PID Control of Linear Time Delay Systems

Click to edit Master title style

Click to edit Master text styles

Second level

Third level

University of Delaware

Mechanical Engineering

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/master03.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAADzCkAAAEAoScAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC0QLBAwkCAAD3AAADAgEA AAAAgAAAAACAAACAgAAAAACAAIAAgAAAgIAAwMDAAMDcwACmyvAABAQEAAgICAAMDAwAERERABYW FgAcHBwAIiIiACkpKQBVVVUATU1NAEJCQgA5OTkA/3yAAP9QUADWAJMAzOz/AO/WxgDn59YAramQ ADMAAABmAAAAmQAAAMwAAAAAMwAAMzMAAGYzAACZMwAAzDMAAP8zAAAAZgAAM2YAAGZmAACZZgAA zGYAAP9mAAAAmQAAM5kAAGaZAACZmQAAzJkAAP+ZAAAAzAAAM8wAAGbMAACZzAAAzMwAAP/MAABm /wAAmf8AAMz/AAAAADMAMwAzAGYAMwCZADMAzAAzAP8AMwAAMzMAMzMzAGYzMwCZMzMAzDMzAP8z MwAAZjMAM2YzAGZmMwCZZjMAzGYzAP9mMwAAmTMAM5kzAGaZMwCZmTMAzJkzAP+ZMwAAzDMAM8wz AGbMMwCZzDMAzMwzAP/MMwAz/zMAZv8zAJn/MwDM/zMA//8zAAAAZgAzAGYAZgBmAJkAZgDMAGYA /wBmAAAzZgAzM2YAZjNmAJkzZgDMM2YA/zNmAABmZgAzZmYAZmZmAJlmZgDMZmYAAJlmADOZZgBm mWYAmZlmAMyZZgD/mWYAAMxmADPMZgCZzGYAzMxmAP/MZgAA/2YAM/9mAJn/ZgDM/2YA/wDMAMwA /wAAmZkAmTOZAJkAmQDMAJkAAACZADMzmQBmAJkAzDOZAP8AmQAAZpkAM2aZAGYzmQCZZpkAzGaZ AP8zmQAzmZkAZpmZAJmZmQDMmZkA/5mZAADMmQAzzJkAZsxmAJnMmQDMzJkA/8yZAAD/mQAz/5kA ZsyZAJn/mQDM/5kA//+ZAAAAzAAzAJkAZgDMAJkAzADMAMwAADOZADMzzABmM8wAmTPMAMwzzAD/ M8wAAGbMADNmzABmZpkAmWbMAMxmzAD/ZpkAAJnMADOZzABmmcwAmZnMAMyZzAD/mcwAAMzMADPM zABmzMwAmczMAMzMzAD/zMwAAP/MADP/zABm/5kAmf/MAMz/zAD//8wAMwDMAGYA/wCZAP8AADPM ADMz/wBmM/8AmTP/AMwz/wD/M/8AAGb/ADNm/wBmZswAmWb/AMxm/wD/ZswAAJn/ADOZ/wBmmf8A mZn/AMyZ/wD/mf8AAMz/ADPM/wBmzP8Amcz/AMzM/wD/zP8AM///AGb/zACZ//8AzP//AP9mZgBm /2YA//9mAGZm/wD/Zv8AZv//AKUAIQBfX18Ad3d3AIaGhgCWlpYAy8vLALKysgDX19cA3d3dAOPj 4wDq6uoA8fHxAPj4+AD/+/AAoKCkAICAgAD/AAAAAP8AAP//AAAAAP8A/wD/AP///wAAAAAAZTAy MDVfaW0EAAAANAIAAAQAAAAHAQMAoScAAEELIADMAHgAoAAAAAAA0ALAAwAAAAAoAAAAoAAAAHgA AAABAAgAAAAAAABLAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAgAAAgAAAAICAAIAAAACAAIAAgIAA AMDAwADA3MAA8MqmAAQEBAAICAgADAwMABEREQAWFhYAHBwcACIiIgApKSkAVVVVAE1NTQBCQkIA OTk5AIB8/wBQUP8AkwDWAP/szADG1u8A1ufnAJCprQAAADMAAABmAAAAmQAAAMwAADMAAAAzMwAA M2YAADOZAAAzzAAAM/8AAGYAAABmMwAAZmYAAGaZAABmzAAAZv8AAJkAAACZMwAAmWYAAJmZAACZ zAAAmf8AAMwAAADMMwAAzGYAAMyZAADMzAAAzP8AAP9mAAD/mQAA/8wAMwAAADMAMwAzAGYAMwCZ ADMAzAAzAP8AMzMAADMzMwAzM2YAMzOZADMzzAAzM/8AM2YAADNmMwAzZmYAM2aZADNmzAAzZv8A M5kAADOZMwAzmWYAM5mZADOZzAAzmf8AM8wAADPMMwAzzGYAM8yZADPMzAAzzP8AM/8zADP/ZgAz /5kAM//MADP//wBmAAAAZgAzAGYAZgBmAJkAZgDMAGYA/wBmMwAAZjMzAGYzZgBmM5kAZjPMAGYz /wBmZgAAZmYzAGZmZgBmZpkAZmbMAGaZAABmmTMAZplmAGaZmQBmmcwAZpn/AGbMAABmzDMAZsyZ AGbMzABmzP8AZv8AAGb/MwBm/5kAZv/MAMwA/wD/AMwAmZkAAJkzmQCZAJkAmQDMAJkAAACZMzMA mQBmAJkzzACZAP8AmWYAAJlmMwCZM2YAmWaZAJlmzACZM/8AmZkzAJmZZgCZmZkAmZnMAJmZ/wCZ zAAAmcwzAGbMZgCZzJkAmczMAJnM/wCZ/wAAmf8zAJnMZgCZ/5kAmf/MAJn//wDMAAAAmQAzAMwA ZgDMAJkAzADMAJkzAADMMzMAzDNmAMwzmQDMM8wAzDP/AMxmAADMZjMAmWZmAMxmmQDMZswAmWb/ AMyZAADMmTMAzJlmAMyZmQDMmcwAzJn/AMzMAADMzDMAzMxmAMzMmQDMzMwAzMz/AMz/AADM/zMA mf9mAMz/mQDM/8wAzP//AMwAMwD/AGYA/wCZAMwzAAD/MzMA/zNmAP8zmQD/M8wA/zP/AP9mAAD/ ZjMAzGZmAP9mmQD/ZswAzGb/AP+ZAAD/mTMA/5lmAP+ZmQD/mcwA/5n/AP/MAAD/zDMA/8xmAP/M mQD/zMwA/8z/AP//MwDM/2YA//+ZAP//zABmZv8AZv9mAGb//wD/ZmYA/2b/AP//ZgAhAKUAX19f AHd3dwCGhoYAlpaWAMvLywCysrIA19fXAN3d3QDj4+MA6urqAPHx8QD4+PgA8Pv/AKSgoACAgIAA AAD/AAD/AAAA//8A/wAAAP8A/wD//wAA////AP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////+m//////////// ////////////////////pv////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////pv///6am//+m/6am/6b/pqb/pv+mpqb/pqam//+m//+m//////+m /6am/6b/pqam/6am/6ampv////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////6b/pv+mpqampv+mpv+m/6am////pv+m/6b/////pv+mpv//pv//pv+mpv///6b/pv// pv+m/6b///////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////pqb/ //////////////+m/////6ampv+mpqb//6b/pqb/pqb//6b/pv////+mpqb/pqb//6b///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////////pv// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////+mpqb/pqb/pv+m/6ampv+mpqam//+m//+mpv+m//+mpqb/ pqampqb///+m/6am/6b/pqb///////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////pv+m/6am/6am//+mpqb/pv+mpv+m////pqb/pv//pv+m/6ampqam/6ampv+m pv+m/6am//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /6ampv///////////////////////////////6b//6ampv///6b///////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////+m//////////////////////////////////////////////////////////// /////////////////////6am//////////////////////+mpv////////////////////////// ////////////////////////////////////////////////////////////////////pqam/6am pqb/pqb/pv+m/6ampqampqam/6b//6am/6b//6b/pqb/pqampqam/6am/6am/6b/pqampv+m//+m pqampv+m//+mpqb/pqb/pqam//+mpqb/pv////////////////////////////////////////// /////////////////////////////////////////////////////6b/pv+mpqampqam/6b/pv+m pqampqampv+m//+mpv+m////pv+m/6ampqampv+mpv+mpv+m/6ampqb/pv//pv//pqb/pqb/pqam /6am/6ampv//pqam/6am//////////////////////////////////////////////////////// //////////////////////////////////////+mpqb///////////////////////////////// ////pv///6b/pv//////pv///////////////////6b//6ampv////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////y0tLS0t//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////LS0tLS0tLS0tLS0tLS0tLS0tLS0t//////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////LS3//y0tLS0t/y0tLS0tLS0tLf////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /y0t//8tLf8tLf8tLf//LS0tLS0t//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8tLf///y0tLS3/ LS0tLf////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////+8vLz///////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////+8 vLv//////////////////////7y8vP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////tWVsvP///93///// ////vP//4pG7kZKRvJKSvP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////5Kui////7x5mf//////////vP+7kZGR /7ySbf////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////+1bK68//+ZMVJLvP///////667kZKR/8O8bbz///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////kq5s////mVJLS2WSvJKR//+7rpKSu7y0bJL///////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /7Wukbz///9LSUJtMVEiQ2W1vP+SvLyRpopltf////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////+SkYv//////21t UVIxbEpKPGyuvLz/iqyKrGXd//////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////u2yuvP//////c21zc2WKSlFDQzyS koqKrIqKi/////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////5KLZv///////////25KbGxLUlJSdJGKsoqsiqy8//// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////+7rq68////vP///7yuSUtDQyNSMXNDi4qKioqmvP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////kq5s//////+8////kaxsUmVtUlkxc22KpqyKrJL///////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////7yui7z///// kpL//5KmiktRI0pSWW1spoplioq1//////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////+1rov//////5Fsbf+LioqKiotD c3OZSqyKrIqsvP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////tWyLvP///5JsPGVti2VspqyKbG1tSlJlrIqspv// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////7WRkf////+1QoqKi4qLc3Jriq68kpIwUmusiov///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////+7bK684rySbGumioqKpnNTUUO8rrtKUlJTSmxK//////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////////////kq6Lkm1s bYuKrIqsiqxselJtbXNyUVJSS1MxdP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////7ySrrttQrySioqKioqKiypZ SkoxSzFSIyMqc7z///////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////+Si2bdbWy8/5GLiqyKsmVKWVJSUlJtS0wrWZn/ //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////vGyLvJJCbGWKpoqKimWuZVIyWTFtQ1IwWTG8//////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////7uRbP+RbLu1i4uKimWKbIpmWVNRZVJTeW5KvP////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////7W7 bUK8//+7bGWKioplpmZSI0JKSpK1Zbv///////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////+8bENsbOL/4maKiqyK imWKZUlCZTySkYqLvG3///////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////kWaRQ3Ku/7tmZYqKioprZYplimVlQotl rm2SvP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////2yRkW21kf+SZYqKioqKiqyKimVsbK5srnOS//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////+9/7xsrpFDu2ySQm1simWKpoqKioplQ21tkm1tkv////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// bHJsbG1sQ5G8/2uLiqyKrIqsQkNykpKSbbz///////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////////vGxtvJKSbLy8//+8 kWtlioqKimsAbW2SbW28//////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////9mtf//vHL///////+8ta6Liq2LvG2S c3OS//////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////////////////////////ibK7//91s/7y1kbWStZK1rq5lrpK1rpKuta7///////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ///////////////dvGauvP+SbLu8bK5li2yuZouLkWaRZq5mi2yL//////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// vJFtbLy8kWySta6urq6urpGurq6urq6urmyRrv////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////0FB//// //////////////////////////////////////////////////////////////////////////// //////////////9BQf////////////////////////////////////////////////////////// ////////////////////////////////////////////////////////Qf////////////////// //////////////////////////////////////////////////////////////////////////// /0H///////////////////////////////////////////////////////////////////////// /0FBQUFB/0FB/0H//0FB//9BQf//Qf////9BQUH//0H//0FBQUFB/0FB/0H/Qf9B/0FB/////0H/ Qf//QUFBQUH/Qf////9BQUH//0FB/0H/Qf//QUH//0FBQUFB/0FB//9B/0FB//9B//////////// ////////////////////////////////////////////////////////////////Qf//Qf9BQf9B /0H//0FBQUH//0H/////Qf9B//9BQf//QUH//0H//0FB/0H/Qf//Qf///0FBQUH//0FB//9B/0H/ /////0H///9BQf9B/0H/Qf//Qf//Qf///0H//0H/QUFBQf//QUH///////////////////////// /////////////////////////////////////////////////0H//0H/QUH/Qf9BQUFBQf9B//9B //////9BQf//QUH/Qf9B//9BQUFBQf9B/0H/Qf////9B/0H/Qf9BQf//Qf9B//////9B////QUH/ Qf9B/0FBQUH//0H///9BQUFB/0FB/0H//0FB//////////////////////////////////////// //////////////////////////////////9B/////0FBQUH//0FB//9B////QUFB//9BQf//QUFB QUFBQUH//0FB/0FB/0H//0FB//9BQf9B/0FBQUFB/0FBQf//////Qf///0FBQf9B////QUH///9B ////QUFB//9B/0H//0FBQUH///////////////////////////////////////////////////// ////////////////////Qf//////////////////////////////Qf9B/////////0H///////// //////////////////////9B//9B//////9B/0H/Qf//////////////////Qf///0H/////Qf// //////////////////////////////////////////////////////////////////////////// ////QUFB////Qf///////////////////////0FBQf////////////////////////////////// //////9B////Qf//////QUFBQUH/Qf//////////////QUFBQUH//////0H///////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////9B//////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////////////////////////Qf////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// ////////////////////////////QUH//0FB//9BQUH/QUH/Qf9B//9BQf//Qf//QUFB////QUH/ QUH//0FB/0FB////QUH//0FB/0H/Qf////9BQf///0H//0H/Qf9BQUFB////Qf///0FBQf////9B //9B//////////////////////////////////////////////////////////////////////// ////////////Qf//Qf9B/0H/Qf///0FB/0H/Qf9BQUH//0H///9B////Qf//Qf//QUH/Qf9B/0H/ QUFB/0H///9BQf////9B//9B/0H/Qf9B/0H/Qf//Qf//Qf9B//9B/0H///9B/0H/Qf////////// /////////////////////////////////////////////////////////////////////////0H/ /0H/Qf9B/0H///9BQf9B/0H/Qf9B//9B////Qf9B/0FBQUFBQUFB/0H/Qf9B/0H/Qf9B////QUH/ ////Qf////9B/0H/Qf9B/0H//0H//0H/Qf//QUH/////Qf9B/0H///////////////////////// //////////////////////////////////////////////////////////9B//9B/0FB/0FBQf// QUFB/0H///9B////Qf///0FBQf//QUH/QUH//0FB/0FB////Qf///0FBQUFBQf///0H//////0H/ /0FBQUFBQf9BQUH/Qf///0FBQf////9B/0FBQf////////////////////////////////////// ////////////////////////////////////////////Qf//Qf//////Qf////////////////// /0H///9B/0FB////////////Qf9B//////////////9B//////9B/0FB////////////Qf////// //////9B////////////Qf////////////////////////////////////////////////////// //////////////////////////////9BQf////////////9B//////////////9B//9BQUFBQf// /////////0H/Qf//////////////Qf///////0H/Qf//////////////////////////Qf////// /////0FB//////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// /////////////////////////wMAAAAAAA== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/master03_image001.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACCzWOsQ7CMAxE7y6lVQXsDIiBhYl+CBJMjAx8Ulf4oAqGzvwIE0IKtktOsu6c+Dl5 jcMdyKajHrzC9T4TLZAuluXJNLOay+c8LfTkSZWliku4d1yFi4zZVoWiU0iWNpiIBoVszL8iJvnp 3hp/8aM6aHQ3bP838Sus6x49Bh5UmB1zTrHhBzx6JRzOAAAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/master02.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0191.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

Optimal Feedback Controls o= f Linear Systems with Time Delay

J. Q. Sun

Department of Mechanical Engineering

Unive= rsity of Delaware

Newar= k, DE 19716, USA

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0065.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Outline

<= span style=3D'font-weight:normal'>•Time Delay

<= span style=3D'font-weight:normal'>•Semi Discretization

<= span style=3D'font-weight:normal'>•Optimal Feedback Design

<= span style=3D'font-weight:normal'>•Methodology Improvements

<= span style=3D'font-weight:normal'>•Extension to Stochastic Control Systems&#= 13;

<= span style=3D'font-weight:normal'>•Concluding Remarks

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/master03_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAAJ2AXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwD6 AXEBgAAAAAAumQL/hI+py90Bo5y02ouz3rz7D4biSJbmiaaiw7buC8esStf2jef6zve+JQsKh8Kf 8YhMKpfM5ooIjQ6d1Kr1is1qI9KuF+H5isfksvmMTqvXbEa4jdbA5/S6/Y7P61/y/RTjFyg4SFho eJdx+HCh2Oj4CBnpyPhIKXmJmam5+WVZ6MkZKjpKqgnqB1SqusrailohmOo6S1trKyaLB3vL2+v7 60aRtwtcbHzMSkwnjNzs/JypvCYNXW19vUd9po3d7f29zZzGDV5ufl40Ma6O3u7+7iJOJg9fb/9O 75V/z9/vvQ8FoL+BBJsJDHKwoMKFvBLCYMcwosReEANKmIgxI62K/+m4aPwIkhTHGA5DmjxJqOSC kShbuhzEskXMlzRr2pm5CILNnTwRXXz4s6fQoXGCyjRKNKnSLjjBIF0KNSpJjzOeSr2KdaXVBFuz es3a1UDTr2SV4gxbNm3SrmPVut0ZE+3buTa3yqWLt6XVu3n7mnzK16/gjICpDj6MEmlgxIwVGl3c OHK/x4YlW44YFPLlze5+auYMupznyqFL2xut07Tq0x4/r36NDHUA2LTR5aqNu9vt3Lyh7e4N/Njv 4MR9DS+OvNbx5MyTkWsOXeTz6NQ3La+O/dL17NwnTe8O3tD28OQDjS+PXtf39OzrnG8Pf9r6+PSL qqyPf8z7/Pyl7P/vD2BHbQVIIELzFYhgPAcmyGAw9zUIoVMPRhjhfxQ2aOGFCWaoYYEcdhjghyD2 J+KI+ZVoYn0ophjfiiy25+KL6cUoY3k01hjejTh2p+OO2fXoY3VABhndkEQ2Z+SRySWpZHFMNhnc k1D2JuWUuVVpZW1YZgnbllyu5uWXpoUpZmhklsnZmWhepuaakrXpZmNwxonYnHQOZuedfuWpZ158 9knXn4C+JeigahVqaFmIJvrVooyCteCjVEYq6ZWUVqrlpZh2qemmYHbq6ZighmrmqKSmaeqpbKaq 6pustirnq7DWKeuseNZq65645urnrrwG6uuvhAYr7KHEFqvoscj/NqrsspBO6Cyt0EZ767TU6mrt tb1mqy2w3HY77LfgGivuuMmWay6z6Kb77IDs4uXouwvFK29B9NY70L34TtbsvjTp6y9r6wZMFMAE 49PvwScZrLBtCTcMEsMQi/bwxIRVbPFEEmesG8YcM7Txx9aELLJvHpdMEMkoG3TyyvwO7HLELccs sLs0wzXzzQjDrLPGOffsMM9Ag/zz0BQLbbS9RSf9z9JMY6Py07NELXUrVFe9ytVYl6L11qN07XUo YIdtndNkC2f22cWMrbZ2abdt3NtwNyT33Lawbbd3SOf9Dd58H+L335/ULbhzexc+MuGIc6344l83 7rjYkEde9uGU/8c2+eWYBK65T5Z3DgznoC+T+eiVlG56I6KnzsbqrKvh+uv22Sw71KjXDtPtuJun ++7Z9O77MMAH7zntxLP8+fGMJ6/848w3L/nz0Fdu/PS/xG79H9Jn7/b23EeC/fdTeS++3tWXv9Hw 6JcR/vpVke/+4PDHn/v89PNu//2/56+/8Pz3XzzXAFAU7RugWNRnQO2dL4HUEyADo4HAB45vgRLs HgUrCL4IYvAo/9vg7BzoQfOBMISKKKABTThAFAJQhf1jof5ceD8Y0k+G8aOh+2y4PhyiT4fl46H4 fPg9IHJPiNkjovWMOD0kQk+JzWOi8px4PCgST4rBo6LvrLg7LP/iTou146LsvPg6MLJOjKkjo+nM ODo0gk6NnWOj5tx4OThSTo6Ro6Pj7Lg4PCJOj4Xjo+D8+DdA8k2QeSOk3Qw5N0TCTZFtY6TaHHk2 SJJNkmGjpNcsuTVMYk2TVeOk1Dz5NFAyTZRJI6XRTAk02ZDQcLMBwAhXWb9WvhKW+JMlaWhJvQOm BpcEpMoseVk8CbUSmKYwzC+JSbpd6nKYyMygMpfZTAsq4JjRhN0tqVlNM9jlltmMpYOe2c1YsIWb 4dRDWC5YznmgBZvptAg4p8nOdhqInMKUp//eqRV62nMd+hQmM/fZusWgE6Ay0MxACaqgfuYTnwjt hGs6CMxsHbSTofBUqAMmStFl/lOBG80oR/WBUYKuC6IbhBlJJSi0kyZwbypdYUgralGKNkuDXXwe Tce4vZum8aVA4WlJ86fTO/4PlZLiE1EHVahTIFOptfTpD/XF1J9KLBFSVVkfTkjVXnJghx2w2ha+ CtawinWsZGUoK8uK1rSqda1s3QDa2grXuMp1rk2wHV3vite86jWrgSgAADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0208.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

About Time Delay

•Commo= n in Engineering, Economical and Biological Systems

•Some Common Sources

èT= ransportation and communication lag

èF= eedback delays and hardware limitations

èP= rocess approximations in digital models

•Sourc= e of Instability of the System or Complication of the Analysis

•<= /span>Sometimes Used to Improve System Performance

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0209.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

About Semi Discretization

•Common Technique in Structural and Fluid Dynamics

•Extended by Insperger and Stepan to ODEs with Time Delay

•Characteristics

èCertain variables= are discretized

èOthers are kept continuous

èFor delayed ODEs,= a finite dimensional map to approximate an infinite dimensional system

•Use Exact Solutions When Possible to Construct Accurate Maps of the System

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0222.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Studies of Time Delayed Systems

•Niculescu 1= 998: A survey of stability analysis for delayed linear systems •Cai and Huang 2002: Optimal vibration controller with a delayed feedback •Pinto and Goncalves 2002: Fully discretized a nonlinear SDOF system to study the optimality with time delay •Klein and Ramirez 2001: MDOF delay= ed optimal regulator with a = hybrid discretization where they partitioned the time continuous state equation into discrete and continuous portions

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0223.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Studies of Time Delayed Systems

= •Ali 1998: The Smith predictor: stability and performance of feedback controls with multiple time delays

•Yang and Wu 1998: Structural systems with time delay

•Nohmi and Matsumoto 2002: Space teleoperation with time delays

•Singh 1995: A time-delay filter for designing a fuel/time optimal control

•Ha and Hy 1996: A sampled-data control system with computation time delay

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0224.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Studies of Time Delayed Systems

•Model predictive control offers a good tool to deal with time de= lay (Dumont 1993, Normey and Rico 1999, Rawlings 2000) = •A non-Lyapunov based stability study of <= /span>linear time-varying system by the Gauss-Seidel iteration (Xiao and = Liu 1994)

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0225.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Studies of Time Delayed Systems

•Positive uses of time delay
èTallman 1958, Suh= 1979, Suh 1980, Shanmugathasan 198= 8, Kwon 1990

èFujiiEtAl 2000: T= he time-delay feedback control to regulate the librational motion of gravity-gradient satellites in an elliptic orbit =

èAtay 2002: A dela= yed feedback control of oscil= lations to control the amplitude and stability of oscillations in planar systems with general nonlinearities

èOlgac and his associates have published extensively on the use of delayed resonator for vibration suppression (see Filipovic et al 1998 for example)=

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0210.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Linear periodic system with time= delay

Feedback control

or
Linear Periodic Systems with
Feedback Control

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0210_image003.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC91Za2xURRQ+c/fdQlu2D1pELGCNUEQKgiRgWio2Gx8UENBsGsOjrWlScEHqFiGm SI36w7SIER81EoIxRg0J+sMYwCYKPiIGUUOMKQ9jCBYbKmCCEVzPmTt3d7g7s73tbdE4yezMnTnn O2fON2fuY48fOfwa8NLDJkMj7z2/gkEIwLM5H7CtzqUx+r3FnwtPTnjogZq7GZdj0HiP2QI8PMFE oZaumyFVjuLAJOl613SAGR6A0nseqCFp0nkTx7PAVnxYvQBVqN9vn/vZC23veGAMdkdhDWINiz7Z LxL9Yqwlop9IJGhdkIeVFvU7DmSJayqjDVN+lLheijXGTLy6v1FZKp1WCLAsgyZYCw3wOJTCImzj 2C6Fx3BsFawDZ2Xl6ahRhZUAf5rfDO1/hKEc+9RaJU9Ukt1fhRG+4ebw0fZOJvcX+DG+XbPYm4gR QYA24aSFOcWGOYX/hkGHUaPAuNWGASZNUH8xDJWSny/MboYurMQN4ZF+UHAVlHTrnzAvyyT+LB4S tr7FiaHgZL+R6rvnhEXbilvW5/pZlMPiBmz9rhA+OloINYizAfEiiNsMMZiG/RiOkDWyVwMVPKZz Ky7FSTX2WxgWYluFLa1tPranWp5Yf9HHFhA2pgL4xbotWSqXsU82Se7HR0/Hz7Z8kIz2qXMm1kvY HimcdOdYxpKet58jbq6VzxO2P8M5sjker71Yp87/M059mZNX+sNpnBhS7D362PPfjbAGo18BQy9q XltZPsw4fCP2KjwjyStoeC315PNKXJEU9WVeH/6m2hP5qhrDg35inKd/dSU+2zokcIyq3Kf1dH95 JS7HvlWRDx5NDnj155LEwyxwU7LZDjYx0QRFrNWwfCJfYpcpfLW8bv28DkeiyewjF1b24R7C2ox1 5dmo0f1t1OjsX2qQ3jGcp1rEQJzaEjuIk2CVQLJJTNRd6e1gdNFW9SLzi/O7sWMNLH63lmMS/hvP 13E96tO4HBM6l2iMqogRVN28g71/pgmee3szD5jMwxgFD14p9j5N7NmwnT//D15vwbtF7Ncw59XC 2YO661+v3dKKdVf+si1VAY8hx/7rvvTzx6fhwe8oB9ycRamcntY3iJz250MZtm3cB9x7iOE0VoSR KumxmgqpfUaxGt9Xy8cv95nnENWF2I/23O5J5tf5MHz6yKX4r1ijfnbJkl143py3fJN5OKXgwW87 i+T7g2rcm4HDkcTxZ8C09k4A27MjmsP/zj2N9tH+M8RrYVKivzfzPio+l9pHC8WzBZW558z9Uf/q 5Tjt7851xfy6AMefwz3+Bbbbt/4Z34Xz8t45i3P2vRO4DvvC4jbo6FyY6eoMle8fVJ7Z2cTfL/ZM KGfdX9YaVD9cvxaojc2o4y3DfKQ8e+NQHc+57oT6DD0s7RnVGTqUc8G6N3YeSd0bh3IuYLx9dm6D UuxD+nvjiDwfXm9e6d44UrwO5d4Y0uTDf/mstt9TJog56z28cLypq3sPlH1YJqpVcrDeJHJhxfIf Khl88QmNPyvG7k/bTWZZLJ6/j9mevS18r9APied/Gf9u7L/oAL8M3zfuyxA3y1aO0C1RrOWYw7X0 oK23bFxY+CVCfpJiLXHmDH+jiJfK/4lCfprC//MO8U/Y/PdL+HME9zXCloxf4XGGf1e/+V1poH21 ROg2KNZy0OvM1gKKBRuY9wahG1PY6vW55z0m5DcpeO/wu+e9VchvU/gfCAyO94F42SZ0tytsvRcY XL4PxMt2odulsPVU0D0vXUL+LQUvk0Puedkj5Pcq/H895J4XOTf3Cp4OKnKzKsuZrXK0dVrD+0Eh f0yxlonZ7vMxINn6nu5HtHbFWhpReLkDW/VYX9bwclLI9yrWUjja/b7qFfIXFfvq49Hu99UFIX9V 4f/MnOHN96vJbxfpto7nDG++Z4sH6SKFrXdy3fNSJPBvYum8LMobGi9BCb9M4N8h/nuR8W8f4wy/ 0paDIQl/nniYj7D0vNgUdoa/GvE/1cQ/Ivx/UBH/+fnunx+iwv8mhf/3FgzujBpo38bEWtoVa3mp 0JmtaofPD+3CVofCVneR+33bIfBfUezbhrHuz5OdAn+3wv+escN7nuwWtvYpbD1d7MxWC+ifIeV1 7RO2DihsbShxz8sBgX9YwcvYce55OcRS/+Xa/e8YNzReQPHeV47vfWdQnt5/CqT/PQuEPx4W5OvO Nqw/iEcZk6GH0ZzBGJeZzor5DDPoH1/qhbg0QsNfxi8J6auB+f9t09qGx0sXNcRLlz62dlX6FzfC vE188w8ZCZB712Km/oF0hslU+uZ3jDVNGT+QmPqG1hO+Ogtp1sBInjR9NqiVeLU4g1uRT1qRFSP7 iCfN5nDo+BS65lr6hhgT/7D4myGeMweOZ0DF6yD4CNr8ud78gI2faeK7fZF3MpxkAOqstKzQE8vM rHEi0VsjOcm8MWdK8JpmyiI+hUeWdg6X6YlkJ320Zkr4zMZIME1nIp85kdTxJWfm8Jm7InkZ/F3C ZRZECjJ41aD1Kqb1qjXpld72tmSs9La3a213aW3v0dpOxWYvlymP5KZ5dVAbEb+QuRHf1UimPpKV Zvuk1t9erb8XHMTqqoNYZTOd7SJ2re1AcqaMz1Qm4xBMzszjM6sjo9PsRJhux0WZFVX9SmJcpjrj jmvXrqSD6aK4kw0cxd1cpkWRESmcfVrbB7S2D9lsW2dJ+hni4SfeP9yJZU4MJwAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0210_image004.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYb2wURRR/s3u9XguUc+8o1SKetBAqFdsSAh9aW7E211RavCJUaAgUK2nSylVa rokkVFIDxhDOKjEWiHygGD/4xZLoB4zEP1WJmEZjjFFIMaZCEDm1JjUSz/dmZ+6me7e91TZxkncz O/Peb97+3pvZmfvm0ugQ8DICRbCHtya2MsgB0Nfhjxt2ZFMf/a5wL4S387ZurHuYcT0Gr7WZNUA0 z0Shmp47IVmGUZYpz4fuACjTAQKPbKwjbbKpwv5ssJQsFBdADQLGrGM/uKD/TR0QCuajeFAM0ab5 80W7AOVO0Y7H4/Re4EVZiPIrduSKZyoLNFN/vngOoYSZidf6NxorJSopwLIZOqAL2mEfBKAR6wjW IdiLfbvgaXBSmB+nhuLHmB8UHgp+N2Ds7Dk4zzTY+ZsB3+65Ggn+NMLHSD+aH4XAJ8x/vgbZLiw2 xgai7CE3wOmTa9jrlZ0QXAXQL5z8Dp8H/jCgBNtUy1LCfw2ww6hLg7HSggFmmPzcH8EnydG1nXAS hWJDeGTvEbHyKLZP7jcflyvxk3GIW9oyJlqamJzXku05iImrv6C3+4jBXBwWE7Dvq0Xw7tgiqEOc ZxAviLidEIZSbIexh2aj+eqgnHO6vnwyQqbhnw2oxboGa3q3SqzHe/d3bwfGCBuXAq4z872lLpUp bNOcpEexv9Y7kmB7/IaJ9QrWlxYtW7eYsYTnAzcoNtP1vWLuj9Lo01immGg2cdDt1wanrQd2YyTW wGxKa8XL7K2JDjjyxrP8+flXO/g6PrN0FfPhy23a0qyd6+4CqsNlrbxmyH80FtJOfdwKFx4MaeMt IY1q6gsfbNRiZkhhVOS/rkYeGrU4q+b2gG3eibY7Xcd4vPprBplb7CFPHdsN3u3NHJPwT73Qyu2o Tf0qJ7jdxKmPJCr3FeXdNMvaID1rHHSFe5cN92zO1sD/G1eAuYnrCtyxwtcNHlc595mbBnSfaDrQ h3Lat/lATbauqdx/juNW7l02cchytAbKZ8HUBj14cQNO6YNS9Gv1xduRtfLjg30karsP2bvw2e2I x+2D5Vj3cx8ANiGGU64II1lSuboPknlGXC252cT7p26a+wxJLba3XX5AN7/MWG4Z8OGOych1lG1u Nil1a2+Z49I3NQ7jaeKQpXDvdsR9xSy490Hxf+A8jL0BwXlm7n1QNno3x5D1SqwPCe5BcN/yxQad OCb9d8gXxPRiUlJuSM4r0dc25Nz1iwEvPfcnfn+mIrTv+PF5wQdNB0x/TX+kj8GTJXz7a7DsP2h2 0Mq92/IdsPs+qOvEbv2oZy01tkvFmDyTvZhr9tudCVQfNgtJfNtQ7hHcbHn862oGn75P/YdF36Mp O55ZNmG7FzMnNsN7ybnk+bEwzVwxh3NdjpXrwxauJH6h0C8W8VLxjzNn+D2YR302/hcJ/dVp/Cf+ neBfiU1Fhi1xlPjrRWyCKPda8Jt0Z/hVMXO9qHko8ZuFfpu4Z6j437uc4Vcj+NUMedUi5pD5Y+Xq vSyzX8swVwNG4gk0/NJBbh0W9oNp5ruW7TS3DLDLrUGhfyJNbh31OM0tsM2tIeUOaPU/K8dpbpn2 6n5h3SPO4h4xgfp0DfUra98v3ldnHp6T8zR5sZyvFeGdl8Y0PAtTvZoV8BGm0U2RWjlcewnKX9qP ceXrYt77Orra9wUa2yOB0N6uXaknKsK8X5wPcrQ4qK3pmMmbizNMZovEvTO/fLs7ZjyemUhaij37 V57otjiKH+WZ/XDNZF+R2T5LYSSVI+mj1edkjKUXVJcy8w6e7yqCc4k/IqwRlLPQibUi9y6RFL31 3jTzSh0v17lcPy/hiRwp5CM99Z4UmyI+ciVh40qMrOcjVTij5ECONPOR6vqFafzNFTptnN6GvsWQ N4PHh209HrT1eCjh8XR+U3k1b13/AGoKZd2EEgAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0210_image005.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYb2xURRCffe/uem0pnNcrVIpYaEFqa6UlRj6ALYhNk0qLpQqWxpSWP6lp4SqU awLRSlDkg6EUjGAllgQ1fjAhgQQ+1GCkViWipMao0RJQgxCsVKkJKvGc2T9323fvcVfaxE32Znd2 9jfzZmbn7b1vzvW/AbwNQg5s4KM9qxgkA5iHUgCSYKeXePQ71zMF/vatWl72KONyDPpGBAX41idQ iNK8GaLtS+yztfnBDID5JkD2Y8vLSJr2LEO+FyzNjd0FUIqAw9a1H13Q8Z4Jd+Fwktzrl2PSP1WO M7HfLcfhcJieC8jUKdh/R0aKnFNLM4T8JDmvxh5kAq/uX9ystU7lAmw10AQtsB62QDZUIg0hrYbN yFsLmyCRxgKoGnKfYAGaJUlu5g0/nH/nBPQyA+r/8MN3Gy+Fyn85ztdIvnNqJ2R/wgK9pejtrFz/ +V2dbIkHoOfNBeytRc1Qng/QIY38Hue7/vRDHo6JqpbHf/1gPtIMsySP1sO1+1kfxujgs/sYbF3b BhrGPAsGiDAFyB5qTvZ0Fwp7vFqsMQSn120T0zla/FQcwpaxiolhE5NeIzqegJiwjsy21jVIOSwm YPtXGXDqfAaUIc5ziFeOuM0QhAIcB5FD2khfGRRxny4sGgnR1uCvfp7fpUjp2RYhvdi2rfWGmy0h bHQzeORzK1lqN3FMOkmOYn+l7XjE2xevCawDSM9lzH54GmMRy3ddo9iMlvdJ3X028rTmtZw/a0wM hziYzmeDu20rNGIkFsB4Wk3hfvb+5SZ45d3tfP7S6038HB+dmc+OLak2qJ9obQGiwfl1nDL0f+dw tXH44zoIvlBprCiuMogSD36qNIZFSKFf5b8eeag0wqyE7wcccyburXft5bnQUdrFPLKGbNjbCCvu E5iEf3hPHd/HdRJf80kJUuJRlz4a9WyG5WygDmaNg6n53uXgezZhZ+D/jSs+6YTEdS5WrOBVP4+r 0n10yA+t3VU72rH3pNfsKE0yDd33n+O61fcuhzi4EzoDRePw1FKz/OxSVJkOBWhX4dlboYfUywd5 1PVxO0uHDz+7FfJ60mEO0g5uA+YeYiTqK8KItlhf3Q/RPCNfzRiq4vybQ6LOUF+G49rBB03xZsZ2 3Q9nnhkJXcVe62EjSnbZdbGubNPjcNEmDm7N956EfF88Dt+nQ+4d+DyI3Gzp8/i+T4f5/fdwDEXn Id0pfQ/S96u/WGqSj0n+JNmCmD5MSsoN5fNFaGsD+tz1mx/2vfgXvn9uhvAdGw7gPO2jqh3CXmmP tLHnUB4vfxWW+kM4Vt97LO8Bp/eDfk7szo9Hi2GScx2boPMj8+tyAQ9ZcE0jtCNvHfoq07eXbdwu 5s1DglePnebPT6/j9GXcVavDUa2fLWo8i1PHSE7VMb4H6xhRw1LHepaPrmP5uGtAyw/QzqYxzjqW ZImPfufVz9hMuabuxixN8J3uZnou1MgeuWNgv1fm6FNPfl3C4NPTxN8teY/HvHlEW4HjNnlWnPJL 6VL3+CwbXcMJ6hpEwbctOavws6R8rjw3Ov5rLDF8qgXtDvbnSPlCG/vJ/4ngX7DY79bwF8rYlGOf ZcGvMhPDXzwsYqGfY4W/UtUN+X9Px//BlRh+CYJfipNXq6UOlT9WX33gFnwjjq4KjMTTTJyzeLm1 W+7vstF3JWn8udUl5bttcutV753llh6bI1L+mE1sNiWPLTZ6HVH4J6W/+2xy61RKYvgNiH/Gwf99 2rcEq/+3p47tbOj1zlrjZmCNu4zyk3Ee0GpXQMbLZF5+plIN9YFikpEDg3zNwP9URAtZJl9hBn1x oFEyl56B/R/j57B2SxHfD5pa1m/Jrlwfyq7e3LI29mZOmA/Ie2ayEQZ9NBoz+g84MUzmiMStE2/f xqbbXvMFkhGzn43JEtMRR7OjKL4drtvtL46/3615JNZHysbRNrvtnn0MNnsiuNFcUU9DtEDekaa6 cuBC5MOYNROUtXTzKE6ZLpOrbcBnY7+S8XGZwYHUyBOplSy+snXAG7Mnh69ciOxxRVYW8pXFqFH5 Ra2s5CslA1Ns7E2RMg3cZRXt02DybSze7Whxl8XiqPYjEe3K32rlJF9pGEiL0dMXecrRMYmNhfhy 8B8FeRjASBUAAB== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0210_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIAEWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABQAU AQ8AgwAAAHAKC5IJCoIKCp8JCrYICasICcAICNIHB8oHCP8AAPEEBOIGBvgDA+oFBQECAwT/EMhJ qarz4s27/yCgYWNonqhUWmnrfuvbxR6dyaii7+p+hDYVbpirEYE7XU/3AwWPQuCm9IQCArrAJLAo aJ1TlnV8I4nJGKzie+2yjWZyNXruoaejA6NYWSnvUDF+c0d/AHp8dVZJGjx0GY6PgCIaDAUVAkmU CgIiJJGek05/kYKghER/lpiaO52mhjmMfZSQZbS4opQCDQMbmQoEAAMOvqG5t7ozI4Y0gsq7vb86 wsTGzi+NHBfNzHHIFoygsg0KBhwHCg0BDGzP39B4tpLHipDiqJ/l5xvp6+3J6LWwwY2ZN3ACB+Iz CGCBOQ4MdBijhy3eNoYUw6RaaMshPwwRzhVMrCdwoTOCtexkhBcOX7YLA8qNpFAOgb2KFj/NI8mz 5yZxL4fJ5FDz5pAgBXe+Q3jnTyZpFQ4k0PFxqb2cKbNaDQjIqbqZh6Y+XCkDaUORABA0w+VHmZov mRYImyAVQAEdnUhqu5rToS+1B8u01fVWQty5Eure5SRprwuzAxwuMFCqJVM5sxj94JEkL5VYPnNG VjC58r3LY4Bq3vTTs+WyoEOHg4E1KJzaJ2Kjxr0MGqon+XjzTSh82+3iJoJnS7QbuXGNzqVAjy69 64QIADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Systems Considered

The system with time delay

The state vector has an infinite dimension

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221_image007.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC91Za0xURxQ+c+8+ebs8AlYtSDFVqAI+aioWUEpIWkHBR6OkEQUTGtCli+6akhaj jfaXoElfYsoPTGPSxv7oj6Yx1GhrrWkbQ0ts0vhqG6NQIlWaaKrdnpk7d3e4OxcuLNikk5yduTNn zjlzvnNm5u69/P35D4CVOpINO1hr6UYCbgC1JwmwzounffR3niMRKmduWlO+mjA+AqvmajWOz9Sk 0Jo+N0G41GDHXOHZjw/5KkDmC2vKKTed04b9MWAodiQbQAnOHzaO/WqD9pMqzMBmHJILycPbVH8a b6cjZfB2MBik6wJcFiQi/YkdMfyZlnhF44/jz9VIXqLJq/0HJwulQ3cBlvXQCM3QAD7IhEqs/VhX wy7sq4OdYK3kl1UqSUhU4C9FTXDgLw/kYpvWekniRHlPl6CHn3jKc+lABxHbpQ6A7q7F5EOUUYEC 2rmRusz5Bpnz2a8H1OebcB1aoeOFW46SrxCj917tJNBatxsEGU8bZIAGE9Tf8zAczOw5tlCzx8WJ Fqqjfo/2mCPgp+MQNLR1TBQJJqeVcDt6TIitPX13yyEPsTGxGICBH1Ph80upUI5yXkN5FSi3CbyQ h20v9lBtVF85FDCfLi8Y8dOp3j88UIZ1CdZ0bUVYX9+9p+Wgi8yistEF4ODr1nlpuY9tqpPy2QTL lhTq8UBgCcAZBVsVgx5ou6PJj9dXgLSg6IH/IY6dRdLdk4k0gs+fIrU0/eZ/zhkzChM6z4iJIvhe Nfc9+22F7ej9Aph8keMaIMmQf342tgrU6cQVTHDNVJMZObgPaVvE9eUfVqkVF1ehe9BO9O3Ciw/9 S/VNAvsoiW26njPfPvSLvg9IfK+a5IDNfF8ScFgM0ZRYcpRkBRshjQQU3SZqS8mzVYqW9jXKvm9q qVWh7KMmbB3yQD1SE9KZomrFm1itdAxXK3ReH45TSiPAd20BHahSgqQYKC9AlSYT5261HSb0ob3k CHHw/XvH4e2QtKWGyaTyj79dy+bRNu0XfYJbfZD2UerQ9/TCo+STm41w6KPXmcNEHCifEQeb4Hu7 ie/JlO0//w9c5+Fp4b3tYbjqcnpwbsuxqrYAUnfy+rYSp6qIvv+O6jD43m6Cg8NSDkSzF4VzOm9o AjntSIYcrNuZDQBrUYZVX1EZ4RLpqwUQjjPqq1lDVaz//pC2D1Eqw/bmK4vUUH7h2XDulRH/baTN DjKi85bd0cZ120QcrktwcBj2IvF8kPXbxsBwOuU4xpCpx44T61vTmsP/zZlG4+j0TYpraohjeGDs OEofDMdR2aAn1L98UIuP+vfv+2l8d+xMZ88p2H8IY/wC1p37Hvi7cVyMnVs4Zowd52OICx1bl6V9 oTCqPVQ8P2h5691G9n7RMyeXdG+oUSh91tIMtPbm17KaYD7SPDv+dS3Lua2lldI99LwQM7I9dDL7 gn42rt0UPhsnsy/ESe4oLsH3bvOzcVruh48bV3o2Theu452NeI150+h7t0n+GPftOXxMf9c9m6Ll jNm7lph76znpJQHpSR5vGzf0FxO48CXtP8j7XopATCtr+R23z3C/1eXb+Hw3v2OL8ldj+4gF+Tl4 p39xjP1C15XA52ZI1tJncS1XhvuLTxj2IF1+BuefK1mLn1iT38r9JbM/i/PnSey/Y1H+VfTVCUOc 6PKXcezLuS5RfoFqTf7KYe2/m/Hiah2f2yBZS6/Nmq5S6C/OI+Pj3sDneiW6BuzR4+7l/HsluB92 RI97gPPvl9jvdE4M9/Fw2c/ndkp0fey0mu/9xX0W8rGTz+2S6HrDFT0uXZz/hASXbHf0uPRw/lMS +4+5o8dFzM1THKdeSW6WxFjTlYu+umGCey/n75OsJSvWaj7i3mSSj05B10/8P6urkrXsQOYNFnTV Y4y9Y4LLNc4/IFlLarzVuBq9T4pxNcD570ni6ov46OPqLud/JLG/MGFq8/1R6P+BSF2XE6Y232P5 ZTVNoutkYvT5nsblP0kicalMmhwuLkF+Dpe/hH/fEOUvmmFNfjHicsNwl9Plr+AX5goSmRd7Pdbk b0P550z8X0HC32eM/i9KnlxcgeSe+TPeM28iP71vpQjfMlK4PSpxMdxiFf2jT5ySDXWEjimEMJ6F JJ2NEIV+xaEtN+OehfS38ntQeBPQvsk0Njf4Misb/JnVu5rrIt+iqcxn+P94biUIYmu0zPBXBWsy iWy+9m6yvXHMlx5tvmJqCVudLmnx+JLUiPlkQiuxmcqZ2Irswop0Hxl71AidUzHHLpmrrWVokj5x TIm9Y/izcHx/OmW4TgAPl8FmMPgrj/83lmbLhm0EQJ4l+irpjlUYM5MnXsCXEIpjbSQDn+lIjs8u 8Yg+O4HxXPHFhnykj2SwkVafK2JOFhu5GppjD40sYyMrfUlj2LuO8ZT6UsawqsHUKq+pVYGQVea6 94d8Za6701R3l6nuHlPdYd+cYjy5vsQIq3pNPeLgPLPxrsa+DvpiInRfM7V3wNTeuxZ89ciCr2KJ me40Mlq3MzSSw0aKQ35whUZWsJFtvvgIPRVktL165kRmjMry7V/n7rQQXiEAAC== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221_image008.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VZDUhVZxh+z7nX+6PXn65ZNqzdLdaiTNQYGDTUViZRN7lqtiGjTIvLtDSr6+hS 7gc0WNQKWmsNhHK1nyBWY2MJjgUVUUNaY22sprG1tQxvzYFtbXfv+/1cj8dz9JiyffDd7+/9+97n /d7vnHO/vXzuELDSBzNhA+t9XqGAG8C2NgkgHj5IoDn6neVIhmVTK1YUPacwOgUenuAtwOypXAq1 NK7F6uRT0I31SRgs5UiTbQPwLVlRRNTEU4bzCaArcVjtAAUoMKJfu2mH5vdtMAm7HqwurF7RJ/1T RD8d6zTRj0ajtC9IwZqM9R5OxIsxlUSV03vEOIC1XuHyKv9BZk3ZK10AZHsQ6qAGGsEHfmxD2AZg E86thY1graTs9KtthX4VNH5L/90LXe+dhg5FRYnczhRBG0V7aO7ErSAQUwnOvf6HF1Q1oM6vXM38 2XrfC833vUzWz/GrWEs0xK9wOfDWJJrHcSGfo/ps8iq+MSxk09KBcqajC2VnSz02/9aC1QFVue8X ngeoRntdAgtGi+MPCxvI79He/X6mey/KkzQg7K7exodPafCTOEQ1OKjmODC/bYF1iMR8ePSyEb7b 0BMq/uUU99VdL6ssnrG9NTUWKrF1srK06mZoyFzdJ7ALmY5jC91/79TytOL68cye0ICisBiUpXDy 5gY8eT98RHoCPSEa62k2d81VqF5CmqrSnlCDGo3qacjWXlxv3lcHRuvEz12WClocEKKdehxUExxs Bjh0qIP98Z8H5VRz+taGpR7lFBOLh7/p6zT4rCsNilDOZpRXjHJroR4ysV+PM6SN9BVBDovHvJx+ hkl9rxcWY1vQy3FciG331m0NLS4lg2TTXhzCb5KWygD2SSfRXbrjhdN3eIxTfx9W4qXzR/NdfXzt Dey70h6ESD+mLTiI46OC9hi2vogX5pCvsH+vciBEfHaBgcThINLocbCZ4EC8vxqcB2XCcChVHUX9 oZLfvKZ4NympkH1uOvZybBONN8DoePtsqaw6BB7Ul3hTWf3VIlvxxUU2ivds9HvWxYehZ2Tixjmq Vs+DXXc2JA5xJnlp4nDwGuI8cecNoJn5BO8VJR/2RgLqmgLs04WZHMCt7hH3HJa5AQbR+j3r4NKZ 7dCMdPVI8+6uSsZHfZoX9y0r1COeWTAb6m/z8yDLUcxVDe+sDDdhbUstCxc4bUPuB8p1ehziTHBw mN8PE+Unlv/zxHmvfnsgxOLqe/7wMxnnWx2pcAHbN195EGrDddr/NRy/euFh6LgzFfKQliqZlSf4 qBzQ3S2Usyl3H0Ze39KeED0HyJKNY71h/UjXl/Yns4f8AEifrLkTuHzMgVhSIty+kgPcPspLiV+u DPPzADEbtTh4MED0ODh0ecksX5mdHy2eEkOnpTs+F8ZbRor3NfbBeO8KjD3eecwbxzthoI/3OTCY KyjeM+6uZPMD4tmjO1jOWi6H2wOI99kX+0O3sb7gUPol7WIRm2QX2afFEJylw561nBrfu8zzmMb3 OePw+v+LqzaPPQqu48ljRveJS+N7t8ld/l/leG3MP0qOlzFPQr7AdVWsTfOWs1gE2B6jlXzSrs4g p7mGPnx+WS3TqY35NmGPR1NlIVrKt+mL+XtG42t+xqPzfafe926TXGQH43fAeEt5KWfc8Ut6JTb8 IuDY0KC5YJ/iEHcDYVNSUaoaYUPzHo2N+fSehXNUZUxV5u5X6N2x9dh2kXuCzCdHZ8xVPALD0w11 jK+wuJa1hA21EhuWmxYGVK3tHmEf0+kvVVOwynWtTi0+pFOPD/l7hsBCvpsnJvG7wuhuUUXslmne nykTPi7sXFX+Tb4CFzqD2G8Rc8uHZSdeSrB/PfK00j7C/SZ1eQWvz0BXkmJNVxPMU66McGdKXfIb ShY9a+h0PcBBhjK6rjI452g38VuWoF9gsJdPVat+A2jX3e1S/gJBv0j4Syu/0mZN/haMiiYT+wsF /XID+69alH8jcii+XfeMI+VLvlID+1+2W5OfiYgGLcRVheCtMdjLlDircfWjaiWu1stvAwZxRQnH WlzNU8ziqlHQ7zDYS6fDalxVKmZxtUPQtxjgUu20Glf2IXHl1MjfLegPizOolb/EZU1+fmQG9Oju fin/iPDXSaxP6OTvcVuTXxW57Diru9+k/I8pf2I9YyD/JUy05Rbk56B/Wkzw7RD05w3wTUiweu5c LG9ImecFzRUDmScty7QPyUXamL+q+Tatj/mNHqsxP/SOAIM7aw7eWbeQPknokS+Rk4U9NsXFYjlB lR+8PepM6GNrKr7/UZulpLMVhZ7WWM/NqDOw/qX+FNU8jfBnuGBdTaPPXxPyBTbVrR3+dEgy54nv Fm41aiyJP9WsC474OZVLUkwlDX4VtGaTOkzS3ZhNypgk2WK26fc2Njl2Uzlj21mcZmfD96q3Weoe AZfc0XFxGO1d8ueMzu8chsHY9uzS7cc2cuyOwTI3azPF94Ip9pni/yG9R9n/WJAb/xjSkYrr4QQD HCQNf4NuCicZIMNpUjD/E00ZytFryIppkOjJlQVsZUvYNYynkK3ciPHExVaWs5XMsHMEeyss2Lve 1N5GU3t36Ox1xFZ2s5X8cHIsQuTKEbZSFU6MYc9XpuPtQys5YfcwCzpiu5cz53X+GNzH1dg+BmPI OAZs7PdfO5/JatgcAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221_image009.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VXa0xcRRQ+c++yLJRXLw+3thja2loCIlCN/kB5iASblpIrUGyIyqstZunuQreX xE1EJZpak9KYNCo++GEajf5qTZqoSYmPhjZUifUVowZqU6uCYtUEY+N6ztyZy7AsuG0wTnJ25p4z 850z35nXfnH21AvAy0FYD7t569sdDJIA9JFEADc0uElHvxvd6fByyo5tNXcz3o/BuRm7Bgin2ChU 07cP5koYZZ3yfTAVoFgHyLtnWw31pjH5qE+EqJKA4gKoQMCZaNt5F/S/rsNKbJJrD4oh2uQ/R7S9 KKtEOxKJ0LwgAyUd5VdUJItvKqma3V9MBUyUALPxWv7GwUoZlBQQN9AF3dAJvZAHdVhbWJvgR10r 7IX4Sn+BqT2EQu13K5C91TcaPkQffnEzC102IBfbB+70wU87n2VB/Nbv8kGqGDvwh8H1HUjycw8f ZrqvMwj+Pvwxtc0tzQ7eUbDxPsTx1Ca8GRxHzBGeoeCR/gPdxoN9rSHSj2umNowxkl3TzVBFs6mx y3WCeYCO3wyeB+lvfGCQVbptn6+U+WCoCOcpcuURvshHx377c4OSP5mHiJIHbfE8wPLkweC+p6YM WHnrpDV+9C3Hki7qtfA0+9xlx0Lrk2a+Z9qAr1b3BBNEH++n2Xzp0g+Nq8zqCY5t3cuxG7LX3e7Z /Z11Iv+ClaMxRLPnWzFNSJNW7ffHOcar+E1Ctmewvnids0wdOzF0X9t5S43/tcJJa5YxJ14Q/s++ 8fbXbxKOOWnRN/VR89AzXsCi86Ap3OuLc8+p2AftyH4JXHup0mvPVKGbTCjEOIvOXLFukxsMdSRq u49lwsjpK5bHnQkbsJ5AbTFKPcdYmh8aX3wql2PIGiAXHsdf4gcEP80fVenFK5KHqP8JigWxMzD3 FCcTsVWjn53f3KIT9uHH/rTqj8xaeKxE1vxsQOp728N2vHZcMsbh5/N1lfsJxIjmXle4dy3CPVs2 7v/fvMIy5XUjbILAD4bI59w+CQ5tD/ehDGc2hCsSdU3lfiwG9y6Fe9rHl/7TM8e+fx6EDI5K99m9 ms2P1GmCL9rTD6COCd3wjwbsWtsTfDKN7RnFNmcGz64Cbyg4hd9957JB1tSnH/VU88TihUp6gGyo wXh7MO5ajN8HASjEdgA1NCuaVw3PvwF3lPzOOQ+gj2o6s6bsc78M64nQ/uDHaaxKE2vXLWKWfanM ThnzzpxLoeMLuE9QuHfHdeaUwnIUhndlhJXD4IypZejYpsdCOt7JrkPcIzEg7+ddh9ph7J1H8A1j agHs89KBFj6O2qQXbw2nyIfCCNo1YVtlNNJMeX/ZT46TMZ3sagTC/BLX6P1bfNznBOpk/mk8CN5S lHcLX9fYd/QXA7zVQY7Z+0TdPO5R9Wg09+6oPaC+hdRz6QZhk2+mTR47b+qdrd4hDUJkSUPJE5w0 NX5WzmD0JOmfErqtC04nu9SLs+CTqHgkvlf4u4nf0/Px/Sw+/DLcF5NRPEj8UoFfHgN/WosPvw3x 349a7xK/kvhE2RID/zROtDEO/BLBo5pTid8k+neK97iK706IL/5jM95F+fELfsIx4h9wXx0/6tqL Xm/luN4uYn9aR1nKGZol4tGZh/O6Qj7SIEVbj/9vyKbh6Ul1EfNyC6OdzltJvPcalL+0CxHltLHf +F3dnb15dZ1Wnunvbl14shPmzeK+SNIisZEgfiQWa7x96rV3LXkd2+O1BePZVY3Xxfjpa4zftVT8 pf/uP8GJYy43cmZUFzL7/2KOizIr82wzLxmk/3qlydeLFBaH0xwEafFyS1k43fEmLaXc0hZOdeZj W3Jxl5KlJJzkRCrHNHHLsRhofgdt/mwWzoI/cuAfAeSNk5YPAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221_image010.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC60VS0hUUfTcO9P4acppeKh9kIGpIJxiMpeBWiQSKcNTs8CFnyweOJpavYVRE0jp yskWQRS6iDSoVbYJoVbVosBNhH3IkdBFH/oQRGWvc+69z948RxHqwHnne88995xz73v+9OEVELAe wmAIbk8DgxwAT8qDHyjykI6+W315UOJrqK7cy4Qfg9ywpAABn4xClOR2+AtZiCGH3MsBohgvtK+6 krxpTQHqveCCVVJZjgE/uW0zXkjc9MA6ZP2I2YhBxdP++YovFCeTvGVZdC4IIOYhfkZFrpIJ1nDp 71eyjnicyXiNv3GxA5J2CRDqsG5xaIMePGUNUhOpDp2oa4YOWAkwjQKVxphm14ug8GsQJm+MwwTj 0PQlCFPHUmbV3B1h45RDfhJCj5hGNJAEzdZdRl00ofPRQdDIPjwBwoeruO9QJh9mHwBhohw7tnFz cLIvySqwHyNXd7Hh3e1QUwyQUH4vUe77FoQI8kSdgEvEHgTRkwDb1Jo8ZU9grbnSZSsE0ZM31pFT Utzi6J/dB8vRB750H+D/9KEjrcZ9H4ICxTwjnS1YGJUFO2VZ2zJjpunid2EAF40hhen5s841/Wgf i6TM74wt1IagQuvuArj36hbto6dMkt0+3ZPFjPAJ+rTUpswublluH8r1PdoTQ3HIZKf1pz8GoczV B9K7+8Ah833wLN0HMWInoBU7sRP+ATDaeUQDRuZKWQxnWWjP6bzJO8hISJQPMZ+ar6ODrfBgSueJ HzqPoc+1gUa5DnnS+x050rlJR2jPzqHoJXZ71oD+0V51HwzxTlwvKmbkP41xxrviYl1FVbugh/dL Om3Ug32PYr90+4qJmvlVfhSj6bXOQ6+lnbn2TLsP89ai+0D1LlK9sN+pM0w+j8574uxbnUL3G0x7 H6x/Vsbg8X3SX1C6A64GWApiyEdERdJnwZ3PRQwyi/5rUdaUPqB4etc9LFvku5rbD7ufh/FlJhvH GSW6gxUKC+P0UhOXI7w3If7kby3HpMl314i39YRq2syQ3hlvXnzDKeZ2VaccbmWOBCuPxJbPSc5+ q7Hs4MtIXNAIk33J94bFP8qZqb0jzWFJ7gZ15MiLLEcOmWOI3zX8AbCOgmPYBwAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0221_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh9gAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYAAQDl ABEAgwAAAHAKC5IJCoIKCp8JCrYICcAICNIHB/8AAOIGBvgDA/EEBOoFBQECAwECAwECAwT/EMhJ 60QY2807z5onjmQpgYiprmzrfkCavqoc0zhrz3nv/x4eUCQcGinFo3KZ7DRvm2cNtoxapNJatjrc VppZL9HKJSOptJm4fDWtL+34KS0/l5NgnPDNzrindXN2LXlfbFCDcHqJY0x8iBIGfhgJFyGKSJeC FpIalJZFeJpafiN4mY91YqNfIDprKEkFCAoBBwKmZpgWs7W3uYF/kCeFjD17RFtqUWGsZMsWBwgL AySnwRTS1NbYsc4xxcapwJutb99epcnlFAoIAdyG2O3v8cYrT+Hsx/fEwrrrguyaQGABgkrkBu6j UPCgPYX40IgzgizIKicRMe4rUIkBggIJXKGE6sARgEeQjRSNAzesZcuVjWA1cwnzig1ICTx9Sglu pL8JOWXsFAgqjb6XWtw8mglQD4+aC+VFBXQn2NJDGT94o/oiTD8ddzRd+4fV2jcfUF2q5Vd2bNm3 OSIAADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

=

<= span style=3D'font-size:83%;color:#00279F'>•Closed-loop system dynamics become

Method of Semi Discretization

•Discretize the period T into an integer = k intervals of length Δ= t such that T=3DkΔt=

•Assume that the time delay τ=3DnΔt where n is an integer

•In each small time interval, the delayed responses= x(t-τ) and the time depen= dent coefficients are assumed to be constant

x

%

Ý

t

Þ

?

A

i

x

Ý

t

Þ

=3D

A

d

Ý

t

Þ

x

Ý

t

?

b

Þ

i

i

+

1

=3D

u

t

5

ß

t

,

t

à

,

i

0

,

1

,

2

,

,

k

.

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image012.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VZeWxURRj/5u12uy20tFuKreGoXFbE2i4Y/APY5bA2wXabQgsxhAAFdBNatnJs jU0s4oF/cSUQFZL+gVZjxJggkkCEyBEkxRBMY0ICVGKJHKUFKlYlPL9v3szu7Nv32leKcZLpXN/8 5rtn9vWXc6c/Bl7WsAmwhvf8NQzSAFy1IwDbiuE0R38ne0bAzrzF5aXzGKdjcCRqtACRPAOFWhqv hXhZjBPjlfHfOCh2ARS8VF5K1LQnjPPpYCopWN0AQdzfY1676obmL1yQjV1i0IvVJ/p0/ijRJ7by RV/XdZILsrCiaHAHJ9LFmEqGZtAPF+MqkocZeEsf4malbJcqwLIIua+D1bAeCqAC2yi2VbAO51ZA PTgrLbdDWjNW6qeKubx7Pjj/2UE4yjRYftfH+cwStMj6lQLsf3UtDLSpoyukvfuHD7S3K7RpS5fw c7finua7Po7VmV7DW6Kh/czAgT3ZNI9jMUd11ogaQzAsxNPLfdX8jCzEPn5bnOMKbey4WqF5BR2t rbpn8Eg8bW19C4px/OWcBtK7fmtXBT87gvu9wl5g2OTYqk3GcJJiP2kH3dSXNtEsbHJUi/eHbhPm bs7b2LDVx9wcFh2w8edcOHw+F0oR5w3EK0PctRCBqdiP4AydRueVQgn3xhdLenl8RG75YD62QWxJ tpnYdmzcFMPGUACPjCNBS6UP+3Qm0bkVzqb7oaml2wfTwU/RirrIgrKbPmjCudeyQ03XusnmoaaT MRo3ZImzTyLdudzxM55gLIZHa6pNpmA120SzsYPLPja42jZALVpiGgylLCraxaRPUXlvT5jH8f6x z7LIpiqN6sGGOuD94qW8Zaj/7T1V2r5TOEbfbCkPadTSHNwJaRdwP9XTHNGXaHmMB50F+H6KDT6J e5e7tzEaNAd3Mo/IIWu21ULl0wYm4e/7cCnfR30+r+gkgC3NURU6SpBNEzaQdsAzmNkOLkX3bhvd s8cWA/+vXVHSx2LXyVAIkes+bld59v4uHzR8EmpqxNqSs6gpmOpKyEttuG7WvVvRPV1Nv/+nuq/S PKW90cobPts818hyoPj0GOyVuB53ngMYOM8VuHJ4pVigu4j6Ms9RWfLTXFfZ2bnossgn5p2isw+i L8hLE+eoyr6qe68nJ0n3KYruPY5yjh+GWppNuaCjh9+7uswFREPvlkq/4VeUC9qOoC9b5AKaF2+Q WJEPiPPzKjRNrOX7qum1xeklndwn+ToWroat0SmuA/7e6Kse1nsGfZXeQTTX3Pwn3jmstxuB32cG fwtEJHyOdYY7pitYLqqqe0A8s+49iu5T7XOOovuSIWj90exq5YtqUX2xsKt/X6RKsXX8xwdR8sVJ 2EYEbiVi9GdXg38jLmV8UluI7TtIRzkHRM4hnlTdM8Q26z7VJvd7HcXAUOyQqCvKoSOv+4R+jFJm kUOnQDwHRnB9dFeIz+/tMt4fybqK5+fry4z3Eojc3R92m4LdJ7DJ9ykeOpgiBr6BTiAuYdOapJ3f beQoeXeodhj7cFyB2Q5e0/vH7l2k2kq9N9RYspp3mc5yQjMYftT8mWZzdz2+/BmPtTM3Bh9rlTKv IsZA94tVrAEYsRb31RxOW5yWvoT634lYy0LlEp/yd08H8vr9ledd5Hs7Nv8VrdzdFyU/PYx3V8YP GLcCj/iSPLZ89ExCDDfdTH43pJnsoP7GVO05VqzJ36LZuYn0ej82XySqLJlYxwm5aqrbAwzOHKP5 D8TcK0lZ1ygkV6N4Q9n5tTwrU+zNtzjrgsOzLuF741OTv0v8fEE/XthfxY8yZ/gbhDyq/iX+BNIz 1kKsT5nwvajUagf4YWgPLDDFt8QvFvQBIYOK36454z+A+vnVdB9I/FJh+4UW/I9zO8NfifgnbOy7 UNAvs7DvVYf4l0329Sr4YcH/mxb8T/Q4w5/Vo+s9DuJii9i7w0KWb1KdxoWuO4mLHWLvXouztngH FxcSc6+gabXALExziqnrdrHWKui/toi1cw7xw6ZYU2PhkKA/ZRELB9IfLRZU/tsE/UUL/vuGOcOv F3nPyqYXBX2nhf7PDh96LHQKf71vEQvrMpzhz+lpD+g2+rkv6S30U5/pNJe2Bxpt9PNQ0KexZP1c yxy6fkaKHxgTWbJ+CrOc5grjO/JAuaJIvB9nWsjybbbTXNEeuNDPW0yeNZsZd9A8C7lafE7vIOM3 nvrekPiES3PlLDnubjrED6Bf7bbhv1zwv9iC/805zvAp7nab3kXmt5Af30LXkJ7eHCPld0vRJz93 MS/na5gm/3EwXJsAaxitaYxxmiKWx1cY/YrnvTROPRrrP9pvuvISNr7rh+tWry+oWB0tqFpXtyL5 awphPie+BaVpOqi9RMz4l2lnmMwWiXNnvNJrw/1+fjOQtKT9bFCcuMT+rkfc7+6Pf//A/KdY8S/3 lwy832OrBxgUTqpikWQbyTOkziTviWMthmU3P/AZ7iR7DE6f3hhO3P9VrqaKbzyj3BPgdQZg7d2S O8o0/vQnRcA0BjMtdCJpMjnNpeCwmPRyJZ+vbAjGeTNWxuALnVbCwZSYRuWeYr4SCI6I2VmulPKV lcGMJA4W8pXLMQ5SYyth4/9ewax+ZNziQMYdMRnlzF5bqVuFbN4k2Q6ZZIvvaeMr9ciD+eSLtrJ1 8pU5wewktPsmvcfRHtqijWQDa6qI2WkqbtnZLNGy3tjKPGZIn560p5wZ0qebfDfZZ13c4/8Fp5V3 Y9weAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh4QAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQDV AA4AgwAAAHAKC5IJCoIKCp8JCrYICcAICNIHB/8AAOIGBvgDA/EEBOoFBQECAwECAwECAwT/EMhJ J6o4600v/2DmdWEpmieqruDIsu5rxkBMy5aG3BWP/5ubDygZEosY47Em4rmUSxwN+qNWk1HOlIkl ZV+G3WWXQPZ2RDG6RwyjyWavZQ3z0ONm2537c48RZSgFCAoBBwI5XVd8bDpqYhuDhYeJcpYrY4yM a1uNTY8+koaIKwcICwOXmpqge3M6S6aoqp1noI54m6+VqjKyqZ4fCggBtFE+yK3CxMbBmHaKurzT Hcocw8UsBAuAzUVWKeFA293UtTDm00/iP+SB3001FwVlDAgF6nHgZ6v9LPQA7OHLxcpfixw20nFJ SASgQBK33iR4AwcPJGooXBlUMfFPuVVPN/bJ2TOiFSeSRzrK++iEoLOXR0Sig/ll48GavRaGSPZF 5otzOH267CkE3k2cNJECzSLUJlINEQAAOw== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image014.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VZC2xURRS98952d/sBlm0LhVKooMYPlrZoJAbtolCNCq1bWqs2KLZgNgEs0LqN 1lhFQzUmVogYRROMGH/xg5qIkQgRhWqAgEQlJoX6AVFoqFoUI7jeO29mO/s+3Vd21UlmZ97Mnfs5 986d2fe+3r3jWeDlJJsCi3nvhToGmQD6gtEAfnh8BI3R7/neUTCy8Oa5ldcwTsfgpvuNFuD4eIML tfS8BAbLjzgwWXn+vRSgVAconjO3kqhpzZM4ngmmkoHVAxDC9f3mue880PGqDqgi5ADpCRAUfZI/ RvQLsI4T/VgsxmUEsI7C+gsOZIlnKiM0gz5HPIexNjODX8PfuFgpXRICLPMhAkthEayEYpiHbRTb MNyNYwthGbgre9+p0t7GSv0tIUSv8NzgB9jf8Nx01vprED4QegYELap+ohj7bxyJAC0qxbGHTwZB GxnWpjfUc7mduK7j1yDnfzirjrdEQ+uZwQeeHk3j+CzGqF45qs4wDAvpdO2pWi5jL/Lu+lvI0ata +2eGNb/UH+eafgty/Uinzpfvg1J8fn3WcsI9dnztPC67A9f7hb+oHFwXgaZ7jMfzFP9JP8RMfekT zcYnW7TBfuo+YZ6OgtblnUHm4WwxANv258PmvflQiXxWIL/rkO8SaIap2G/GEZJG8iqhjEfjjLKB KC1tPh6E2diGsCXbZmLb23pPnDduBfAKuyUtlVPYJ5lEV38iCHeNrmr/GNvHsN2A7aVQzuXszp98 +VjG4po/fIx8/m30aOu7YsQDASH7k2NWeppTfULF7BPNwQ+6897gsLVAI3piOqRSGsrXMhlTVB55 OsL38caJF7NcNK66rkZ7b/lSoLa5tIG3DHHp6g9rz3/aANuuCmu99WGNWhqDX6q0qaijrEbmUDyP +yHGKvh62ht8ENfe4XmC0UNHaA3zihyy+IlGCNxWw3kS/+cfbeDrqM/HFUxoH9AY1S6ZVxTbNOED 6QeiM/tBV7D3OGDP0rYH/l+/AqTHr+fDBdD8U5D7Vcre2BeE5eur2tuwbsid3x7y6Ql5aRfOm7H3 KNjT0XT0X8W+RvNWDkSrfw465rk2RKl0RxH2yvR05zmA5HmuWM/llfYCnUXUl3mOSv2eq/XrPr8a Qxb1xLxT8vnp6GXy0MQxqrKvYu/35lqwz3DYA15X+acMUi0dprxQ+ho/g2MyLxBNhOhqwlwu5YVd H2Jc2+QFGhf3kXhR41RLkGyN04tgMM4oTif0VfHxU31Gjqc7UWf0Ir2j4w88f9gAJ8TzYvuCgehP WG/1sgFJO/uE4Su5h1Q/oFoPmP3gNZ0DTueD6jfpK5+zryBd96j/ylfEJFAR1jQxNy5YS5Zyekkn 10m9tkZqOc4HEPtbrl/CZfbiGJPBCoY+OUqVhWi70VcFs4371MpV8xLP7GzrWeEb4k7lxm/qflNz YDIabwqyUtX5bGPT75DPE/NIeQoZZDAXdv88dC6kSrl922eno5QLz8O2WsRsNfIYKufOOGa0Tc+c ivK8GiqI55FO5NWN808++Gd0A85THB3A54e6T0eP4lwAaXvpXKHYxj7p04u6fnRomk7raV31OmPd Zi4nV1RDr2ohyXyPaT9mPUv9Dv5PJXb8DrFgzl8TxZz8z3d/kTV2nHSYL6oseVgnCT/W1X5ZwaB7 K42vFmM3Wm5URiGsZoFxT7GTpSuy8sTaSTayaL0bWT39NdpLpn0s+U8S9BeImFL573PJv0XEjYq/ 5H8h4Yy1BOs5Jv53Iqi1LvhT7N/ggM80QX+FDT47NHf6H8R7z0umOJH85wjf19ro7/e4439lv/EO I1lc3S7WrrSx5amM1ONK9Uur8Mu9NnZ94z07v/gU/u2CfpVNXF3lc2fLVCEjGW7rxdq3bHDLz0wv bpsEbh/a4HZrljvcmrCuc4jnLYJ+p40tmdlu93tiPKv7fad8Z2PjlzezU9/v+wQ+X9ngU5GT+n4/ IOi/t8HnxZzU93ufiK0zNvofHpHe/e4X998JzGrLilHpi9t6rEXM8AvRmu16P2D4RUsatxEet057 vkTYcxmzxtam0end83OFrIU22HXmphe7RoHdChvsducNH7tktrUI2x6ysW1nvjvb2vBG9AUkz2er hG2dNra9M8btfvUkxIRf4U98aWyN+A6g8j/jkn9Fvz8hX6r6rxH6P2ej/9qx7vgvg0vYOod88Ip4 37zZhv+hgvTmg+3C73ts/L5kvDtZi9GW1S78vkfgtt/GrpxCt373O/p9v/B7j43fby506/dHdCe/ 9wj9f7TRv6/Qrd91HlfqfwXz/4O1+P/gCNKPVO7iAdGnc1Vnfq5XtiY/WuVoU+AkozmNMU5Twgr4 DKM3EbyXyaknYP1L+yGm/OM0vilFli5aWTxvUbQ4fPfShda3H8TzEvEeMlOLgdpL5Dn4VcQdT+bI qSv+oqKlMTLkq1+Dk2ZZz4aliS7W953leo+jHoodZcntyFAQsWIkZdnIGIauXhuPOsuSdkmc7Mcz hsFrePLd49Fnh3l5csx9Jv2GY4vPpKfqSY847+nOMsYzBf5gAPa7SEqhLxLlWePFxpwVyrPQaHGa PE7TE8qOe0bOTOIzLSF/XDdjpgj/HdNMJJRh4TaNzxyMc8uIz8wxvtOGAkPoe7ujvoOyW02yvfHV 7Xxmasg3hIT1LiRs4jRNoSyLdVscsdrpiNU+R6wOOGLV5wIrP3O2JEvILuLf/poiWWBFq4QlR2uu CxmNigxnTi2cU1to5BC4r2KJSPniM518piLukcE1a/jMsvjMIIavsOQYbuc0i0OZQ2i1x1Gr/Y5a 9cS1StzN1l2s8/zxD4qmP8bSIgAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhOgEVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQAv AQ4AgwAAAHAKC4IKCpIJCp8JCrYICasICdIHB8oHCNsGB8AICPgDA/8AAOoFBfEEBOIGBgT/EEgg 1ryX4Q00/yBXhWQ5jWaWemlLWW4swnJtkwfDIHVegCxS8LbxEU3G1lB4/CSbqSd0GtUsGrUGw/FZ Liffo5ZL5YyVnLBEfTuXSe63PM0mGQoJhiGNYddld3l7cwCBeisbdX8xhoOEF42PkjptAQMMD4l9 lEBlDZaYj5+XmSVenJ1Uo6GSE6ulKQo6GjqwrRmzNQIJEloDfZoharPEbLu9DL9yxwC+QLR8THTF dczOdFPWyc8YBQwLAQfKTdSo2D2DBgwHwCrBa1QH6evRN/IS6uydXvXwU/eF6HXxZ2+evoEdJuRw IOBdK3MEQyygFsAdGFPPqEmkKGdisYrR//hhnFaMhEdiINtBOTkrpUoME10eKedn0YYCPCYgEBgx Ia6XRHBe2Hmwg00QQnXyBMNJJFOHQXNKILqJ1tEPSacuXUPJHAEHrLhig0jEHFmjRgcsGAcggA5H QTzEBWpDLVu3hy7esHsBryOfctvNpVuD7wS/egPvXdv3rTvFAApk0vLjosauVCBaJYaWmAIJl2Z9 JpjLos8joRmMTq1ar9gUqVd79jeY65DbUGKDng057lHdAFiP7i3hQddargVP4Zz8MZpUzR9ChQL5 NELT0gFPJ0fbRJjqcr73HHnO+i200akzH/8z/aOSZufA/3NW7tUY9V8/F3a+/35p/gUo4ASAEkQA ADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image016.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYa2xURRQ+9+6ju0try5ZiBYotCAG6Ii02mgh2y6NUhdLctkARK1CBrrbQbim3 iU2shkgFDWgTjK/QH8RHQGMCCcYYJJIQJGKaKGp80SLhIS3WiEkJxPWcuTO307t32+3DOMnszJyZ +ebMd86cubPfnz31JrC0B6bDFlb7dbUCXgDHgXGA5W4vyeh3pjsZfKmrVxQuVtg4BWa8YpQAV/wG CpXUroH+1Ix5mtRuTQKY5wDIXLqikEbTnIdQ7gNLcmF2AgQRsNfad8EJLR84YDxWEzF7MPt5ndaf yOvpmO/i9UgkQvuCFMzJmP9EgY+3KSWpxvhE3tYw1ykG3rp/cLKU9gkKMJVBCGphEzRAJhRjqWOp wTaUbYCtEF/qKNXUjzFnYz2By9L/8sNnQWRy8j3+TK5nCh8r5B079ykFboD2t+crBxbUQDMCtHDF fsL2zr/98ATWqRSJ2q7wxvCGqmfg9fGraKeqgpgKn7cweZWxMUyk07K+clBpXVVTe7FNWKpDa8zk vAPvi0RuRUi/Dy+FoPW9ZxnGzbVtykW0YXdbMdOhHed7pHnL1mjqUzuM5gzJfsIOEckOagw7CF1H bwc/w+ru9sP4+7v0jnePmj3JvMyC3cp3TkMX8k9itbrHDz9ODte7hN2+TWOuSz80r2BCuP6r5VsZ dlnatAc8W37Tj82+qE9Exndz/YM9hNSlF10+wjAOYpsy9b2M5aU7TTc1+4mh0o0XdFn/9wNdep+i mPoCX//soU9/Pkw4WpdObRoj2yHcka1Y7aBK3DtinwFGxXaoQvZzYeRpkaPozCJcJhUCqOfcM7f1 PHHAUEZZrjcpqXDiy9u6x50KM7BsYToAlDCMwfmh+fNOZTAMUQJkwAv4S/wA52fN14scF3y+LBp/ jHRB7BS0PekpzsoSXGftL/c5CPvV52/qJfv7dAwrkSnX/ZD0xcpmQ19DL6HjD970Adx3IoaVe4fE vTMu7uePinvSc9YIeK9DaSbf31Dc2/E+C0tK9W8hV5jbU8uaifc5fM1YvNN5qUTePdcJt5/3dBve hY6t+hymn8w9TnnOyr0zxhmgM33lP40/Rnx/ElIYJN1tj6gGvpCpfP90vitRpnBZ++9+2JwVrl+W qBw5jXVmAYxj2emN9d3YbvomDURJY1pQTiVzILxcSQ6QBoWobxj1LkL9a6AOAlivQwntivZVCDnM lg/m3GC2rcM1lpA9uo37ZQGWnY07TGwi3M11FmMp9WFdtsOVxiNRZ8Alce+OfQbGiPuxiy8zYRbU XfXzuNIfr8nHm7iPBxMc6hzo9x2aO6VnJZP38bhvjS8s/eGHk5U39KuY17qVG2Ks6K9L1tR9vZoK 0zQ1r9dX0P7GbMdHucZYiknkUySTuX8RAazcuy1nwM4mCTHOw8C4lDMmdwL59HBjUwlKQ6bNBvfZ we4E2WcpNj3t9jUMFps6Udfj56PvhE+uRccmoWPryYwB56H5WvSdkCBx74nN/Ridh//XrjBGdqWz mHh54FkMXos+i0PdCR7L/WD3TvDGdU+PhrcQW+Pg1GyFzvg8h6YaH6eaut65V6FGS/A1xc3vh817 qyDl8VIVNE2luPDOS+uA5lGd5ImSjuSfJKMs7rR1uW2K/C0vr0/jTiDO0fpatkZBUQ0rKx41ys5Q uRnDYA3Xk3OWyPXLx7w+XKp2FJeq4jElrynbhNa02oR0mcptId5vMz1GjJLfD3IcK+NZJC//NqC1 V5Wfy1fg9Ock38Vly6NOhZFK+H3QZPlmE/h+871gvH1l/DQlPvw8vJe7LH4n8AN8PJ2buy34bWp8 +Od7jXF2/OTx8Q/b8DPJMTJ+XBI+2T6Jx9YsC/4hxC+PA59iwGOWO0vgL+Xjl9von+yMT/8AX8OO nxI+vsIG/7Bz9PxUcH4qbfhZ6BoZPwkSfiXHr7bBb40TPxv9Z78lRgr8ao5fb4M/1R0ffg4M9E/Z /xuk/5as/n/cHR//nb3n8ndZYrk1nuTjpi7h+DuwPUH6Rp/A9XEoHma3ceIPAUhUp8Me1qfi1zmV c5V01qOo9A8U1bxs9BTMt9SLEemmMP5PCtVuasgs3qRnattqN0Tf1oR5L3+PeNWIDZL5IokLSbHT xLixqkKDPumN+epg8+cPPd9h0aNnhPtw2ukxjPkuU4+BeD12+8oZel9uu/nD0CfB5GdQnxmGRh5W Bvi3+0QnearwW8OTBAN0L+b6JnGX3B70mLYWPca7Iy+YbGopegKs53zQG4WWZ0Fz8p4MvA+oJxR0 mbYQc5aynkAwIQqtJCZahQXNbfZUsp7soM/kWPRUs54cU+v+/TQYX/XY028Hex7Z0xD+BUanmElU FwAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhWAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQBM AA4AgAAAAP8AAAJthI+pC+EMozwuzIss3ls3DnkUJ4JaqVRPmKCR2zXrAtPZLFVgZtS1zYtNcKOf SscatZLBlM1Ial58S+fvgxFpoRRPybUyql5Kb9J8PNGQO2cP591qlXRp2w2s47H63p2ZYvYi+IZy tcP2Z+JQAAA7 ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0214_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh3AA0AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAB AAEAgAAAAAECAwICRAEAOw== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

General solution

Assume Ad= (t)x(t-τ) is a constant or a linear function of time = over the small interval. When it is taken to be a constant=

•Zeroth order approximation

•Mid point approximation

Choose the zeroth order approxima= tion as an example, a one step mapping is

Construction of Mapping (1)

x

Ý

t

Þ

=3D

e

A

i

Ý

t

?

t

i

Þ

x

i

+

X

t

i

t

e

A

i

Ý

t

?

t

i

?

t

!

Þ

A

d

Ý

t

!

Þ

x

Ý

t

!

?

b

Þ

d

t

!

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image019.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VZDUzVVRQ/9//4eDz58oGGHxhqOjU0RJ1u5YiV5mYgMFBWZCg88a1AyI/HQuPl yoitoFmSlRttWmtZc81pUzfdDEdMN2e4bEuiD5lfCBktnNbrnPvx+PN///fen3Drbpf7dc7vnHvO uefe/+P7c2c+AF5uwXSo4L3jaxjEANi+igNsBx00R39nRiVAz7g1OcufYJyOwaK3RQvwzTiBQi2N X4Sh0oV1mm68+AGADBtA2rKc5URNPM/gvAMMJRJrBMDjCNhvXPslAryf2WAsdmOx2rE6ZZ/kj5f9 FKwTZN/n89G+IBFrAtbfccIhx1TiNEEfK8cFWKuZwCv5B5l1pVmZAEshuKESXLAZ0iAXWw+2BbAJ 59ZBFVgr3qo8LeN8rvban04O6i3K00qxnv/kMJxgGpTednI9EyUtqv5TGva/6HEDqg2lm/I4r3Yu X1tQUszlNiCP97aT419xrOYt0RA/EzjQMpbmcYyymdzQ0oTVYmNYSKenBou4jEOI3Vol5djytjZ7 8jS7pKM11Kk+UerU8GkdZPzhhM+za8juvpu7c7nsNMSzS3+B8El9+TYxnKHzn/KDL0Rf+Ucz8c8J bag/ev84IZOa7r/rGQakG3k5bsWvnoGrTt7yQFXyxk1bvPCa8OMK/DNwQ/hgVzzb+JAKGvIZ0vww e8BD86QuHgmIAkHfft0pJQ+VmzhX+904juPF/pL5Ax6aJ1qie/+6kPkutt1bt9UoXJC4TEdrxFMy LqFO4fyjWfAJ7eWqyZlh980nAHMupEJK82zbY49wO9Sq+D3PbFp302yb1/uXx8hzEPf8cYawG+UV uOH063QU54knoy9fq+5JZ0+WlEE2ng1aozFvn1VzTkhJbGIVdWJcjTgbsZZjpfErE0t4u4uJ3KZK 6x0801oB8ufz81Y4bzdT54XK6y1unqP2T3mYIV0s0R6uqQzrE5vO9hHB8xXfyxYoQ+svgNEWL7c3 5iKWBc2bizXvGZ6XfID2K41o4hLLac81woYbmsrg7PE6bgOy8b43Szgf9Wle5mh/UQk241S+psm1 Cc4iINsRvaJTfEqvk+4iuNSeCl9mDniORLGW9l4nvydoTsQEa3lU3ikrsU6RNnwJ64+a31ZQKms4 20fobB8ZxPb3L+7/X78CjM6vSv+ZMAuqMdfo0jTsRz/VfLhqey3W1qTC7XSOh9u+3me0faTBD/pc FCxf6en1OMqHUZbOT+aobBzq3J/KLIjFys89tdUZJbxlmHPIrvvaSoBsm/G8sDfNke0vID/VM7o4 UXZmMo+p+8xo5zm6e+ks+mFy7yo+P9gr8qPyZ39cwRBOnxNOrx3wXFsrzpmifbJP3DBKN8P5OWn0 YZTO9tHBz4/O9vNHYfnwfk07+Ja9liX52xRsQyHyHNWZim+bVOwlwSy0w7yOe56XmZinOapClOgT 7qlv73nsUUkwA9tqnKX33CzECO/XJFMdd+Iq+RWkX0l2uNwVHSSP2S2dgdH4YbitKE6TrzmlfURZ 0Rs6Tqt1cfqRjL1QZ4DidDRngO4OivNuptvGfzsDd41+sI8wd+nv+5ggb637l6+GYpvejyON7VZ5 X1Bsh3oPLZHv5PK9gx7CKT6a4vdVA2K14/o7r97xtOI63SWXcLyz/Z7nKq6VIm0z3UV0Z2Of9OlG XfdccXB+4svbI/i+vuH06wpSr1YpSbNw38cY/KD/ZtT7c4pcU9+Wd+PEPWPl20bv/0JZVUnG+qCM 1dVFF7MYtJ+k+Tfk3NMBGU+UPOxnY7all2w4uTadXPqWjpP5aapB7jIcFFmQS/7fY8g1Cn+qpE83 2dcAs7avy/2gHTDc5wo/XdIvknvQ4+/VrOFvwfuzNoj+CyV9lon+Y23W8Lv6nXDAQgxkSd4cE1lH LMqqhTqeI4O9iZSsHMlbbCKrIcKyXyCYX4ol/ToTv8yNtOoX2s/wt4TCr5D02+TvT3r8+Chr+Fn9 SfCz4b5U+DukbxpNzkVxtDX89f2rtp8OYv9GSf+eif0n2a3G1XD723X4rVL/Qyb6PxdjDX9pv/iO Che3xyRvm8lerjusydogc1y4fNUm81WHyb4ax1jLV248IysNOV/hd8i5TpO4umgRP6t/eD7U698p 9e8y0f+FWGv4VTLf6u8m4300KR6gB+nj5Z0C8vfFZBmHNmbn53WMpn6MjdWmwy2+pjHG23ksha8w +kLkvRhOPRnrXe03n+41In4rdVe6NqflujxpBZsq1wV+8RLmXPkdHaP5wLw3HH3otz5r6CwEZq9f YzYiTM1sx+L1VeYO+Uku+G0B/COTH+HHGdpR4G4VjeIJoXNmeJ0jzXRW/PPD80cF3TuMCCfawp61 AP+ObK92P85QjCvp1KbLb9fxEdOhz//Pi+ARrPSkvJLpmCiPR7YrOQS1JqlT8UVG1OUuh9+CCmcq X7nsGuP3sVpJ5ytbXPYAnoV8pQt5guuXxWlqXfEm0aRocoLKLjbIjvSvVPCVLFeCPybUyg6+st4V FyCn0a+v8oBaaRX/v3AlhtjJMU6zwRUTwr5tnMbtivR7X610SH0dATydfKUKV4ZHSGBk2PjffwHi BjIwehsAAB== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhfgATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABABz AA0AgwAAAHAKC4IKCpIJCqsICbYICcoHCNsGB9IHB8AICP8AAOIGBvgDA/EEBOoFBQECAwTnEEhA 1LxYWryz714oamN5CYvCEOaUsiUIbHIo122G51NjMYZcQKE4mG6T3QXJGylzxCbAQPAFnEsiLamd KQYg7ZM3jnV5jami8LEwSRIBIw1gCGYcqUac1HM6ZQQIAAIKDjZ4S3kSBQoIC3eJfVJuH21iO1E8 KWJXWXCToQApbKCme5iWOn5cezqVAYcSBmuKW4q4EggMDKKSlKp/qW2+qAAOpQBDdnC3JGETCAUV stBlq8F+mnipbpwJqFuA47lRWgterXpnxU18OJVH7Epl19qsxHnbwNhH+CL2/gn8dQrLwFwHW0QA ADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image021.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+VZfWwUxxV/s3c+34fB9tlBRxLMURI+DficoBLFyYFKALU1/qihbnAiG3wmp9jY xIRzA0ncNEkJVQRVUpO0RHWl0KZSWvFHFCoViYiokVsRyaStSgVBbpXQUHBwW1dNFcj1vdmZvbn9 uNuzLbVVR5qb2Zk3v3nzfu/NzO79/t13vgc8PcwWQhevxbcyCAB4nqsAKIGjpdRGv4t8pbBy/lfr N3yBcTkGi97SS5Sbr6NQSc/dkEkPYMPnlOdHFwLUeACi99VvIGka8wy2zwJTKsLsBViL4yfMfX/y wuBPPFBOc2L2Yw6LOs0/R9QjmOeKejqdpnVBGWZa1F+xISieKc3SdPkS8dyMuY/peG2f4WAlHZYm wNQCSeiBBPRDFDZjmcKyGXqxrQN2gbtU42vUyjAvl6ADTdpxzKM/egNOMg3a/xbmepYJ2ZNr0cK3 3BYeffowW+cDGD56B/tBXTdsQoBBgXEen5/+RxiWYp1KmZYK0yIOHCnfijVnvBYbvFUmPG67/u6O /ofgSdLvp5eScODH+/iYu7a9wD5ADp9f3Q1HV+te4RcZdE5udO7VH29X+JM8pHPUJT+aDT8ntUx9 +vx04ohejI4ofAXH9yDeCliPv/2wAx7Blj1YfwzRqOxFzDr0/w7Yjj3dcC9MXtFtVepj998m+cXU fjkMf1g6maJ2UhdDAtD0XH7kL/oY1cpXsW3gNzdxnEGsr4lNpqidZEnuJSwJ+0Usxx7du1vigsBl iqwZT85xDnVS+YGxG0+a+dFccEJr+cgmZtiMcQKw7L15MPpEBOpWcTsMMLHGUebRXsL2wcF/psxj Xsc1/7BGtxvtK3AlbOh0AttpTHt1k9Z3qZqtb9sB66CJm5CeeblNtoUhUnaI7dynP/chzkOYOzHT 8xM3t/HyWRx1vxrnf2/Ujq9pxvFNGgG2rHyByXih9MyRJN+jXq1azkiO8hu7e7I4YTi3mROPYnuv 837F17IHvTYJd8B0k74vNGppFofD/a1aGa4tTZss2q/de4jpkQNwvEu3YdehHXDmF/u4DcjGrzzX xsdRndrFHm0kucG2L2vSNNE3N7wFyHYkL+XkOKnXqeQWGN4bgZ/VTqbe9LEjI+Nhfk5Qm+4T7Mjd 4kz5EuYqYcNHMF/QDFtBu8hZ8YB4Ztt7FdsXOdh+5vz+P8srwPR4lfovgiXQh3uNsk3Dq8jT7u83 7B/APFzRsp/iWLX9mXGr3xeZeFD3Iqf9SpVXcSSHPlfxUzstG+eK+8b+Zo0yxT2VfTVtvKS4J7u+ 8ss2INtOzG3iNqY2sv17OJ7yO4qfSDsTn5nZrXZeppxLZOdbxxt4+yfj+v4o+Vzrac7gXAvD2w9O pi4/qMeZlF1/TT9hpG4qh2hbZubQp9i+2Dl+FNvHpmH5/LxGX3/eP8AqjDKCZS5Egqj57TyIjs7D WgUsQTus/PX11GNMb6c2yvpUep1w3/rV9ZTfVwG3Y9mHrVHMSxAjP68Vtjo+hb3EKwheae6scwOx zbYvdtjH/K5iYDo8ZNuK/LTycljYR0+bxnP7aZ/ip0eF7+WKAfLT6cQAnR3k52NMWcYUYqDqs/lR Mw9+yH73cLoLT3WvU+8HAYe72cztb5lYoPtmobEwLM4XioVc96c14l7d+fInKcJpPRExuD2AWCPY /51v/Cs1jP109pzD56dGrqc+wr52lD1MZxdxhHXSZwx1HfowyMfTuMYhfdzPr4QNXUHoNSxm0kz3 g/1XrGdUwMSDHeeFchh0xWHsf4JDis+SP2fHfr74pLu2jM8XxR3ezCH/bnE1Oz6l7NhV5/ike6OZ w6Bi+5Cz7Wfs3ea//X696evW+zW1yfv1NQQm3pPijk3Wfg3z572F369DLmJJPbtKnM+u/xt+CPMc 8vK1L3bzOcewjcnNQbzTlihZJpIdwbMrsn43x+z/5uZsfu5q1sz8lDicXX7xbhVRvq9tu0m/a7v5 vqPuhy0iy1SJeb6wz9Ytv4szGDlF7d8SbV+23Pr01Ij1dZjpbT7fvB5l3jni+yTd0RaY5r0PH7a4 mLcTn4ZMPivxFwj5apt1TTJ363p/Ip0+ZnqnkfjVQn61WIOK/7LmDn8PfWRx0P9OIR+30b/c4w7/ Ir6QH3PhA3Extt5mrjddzjUg7olOdys5V70Y22oz1wGvW170ddnx0irkO2x4WVE0NV58Cv5OIb8X 9G/wKv5snzv8OOr/R9M7g8R/XHBz0CYuWovd4W+f6IW3Hex/UMh/18b+t/jd+lWrdsy0L0n8YaH/ cRv9Hwi4w79nQv+WpO6B+fzqhJA7befDwcL8Kl+8nBZj37WZa1vI3VxdYm/Nt0+eEfvkWRt7fhpy t0/KO4N65kv8s6LtvI0/byhxhx+faNSGHPQ/L/T/0Eb/Cy7xd8E+GHLwt48FNzds8CdnueNiuYjH fLx7xZ2nlFl5v7d0ZnmnOchulcy6roulU+M9qOBXCvwqG/ylZe7wyW5DpnulxK8S+Itt8E+5xI8J W9n57WJxL40xG78td+u32fqr9o8J/e+20f9CuVu/zcZX96s64UsbbXzp2+HCznf13ijxNwr8BmY9 B2sq3OGvEuegxGxgmf+fzZivucSsNd0TwOZOuwvvtJdQfra4l4L4n7ZS2NDD/PzMD2nyT+0SbSE8 zKhPY4zLrGQR3sPoDYLXAlz6Vsyfah+klbcY/T/nZE+iP7o5kYo29/Z0WN9aCHOF+D8ioKXBvpaN nvnP1B06y4E5bmjMCsLU7Fasf9HYkcz514Y+3mMZX9j8XgMnsyLraqWMHJND59r8OhfZ6SzHx/KP 9zmuHQrCKVb8zuo/7u2iWXygMHv4DZxsvaY8p4u1B+zGF+A3QQfdbTkpADdk4aSYl9Xiv5I53oXQ zQDyRbq0G51JtcGbxTayLlGZQ1oT0vPw7ZekOxNBY1USZwHveT8RMmJB9lTznj0Jv2XMnbznYiKU Q784lxlIzLbxQClT7zh3q2nuIqNnJ++JJ0qN2JE9j/Oe7YlZlnkOGvpKBmTPMO+5J1GmsOSs7wlD X+d1n+YyXYlADjbOcJlkosjwOdlzVqwuaBlznvfsMnoya/iY9yxHizhr5WX5tSpl2VoFjJ5Kps8Q NGJF9lTxnhjimleymDmtJMayV5Kxbx3L5ilk9GzkPasSfqOlgbfUGv4l48saVx4ejf8GH8frXign AAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhwAASAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAC2 AA0AgwAAAHAKC4IKCpIJCqsICbYICcoHCNsGB9IHB8AICP8AAOIGBvgDA/EEBOoFBQECAwT/EEhA 1LxYWryzB90nfuFodsKiMITpeunavmI5bUqOqfNY4rSQjcYhki4NC8NgpCUBy6ZnaOl0ArmD63d7 CaVHsOaiE2+HZm5RYiAkAz5yDqiZgxQD0M1u7oqFfH8kgX1jZBkdDQAGCgVTVWuGAAIMilACknpS c2WaYD9WnzVfiGiIkX4ECJMKDkdqfgAFCggLmJmmNZ6HpZw2oIWmnXFBsbEqnHBymbu7Ko7Gv75U U4LLd6XNd77ZdcxUkLG/EgGubI2HdMa7CAwMvMxE1L2cp9fa27qDvLAcw6HwHEADgIXBLTpfSAFA UKCCOU/hjKDJRWxPF24R7T2SU28MNz2kTNQoQJagTpmInf5ZnLPAG7ZNw/AFsWKHWq6JfACu8wgP EKFBKfWdKBTGWrd0FL2oy1ckKNGi8LY8jWp0qtWhV1HFq/g0qZesYKvRiAAAOw== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image023.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYfWxTVRQ/97Xr1tJt5ZXhEHBVhBCHZBsE+QOyGXEQldEtDPhjxpGNSQODTRxv kSYOYhBJCDPGEUCT/SfGjxAlysfMFhLIXCAhOqJ/kWkACeNjAsYSFus596N9vL22b7jITW7vefee 8zuf797b98v5s4eAt1swC97k1Km1DLwArkV+gGzo9tIc/c7x5MOi4NqVlS8xzsegZlCMAFOCAoVG et4MyXYJ+zOm5xeeAChxAYReXllJ3CRTh/M5YGlZ2N0AFQg4Yl373Q0dn7tgMpJ+KatLmvRPlXQh 9mmSjsfj5BcEsOdj/xMnfPKZWq4m+P3yuQZ7CxN4df+gsKl1qhBgWw0RaIYNsA1CUIWjgWMNbMW5 9bAFnLWSu2EtgL0Y6Z4KjN70Z/UTFPdPFrC2OzqckHYGJC+a3htC+qurEUCzoW8grL33lw7a+Wpt Qd06rncPynXc0Tn+Fd8aPhIPyTOBAwcm0zw+yznqS/PXCMdIH84vj9VyHUcRO3xX6nGF2zqNsKZy RmuNd3VuH9m057MdiK/DFy+2UtzjNz6q4rqHjggZJYdL7zZuF4+zTflTeYhbaJUTzSYnPVqS/u85 YRs7Cttad+exjRwWC7D95wI4fqEAKhHnLcRbgbiboQXmId2CM6SN9FVCKa/GxaX3DBJtuaHDMhwr cCTfluA41La9dbmffUvY+CqAR/qteKnFkCadxEfPxDs4rEMP9ueW3DeIPoRduR0ewXnJR/ovS75R yRNAvJikZyDtviHWic6UEy1FHsj2azbvBpuwPNRonsp7Rvi6njLf7SwIoS/35VR4ghOeb4CH8016 lD4aC3FMl2/+bg/OhNCFmUgFoQTjP39g1HiHiXmaoy7iFcyYB5cp9u4UsVcl8DY0YPRL4dFb0u7+ 6+ntpk7x6Ptx1MjBPMzGMYyzEexzOUb6+JC8NbYA+3J2JfDFSLy1uu8HokepzhA7gIEgO9X+NYS2 dl3xcZ0f7rxvhLtiBu1BxzH2uadXRRUe2aVsPHp6ujX2D6yxd5tin5U69hNU9483rzBBeZ0Dc8H/ hw4in6JVYB5aD6+KtmPvDq6OXmAu65nQa419lin2ntTn8QTFx7Qr4NkYZ+XQuW2dNvIxP3fjcLta q3fv5xpJS31rmOtt2t8A507tgEBXWCtBnk8/qONyRNO8vIMkmrpAlPRVa5pcm6bXIiX4FZ+SUzb1 Rmqh5OxM+LrsnvGdhx3ov6nzexDNdXT8jblgB24j8G4m8vSqvBsdobuXO1mn9bKbYw+IZ429x7L3 pzoTzHvUePn/T12qjrId7Z9lj23/7JT1lek9WzwsxsaDMYNw1n1fKPXrsAex+ofFPth9UOyDv+Lz rv5R4xqu1SMv6WmiWkA60/5p3h/Irk6pSbPUURR5rXWUnSJv1lp7Sq6pO/mDXPH+p7oTmnO+WnbV 8rAXyfdsTe3Fcgb9vTT/vpx7bcyuKxrtce2wKvpTmjpSuujOm8tvCgBPW3QNI13rQJd6T81njcIv kPhFNviLmDP8YrzPdFn2U4VfJPHn2uCfc4hfKmNqzqPCXyhzs8wG3+tyloulI+I/YKa8V0nZRpu8 d7md6arGun+FZc57k8z9Jvn/1qzrPga4eBx5z+RXs5TdYePX6x6n9QzgpJ6jsh522uRrRfaj1bO5 HvZK3w7a4BfkOPOlGP/r/OYgbt1S9hubuL3hdaaLep6Dejgm43bCxq/dvvHFLZNfJ6XsGRu/rvuc +dUk39lMfp2Rfg3Y+LV30qPVQ7YJf0DODdq8Rxcd4pdb9jez/YPS/ks29m/yO8OnO3uX5cyynlPT 8bC5ivx05kxR308kTfu5i+XwfXeSpj5u+bVZcIuvaYzxcT4r5CuMbpqc8nLuGdgfaJfjpluK+PYU ad6wLVS1wQjVbG1eP/afBWE+L/+veLU4mKmHMZNfT5xhsjFINxPWsXEhaWPkEzewhkjaa7yQd9nJ j0O/2y6649CfZYrE2NgoH53wTDRemriWZfbLY9Fl9pjGefIOPdU9C24nPthaq0xZR19ey3xPysJt j+XZ2Ct48B8954nEshIZVisFfKU45kvkTq0U8ZXSmDdho9K4UHzVjAXSWFXFeapjU1NaFcL9UlmV GqfZgXdRi3dJS/dK7/LTaOjmPOGYnkbDMQeWnuQ8TRiv1DhnLJZ6EisDfKU8kYekzCBf2YIrD1fN 2Gpx8d9/AWmlyUaCGAAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlgAWAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQCK AA4AgwAAAHAKC58JCpIJCoIKCqsICbYICdIHB8oHCMAICNsGB+oFBf8AAPgDA+IGBvEEBAT/EMhJ q70437IYW4ImjplnekeQHR5CvnC8MoaUMK6sW4EnFYwGhgVoLHbIpGXAOFAcjIES6ZNULdepdqeI UgQMxZbCGF2z5LLu5vM4xrGGmiy8sMtu0rykBu4nJzsGQQEHUmZ/WCcmfIoZgw2Fh2aIJikYaDEs DwRYmHAAmUEam50Vf4uMF5mnoYmJGXIqn2QiqawSXZMATGKtE7IwsKfDxEkCDwxvgHOooExOEyy7 FsjKaSWIja7Yq3hlBm8dNYCugaGgACzkg9HME+EA47W0GT0Ms6tWzqn7oVDfrlkpRw8UBw8PCugD ANDcMnT1vJ3zNBHiwmIWM2qEQySix3TFHkIO1HAmDcYkBD7kI2jrpBJcMP2l2zIgGSqXM2dGAAA7 ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image025.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VaC2yUxxGe/e9sn89nfD6DsXnEbniD62JDWidAMQp2I162CVAarNSJIcESFCiG o8VtroCCc1VlEihpWpUipS2pmgJSoyZSomAFFNECkkWoitSEuA2hJuaIS0kLLeU6s4+7vf9x/v1I s9Levmdn55ud2d3//nTu7R8DD4+wSniC50pWMcgG8HQWAeRDYZDq6HdyZh7cW/rVpbUPMt6Pwe08 Sg36KQU4noVxCtUDbIBkWIwVFVr53OcAfubFITVLa6k3jXke60NgChkYsV81ju8zt/3VC5FfeZA/ gABGnxwfADF/oczjEqBY5uPxOK0LaEHE+N+xwi/LFK4bon9Alpdj3MwEvca7OFgL+5QIMKyAFtgI 62ArCmEZpmFMl8MmrHsMvgHuwr6MBmMzRo9cC8WZB+sNZPFj4u83V1o4n0HZF+vfL5X1JP/IkgZj zychMHDMrMbV0Ip17TdCELkhpPqhfxVPqQ+NNwQdeD6f6hsMJusozstbJRZG68f6r9xayeuJn2Cm nMfTsK37n/WGT/aTvD6leG0/shNm/iMEv16wheQev7Z/GZ+7Cemp9VG4dLAF1m4XxUkafgqHuCmv MDFsMHnDSOaHjgljkaJtW9ZgysmiAu54ZxS81jUKapHON5HeQ0h3A2yGMsxvxhqajear5doegqqK m2Euw2shWIhpNaa0trmYdm/bvuXpEWw90SbMM+W6VV8KtzBPc1K/zl6Bo8LoXSwT/scxPfuxaGvH vG/U7fBZ2fcApocxUv8XMR3XJ/JFSBcwTp97O0z5SzROw2Q6RjMmhgMOxHuPzd5gw4ZDg5FZezNc /1HIEe8drABKX/6BrzqzYNjxBkjFm+ZR81FahGk6vPneuDAeSrvGY64AZqKsy/9wJ/xtJuqpjqKQ V0EKDj5cjxkHjwMOXmcbxZfTCs2IRAUMPghe7da/S/IOMuXrKvAfpfwd0gVce5DsPaZM6nk34nnw Qz+8hPJ49nu3w/UHb4XJTryG5dy36toUvak4pl7ZmLfHi0wmI3cBbdh3T6+gcxr3wCt9dW1Vp+ra iM5lrP/topthGr+3cCvnX8l1quRj+vnxsB5pzv0Cx22H4q2LeVJsFNjsB68DDhmucKiEoYR77paU dqFu7a9BvjEef2ssRCL/Cr+O+aern2PV32owmo43GN0473qMO8jmYJyM8RTZCZbgCZpkxFX0lXCL AlkGypfJeXR6HbWNfD82ddYb+7auNuZBPa6J50HNtflKGVvY2AyiTZR5ukbVhaAo2MGe3CnKp2Ih 6MR4GiOVvzumkaeKbx2H6sMNhhmHDNPeUDiQPS2Pf5p2CW1m5AO+36H7v08pu0kSLOsJwUNy73t7 hE0+/+yt8ETSGSxTBM3WvoTlL36ddF6EIHJJ6xkHs7nSlOJiJmK8XmTo9gpboVNoIkCOpHVu1L1f Gs1YoteFxFxenv/Oz5e1XZS8tZv4KJL509herc307rVU/0B+3oxDpgkHvV5hkuWAyXDaKGVnq3rS 21mKZL86f38nTHZ2Eqa05hZpH/qXm9UWAihbmJQbzX03x1+RzhbWI73JPX6uU7otnHrVagsVj+3P TfPomFxDGmZMsjTZ+5xlP0z74bPFFYYJ18kwFdouh0DgKcJxrN/yk7q2HRgPF6xoM/uHizay92my pztH4afqE4QcSN8GqvMRabNINkULxVl96+5lfMQTHc1w9vWdwO1/J9lue/8vbUJcXYhobkPO6aTz N5HXXR/44Y0YyT6p82djVp1XPM784TQPmHzCj2JW2Wdrsvc7+OPh8wOfHRakq2QzSiUGFFbHrLo6 HZLrjWD7uFgdr385JvR+JUYdC6p75XoITj56M3wV4+/wPEB9mUn2dAYwy97vcC7KsbknDO99LenH vFfd+dM+zZ8GpT8luen+dIbP/+d0ekz2Y7aU42UHfzoxlupPq7CchfNQOhbTHFlPdAgzNb4RJbEE HubpBpTMwyiXZrQWLSiXlPsanmPNOOSYcLDzxwGHu1uqXZoFQw0RLqsGI87mc53pzOXvF3FAPW7y dvAZyT53PSrOjGZd/+kzjXwc5aneJ+2NCiDPHF3Ybsi24hBpteiv+vk0O0XhRMtKIJqteFf42qIN fM5urPMoAcgzrM+k9xSo71rES9+nKX3qllv2RkCTfa4r2Q/FZ362uAIMDVfFP9m4wN9CoJ98q3vT ++P1vVafkOtwTxjhCofKYZMVref4FbzzoKxU2+WP0tvsQG/SZlf1Cju8Uumyps/03qDb7Cr5DrRH nm/UvQ089caCPjxfoh07Win6NmLffOVv8S5JdXMkA4sxTpDvqHS+zUhzf9RxoPujGYcRmuzznN+O /k97YHC42p2B7HAl3zwcuKo9QLi63QN2d7Q8ky3SfbbCJOh8XhomTMRbwIvd9QadVdRbAJUbsUx1 TRipTG8BlMbl+0Vi7Wg/IiXLDXXeXFG+n9Gbs/LDa1+4FSafvfpV4YGDWN+OZ6xT8nxz+AVx1ryA 5V2n74R7sK0J+9I3hrWkz5jX7VLAxi4RfYu/0coUAia/YYdJUJN9vvPb0bCekdz6Y/jEnd0O2Phj 5sIfBxz88cVYqj9mJn8c0KLuj+kN0NEfR6xvR/lpvjk4vXs7vcM6vQs6nYvdnNOcfJf+jUqf9x7t zEnfshpHAtxBWTh9S9HXuEJG9dmNdspEKZdVK/84n8HpE9Q2Rt6dllgsrQj0VktxBHOWm5prpLwJ kV+ZYpprChZ6oP+5WrDv4jRYqLnGyPeQ6fIdVJ/r+8zduub1ie+QdnNlmO6fat5yOdf9GKeZ5n0V BV/qYt7V6Kt/4SDDORJ3ul9UmOhvw44PupBhK5YWm3RP0V8g9aDGhn6XR+h1/xjF43PT8A+S/6CJ /g7sOMsYOv8eyX/IRP8dbPg3c8O/8D/6u5qiXyP1bKnUZZ1+ntcd/Rl94q1bfztS9Jdq8jLzv9cl /Qq5Bt0WKfprpO4+Kdt1+ssz3O2LdfReoO2L6x7xX4HzWfp/BSBx+KL/CfB3tSlWW6j4Wi/luk3a B52vEgT4mAu+CPuTaeyrmiss63ZiHGua6wZ23D4IHQlo9NvkWnZLXnT6X85yt5b3+lIxzNXo75YY dtjI6ohL+gv6BIZ2e7RD0j9gQ3+Nzx39VnmP0O8Biv4BKZ9D0k7r9H/pkv585P+g6ayr6B+S/B+x 4X9utjv6jyP9vQ74HpH8H7XB96RL+pf6nPfoMcn/CZs9WuN3t0fpXPsX07lT0X9T2rQzNr5xco47 +iSfk6azlaJ/RvJ/3ob/qy7pl8k91t/5pVfORZ/AzOeXzlx3czVgXOTi/GIw+ncAyo5ZffuEPCFX N3bDzfklW34/K2ZWjPbmDf38outbsfyOPYlZ8QoHB+cTnOz8FPnfhdnMujcX5g+vnb9Pvnnez6x2 fnRocHZet8MPSLnV2qylOTR0O1wr6S+2oT+6YGB2WL9DmO8Nm/BgfgX7j5BndJD2YqTUSQ/zcT5y DHVbCBiV8Ajz8j3BeJ9yViT2Id0seS6b9x6H8T/G5bh2uxX/oWvZuG5r6bJ14dLlmzY+Zr3NEs3P y/Vn8xeBZC6VZvKrgjuazEIpluCODYiS4cjTvsQVtrW5Je3jiaDkcUepsn9K3gRvgs6NQa4tI0FH lc30BrbCTLvxA+AnS45/f5By8VnkOjB5ZDtqzUD1z69RSpVtzG5ts/pfW0668S6wCZh0JjZIGefa 7acB8DEisR4lcxvMBkAvz24vDQCpoI0VstoQqy2w7mmrDjnrghmTpC1VdCktk+eDQm8lrGEA9pZS cUsvFJX+EvX/k2jIhn/RZwJaferTEs2wWZGiM4b3mRcNWvp4E/tN9S3nfVdHc0wzlcMc3tIazUis XbRUoIcXPHhNYwKOY4KWMZmJlhreMiPqS9gS1bKUt1REsxIIKa7X8JZ10YANZqLPKLyzUp8F0Vwb FEWfYrxrpnKVkxjdxlveS8wdSLTslnQDptWPwptZ6upzEy0HeMv8qD+xl1TLId7yeDTbwsER3nLJ ZvXHeMvaaF5iJ6mWNyW13MQeUS1neEsZUnPWv17epyFa6Kh/k/iJoj/9y2ZO+pdcQzHrH8EprH8E 72OpCCZxeoA54VTLFE6pu9e6a/kfXOB/1067t5YxAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh2gAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgDP ABwAgwAAAHAKC5IJCp8JCoIKCrYICasICcoHCNsGB8AICNIHB/8AAOoFBeIGBvgDA/EEBAT/EMhJ q71Yrsy7/2AojmRpntyiomzrvnDcHgsybXKu73yfCSrGLbPyGY/IpORQoOAkhkDlGSoSWVQl0qql NA7OpwFAzX64lrLJ3OWhp8eGI0NT4dgdOybLB+E1f20jentOZHZ2CSwOeAMCZIYiG28aYWFshJVX OQQKjA4IBDmTeFZ6AUUGCwyia3gKok+ZZ7ORlWqIen2bMaoKUgE0YzGIhbI3YpR+gVjIFFGQmmoX Zn/MJQQ1FQgLrS6yYlJ3Q4ATqtdE6MtF4M+a0dHWaWmTgMUnCguPFEAKrqbOoLyrF1AVqxPKSBzT lQlMvFzlqO2KuGJcC0bU5igkx7AImFyk45Al2gPyTUJJtjA4IteMJbx3KCjJLGkR5oWVHk6+zKMu RUAOsFKWmPhSJwiMaTRW+ZkhaM5rNKv1TGf0SJlpLbgNqADEhqGoh6pKsjZVrE9B1IZgZdF1W7dB OlAtkFKoylSSLtuMI7gThS9g+YZFTHGsBci6IBjcJWm2B7urV00I4KaiwT6hjBcjHNFAM9odniUA eYD4s0QRnU2r7juiwIJfcFa7SBBatuHZjCLbRpGANObdwIP3SODVnvDjyGM8UCH4HbTk0KOD6OzQ VnPp2LPnoVBdu/fvAXGCHz/eKfnzLCIAADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIQEkAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAB AAEAgAAAAAECAwICRAEAOw== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image028.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7VYa2xURRQ+c/dd+ry0UgW1gBBCV9JtaYKmSInQ+EDaYAsSTeUh2IaCbRG2iU2s jygYjTUkJgpGEk3UoMQfJhI1YDTBqmCIKBDB0CLhIdRWRCLxsZ4zj7uzs3fbSwuTzM7smTPfnPnO mTP33sP7974OvDSwybCa99hiBhEA32u5gO2xMSSj36nBPNg5bsl9NXcyoQebK0UL8OI4gUIt/W+B ZLkHBZO0/w9MBCjzAZTMv6+GtGnOYpRngVECWP0A1Th/0Bw74Yeu93xQgN1srGGstuzT+tfJfjHW 62U/kUjQviAfax7W31GQJf9TybGEfrb8vwhrKxN4D/2Hk7XSrSjAUg/NsBZWwXoogYXYxrFdBI+h bDmsA2+ldXytVYe1FPshKSv+w4bPqpHJ8bfYc6Sd+VJXyQ882830/twgwPZtFezNqhZYiGBdqK/G j4IY++qCDdTfPLsFwg9uYcTccBi00aP4/9k/bYhin1q9BKHWegTtJfs+ONUMm955Al6qbIFtWMNy XZo/R/oqrM19ZKP4O0Xzn/JDQvODlcEPTPZH7webY50/b0PBzL74kYFPnZE82U6EF9ghv7CF4pNY aOq34afx7W0B5bcfinjo0g/Nm1vY3rZvwTroQD2qtMYybE+NE6FXj/37V5yIU78kOF0GFk7u/fdJ vjfeBuDdU7voOIh945zbHu2L+1Gu5pA170b74mWBKsdekOvv3/HJsfdpzUV9cfpv+qH9QCkz/WBp 3PsynwFOxeOwEtkvh5GXYujtIa+PhSjaOeObf+IrMA4H9wmZGAPep9rBxsLnX/8TDwfHwhRsu7gN AGdQb9beYmjCcUB+GjROOZVyDZqvVypPY63ANQHPxytPXY7T2glKGqh/EuUM5+b7BQaTcToPbb1w NMC5pzl1r/4VpzkTfrMh54vaTmGvsEvZaHLfixgm9z6Ne78n7itGxT3ZOU3yvgu3U/29kJV9NzTv rcQv1lmoNxz3mXin0rYVuaIKYu3pUv924v07wTvZonivRltr+gIQ/o1OYJL3YoN3skvZ2P1tcRr3 J12492c4A+TlM9c0/4j8/jDkc0i62+62BL6SWXL/dL4bUcakbPuvNqye2N6WF2axHuzzuxDzWGnx hrbz+L/jYBGolnS6UE4tDyC8XEkOUAQ1aG872n0X2t+CzEWx34oS2hXtqwZiPNZnxS7yfNWKa8wj f5wX90EVtr0bNrYtCbGNlozjoLRZ6YL0h+6H4+g70w8Bjftg5jNwlbi/evllKkyD1rN2Sny/jXFG Md6BdfvY+s7qkM+aDsnYIU4n9Ndy+V/yjmiQ+QWOBpJmDtjwZePF+FmsH/tYt9IVNxG60l9rfXh6 JoNJtVblYCJB9u4sF7qUkwpc8s9zLP0ODhpnwM0noQznITUvxUaVl7oOijxEMU25KRcN6D4sZGIs s8/qUNqMdRPqHTkgfaZ4pY6MWbVGpjvhR1vwTvmd1lZ3Qjfawg6K3EQYKjf1oq2XzqTfCbvOpeYm skvZ2Iv26T751+U8hDTuw5m5v0rn4dr41eT4WvuVzmL26dSzWH0u/SwOl4vCGe6HoPHc6nZvRDzd 36M5J8nC8Dk8weYA5YBBH/YpVjEnLPO/zFekVeg9g/qrX14J+z59Ag4U1lqUN97Y/JCYh32Sy3cm p9Acldss47l5qNy2rz89t/U2N4C6uwCEPZly27yB1Nym+wrN2mP6KpLBP5Eh8pv+3qfr36TdDPR+ WFQocqD+fqLj1MuqSkTedbSPxQ0/zmHQs4fkz0vZgrRTJ0qdvG86jGdChW877yPi3VrHL2Le8Cvx 3u8z4lrhR6U+veDfbOBvsbzhHx8Uem78VEr9O1z4ucE3Mn4CGj7dcTkyH0w08Hf4RK4YDp9yzL1G zCj8+VJ/gYv9eX5v9kflGm781En9pS747/tHz89SyU+jCz+zAyPjJ6ThN0r8Jhf8TR7xSzF+XjVy sMJvkvhtLvg3Bb3hxyA1PvX4Xy/1O13if3fQG/+9Rvzr8dMp9Z9x8e/80OjjZ6vUf8sFf0LEG36z ET8RDX+nXG+3C/+xLG/4swfFdz03fnqk/iEX+3eP8YZfhvV7DfOQ1PnZBbM7+8o4V5h96rHcBfPW HG+YMcPOAalzyQUzkTMyOy9LnRBLx9yW6w2z3LAzJC/4XBfMdXkji2E9xmz5zW8GS4+xMfne8Ddg gL3N3GMsJu2f5WL/LwWjP4NVLPn928Tvsr3hr8H6kfF8Yj6TVOAzySnURzdCofYdoVDmNB8+MVHu H6M+WkK2NRkaGI1ZjHGdGayYjzB6YuS9CNeegPVv62RCe2oV37yb165aX7JwVbxk0WNrl6e/URDm rfKbScRKuCA5X008ITE3S8TT88rmIT87ivnWUPMrhp/vM+zoH+E+/G52XMH8gGNHKl6/275iw+8r 6Db/CuwJGfwEHM978JsH+8IGbjiNh2Ss6hpR+X3iOv9kWMJU3ItIVDMp15Rn3SBD+nEIO7GiRsT7 RyXkObtUI1E+chz/m2iVBppfjtyIz6SMZ4uAswc1Zz4fiUIoDa0uI9pSAy3ojDTykVLIcnykRpr4 SMyxOrmf9eKtzBlJ2taZ0bat0oKww7wa2clHZmMWMtF6+EgZ5DqSQw6+kvRJK5M6A2k6l7mkXNMJ sVQ7k9bYfGQDRqJpTYxl2lsVH1mDOTc1vtLjysej9X9owIasSB0AAB== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0215_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhxAAUAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAC8 AA4AgAAAAP8AAALZhI+pGb0PI2pB2ouz3tnxWH2iEY4mQF3lk54qc65oJ8qavZX4tJNH7/LBTDLg kGMMQnSWpFC5KHoUlCmV52zlPtrar4lxElEenBV0BHNH4uVXkoW6mVHae8JK/2xtPbZqduemJgez sgN4hicIF3a1FsNY11hIZYVo90Q2uKk54+fIkhjoOclZiceECMhZcZhH9ynZ90X7KHt6a5vpqoi0 ZyiVWjXbGbZrqWM2dUlsDEyizHPk65VXuujJh41KSIk21g0ajRsVS1ZULu4N3m69voeMVA1fb29Q AAA7 ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0216.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Construction of Mapping (2)

Define an (n+1)×N dimensional extended state vector
Mapping of the state vector over the interval [= t= i, ti+1]

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0216_image030.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC81ZD3CURxV/u3c5LiGF5ELKdQLx0j9IFdIkIGmUNrS26dmUEC8JoI0Ihn9XCxyJ 4dKWmV47rUScTlIUqBk7gzPpDE6tY61asCrMVCvjNBpjHYeZjBMlYGpBA4YxtdHzvf1z992X77v7 Lokz7sxm37f73m/fvvf27e7lDwNv9YEovawGdgrqjxsZ5AK4dvgA8mDsBuqjv8s8C+Gtkk3r6z7J BB+DwVtkC9BfIlGope9HIVmexo47Dd8FHwa4NwcgcP/6OuImmdeA5jIV5AE3wDqUHzeP/dkNsW+7 oBDJfKxerD5F0/w3KtqP9SZFx+NxWhcUYF2I9Sp25KlvKptckj9ffYewRpjEa/0PChtKrzYBlmYI wx7YAR0QgAZso9iGYB/2bYO94Kxs/XwjX4f1meu+RN/nyATtX2jf1vZF+NSiTws9CxQvqn4mgPQr l8LAsW08JmX5T5v4qtbNqBNA9zUfxK5JvIt5G0VLPCTPJA4cL6R+/FZ9VO9auFEuDAvp9MBki5jj BGJX6HlcjZ0nftbE2bUGZXmA7f/wCT94NS9+v3zPfrJ7/PLXGsTcI4+v55oHpE+e3H5Aft5m8J/2 Q9xEa59wC5/8hCfp2fuEuWP+zv3dPuYWsBiAXb8rhlODxVCHOO2IF0TcRyECK5COYA/NRvPVQaWw yZ2VE1ESjVz2wX1kS2xpbWuxHek8sP9hYIywMezAo9atealMIk1zEt/5XX+KjnW+pkbcMPKexPo6 tgPFN1cvZiyhuTSDD0Zx7CNr349OYUt9BYg3qeglSLsvy3GijT55YdwHZp9wGz+Q7mMWe4PNmR+a uaduItr4V5+tv7tYEQS+85x3nadozv0NkOpvmkfPR60f23T+plLxzlIIDC5Fqggq0P7lv5qKPs5k P/VRlfYqSvGDF9dj9oPLYHu3fV4SS/gStKH1K2G2JSZiM8TjrBZ6Ozbzs6Uhyj9xON/Et7p7xIxh 4jvUJObd2dMGb7/xBAx2hngAeV78SquQI5r6VS5OFJ1IIzjO1dhNvhakJL/m03JarzPhFhjpud31 3aqJ6I887Pi5Kz5xHlBfLPZP9AU7/gl1dtRjLVU2bMc6zBO2gq2qZspLboPtcxzZvmoWVl8Kyw/6 Ye0dIqa6dG4eZC4+/oQf5PpSC8UTUy3FJsVY7JdT0Rd/MRX9AVbN133kdtd9raSf9Ffk0gqheeRh 2Tcl4raHGffVSex7AWs97sUH7pmI0vf2ZMqBzXmL4avrjjCKjYf+RvIhsW+Jz0mMGm1P85ptn2PK P3Z5ybhPsuXXvvXY5LS5861PxNLZCz54+4LMx7/BNjiG+RjpUaSvtk5GJ/8i+XRZXQUpZwDH2wDJ A8rtKtxw8BFsD2NLOKsT+rlh9ag6n78xGZX5xi/vYdjfjb79ObbPP/V+9ASO0/56B7+fPjcVHcOx ra/7oZf2NO2R1/0K80I0hjzNuy5ESfcJpIdH5VlC+D8e9YE+iiPvpp4tdA80+9ZjsP08e9vDXN21 /t9zGu1Pc06jPp3T/o7AX2ZSv3p1+zqJtdqdPqcB4pltP2+We8boQztMY/6cC3yXKS/o2PE6ysmr ZnUWtuLk3KWfJwyOYduGVbejT3Wk8Ju/td8quLRHjr4p0ULCSD8oB91XyKsdsHJ+C97vkPxtCCVa RN8I5tQT3UcY9QeID8eCz0o+kjt7bwPHa0tK/Gl5QRcrZUSf5BP3QxXr+YY3lY6diqEQN8eO1+SH bPqNsWY+Y0sTGUq+yQ4tBvg37hG7N4ExjppV1etYgPWjao0bW35fy+DcGRorUXfUh0z+1fuyEenH sA6liU09V4E4raVZK01zvYf0Kcg8VximovUmO2j8MrUOwl5pwr/MnK3lrnF5D7LzyzJ6E2DNVbKl GsPAR2ObsK4gPIXxoMrppO/H3Nf5KRfVMqTLjPkgttyAkcl3n1Xr3W2x3jqcdMqBPbtgw0EnvntE rXUf1irTXJWYdF525DufyMNGTNL/ANabLTD7HPiLcF5yYKvDaq6jFrYq8TqzFZ3thxzY6qiK8z6L OH8D5/q+I1tt5vWmvK7x+1QM9lv4wpPrDL92XOZi41mk8fuV/q9Y6P9Nh/iVylZ29qG+b2ENWNjn VWd+5078/qby+68t/L57/tz6fUDZbcjCbt58p36XdxUrvw8pvw9b+L0pf/Z+H1b6X7TQ/12H+FVp /D6g+s5b+J3s48zvGw6+ZJP/P1BnzGIEucOE/8MFznzdifbpZ5njqpzJuKph0+PqdOHcxhXNQX65 m033y2d8s48rwqW4CrLpcdXvm1lcGfUPKv1DFvp/vMgZ/l70+zGTTWie+9n0WCKbvJrF2VGi4uZ7 GEwVFmc8MzyGjGf8GoPcRQ6257jGf3bezPBJzgn+UN7M8EnOCf6HFswMn+Sc4N9SODN8knOC/+Si meGTnBN8HQf/S/yZ6l8B9vhzddfdqX7va2fJu25R8XXeK2oZ0mUZdTDmjQMs+X+xQtMeH8NHRA/P /n4IFu+mk/huuoT8lM8X6f+9KZrW4GJesa75XD9A83kNvphpjDMmeMqZX4ww+nVEULmCm+z3AR+N G17Z8n9h4T07OgINO6KB0L4926b/IkOYK5U9c3kcjFQqZvK/Oc4w2TSkKwntWFZI3Gp18heEtnDa n9OlvCudfFVmebdhJdPXpnV0wmO2Q3Z65FjJZ2FHT1a66jnNstqm2WPwhD3T+GNVZjvMS+Ck/+aG /aG1pnaF+l3zRncNHGEA1tGvV0VZoypvmdpQjwUXWKxT8qzE3Uw84WBOYj4tXSb/kxssmKYrZcB/ cWmAJKZXZJHbXG4Ioq61olYjXZ3gT7VJrmjHVQaxWsFyfMeTDl1pVlCOb2W9AtlTqnqag/PTIB8W PDuDuWlsc9Rkm5zESJ8YqQ3mJWJNj/SLkcpgrgltiUJLr9WbDrQasNVqyFarYTFSZaHVQEKrVP8v xzcDjXQGl6TRt5xl1reG2el7N0vVNykTFCN7cUTrKVG09RbxNdCYGlexZBwSRxH3IodVpJFsLKNs zFb2dEbZ07ayVzPKXrWVvZVlkr2V2cluySi7xUbW68DOW2znzSS7xkI222yzG3kiolYjXQ3WeDq2 bsC7U+o+1Blpeo6VP9L/F68lV37gJAAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0216_image031.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYa0xcRRQ+c3dZlpXHchEEC7ItbUOlNlAa648+MCol1m43K9DGYKQButlYLBS3 Sy2JizG2/iCl1UDjI+FnjY8/JqaNTWiMMWjahPiI8R+atjaFRkRUiOh6zjyWy927y6WSOMnZOXfm zHfOfGce9+731754C3g5CxUQ4trnBxhkAThK8McFuzKpjX43uvLgWO6BffWPMW7H4I8RUQMEcgUK 1fR8BBZLP8o6w3Mt2lQ7AHxP7KsnaxqzC9szwVQyUJwAdQg4be77yQmx9xyQj2o2ihtFlzr5L5J6 MUqJ1OPxOM0LvCh5KL9ig0c+U8nRhH22fA6idDGB1/IPDjaUQUUBlkYIQyd0QA/4wI91FOsgHMW2 Q/AC2Ct1e4KaD6UK9ct1yN6a9fol1EfeqWWRGR0uyTi90jYe/zvuQ/3Dm2HAsCGGba/+roPmD2q1 LQcxIoDTOC42o3P8G55mXpMNjWcCB4bzqR2fZRvJzrxmMTEsFNOeuSbuYxyxW5UfRzBSF8ExM37J PED7bzrPg1vaVuPz+492E+/xqTf83LcXxysbEDkZbT8uHjcY8qfyEDfpKieaRU4ua4v6f88JK40V R7pPuVkph8UF2PtNIVwcL4R6xDmGeA2IewS6YDPqXdhC3shfPdRwTh6pmY3S0K4pHR4nvrGmue3A eiJyvDvPxZ4hbNwKuM/EvJUtlTnUySfZ/RD6MXor8rHsccLEpMB6E+trheu238dYInJBgw7Xse/B HfPRBaypzYt4c1IvRd05JfpJN+bk/LQO5pxoKfJAsd+y2Bts1fLwtOaqn40Gbusp893LCsD3wYC7 zlWw6vkGWJpv8qP8UV2Mdbp8U6n+tgx842WoFUA18r/lq4XoS0y0UxuJ4KtgSR7cOB9zHhwG7p0p uFdL4EVoQ/Zr4O7LYtxjt9PHTUJ8XPlyIUpxb8A6gK10DlVyjPT80HgztwAD7lcS+KIm22Cux036 Aq0zxPYiERSnOr8mMNahGx7u82z/fDQwNBelM+gicp/z2f4+hUdxqRjdV9Ys4b5vMnkPOA3cZ6Tm fpXW/f+bV1ilvG6ESsj+WQeRT3nXIbfdb+/v60UZKWjsG2cO853wspn7DAP3rtT38SrxYzgVIKDF 2W4Y7DmoxVyo00tEPt6DzjPcI3lprQ1yv4fPtMHVT09C9XMBbRBt3n29hY8jndrlO0iiqBeI1pyg psm+Er2J38dkr+zUOBXTaLgJTp/b5Pho62z0ExcbHruj8/cgaovF/sRcsOFfEPg1JvK0V97QF1C2 OxfXaasUI/eAeGbuXaazP9WdYDyj7tbe7PcB2afezwbcYi2kej8w+mqUogq9opZLzpubvtvNYGyU 2k/JtqeSdqAotN5P4Jr6Ok38yhe9n+XzW0O88xp9TaK+3oavMGxy7DWdOwq/UOKXW+A/zOzhV+Hd NmTaWwq/XOJXWuBftYlfIzk15lHhb5O5oXNirQk/y2EvFzunxffAcnn3y7HtFnkfctrz1YDyJFs+ 74dpfaI8bzGveSS4yVbeGd+ry82rU449aTGvZ1121zPYWs99cj30W6yHhky76xmWzAss9vUF3Nc3 0Z726L2y3St1Wv8O5ubr9B5NfRhmaxX4zUp9Gr77Ur2FFfMeRqc017K4dSnKX9r1uOGmEN9t4c6O Hp+/I+oLHu08lHwrE+ZD8q7P0uJg1JZiLn552MNkSUh3EtGxFSFpSeMTt2BbOO0VKMY7rMavwL/T it0V+M8wMJHMjZqjfRsjMtWbmfhfochZAecSfyqYs6lQ6d+BrZ775QI5Ecq18CNs1uLqJJtwKCPB pOop5D1VIU+CI9VTzntqQlmJGJXHbeLLO+RNE5Wf2zSEilJGVYbnkIoqNU6njdn1mXAUr8l8Ovjv vzokQ7JIEgAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0216_image032.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+1ae2wUxxn/Zu9szsYGcwZj3i7h6QDBxiU0EF6xDTQJD9sXIHVjCI+TCRAbAkcK DUccCm1VDDRAaKCCqH9QCVEkSlOVImhJW4pICy0paXmEgEkIrzrECFIQ7vftzt7trWdu5x5IqdS1 xjO7M/Ob7/e9dnZvT7//x5+AfvTQNoJfb93zMUgDcJXmAbSGnCy6Rv/7pLaFnnlTny19iunjGBw8 T7VG/3DsrrZYHqPrAPMhfLTFARss5w+KAGZm4pSSZ0tpNM15kdFatiMFixtgNPY12vsuuiH4cxe0 w2YGFg8WL2/T+jm8nYulE283NzcTLyBCKCp8jhfS+Tkd6zzG+Ax+Xoalhhl4lQ9wsuVYb6oAjwqo hgUwBxajEiZiHcC6DF7GazNhIagc8+GN2174NraoNg86T1n04qKZs16CCe2nQEnljxmppOKWV194 QC9f6NoKvPYAazonjEyuPsZ10ziwXEO6/yauI77wwtoxtaSP5q8P8ulrfRPnNbjD62PXR/M6TNEx GhD70+JybUd3ny4TnTdyGWieaap+hUZ/CpffxKJaw/Wpb/0XZZqHy8TXWTl7qXHa22I/0w7NtrZp E01gk99q4XbiNmFdg7lLatd4WFcdFh1w2d87wK9PdIBSxFmEeOMRdz7UwABs1+AVWo3WK4UC3RuH FTQFaGrNdS8UYz36uqGzEVhfWLK0dlwG20fYLiypnLc5lo672KY1adw//R8HrizZx3vccOGagfUm 1u936Pl4R8ZCkr9xjfQeOT6Lr/0e9tGaXfHcjSV/xJcBaltt8lajF+w20SR2INmvCGKDJc0OFVpq aVNg8lWv1N7LWDbk7f6RZ3RqdtLtDRBpb1rHXI/qXKyj2ZuOwae6Qd6JbtjKhsGo/0HH7ge+w4zr dI2Koa/sCDt4kI/dDi6L7t3yvKRTeAVmofYLINEjqPsm5g82CtYvnqbVrNVzSTMMKtdmuOv1Faux XOhUrq87t34WHD+wHLJWl2uDccz271fq86hN13kuDh1mIs2aVK5pvK+Tl/KSMd4cZ84z5TpU7QPP 4S6wp7Ap8KtUtuXoDa9+P6BrweAdtAXbMpzfO57G0p3rcBGWs1pIVzCDF1te+siue7dF9ylKui9M QOvdIHd9f9eIx3SfWsa4jk4wl3ahvr/L4Bd5kD8xXpNvko8F/3Q/sP0P9wO/xGKO2/v7LlBcSfIZ 9qr5ZIAuec23jGv3db+tZ9a42oXX3sLyNMbiuDFNATqfHU45MDq9I/xw9EZGvvHMTa9uO4pbGqfi ozbdH7LrPsWWf2R5yRonsY43bZsqyWnJiyuv7kuHL3nh+CUjH/8V6/FXMB/T/RXbn1feDdz91Bhn HkWFEJHTNdy50HzAef52k1bMw/oHWBNOUcj33FDUYOSh2VvvBox8k6ufZ+H1tWjb97DesOrLwA7s p/g6heevH70fuIJ9M97NhRnIfQrFyLu5HPNSIIhjKvyXAiR7E7bPNhj3EsL/TYPBSfepzyLvLcNI DpttUy26b6Wk+yH/E7rvA/0wKXpbrF/79qQVy7DsyK5YQfGcD+H7ZSXqruuNSfr1tQ3GPduue10n l71w5IWmwGcvGLnPHHvqMr/nYK6lnGvVPeVJu+5bSWLAo2SHwv/bIUl28NjsYLXPw857sY63xq3M jx4GL9G6scofj5xfpXUftp6TqR/rvdvMK2lK+6YhCe1XM1EozWW0Xfi3GetZWMy6YdXiiPH28+8x Yz/7cQoJpekYofcRj2Ln80an+wbF+GIY2NqHz2DYXEP7KZ9+7QLue3as3cjoeh6Nw77xq41xNO/w 2IkaPlpE7HvN+Xq7AxdmjbFHY1xBQb7HzrDYxbJvumfPK2k2O6hct74Dse59u4d2Dsa7kms9DJvL ntWtvlbBCx1D+fsZH+f1nO+DUQyOHtJf67iMa8/YbGo+A0zG9nh678DkecJci/qf0nfSAFNta83C k70Ka1XzZwerHkz8/nw/8w0B/mxNjcuTjcbzicwWfehZHUs6n9vdxLCMS+frD8BSyvung/HOjeTN San1POGmMgTbQ6yxG+xnwXCy3Tw+Lsi5W/kWoCMsS3XmO0XRdquwdKZYxDLIttabKHjXVHXbOfG6 yHk1CniNzFTjNRjL38CZ1y0sHWkNBHzUtlb/Nmg/hbUmYjliy7smfjPHTxPgX1fEP91o5Eprjjfx CZdiNwvrfBv+623V8M81Grax62caxyX5+wvkv8bxNQf8haihzTYdeSwc+nIOBcyIGesaxe3UOIyy 6chq4wLOYbSAw7/axWdjqw1GcvlLBDbY7lXDP89t4BQbq5kRG1tYy9g4kaMWG1TaKMT8Vq63nwr0 dqejGi/VmJ/Hc/drgtxNueyIQu4eg2MHOPAin15JtqJ7Js/L1rWWomE3uJx9ejYy2xxDPhvG89lU QT5T4RZLPivh+Wy6IJ9tcCWez0p43pkuyGcq+E75rJjnnWmCfKaCf66xyhUtn5XwfDZdkM9UbK+S z4p53nlekM9UODjlsxKez6YL8lk8Nrbns2Kez6YJ8pkKfiz5jGKDfrWaKshnyYyNTVxvPxPo7UDH xGPjHY6/W4D/Wm58sWGVfzfHPyDAb98pNvlV8vFcetFNNhLk4zYsMbtY/e1V/htAkO8vrWt1xYFn IbE9TFB/AsT7GT2+2fBXc/xEY34L57ATy1rbGuc9ahyixfxOzmGvgMMradHxr7YyvhU41tb6rQCE HvLpOwE66Hf/sJ9obll+2MO57hfY6/F0Na7nbfayxtF+zvWQgOsORfxocXSI4/9FgD+0tRq+ahxd 5HF0XRBHdO9XiaMJ/F2JUxzd5Ha5LbDLjczE4+g21xvJbNfbc22SE0cZzOCQw1rG0S/aJh5HhEsc egs4lGTFZnuRDR7h8uezljbwtEs8NvK5/EUC+WvbxRcbVvmLuPzDBfK38ibuQ8O5/BUC+Wu8yfGh Ms6hUuBDf85O3IcqOYeXBByq2ifuQ9Vc/hqBDXp2iM2HVPZfc/n+a7Vg/5XM+/wmzmubgBftvxL1 rW3cLvsFdumVmxzf2sc5HBT41nc7Je5bBzmH4wIO2Z0T961jXP6TAhv8o3Pi+ekkl/+MQP5RXRK/ d5/h+FcF+B90iU0/Xfi3hm+n4N46peW7XWb54Mb6bneoZd5MD0jf35r4uzLiw6d5KvhP5MSHT/NU 8Md1iw+f5qngkx7vaPHpn+RS0X88+KbdVPQfD75pNxX9x4Nv2k1F/2MhPv2TXCr6jwfftJuK/uPB N+2mov948E27qeif4uRhxle88avqP/H6p6p+4tX/WJDjJ+s3vvss8rt6+o3vcrdaz++6UxmCbeff +EDwe25aHsAneM/CRytoz69n8Tat4WIeXfbWmvljeIa2EXpo1Kcxpo8ZxHKN787pC1G9laaPJn73 tIZmyy/+xrfz1QvmLM6bOCeQV/bygpktv9QlzIH8e8s0rRmsrUjM8NffapisBdKNkHQsJiRNxM74 mmFWddTPBI35rmjzC53nuy1MWnIzZVQZY9dDbDxSos0f4jw/VUUOBX20CuGYuMnSj8oYUxd2TonI FompIofzug8fMxncY+dhxkSUmFLwRU8IR3Yezm1mFFM9gH/DmuPeCF8L5Ul75jLZUvYvTJ/Mk+F4 f47A9saYcszUNKbanxJaz5zdX+950p/VQkZ6kvyPZhAPY6bpd4DeLjfeUTQYr5d6bNeHxkfqIl2v G3GejEEvmGd8IRmFQT6sCjGQ41w0vmD3t5Hi9IVb+piJ/syQ7c2eZr3ntD895B1mT5qe08/5w/6T znuyGBFeODEdMkM+Zs7qq88aFcILy1DAImUIrzRS7zmPK8lZrtbHTPZ7o7Dcypy0Vca1PsbfXoBj 8PPBSt36s6vTIRqSs959Ur37pHr3SfXui6J3n1TvPqnefQp6L+N6j85yE5OxfIdFsgzP2R2aI1s7 yG0lWtvkUAevglhbdbjllGmrDraAWFt1sBPE2qqDPWBqK5JlHewHMcs6OATOLA0/muBPj8LyppTl 7SgsM5iMZQ6TsXyEyVjmM7HH1kERk0k3nMmlK5NKVymVrtrRY4NRPDaMs0kq8bYoEu+TSnxQKvEx qT5PMpnXnImIjfZaAcyIvM8Ew/clGpGtuXCE6M5Dcz90nPuhdO5y5jR3OZPNbXKc2ySZW+XIt0DK t8qRb4GUb5Uj3wIp3ypHvgVSvusc+VZJ+a5z5Fsl5bvOkW+VlO86R75VUr4uBX9ukvqVs2/E71dV CdhonWBurLvLB5gFMjUq9diul+wmzX1my52z8dX9fwHI2KqQokAAAE== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0217.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Construction of Mapping (3)

Mapping of the state vector over one period T=3DkΔt

The stability of the control system is determin= ed by the eigenvalues of Φ
lmax : the largest absolute value of eigenvalues of Φ

<= b>When lmax < 1, the control system is asymptotically stable

Stability criterion

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0217_image033.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYb0xcRRCfffeXE8rxKA01UK6xNGixOSjRRtsU/50mtdfLCbQ2JFIomiOlHKX0 aCXxNEbrh6YYI5gaDZ8MjZZPxjSxEdIPPTSYEK2xHxtjqyk0ImKkSnrO7Nt993j37jzaS9xkbufN zv5mdmbe7r778dvLZ4G3t6EaXuHclX0MCgBsJ/HHBWMuktHvZmcxBIr37Qk8xbgegycf13qATcUa CvX0fBhSLYb0gOG5vgjgRRuA75k9AdKmOdtR7gZTcyDZARoRcN489pMd4udsUIJsoZirCp7srxN8 OdJ6wSeTSVoXeJHI3d9R4BHP1CoUTb9QPIeRokzDa72Dkw1tSIYAWxNEoBs6oQ98EMQ+hn0YelB2 EI5Abi1eH1bakIh3CVn5HyrMfPI5XGQKtC2o3E+v0EXX7/iQP38jAjRpEmVv/qmCUhJWtrXuhy6U ncI58QWVY133tPCedGg+03BgpITk+CxkRDuLW7SFYSOfnl1q5ja8iD0q7djC/aMbcM5CUEQe4BD6 6xa5IF0/Pn/6RC/FPTn3XpDbDuF8tyHXODRx6Lj2WG3In8xD0sTLnCgWObmopPh7zwk7EC/v7y12 sgMcFgtw4PsyuDBTBgHEOYp4zyHuYYhCLfJRlJA1sheAOh6T7XWLVPoQnVPhaewbsae17cD+Wv9x HRtfBXCKdUtdakvIk02pNzOr8nVfxX4S6aEdt2PEfyzk86JfmlW5fRon/ishp3ZsXuMrENs+p+kQ b8zJB6hjzomSIQ/k+68W7wbLWx5eUJyBxVjoppox3wOsFHyfnXY3Okvznm+AlfkmO9Ie9eXYZ8s3 Nf+VSvDNVCJXCn7MxdZvlmMnmSYnGZEWr9IVeXDjesx5sBlib88Qe5EuOAYdGP06uPuW8nvqZna/ iSgek18vx8jvauxDKKV9qIZjZI8PzTfHFuC0+w0dX+tJd7rEU0P8MtUZYnsxEOSn3L+uoa/D1z3c 5ruv346FhpditAddwNgXXdo7KPHIL+mj//0HbcbYD86mvwN2Q+wdmWOfp7r/f/MKecrrZqiBwl9U 0PKptUaMbe+HewcHkEZLmwZnmM18Jrxmjr3DEHtn5vM4T/Ex7AoQUpJsFwz17Vcmj4To3E0Cnm1t 9jPcIlkZfUw7t18+0wHTX74K/pdCShR1Pnqnlc8jnuTiDqI3eYHwFYUVRYytV5v5eUz6Uk/Okz5N RJrh6lQljNcvxr5wspGpWyq/B5EsHv8Lc8FGfkPgt5AiKN8tTugxpEftqTptE2SMPSCeOfbODHu/ K/MZbMhDwz1Ef/V7zpDIyd3uObSf055DtYlvMa9N0g2rnsJc9pyx2dSeQ1mz2nOkj/7LlXrMmSkP VvciV5bz2Hg+GO+wxhxuEGPyrruAgH+joUx3LaOtJkGyrUGqEmtvaf5hF4OpCZIPC9nzabuZ1mjv OIH0XRb/pS38TOB1XSa+H4y2ZpHfloOtLlH/xj1c4pcJ/CoL/EdYbvhb5rU1G/cpiV8l8Gss8Kdz xK/jX2Yr8yjxG0RuqK43mvALbLnlYue89m1llQuXwVZQxK7dYi3D9txsjaOhWmZdV+1CP2pRV5cc +a2rHpGXmMVazjtXV1fGd838fqn49t5AfXpX1gq5V/AUSxtz83q5T5Efu4VKNWabxhTGeL+VlfMR RicP5wq4dgXSP8rPScPpp32LRro7+3zBzpgv3NN9MP2mQZgPi/tLgZIEI7cSM/U1lRsmS0O6pXvH VoWkpM3XT5SOSNZjXZtvs5q/Cvt2q+iuwr4je0wlUsN/IzktYitjlKoFaZX6WnEur7NvglP6nyjm TEtU+jek3nO/KJ4TiTUWdjSdjVi5pNOVcOhRliNlfGRLwqPHT45U8ZG6RIHuo7TYoP3TkPCmWXTq OkGuM55Ym+Zvew7+HtX9XRmp9AjZ+O+/zte0dwoTAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0217_image034.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYf0xVVRz/nvsej8cT9PFA91DQl7/mnNgD+kM3DSwjKoWXIGlzDQcmTEgM8LFk SZbaH9GsHJi6Yq42W8baaqYbM9avh642t3SRfzRqZpS4vZQUF4u+33vOeRzuuw+u8bbOdu758f2e 76/P95xz7/3hu2+Ogl7cbAE8q/fWljNIArB1JAM4weWiOXoudswAV/pT6wsfZjofg3Uh3gIMpHEp 1NK4FsYKw4n5yrh9NoDfBuB7ZH0hcdOacpxPAkNJwGoHKMD1YSPtFzu0fmCDVOyimWgngEf0Sf8s 0fdizRD90dFRXYcb6wysf+KES4yppGicP1mMN2CtZ1zeln9wsVIOyRBgKYMaqINt0AA+KMY2iO0G 2IlzW+E5sFb8pwNaz5WA1tgA0F2A0Zuz0HMW5zuP57Gmmx44K+x0C17bg7WoBeCjazWg0dydgPbK Xx7QAqU0hMO4hvjytmwCvxi/hpV4aJ5xOdCRSpHH8RU+R3X1jHLuGBay6dHhjbqOAMpu7RJ6bIGm zoxSjd0sFpEHqLrl0XFwCl4/jj9cs4viPjr4VrGu24d2Sh7gmOyt2s2HixT8JA6jhr7ERDPBpFv3 XCdBI1QiKg/Afy+sutXbtOvAdFatC8QEbP5+Jpy5OBMKEdvnMfpFiHUt1MMy7NfjDGUA5UAh5Ogx WZEzFKSl9YMeWIttAbbk2yps+5t2R2TjVgCH8FvyUhnGPukkvh+3/xwcaPpEd67vugd6sC5ddTdI /XewamKNJgOA+q8KnhFBd6O8YdHPxL59kNOpr2JyJOwBIyaaEntb7P2gxD5nCrEfH5/FsAS8v3ki OUllHfqx61hJSzPWzrSylovMpi2VG5JsQHrmjRJ9vvP62Fo1PlROou9fPjMU/B3raQfrIF4qg4O8 PYR5fKhhkwa2Uq0r7Frp7JkDXbmc9yvkpfOH5lpb7+hz/UJRO+GMFY86qMS5r7VIfkKFqJjR4XmY L5PtB5sSe3vsvId4nUXxii3h1oi4UWyl7JOTyKa1UvaIkG2MLRX7jfG4jUTsMOAGpdrqsGtPX29W BDffIMeN5tTYV6MAY+ztMc4fupoGTPYAixsOZZqjcCgY+MNjinczSwPfqTZngSMNTiHPcaxPIP+j a4aCNPYJXrrnvsVxt0KncZUSyyUXvHCs4E3mvxXQ6PwpOFqGGjgf6SY9Uh+1Xmwn8pGLzoIVYi9V vT2M+KfBps+8+jgd519Fu3uxfeOlu8FOpKs4DCDNiEOCEntHjNiPP39yp3D+ZIHvYhaQzb0Yg+UX RoIvoHz/JT5HlavjfYpJz/mRoBPtXoRtK87uoLiijMnjMxZX2QK0Offhk+IDIj6k+3aK6zHiH6E8 Q9luTE6yU97b/Whr+68ufQ9QXAPtw0G6e8+gnJQvSlq4vdwuaeORF72Tnj8OJfaJsWMfp7z/f3GF OOFKZ18ynn0cT14KTM6+cefP9eh7N9Fw/sQ6l9R9ouIWS47E02npLs+b0l1uNRbqPVCt3DGHxdmu 5vhJcbYcN9zfkrdf3N90/uv3wPxSLT/MOojWgjzyXboI+T4Nl7RkZ/D1FUfKtIUH9sDHyFOT6noX IJu931en91WenrRstup+/V5rlrYZ8dTPPgOeTgsY3ivmKr/xvWGuoMnvG5ub50is92v1fa9MVBC6 04F/x5Gv5Rsv5zPo/ZxoB8XcuqidzEsA+134/ryMjbdNyp8r9C3Hep9B/nlmTf7qMP9GVGMl5a8U /CVY5xnkl9usyS/C+jiLveekricpzlifNvHlLBq10YIuOmOaDftYyt8s5ipNsMhJsCY/P8zfT9X8 kfIrhf21JvaHLMrPETkRK4elrjqx9mUTXLY74ovLfuHX6yZ+XUicOi5tYq7DBJeHnFZxKdVi4dIh 7O80sb/PovzcCXBxKrpOiLXnTHBpTrKGSwXm2HvMHPdzgv+SifzMaVPHXY3bZRG3n0zitjc5vvnc L9beNvFrXkp8/RoWftG/NaNf+6Zb88uPn1YHDXeH8b7IwPviGvJPF+c/iHszXfhuY059n03T5A+7 ZG0BuBnRNDSO2uXMq1OYRn/gqJekc2di/Vu7Oqq8dfD/aTV12xp8xduCvg0767ZGvzWSzGzxDZak jYLaGy+zO/JJ2lhZM+HPIC6Tmdkk1+dMvl4z0w/WfbJFeXIjYgm7J0n2qPWKJ7mTe5Jgtv4e9DsU T6J9kzZKXdFrJsAhb3LrE2PqtGKXQ8lRiSu1y8T3zyz7AkhlAOYZKDOJ/jTnumaLpO4KpUdkScpc /rc15I5YIikrdUpRaJZJzDhPFr5pEM+OkDMSRUnZrFPyQ66IP5JSqVNyQkkmUZC66yzo3h9Td1tM 3R06JddEd2JE9wmdpyKUGWXVuZhWjWm4bMG7fgtyhnUef0SOzINo/G16zv0LGOM4/EQZAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0217_image035.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYaWxUVRQ+983CTC20TFtaasEBWwIUmhYSIYalRKhEaGk6XSTyg60MJR3oArwi jQ5KtDWyCIqGJTTaREkwQTQpQRTiD0VTk8YlSvQHxVoUChbEpCBxPOe+e6evb94bpjAJNzlzt3O/ c+757vbmp2+/PAg8dUAO+Hmpp4qBG8B2OhEwX5hAbfQ7yZkEL6RWFRc9xbgeg+BcLQdYkaqhUE71 WhhMx1Ae19V7RwMstwF4FxUXkTaNKcb2BDAkB4odoBAB+419l+wQPGYDhAJ0E1woHlEm+2NEOQNl rCiHQiGaFySjJKHcwIYEUaeUpWj6iaJehlLHxPz+w8G6tFeGAFM51EAAqqERvFCCuYp5GWzCtlWw EWJL/Td8ShfKuTs+ZcHiWqB8+TNaPr6lDG5inix8Jd0zhRjhR7M9XTv3sgVOgLbDM9nRObWwLxcg KBz7Bes7//FAM5Ypl4nqI7dWN2wGH7w9uhJrPoUhJhPj5iZVahPDRD49PVABGBpo+wx9uOlTCEux +ba0fY5jbpaIyAOs/dvDeXAJXcJIf24/60EO+/aXcB/OIZ7UAY2TF9du1ao5Ov4kDyEdD4o1DxAf HjZy2+VpE2e5/L+pHVN61DE4i9fEGii85oEL/m518eWPuXY71kmo73XMe9PDSyncT7Pwrb6kyrYW bPtgWrc6wBhfgzItSG2oBzj963HCKetWqW7UaejKZSSdqLPa163WK6GQUYd86cP+4L4AmPXT+Obr HihuDYCeB2o38qBY8GAz4eGMEk8emD2YsaW+xcPsHBY3f9P3aXCqKw2KEKcB8RYjbi3UwTQs12EL WSN7RVDA1+Psgls85nV9HlhI3PVpPM3B/OKWrWFsmotTxE3qUhrAMtkkPemVK+22evyqh44ktARw Asudf2lrvwXL1N95Vau/iXkbCtl4D/Osfg9MFTHNQmw7ytQ5t1Uq63l4B/WMPNgseCA//jDZDyxu PJQrzqJbaukVjyXfTSwFvMd3uQqdKXHnG2Ao32RH2qM8A/NofFPK/2EceLvGYSkF8pGHvG/uqs8z rZ3aSLR4pQzhwYXzMfJg18XeYRF7QTFshjUY/QK4/zTo9/kr0f0moXic+/quSn7nYF6KrRtQJnOM 6PGh8cbYAuxyvRTG13LSXTQ6IUDlu7TOEDsZg0J+yrvjIvp64PcEbvONHbfV0gMDKp7xoVMY+5Ff LGuWeOSX9DH/rSm2e90JDl3sndaxj9O6f7i8Qpx4nQSTIfGyBzQ+tVSIPNQfWtbchNKWUt7cxWxD 7uP1VyPPH6fhTpA8jLC+j3WxmgHxSAzfKCE2H/Y2Pqt4r2OZHnMXfMpK+x5ukRhpe8XH7a7bswY6 P90OhajnRZ0jrSu0cVimdvEWDCd5b9ZhvyL6xnoq+LuI9KWeHCd9OltTAYT5M9639FYj3YvYxmQA QPMnUScyke55vDsyFtZzzMaXS8CwB84aeRihi73LIvYsbuv04fIK8GC8Sv9pD9T96QHF8C6LtgfM zh+X7g4OBoND9ob+brZ6O1nd5fq7xWys/jvEHdN+exDOa7iN9vG5TPLBm8U+o0qwcB9ziu8n4iM4 q0Ix44PaE3U+zqex2EYiz+raJ/ezD3troOX97eIuG7TvEfvxk/oAH0ffRJTTPqNc7jOS/FZfmF65 z8g/spn8UbnSdaJckXt8/exBm3rOyaaRc/JlvOBCfh9+hVfbHVwgVpyXC9F/wnqF7cqKH+czOH+W 2g+ItqURu05LpeI7bUmUdSRtOXQ3xmMGW0titLUN5bsoa1PaIl7omztTfNPrbT2BlZkx2Nog5qW/ 2yV+psDPNsHfESN+br82Z/0elfjZAn+6CX66Ehs+7bBXLXjPE/ozTXjvUIbHu/7cl/jzhD79XzLR gH/UFhv+SYxPt+Fsk/hVYj7rUCYY8Mc5YsOvFPhW5yXZWUl7kf6HELE02kpHxbVinVvZIhx60zVh C63dJoF1r73ZKnB2m3DEXPHdm7vF2MMme3OpK75786BY2++arO1Z7vvbm/q4tev+zzPG7ZD7/uIG JmfsJTxje1F/FNbF34r8j5VUMV8bkkRnxiOKPGETlRzo4H0KYzzPYxm8h9GLgpfcXDsL5V+lJ6S7 PbX/8GoC1Y3ekmrVW7YpsCryK4Ewp4vvPrcSMkeC2JGYJdLgPymxISkRSNfCPrFhIdkixodfFmtq oj4rtPF2s/HDsO8Ix8YkttKPGff2wxkxng1rHiNEROnckp4NxjiSv0geZDyH6lqsv2F45uL5NPHt NcaeDafCr4yh3tHbZUZCpljezX6Hib9Sx8F1tvlHmcxA05kAaVxng98R5lr2ZPKeXH9COFayJ5v3 FPjdEV7lhb2SjMmeebznpD8pzIXsqdLOG+yJZCeR64zDG4XO3sCqJhiFt5o7SlxaY4jL7hjicsQQ l0EL7QYLksVI9mz893/P4lsYihkAAB== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0218.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Optimal Design

=

•Control performance criterion: <= /span>

<= /span>The decay rate of the mapping Φ over one period

Ω: a finite and compact region<= /div>
K: feedback gain

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0218_image036.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8UZaWyUx/XNt+v17trm+DhqcICNIUANQTZHSSkS0DjIJA4ge+0mjSk2hoCRzWU7 6zZbxW1pwhVhkiqQQoV/QEtpilDjHlIRsZIqckoiba2kTVo1NWDASUBdVEhAULbvzbE7/vb77C9g qWPNzvXmvTfvmjef//be2z8FXmJsMjzNe9srGQQAPA+NBMiCYzk0R79TfcNhad63Hl/6MONwDIpj ogWYkiewUEvjekiVN3EiXxs/8iBAoQcg9MjjSwma9nwX57PBUjKwegEW4/64de2cF1p/6YGRcp8f qyn7RH+s7OdiHSf7iUSCzgUjsA7HehUngnJMJccQ8IqPMqxbmMBXdQc3a6VNiQBLGOqgAdZBI4Rg ObYRbMtgM87VwCZwVbwrZ81kHVsboHNEubGkpJ63Tz4q2ok7yqBsWrmx/boJhdhWYj21GCWcN8WM bW9jS3wA7YfmsMML62H1DIBWydg/cEx7FpJOr5tJYjT2ENH/mOATJzXWYp9gDE95c/zz8mYUzZ12 pP3ri3UclurJWeUGVTXmhzfoBwElbr+sI0aWGbRe89TLrBd1+OK8ejg0r74fDJUirGufEcMHNP0p PSS0fmtra1InhrNOYGh0ciNCJnUbZcLRogEO97Fv6xCPGsLmVHkI682lZyPkCktxbce/TZhMfG8U uEo+F7guXzZh5NyzkdjPO5J7h8v2ftjF/upN2T/h33DFhL/nbduaIadz3x/DXYN+aN+S0du2vlu6 ieMOj8mf719/Hun1RsaiBnZJ+12MOD5afzZScul1juMIjqnS2h5sdZ2AjU4MB50kND8hm+iz6OSU MZQ6MTkfnX0mHMNasPBmhPrP94l5btt4lgIRNnjZgWvRPnH2vubXlbuB/xNx9lO49h7K7CssZTy0 psNR+5M+k9PvumVC7Ez+/A3j75+PPpKI43z5mnMR696mqyaPNdDz3+cYcYMtDbfg+rXPBAzZ0xTl R1iqce2jr16L0Lxh8ZOuT800nXg02XttZC/9gYumCWpR+rPh7ssECMUmYDsKXsMzz/rz7cj3EH/h +2KOqiAn+i1sFHS+czvi942CB7DtwdnHsE7nOAaWD+0Pvfain3CoFiOI/4f4S/IBKR+iXW0G5xL8 bbJzxD0CURGfTMr1T8jrby4Fue72/eBmZOUrNyKkt0NIJ+fNFVHBr+BL8fhh14R+sie9WGXv1WSf 4Wz3muyL7kH2/1+9whDpdSpMh3ivCUKfMl/A+a0HV0RbsLaPCkdjzGPosi+1kX2GQ/zxOd8JQyQr iW9XmOMLYdteWcb7+0HMX/46SqO5jM8bPrG2Be/CajlHezDuMfJdjHtsW3OZkZYMaDFBlT/I9ixW nw/KvBKvG557diKfO8MDwq59le4o1Es1Aoaw9uwID3Yn+Cx3s9NdocMrXWU66IoNmc+kYnTXxf4x uueiiL+leD/P1myV7k5+T+H9GUeYML9Hvan7C9cLL4l7owR/RuP9mo3j/FaEa/gtn6M1giH66t7v iJvJeERrfoKXdBXupkuCpx7FEwielNIULkD/6t53I0L3xgHcc0Du03X1tdUrolZdZWqy97vykzn3 5Ce6fMjvr50z+Zwq0y+l+32BZvcrcf2+Kyv4fFTK3Cof/lbBmPXWd65FPsH6Ox/bH5Xy6OoTLflI W+MTBngwb44HX21/JhdOzBaw7QhL7weaa239gs/1SEItMk+eSvkGyZ+l8stqWdG645Mwh9FlP/HO pJBV9n6HeBWw0UP6vTH3nvSwZEPK7UegFBFbZx3mXFSysJLMF+uxB+NtJuqE2jxsCeb7R5ZHS3BM nnCjN5XxFshz8dwX13U8pfweXxEt1fAQPOEhfav9VZgJlkI5b+sxMyzHvLAWTy54fBhWIsek75MX hA3sxB/Ka/dcEH53DP1up/Q7XQ83njsfseoh4BCX/JY8V49Xg837v+S8/rYhLuzwMwe6zIH/TIc3 UtA5JxyifLwB2he/xGZ+KvLvcMFNfof0YW5A4+rf54IX12jQ+ZnIvw4gDMXkGI6r3rodIVhVCt8W OcSWp2rBzEde0W9PVpYbBE8fIXJU7MC9Id6rgx2/eJb7eNH+Oq7fIxNnsBju6ZxYYTwv7aJ+wcuM 3rEK9scSFmAGIziq/O2N7ZbCKt4SbaLn2VvF91DV7SvH5j4MOvh5lqt4W3RPfg747jm/vkIgHNNf dkD5h3cv++Y0fKZjVWd4em8tvPvHZ4HkRef72c4qvo/6NC+/mSSL+uDBcxu5Ns6s4N8PCF7BqX2K tTfqKrgMP0Qe6ZsGwfbgHFMCAPH5IFurqhBsF8b83OKtHGfjj5b3f6s2VxhWPWQ5vFutMBO1+EXf forz0nNLp/wmnLwDUrEwJOVTWfHBIgZdb9D8C/KdVpqW0YsS5l5Ux/1tJhP3TvcAb2397ReWdaac +wb/ftCfh73IbIWcc+JhJc/hE4luy/tG4V8g54pBfMfT8dd43OGfF08kXrHk8Ap/sfSnchv+v3CJ f1lc5MZOeacel8NaJbyrbHR31St0MRjdf8WFjgezk1Vy724bWi0Zbu2khvNEdtJhYydO95Y6625J t81GzgUomKiL80ble0+/exT+NknvsA3+Zr8442D4K+MfLDrroK/DEv441kkW/JUBd/j/ifiPOsgt oNE6Ln3gtI3N33JJ60Rc6Mop51C0Tsu979ica1qWO1ofo38ddWEDZySumI2OLmTdnQ04+Ve3+g5t Y/PLst35V4/Fv6w5U1jm6hfk3rksnVZDjsCROQCtKuw3QjOsgY0yAwU4Ks/QLWl0yNoi6T6BdZHM pyps6P7KFHSNQc7YhDlXywD+rPvYavlA3sTS9ffSaLc+1j9W6jErqMUsyl0oLu+1obVnjIjLbmOW kuELDmfM0s54UJ7xuA3dUbnuzrhQntHOBzpY6v9SVp3tG+cOfxFcN7otuYU1n3gS84mLCD8Mx6OT bzDRp9jiYX5+D2YZ6p9d2cZkiDFaMxj/egazWC5fYZTJ8V6AQ9+H9ZbRm9CySfG/qLqGdY2h5esi obLNDTXpWTzhfFB+swwYCVA9sgEbnOAeJ0vDmUjyeSVh/W+AO5yGZX9bMmVsqq0b8EOe2O+xo6/2 Fw2+35t2kt675CRDk3O6vBSMlQb7Utz6BuJxzuD7Mx1P209ucwfH5E87W2by1Oqs9uPMQcaQ9IGE BQOkja08+NJs/cpd2nrAnV240FnQYg3WlZnyW+lY72T4CwOw91yFgyLR7OB4GZcb6jZhrPHDMFvP VB4W4Hsm4CuC0D8WH5b0HbWygK/MiweTXqFWivnKsvhwG1tW+hOweRh5Gc+XAwPwvUrwXdOCfGf3 49tqNQrrbo41Gs9I6jggcbWJuI689edkPOaRjGeCWWn4/UmY4xzmRHy0jSUrmNMc5mPE48TdGQt3 6VLp5hA9Sanodm1KOhe4BTQ2r9m4rrYJb8ph+OdH+WTjb1DCLGJkOk2b/TZSS8lkNVMyseogIHUw AW99pQOiEkjDFkxiO8ixLUxKmCVXOvhKUXyYxarTrdnDfeF/Hdkm8YYiAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

i= s a function of the reference input= r(t)

is due to g(r(t)) over the interval [t= i, t= i+1] in the jth period

Mapping of the state vector over one period T=3DkΔt

Tracking Control

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image037.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC91Za0xURxQ+s7vsLiAPl4dQQUGKUaEWsFgTMWCklD7U+qw1xPgAlATr+ly0hmC0 VX8YwWhtK0Z+aKsJjT/YtE1jsImttbUmhNqYplWxbYxCiVRto6l2e87cubuX3bnLZRds0klmZ+7M mfP6zjn3sVcunf8AeLvIsqCaz44tZhAJYM5IABrj+CL+jrfGwV/pr88um8X4EoM30pUR4HK6woVG uq4FX2vHhXGa6+u5AHlmgIwXZpcRNZ0hJaLAr0VgtwCU4Pk+/71fLNBwygwjcToCux27Q8xJfrKY p2BPFXOPx0P2QLxiDvyBC1HimlqMSaEfIa7nY3cyhV/FP3hY0xpVF2BbCDWwFqpgI2TAHBxdOM6H dbi2At4EYy1veyGLx04MfyqqhV1/OiAH5zSqLV50oj1Tgh4e/bSjY1djv/lMK0BL8xR2DHmUI4MG oaTKc6Ifz4n81wHh8FChqrznQMt9eu4rrIVm7IQN8aPzdoGVXXO2cotyma3BT8XB4zdXMTFJMDlj 8s3Dx4SlNaRsXr/bztI4WwzAuu+T4LOOJChDPhuQXznyrQUn5OLciSskjeSVQT736bT8+y466vzd AaU4luBIthXh2LV5y/p3Ytka4o2pAFZht0pL7QHOSSbR/bj6huvW5jaxY4GuHoXXQRwvJY17fhRj Xs139RA2/enjhewvcY9kpuG1Bfukoocummsxea/PEYCJSeN7s77v+e8mWIXez4fQmxzXOpYAGa37 7CXWhGHFFZAvyVHl0ZiC40C45mEhy+igQpgAeejnyd8+cm1jyjqtUVdQUubE94tvHrm0vq+T5INZ Jwcs+nVJg8MUCKdFsxyW6amBZBZvUnUiXRpeKkRJSt/xdQUoc/AWxeW9GEPYa7E3LMO9TYWsceMS E53rxH3qyQxE1dagg3w8rBiI1ssTzy637GekQEPJAWYV9bt6/yqA1kLGdUGao3srlHM4p3WtTzxU /FuV9UZR09e8mMM+vlkDez56izusX11COn8cLBrfR+j4ng1Z/fl/4DoeJoDztoPjqvI5jmfXH5m7 vQ57S8LC7R3MbNL6/rvewPoToYOD1VAOhFOLfDmd2zuInMYalY1jA9cBYALxMOgr4uFrgb6aBL44 I1+l9c7l6w96lTpEvRTnBb9G+fLrjgPOLbvvuo39Eys7rNKW3hH7QjctDl0SHKx+tUh7f5CtW4Jg OJx8rEF4qrFjw/HWsObwf3NPozg6c5NwTfJS9HUHj6OUHl8clYpnC2rTepT4qHz/gYvie8mnKfw6 Edf3oM4XcGza8dDVgvva2LmFe/6xY3sCcaFiazdUFwrCqqHa+we1tw/X8PeLxjE5rOvDQt7d69cC jc68Cj4yzEfKs6NfVfCca9kmr6HnNTEjq6Gh1AXZvTGUuiC7N9o1vo/UvzcOy/Phk8aV7onDhWso 98ZInXwIpVYPdU32v3eMEXvq+7ZttHJW731Pq8NC0dUWi32siPnFi34oZnDhLK3vFmuvBkSN0l4T z9mdfs/YKn+LOE9+zfDjPwvnBwzwz8b3ileC+E2VFSvOpkps6TRoy1WUdcIPC5V/qqAfJ7HFxYzx 34RXdTr6Zwr6XIn+dwzyv9a3wHTCL05U/lMF9mVClpZ/vtkY/xl9yvejgeJqnjhbJbGl3WJM1kzy BRsY9ypx1imR1R0RPu5OQb9Vgvt+q1HclTyR6V8n6HdK9LfZjOKu6D8QLjvF2SaJrFbb4PJ9IFya xNlmiax6e/i4NAv6ExJcsiLDx+W4oD8t0f9IZPi4aHPztMCpXZKbJVHGZOWgrBs6uLcL+k6JLZnR 4eejTSPrMt2PyHaJLdVIvMiArErs7+rgcl3Qd0tsSYoJP666Bf09SVx9HhN+XN0V9I8l+hfEDm2+ P/Z+owiUdSV2aPM9Wjx5JUtknYoLH5dkwX8sC8RlTnxouNg1/LMF/+fEfyxa/s+ONMa/uK+hXw5G avhPFw/t5SwwL7Y6jPFfif45p+P/cqH/Aon/ixIGF1eyGrVU6F8j0f/lxMHVqIHi1ilsqZfYcjDJ mKzVBuO2XsjaK5FVnWw0breYjeTjXiHrkERW9ChjsjZgdxuw65CQ1SKRdXZU+PnYIvifkuRjZUr4 dfKk4N8m0f/nlMHFs8qzjfn+R/XnuSM1tNoLknexdHwXu4n09E6SqPnPMVHYaGZ27stok/qP3whT FlxktGfCN2AaJ7MUvsNM9MGdZpGcOg3736bfPJo3duW/05q1VRsz5lS5MuavW7si8GsX8XxGfG+P NHlAO+vP0/fvnzGeTHZe+YawqiboxwnlvElXE26dymnKwJzMAefZoCyx6PIZnEURGotUH/mvmANk DsWZCMlZxZbeEH1iHRJ9g/izYGB/2mS4DgIPu58+xvAJHQ/wwyNXfCNPtmTBJQYgz0JVCj01FEQ9 JRK7zh3rzRNlJxWvaSfbHSHRSD0dy2muuqO9Oqo7qXxnk9secCaT71zznonw7kzlOzPc8UH0ncdp ZroTg2hVpauVU1erOq9W+rJ3en2lL7tJV3azruzjurJ9vjnNaXLccQFatet6xCpo0vF9iWgq3VEB sq/r6tutq+9dA756bMBX0UxPdjLrL9vm3cnmO8VeP9i9O9P5zkp3TICccqYXcUuZ6lV9S5ycZnVQ S+q9lujz2ctpNrhHBOFzSNcjLUwPjZNe69SVNtYfH7VSBFYIM69f/wKJI84bViYAAC== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image038.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61Xb2hcRRCfee+SXpozic9LvFSpwZpiSZVL62GEQlJO00NsDCG1VU9ISWN6cLGX f71Aix4YtVJKDhEEbbFCVfzgp9wHPwQsxX8fLByRIiKtsbFRqYX6pyIofc7s281tXu4uL6QLczM7 O/Ob3ZndfXvfnv/ibRDtOdgEB4W0bi9CFYCZXgdQAX9XsI5/N1fWwuXqvbs7oyjsELbtczjA2WoH hTn3k1BoXURNWv82Ag+bpHtsdydbs08r6SvB1TiyD6CDAK+7xy77IPORCbeTGCDyE1lS5vgNUg4R NUrZtm1eF9QR1RL9Tor1si/mZTj2AdnvIUqhgxe/Sc5ay6oUUOuFBAzBAIzSKruIp4n3wCHS7YcX wEvDIAM91I1BkX+pDf1pQf6DHMygAX1/WPDd4I/p2M/TYszgOTRkoelLDM50ULbvus/KT2ZxJyXx 9Mnt+O6OJMRaADJykt9Tf/KGBVtIZq7aFvFrwVowZKmCPB+Q+WQ6EUnCSSKuDeOxv1/Wyq/5Hjjs dJu1+qk62C5Z1cQoUpMZoyDfgppMZ0Ljw7sCOC1gaQNOfFMPn+TroZNwRggvRrhJSMFWklOk4Wgc r1PsZgvaWv9Ks2vqNwseJd5BnNe2g/jc+OHhYxb6GNuUex81W27/kMwx2Y5r/8v4tBzxwdxVB+tN 4ufr7334TsTFmU9e5dosta+TsT8rYs9jek3sH2zbXROjRB3M0mdDpG0M+qkS22Et7eCuFvx4IQHH Pjwi+q+8lRDnOLuxBfM3IrVEmBseAuapcFxwpPxnR/cZpz6Pw9mXIxh+L4LMWTd3PIKz5M/0tdz/ Ub3yEEEb24U/kCyU5Nvnm0JeVKbjDayUd8jzU/2Qz0SQMRn/1Otx4ccy6/WctBNnHZPM0ZK1Ga6z QdfTS+46mK46lKqPbq9q5StRK7xlZ8ZZb2phq8Of7adTEcED1ywI1U3h4BGnn6Q+6/qIuP/ihrjg r5LXMxoa55RryblED/uA46+0D+pml+6DHPnntH3AbTPcD6lfLbEP1FzO0FyH33ny6ATR6Tt6j+bR NFaqla9E3fRvS4Wn89O6htNTyJHYl8fXtp8Dq9jP6IrPT4PUFVkj8tkZSwr+9OMOn0vsET5M168U ch+QxPPjmN3nqI7nCuN6TFdNbrprwvneKGuhvvmjFY6+1DdHP2O9klSrIbpHzvmpPRfaEb76lPWv Sd0TrmrYsnWTPAgX2mfLnFsVq0b6NhaJNesx1kX6fr3vYV2N0re5SKw0eos1QuvKeVhXs/QNF4nV YqxuXfqZU/hhaf+IfH/q+HmP+GPwX3qixPzbpH20yPxjpjf8S3L+CjOqvZndmNdWianfN+49f4I2 /ALZ894KqneAlDmHJvrFmag21EM8YGyi/wg8ZtCtyvxBDIkRNPhlzVKVsL6b6F/jJ1u7zZx3cmJo YLSpayDd1HNoaP/yLwpjPiDvxCrDBl1aill46XnDxJJIYnbOTdufKPtMcZAMDWk5trJxx8BVzdZ0 xYLys25dedY+wfmrzP8tGnxcSYDimVar4lt72/oNsniD8zVF1qlsaoTNxfnqMjiNwmZkPlAGp3kR R2VCjYTFyNi8f5lPmxi5RD5KE13UFPJXfP2m+P0fGVwg9gQPAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhYgEbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIACgAt AA4AgwAAAHAKC4IKCp8JCpIJCqsICdsGB9IHB8oHCMAICP8AAPEEBOoFBeIGBvgDAwECAwR2EMhJ parY5lt57h/4eRM5hpQJkKoqouuriYZi27NlCwtTdrgURtFQCATEX0oxKPhySiGQE4wth7JoaWFE NrSrVhZqETgUjoO0JF67LYjABohVmlo3G2MQzdfDd1gJeWhgJyhiDgQTA09kh3MiCQw2aXJvkJge EQA7 ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image040.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYa2xUVRCec/d22V1qu9y6WGKxS6UELZIWWDEGQo1YGwoLNm3BWCNQCi5SaS1l QZpYiFEkIWDE1mfsT42CBBOBSFKiiVQDsfERH7+KSwvhEWutsWjjOnMe29u7d7e32sSTzJ45c+Z8 M2fmvO5+f+HzN4CXc1AIWzh3ZC0DL4BrlQ/ADQUektHvHHc23O9fu6rsQcb1GNQvFjVArl+gUE3t bTBaTiLdaWrX5QA86gIIPrSqjLRpzEqUTwFLyUDSAUoRcMDa97MObe+5YBqymUjkpCF5sj9d8rlI MyQfj8dpXkCuZiP9igKfbFPJ04R+pmxXIjUygVf7Nw42lcMqBFiqIAINUA/NEIQw1lGsK2E7yjbA 0+Cs9PaH2FmkIuTPlGL0bp9tnEa+862FrGXQgNPST7/URde7gsgf7Y+ARgCXQ+z53w3Q+kJsYe06 2Iqi/TiubdDg+H2+Gl6TDo1nAgc6ppEc21JGtDS7RkwMC/n08HA1t9GI2MevSDuu0I6en3DMYFhG HmDTbwbPg0fqFmP7/QeaKO7x66+Eue1OHK90QOSka9NO0Sw05U/lIW7hVU40m5yc0Ub5/54Tprfl tjTtN5jOYXEB7vomAKd6AlCGOM8gXjniboNGmId8I0rIGtkrgxIek/tKhqI0tPG6AcuxLsWa5rYE 696WnU2PAWOEjVsB95mYt9KlMow82SS9H7dcjF5p+Uj26NB7TWAdwfpCoGDxbYwlPBdhMOAS9t29 5GZ0BGuS+RFvWPJ5yOvXRT/x5py8NmCANSdaijyQ71ds9gabtDyEmLtsKLrmqpEy37tYDgQ/OOgp dedMer4Bxuab7Ch7VOdinS7fVIq/nQnBnpnI5UAxxn/+lyPRZ5mQk4xIxCtnTB48OB9rHlym2Osp Yq+WwA6ow+iXwL8vo353X03vNxHF4+wXI1HyuxDrNSiNIM3lGOnjQ+OtsQU46NmXwBc16VZm+fYR P0LrDLH9GAjyU51fvehre5+P23x5783omvbhKJ1BpzD2t3y6ulXhkV/Kxx+6Z46Jfeu15D2gm2Kf kTr2k7Tu/9+8wiTldQ7MhczLBoh8ilKKsW16c3XrLqTOnKrWHubSLHfCc9bYZ5hi7059H09SfEyn Ap4/cbYMDjev03pO8ns3DidCbL1+iFskK43HQpzffKgOzn+yB/xf4V2OOm+/VMvHEU9y+QZJFPWA OPtOiN8DJJthVPMzj/SVnhqnfOqKVEPxq3e5ji0Yin7sZh3dNwz+DiJZW9sfmAvW8QsCv8BEnirk Df0u0mJ9dJ2ul2SOPSCeNfZuy9mf6k4wn1ET1Z8MW1af75B96m13dCrAnxjHVG8Ls60qSWpRZSHN kvmqqf5uGYPuLn5OSNnKpN0rCu2V3Uhfp/Ff2fLLPAXke9ls65p8x45nK4JnZoXlzFL4AYmfb4N/ L3OGXzSQC+2Wfanw8yX+XBv88w7xaT+9aMmjwl8k57PcBt/rcpaLpQOgDTjIe1i2N9nkvV13Zqsc 9/EKNn7eN8vvkads5nUTA7zCUd5dWoWDeTXI9h6beT3udrqeQ8zJem6V62GvzbzKpzhdz+L8slsP B+R6eN0GP+BxNpciXAwXHcStU7aP28TtCa8zWxvFs3LcuJ1Ammb6bjbbehKfNUUTiJvC/ND0LW7Y YD7CxsfcKjHN5631jP0Mz9h+1Kfz8lYp90uecuXCrz86M6Zq6gM/UyuEc7xPw28YquezXN7DNLr0 iPNy7Tykv7RLcdONL76/Iw31zcFwfTRYub1hQ/LrijDvkW82rxYHMzcWc/QL0hkmS0K6kfCOTQhJ SxqfeM3URdI+ZcR4l934CdjX7aI7AfsZpkgkx0bN0YnOxPHMXlA9j4n/kqbrs3FlAdhnXqHSP0IL fHlyMe2OZdnYEToFuJJJJxLLSERd9QR4T1HMl4in6snnPSUxb8JHZXGR+Lcl5k/jVZjrlMemp/Qq H+8P5VVqnAYHs2u1zG7U0wNydtlpLHRynY02s1EWZuHJpiwISZaUbE34rnKZnEMX//0HiofSIbAU AAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image041.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61WXWxUVRCeuXe7tGVDt7cW1qSQRSkmFEkruYEHDCXqloispaEFQh8KpepuWmkp ZQmYsA88YIyhQRMTE2N80RB/HoAYE0ggPBhDINmAaPSFVZEQrQlUjBUar9+cc257ud2WGjjJ7MyZ M2dmznx75tzvL339PqnxFNVTRkkHtjBVENnby4gilI6ITn6XRqvoWPmWjannWNkxffey5kT95dqL cJn30uRYAHoyML9qE20DJV/YmBJr2ZOEvoxCQxSI2wyHt8JrP0cof9ymaogxkIR3jCzx5xs5AXrc yJ7nybkoDqoC3Yai0sxl1FnaPmbmbXIe1v46/8XmwBj2S4CxGXXrox4axCnS4DnwNtoN3Q56nWY3 ut5yuRkk8hyjS/zpUOHjU3SGLeoadVSecWPredc8qdnnNzKEtKn1F5cP/+WQ9ZHLKzu3Uha6I9iT H3WUr18rOxQXG9nP2g+9Vy16zI1O6NmqDn0wDMmpZaxdx4DvRj+O7e4t/Ig9o2lTeaJdyLfcYKFs Mf903YDU3Rt5J61iD3/psm9DGpNDu/bpaX0APx8HLyT7mFglMDljTcoPjwlzPjE0sB1cucUfcP+V WvqqUEsp+NkDf+vht5f6aTnkfmgkmsRLUZOqyeqmOzl1J0Ycel5qCS5nWwNeHNo30BLjk+IbV4Gi /j0ytjLGIEtMsfvh1Z9yN4dOmpUIFX/Xvt4Fv1T7xKoFzBOZ6zI4dB1ry9b8kxsHF10c/saMXAc5 MqLXRX4QJtY0OEjuN0vcDX5kOLgcTd3Jtf7mTIv3fq6h5GdvlzdHax453kT34y1x/HjCE+Az4S2j 8duFlCwshFRDjaj/igvjuQOs9aIT0vWqCeNwNoyDTaV7VGT6HqWOs5e6gUQTPcy4ePogdaKfDA9u tYpf6F5FJ1zuihxVNcs3H+Oo6a2vHO2mQh494LjLRdh88Gan3gdZ9LFAjmvBRSdkcqbXWhpYetuR Tw6a2mRU7x5e1MBzAda5D10+NdCn9q1b36v4thc1L2baye9l/ZfdiYsRMyT5qZjnEe+8XudQzBAO f4dxkHovMlj4b0cadBfG0/Wu4F3abMgHSPr6YpNHR/vVtUzfnJW1N4zupRAWnhmtkHfqv2vJWHYg lvwbqwPvcTBWBSYNs4iVofHchoDPqsAb75TwuYkf7DNLtrUh9L8O17YbdAP28zB/zOjjRhYsbLwq 8rkw1/I/HGJWPb5pZM1CbxS+ghNqhS35EhCpQlnXge5Z173ArdHveqavZzCZ7skl23b37ZjaRcTn 00zGk0dB6X6fky/T7HzyFE9/TGTH/8uTNfM5dW/ozszYGLQnW/HlrL9P5keWoLpEpU/vn0Ju7DOV daagO7PxKTaWsVlM+j3LZMuMZp7RZKGZPEPpHGz1+x+tuu1gzAoAAA== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkQExAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABQAP ABMAggAAAIIKCqsICcAICNIHB/8AAPgDA+oFBQM0CLrM1TBKUN50F1cbeZ0epy2VYAyOWArFEUgf wIopSdt488QzXAgsVw1AmKEgN1hGkew8EgA7 ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image043.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8VYa0xcVRCec3dZli0tcCkNVSrbKA1a2kAL6o82xWjRREtJA30YflAeNmyKLC2w tCVxNcZak6Y0RjA2Gn6YgpESEx8hipY0xqApycZHfCQmrbGVlDYgYkqVdJ05j93L3bvbCyXxJLNn 7pw5M3PmO3fOufvj2FdvAW/DkAcHODe5h0EKgOOYByAZat0ko991rjT4NH3PjrLHGddj8Ktf9ABv pgsr1NPzQYi2AaT7Dc+1OsA+B4B3+44y0qY521HuBlNLQnIClKLBKfPYb04IvueADGRT5Vxd8uR/ leSzkVZLPhwO07qAQk1D+hMFHvlMLUcT+qnyeReSnwl71bdxsqF1qRRgq4RGaIIGOAxeKMc+gP0u aEbZfnge7LVgXwmrQSI+Wcqy/9IhdPYjGGYa1EzrPM50qRsOnw97kT93tRE0inOohL38tw5afwnb XL0XfCh7FecEp3Vu64pnN+9Jh+YzYQd6MkiOz1JGtDVtt1gYNorpydkq7iOEtnv7pB9HSWvoF5wz XS4zD1CP8bolFqRbiM/vP9ZCeQ9ff72c+67A+W4D1jj0Qn27eMwz4KdwCJt4hYlmgcmwFuXvHhOW E8xuaznuZjncLG7Aju+yYCiUBWVo5xDaewrtHgQ/FCDvRwl5I39lUMRz8mjRTICm+q/r8AT2pdjT 2rZgf6mtvSXNxZ4l2/gqgEuuW+lSm0WefJLezwcuB8bbPuTr/mlChxGkh7bcChD/DhLJp2Q/O6Fz /zRO/BdSTq11SvA5aNt5XegQb8LkphkTLQ4OFPu4xbvBlgyHEuYqmwlUXNPj4t3BMsE7cNJd6spc crwB5uNNfpQ/6rOxT4Q3tcLv14A3tAa5TChELDZ+Mxc4yoScZEQiX5lwp3fDYci9M07uJVzQCnWY /SJYfIvGPXotcdxElI+Rr+cCbsQhD/sKlFIdyuc2EueH5ptzC3DS/VLEvuhJ94TLs4/4OdpnaDsd E0Fxqvp1CWPtvuLhPk+/eCtQ0T0boBo0hLlffmFnp7JHcakY3SP3mnN/25x7pyH3SfFzv0T7/v/F FZYI13WQD6l/6CDwFK0UcWg5s7OzA6k3s7IzxByaKfeT5twnGXLvin8eL1F+DFUB60+YbYOuw3u1 rnE6d9HvaTyrnae4R/ISek2c28+dqoOLnx2DD1CPdN4+Uc3nEU9yeQeJNHWB8I+VME2OrdareM0j faWn5qmYzjdWQW97Ngxumgl84mI9ozd0fg8iWTB4E7FgPZNo+BWkRpQ/LU/ofqRHnNF9WiPpTjXH Faf2J8c/gw04FN9F9hdec7okJoutOVTPqebQ3sS3mO9N0j2T4fnYTs3pn4jWHMqmVc1RMRa+8aCD CxFDZsJhdFIHMw7JCc5j4/kQDzc7c433X6Od++SYuifrywD+wc0S755m9FUpSbUVSLkyb7urftjG YPQ8ybul7JmYSiga1Z0jSN8miF/5Wo6UwU9v8e1h9DWB/GYbvnzy3THWf2U/S9rPtbD/MLNnf/2U WLOxxin7udJ+voX9izbt0x47bsJR2S+W2NA7sdZkP8VhD4utU+K7zAqLZIOvcpm7Wou1dDvt+RpE RwXMel/VSn2/xb66kLS0+6pZ4hKwWMs51+L2lRGXoFzbKQtcjibbWwvtq8s23sduOfesRd6+dNvz VQ/x94Axb+/Kd3LAYl1jKcKO3bwZa5S5Lm3AunQV9anGrJTydMnTHnTg1ye9Z8s09QdDqpYHw3xM wy9g6jeybD7CNDp0iUvh2jlI/2q/hw03DvH939jUcNhb3hDw7mpu2h97uyObG+SdMUULg5GbbzP6 BWvPJouxdCMSHVuQJS1mfuQUr2tMeJUS8x1W8xfg32mV3QX4T0qcU2Wp+M6WXBa5VTmK9RVfN7pv 1CzqC+S9aZXzAfg88ieXeVcoq/Rv1SbPPXKjHfGtsPAjdNbiLicdny8pgogayeIj632eSK7VSC4f KfKlRGJUHovFP0G+9BiProhOOdcZ9K2MibfWRryHTPFGfQdlvGkJMtLNdeot4lMe1kBfxMN8LGIx ENew/wCsxvVBDBUAAB== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0220_image044.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC81ZDWwUxxV+s3c+351/c46NUWLLCSF1jEE21GlpcXDaxkFgXAthN22plBi7yBcM xgSOphF2fxJckRSaH5P+RLIUIVGaRlaMWqpSmRqIKAXk/kaqUOtEJWoDbhzqqiahcd/bebO3N7e7 XmNX6kpzM/PmzTdv3t/O7L1x4fXvgfmsFJWwxWxtbhEQAQj8MQaQDYO5RKPfu0N50FLyufX1nxYm n4DTXbIG+GiJRKGa+lsh+dyDhApb/9ulADcCAGUPrK8nbprzHNBa2pOBJQhQh/Mn9LG3gtD7wwDc wvPCWGLcpvWLuF2MZSG3p6enaV+QjyUPy3tIiHKfnicNya/k2IClS0i8TR/iZNtzUKkAn43QAZ3Q DjuhDBqxTmC9AbYj7RHYBv6e3sM14mEs3/xXLKk3UwWSZgRqHstnWYkXRf9PGbZ//HYHoNhwkuca F2rEik0PQRxpfddi0HtN4l2Otpg18dB8IXHg0C1Exz7TqNTmtciN4UMyPTjVbK4xgNgDh5PyjP4J 51xrZM0DtP0zZtohzLxV2P/R/TtI79NXn2s0127C+YoHpE2G23bL7mKb/ZQdprW2sonhYJMTRrI9 d5uIYG/xrh19MRE0YdEB9/yuEI6PFkI94nQj3hrE3QpdUIntLqTQarRePVSbOvl49WSCpnZdjcFn sK7Dmva2CuuxXbt35IXEFwgbQwFCvG/FS88UtmlN4ht8N+kX4cLricErMSD7U32ex/qwTWPnr8j+ 81gPYKE1Xsb69gnZLkZcwFKx6nqC2n++krQbPRSruk0MFzuQ7H9ziA0xb3aoEaH6yUTTOzFXe+8R BVD2yjPhulDBvNsbINXetI5aj+pirL3sTU/V70ugbJQSZAFUoa6XnbuReFxIOtGoSH0VpNghjPvR 7RCw6T7onpfMLTwGm1H71TDXp9f0Tcw5YjUc3PmQMXHVzD/T8BTmrOABc0XKN3Wv15jtLx/YDOd/ /lXIH68RY8jz0rc2mfOoTXTOxdajEunoQI0weGxhrNm0PfErPjVPyTXc0QyDI7fBq8snEz8JiUNn x2Pm+4Bovb3/RluIQ5/kd8c6LKWsw24slwxLV/AwF7vuAfF03Qdtus/wpfvlc9D6AWH36yPoSy9i WYex8OD9kwnqt4kkd1N0Aeyve1aQbRr+EYP8kzJuiM+Pj+h+DfBM2DNaNL8uH/f2ayqEe/JXNxLk 14uxpsMD5bByxLDrnmyu6z7DJQZCLvln/mIgGede+UTXx9l3Zq+PJo6jchPDO5/QfKdc9HULX9Ul 8GY0WkrtG5SXETsfHZnkVO/7MZS1/3IUjmjvAQy1Ht0OIZvuM911D/N1Lvp/zz9VL9wT0PMP0VT+ eReBn8LSwTmILHgEy8eCs88/mS4xEPYVA3PJRUm//sFN+PVB0onl1968Tn5NMUh+vef7n30CCjY+ MSoCBq2tcNz8+hjKOnI5amr9O1+7nmjqn0qQ/Z5GP88ZQSyOE5JLyUjvjpliIKzZRNmB7hZF/1M7 SH8mXybf3ocUKsfNsQ4tH3nHC2XEqp/NLl5U1LjFi+J3ixcAyfMKxsnn12411xzDGBKsoKqnpTzZ Nj173RMiHu8He76aiZ7pwhN24YloZ2G3M7JTrEZ9nRtWzOm8RnmJ9EzvDSc9X2SbjH+lAd7Hou67 5/Au9+aLDXCQ7ic4f+BcjSj7qbTJYs5VZ8R6eRfEseA4ZbOdsDSrGS7QUbmfeJtN2hhiDPQ9K4he Rnw4tuZJyUfzTn6q0cCjdYofqflmu5CF6pfrK9knjnv6SFqsRl18xIs+W9vavxnYz4qlPKa+LWxB NXyAQrrdbe1rbeQCvAbd++9kPbQ0/2G1gLPDNPZrpjVoPqBikM4Ubdib8JBfrUXfROj9tYDH7WtF sPNdH2vFsbdO04PCX8S6Ju++S8OPGv72Ujsh9+Jku4htrVqe+0XK79pah3DTZ3ysdR+uNSKcdfUl 1mcr35ft+N0ZSZoXvjoT2HOSwm9l/E4H/F/4xK9FRR3WcpjC72T83Q74rSF/+FWw19gH7vox3y18 5rHj70L5XxUz4z9K73wtHyv8dubfzicJO/64T/zVqJ9+F/1sZ/49DvJ/I+QPv5rfz2555m4st2PJ 4rnqC489PmlspS0vLGV/bkVhtyDhJVTKW7jeFPeJTndexdftwtfNfLdxbqF5a7F/r61faRvv1sa7 edwuz8u8Tikk5bieKVO5XR47X7fGZ7NFb7lNBzPF+37W3RGHeF+Ma53y4c+rJs4OD7nE+1GOl2MO 8fJeJLmmF/425O13ifdjjD/sgL8v6g+/FuU/7BKPw4x/2gG/Mssfvle+Os34Fx3wEz7xl3jE40XG f8MBPyfbH74ej7p96RlyiPdJtO/gHPPVa+qbpUO+2hr1h++Vr04w/xkH+Y0sf/jV2Nvn40xyiXV3 zeFM8vdsf+/xNdijfDLTmWSSzyQfOpxJGnL9nUnoW0P/PORhlcP6cmUOO5Unc9iqPHl2+k1eau5V fEMa3y/zUnPvKe7fa+uvtY0PaeNDPG5fZwvLQzn+t8xP6xFd5xtivhGNzy33zuQPBfw/wCKR7g8L 8/35Q6v85D6jP9wlZPzQf4of0da6Ex3l8VnkMYV5h0j+T1nggDkg/Jx7Jab9LqCf/3vRsd5GfvpD 9Vam53ObzskBETZ9M8tQf35mG5WwUtCYIYTJs0wUmyPCoEsctSImN/nvB8Zfp203SvnfZEdn+86y xvZE2YbtnY+kf3UjzKX8PTtiTIO9lYqZ/HfNH6ZIQxq3pBOzQjKcdidvy5s7PD/tyvkBr/nLZ54f 1OQYv0k5Mpzmz0IPIT9y+NhPpoUncf5ykzjhNP2ofTr3Qxo9U6OHbR6T7kM+fGHFzDJHNJnT+35k SMad8jCqK/mbeFFwCXxCADhHlUKl0+vyaAkHals832EdyXMHyP+N4/EMaz01e5H8xx5np+4jzByl eBMmjvvipRpqOd7RaKTDQs2wRloZNcuykBrplP90xCMaWi6jPRoPW9ZVI+3myOp4VEPLxVsWjVTH 061AZ6f3DambpEai5vtoQbgI9qLR+2AZPI/1XovaY6P2mPq81SjEcWoVGAu4RbQei9bDsytwJuFW 4GywMCW1h6k9llypXiX1NCGirlbYL//5j5ekWeGoObLN0k7SCsc0KyTnDLta7rQ5siRN1+V4gk7V ddJyR10t95qr5U5YaO6efcnkWRMv8vDsSW33/j0gV1RAEEsuMkxZ1Bym5phUaW2iSmsXcoto2RYt W8jZmJcE4S7DYliYkpqD1ByTqlvcff8F5nuu1SOyF+F5RllSUvKYQrGemmXSs0vA9MD/AqgytjPC JQAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

LTI System with PI Control
- Example 1

The System

Parameters

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image045.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC91bC3BU1Rn+z93sZvMggQ1EAqghEkCaUjZxgI5YEGlKfPBYg6ZObMAEQjRAgtGN lI6pVdS2s+Ex0xGfmVGmONNWq3Z0OjilFR+1ljK0nTqp8RWLOIikHTpNAN3+/7nn7N6991zu2Rtw Or0z/95zzzn/d/7HOf85/93dv/3xtYeBX48bO6GVl7asYpAHEKiqABgDpWOpjj6nh4qhovzG62qv Yrwffs6gu0Ef5QAnxyFFeT20Q/ragR12WJ5brgRYMwZZvnldLfUmnh5GY9muIFIOwCJsG7K3fZgD PU8HAIeEQqQwUkSUafxSUZ6IVCbKyWSS9AJSqBjpn1iRL57pSoTN/oXiOYbUwUy8xi+Q2XJtT5kA oB7aYAOshdvRCMvwHsd7DDZh3RrYCDpXO9z77wjcjCW6y4ueg5tv2bym+TaoG78SljfuYmSS+n9F +MBV01bxun2L0NqTp0UO3budXRkC6Hu0hj2xoB2WfgXtKoT8+wJzjEttY1zKPyMQ+EY73G/qxNvX Iu6BAMBDt+5g0LXmDrBgzLRhgOkmmFm9Chbi3U2eR2YDbw8LoovGaLnTfKy0+E/6IWkrS58YCp/s M9Ll0fuE3dQz8Y7O4hC7icPiBOz+8wR46dAEqEWczYi3FHHboQOqsNyBNTQajVcLUW7T+dGTcWLt +DQCS/C+6FPTbwvw/v4dd3Y2AGOEjSaAkNBb9qVrGMs0JvVLlJk6/+VYBPYhzVowEqfyw0hS7RVD Jr5cR8KdMB7rZ+H9e08t21puLlU4iXzPInW2D8btPiE+u08Mi+0D7rbnn13QjNaPgv8rE7ublXCS fl0UKjmvfgXElWNK0vHrs51l0LeBok0JzEHbzn7zTPzNXLOe6sw24GUiwrXbvlth+4DLGshxj0sW P9TAaK4CtotNTbZBKes2pEwTeWyO4XMMw2jM+P7rjSRVavWRCKuPR6AFqR1p++SYMXZGzOj7+DJG fIexnaiUgYjaFu8gTpItBN5XYiLv6pxevlZ6Fu1kIRG/1/U2w6HF2Cdo4j/2YCPnozKvt9iE7Ex1 RMJGUD97F/v5kTZ44Kff5Qaz+iH5eTJp90OOxfZBF9uzcxZ//j/8Oh13i45PItyvEucp5O18ZPnW bqS+kvqtHcGAkWH795y2D7r4IaS1BkYTi9Jruuq43pre//sz8TDGqEq893AZAPZiP11byVgHYm+2 22qWJba/hTJNOb6c1w8fN+MQ0RIsP9cTSq+vExF45Tsn458gXRtiEdl3yQmzXcqW4YfkCYcfQhbb 52rZvnpU83QS6Yi0m6X399WCUMKhi3FdlYu+xcIP5BuyIfmp5/Uz8cdePRN/AUliLrrE9Nn2mWUw VBszQrVoE4zhUpf0flPCsWm/oTm3F/s8hHQN9v/WlSfj1nEPYP0LljZ6tl7rC8rgEYxd5TfHjPWf RaBDjHtAjEvjZdo++Z7d9rkW24fdbX+O4s/5n9uqOHCu5jYo5jbFsiuG8tuPVpbBL6rNvlPQF+Ps sR8DkN32YRc/5LnvA+co/nSh566Hu9CTXejHDfgUR8QuWI+lFVCHn1ehXzdizWa8m3nXZWzOkrns 8I7h+DSS+UiEk7zIxo/i80xR17J7OE7+bfjlBeZZHusfQB+/xNtH4n3YjvMx+QY+3/PGmfhRbFuN fd/HVtJsNefLgReOmGfRRXg/9IeKeeUjxF8xj86d5P+WDyOw1SLHQ0fOvg/sx3a7H/Istqfc7eh5 3YNxDg7iuh40z9tU3jmYPm8vPWqeq9dPmjqP7PPoYOaaJz6KEe/gffjjSKouPGEkPox3iin78f6W wPwT3iXmRxxrOE58ORbMy6rN830SD4WJb38QNzB7JX5AvtZxy7feivcf4p1wgMfeD1Nxb8lHQr73 P7+7UtwZos8S7bb4c7fd9vkW2xe42B6+ZNvbz+k6tree0/cNZr+n92HtRhH3vG1fopTxHh7L0p61 2v7asDMHKLDFH1VcyrP5StU/x0e9Nfew5oOq+pyznNlU/XNd6sMuOPka9eH/Md1zXXxkxbefsS6S 53HxXqp5hlnv9l7EKlu9ILrmIhUhrRJ75w2r/rqQwRu/4a/QAmbdtY7Mw7xWiHz0sC0Xlfgk/zyh 0w02/KuwfFwDvxLz72vOYk85VpHQpUyhy2FNXQZwrD02H0n8MoFfodAlzvTwu4S9VPJPFfhVCvlP aOK/a5M/ZMEn7PlItUg32vCjAT38K4bM96xua2E60hTLfL1IYlj6FYrxqyxzcB2Y738JYzDYGc7l VIPlGutYPTMtGNa1LHWMi3V+nzjDWHX8Ao3RHfLWcY6YzxLzaYH5ogLzszw9zKgN85TADDMn5pNF /uSMC/+S7g0K3V8J+NN9vtC9QaG7H8xTApN0b1DoroMZVei+Tui+TaF7EdOX0zq3Jf5ugb8X6QEb /pmwHv5CXDgf2OK8xCfc9Ui/Rrrfhj+Qp4ffOmT2s+53En8fEr2gfw3pQRt+Dh4cDoA3Pp1nfmI7 b1jxyT6v0ndDCvwnNeSvFrqr7P+OwD+msP97hf7sb40bxwT+iGL+7B+jh19tmz9W/44I/+Yyp393 FunhrxzKnPOERZhlCsyW4tHPmUlYfzvepynwfzTW9InunJksvkNbj2vxZ0HnPpFKC3oy94m5Fr41 YXDdCyT+urA/fOLTwa8r9IdPfDr4h8b5wyc+HXyy438Mf/YnuXTs7wdf+k3H/n7wpd907O8HX/pN x/6LwZ/9SS4d+/vBl37Tsb8ffOk32TY2z/ytQGkk47cCqRfD9DsBuuh7/7P5yo8s0sc6vqI1dT7X ot+1rjvX/M5lXfv4tf9iAM9z/Whzi68LQa5h6dxiY6QzfHUJUQ2W3XMLr7x5GTP1aWTOXG1XSXZ5 s1de2yjGalWMtXb86PPaVoFP7+zseW3+hNHntZsE/haF/PdMyC6vdXs/JMfaIsZ6UJFbzCjVG0ue E938ku08/LGYh09Y5uFXJ3aGV15AVIPl7HLc58V77d8qcsd4mb/ccUBgHlNgnprsDzNomJglhhPz uov8YZLu84XuDQrd/eSjAwLzmAKTdPeDSbrPF7o3KHTPBlO1Zp9hZr7yMnPmK0vL9M7+t9H7blCf /V8WZ//fKc7+Eybpnf3bwHxvp5L/bSH/EYX8eyaPXv5BIf8Jhfybp+jJ32HLd8M2/64T/t2m8G82 7xvkfvrcRH/nAeLTOW8UT/aHT3w6+C9e6A+f+HTwf3WxP3zi08EnO/o5L0m/6djfD770m479/eBL v+nY3w++9JuO/f2cJ6XfdOzvB1/6Tcf+fvCl33Ts7wdf+k3H/n7ynWzWl9/1qzt//M5PXfv4tf+X ke9MF198zzfS58zryzvDX5tKVINl//nO5YapT53hPMN3Tz23+U6dGKteMdbVFaPPd+oF/s2GM985 UeEv37HmIM0Cf7Pi7HfokuxyENW75LvE2XKb4fweb1KlHv4tiP+Ki/23Cfl3KOw/UOkvXwPF99Vb ZuD5D/vT97bjRf1YUSZ5AizM/VZgyD96FBo74XGD2gxm/jJiNpvIW5hB/9ygUh7vTevmtPFR0vKr E/N/GG0b1t5evmxtvDy2acMa569MeG4mfrubZyTBWsrETP+TQA+TqfjN3381t531x18mv+EqCddO ItV4IwUc/CwrTXJccbLTKHg2/mpv/pCKPws9cl1xWFZ6hAX/cZ/2zHPwZ6dHfkqPTL3CKfzM9oDn c3qmyblrrwk45oK9R8hRk2vjyXN5zv0S5A3ZbBSwxA45O+leJX7DXJqzE/pSccgeGeSoFKWr81eI YNPdX5Rau2bLcnymlsr+oEJCyV3E+wz0F6Rkli1lvKWrP+zgmcpb3k3xBFMtc3nLFf1jHVajfPaU YU71tBwF5pkkkAMt2HIDp14s96b6Z86+Qn4fYgUp75kjT4M4H3kOWkHWPM1ropaaU7Y+MQdXTHBZ a07ZcHosXFJL2bKbtyzsL055XLbs5S2t/ZHU/DNb7oN9vGVjf35qhZktd4qW6v48xzjv2MbJTbUc EzxFDglGeMtKix65TC3TD2ASkzLRzBlvRGFDpkd60h4M8jcTAexh95Hk7fXk7XXlPezJe9iVdw7z 4p3D1LxNnvpGXfVt8tQ36qpvk6e+UVd9mzz1jbrqm/DUt8lV34Snvk2u+iY89W1y1TfhqW+Tq74B jfnsxhvVmBv+51XTKHyUUPBmG4cvx/2jjlMvltV+U+9Dy5jch9x3m0bmttu0MrfdZhOTu41z15d9 tjAZD51je2n8GGqb4NSL5V7PneZ5Zt9pBhw1QcO+i9i5Yg6umIUr0zo98Azve1t/oSNSv8xb2vqD Dp63XXn+wVs6UjtOevdISyDn+h7PGLrHdZ0c9OQ96Mp72pP3tCvvhYYX74WG2/rc4xlD97iu7YOe vAddeU978p525fXSN+qqb8JT3yZXfROe+ja56pvw1LfJVd+Ep75NrvoGNOazG29UY274n1dNo/BR QsGbbdyfaRgwl1MvlrOJ+5cb3nG/znCL+/VGZtxPx/RmQ32WXgF38ZZb+sc4xtlmZO4VMnNwZlYB bsr/AoAU161uRAAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image046.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61Wf2hVVRz/nHvvm9tcbt6e85nDnq2Glo3lHP3jciMSwTnb7ZUsIlw25mpzm8qu hOCDpCAKFv0jNWh/RBRJ/VEYhKAQVEKGlBYt/3AqmuDWq5SEwtf3e37cnd29yVP2he8953y/3/M5 3/v5nnvO/eXkN+9CyjBq0SN7tdsEygD3bALwcNxjGz/rSioxXLZty8bHhYwT+OmEaoFMmULhlsd9 mBZGXWmNX1sINLhA+oktGzma57A/gZiwgdZtIcBc3HfeQ/ZjF4upW0FaSurrPq9frfsp0mW6n8/n +b1QRVpJ+icZyvWY5S5HxVfocUA6KBTeczdpsiUjhgJ+Z/SiH93YgzTaqQ2pDTBAti7sQjEikkQH koFI8miBtqb+9nHqwy9wVDjY/pePX3smwk2XP5c+h3OoHkH6W5E82kJsL7/fP3VwRLSWAGOjjeL9 9X0IHgKyOsnfaHzwuo966nNrpF4+fbiP9UlMaP+5Z98RRyipQy+9LfBK994uHECa8sm0iySvy8p9 VsoEn70KaWcplM9bTX0YJRW6VqV6LSrBsReH1fABq36mDnmrDs4cddAu7MUOqsQjuHPx5dpXr/pY vG4iZO6NVOp2Jd4QP3t6wYTaczsnfYwv3z1k9m/q9BK1lxNqXmty99D3bbvANc4sue/R0p4L4Zer L4bVjiA0SHvLJCNN1/cDGrNyPm9Se2lptE0jPzP01AvnQzv/j9ZMhDeEiPKFXv/kJ1+dPcw4wUTI Y46J1eFAvA6Oxb079zcwT9zP5KcOq5C84kt+jGyi/Ife27p/H+nY3Zn9gwnXedB8hJwn+Wsmt0r7 qOYuzo/kbsrH189fC6+QtpUIf3RS2X+fUm32SOCMXV4n4AZOR6780FhqGT5dq2KPUyyfOWzLZv+R tnM6gX2k60nr+LxkHBFxhO1aienchtg3sOLmvek4967FvTc395if82f+uOW6DVLdmFt7r94Km+ca 7BsaO86tlD9m1s3EmrWjuiFwmnPlJ1pqp+tWM6XqFud+J0XHufcw8x6wa7JC+8x9kStR15R9Xtnf T0ar+VAW6buQ837m6TMbBL47xr7Xta0tVpe8liep30GX4I+xfAx+SuOvKoA/IIrDb86pe9bmweA3 mrOENB3D/88pDr8BKn+D2Wr2XgHMH9ziMPn+6rUwN+uYzgKYL3t3lmen9R8Tx2xOFIfZpDHtfRXf Sx5d/JconvdIUturdJ9r4YpSudcWmssHFU4t/bexz6HznNt6kZIe4fDfDvfKZHQN6b/Oxbx1eqh/ l97+7j3p9u4wHQz0d80+LRjzYQGNlC+AFN2+O3pvefwrJFEok9uY7xSaj+LfxLU4MYjcrhHqv6va Y0YNv+qNTeb877i2/B5NXcf4ogjBeFLS0zxeFa1mPI3S00BzjKVVWurHF0SWzbNiOqWliSwzs56d rSuf/wOybGcNzgsAAA== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image047.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC81Wb2hcRRCf3Xt3vZwxlzySeDEql9YqNlHSGKlIQxKMMWoa5JFLsZTaENN4cklz F9NXEOTAoliUFgQFqZgPIi0VaRtB0EL9VFJoIfif0w+NhraUhFZbTVT0ObNv9nx5uchV8sHh5nZ3 due3s7/Z3bffnDv9Nijph3UwpGrNWwWUAAR2hACC0BgkG/3fFYpCX2Trls6HhRon4MiLbok+EReF Smqn4B+xUOs87b0I3hgAiD+ypZNGk89atIfAJzSzAdCGgFf9fT8YkD0SgAqslqKGUU2u0/zVXI+h 1nDdcRxaF5SjRlF/QkOE2yQ3S3d8qSfuUeHibf8LnT1yUFOA0gtJGIZBGIM49GBpY2nBbrT1wwgU J/HfLAmkKGvYFrtmwvT7H8FJIaGV4yznsSfbkOHaO83pfQdFOxI3ceh+8e7mFPTXA2Q5sO+wve8X E1qwTqUWagdcHHiroo9WKgViCvZrifa5CyNB+6OLCaDAjv1pyTZsE5YMWOMTv6PPzz3MPMAzGG+Y c0FjCePytjfELObw9QdScAi1lfvDDN9Efnvc5npP/nQeHE8e5Ap54C54HgYwExvhv4up5p6bM6Gi ecYm7rVEuayD/eJrgycMuit/dt6EXG0mHdR5+7JKbV36I7/2ykz6bPeI4ry3au2m8NCP9sf3zNrV yNB+4eaibZ6QZuyui5MK4z1sk1I8r2F54Zb8NoXsc4s2Bbv4q9uv2/Q73DBjLwqRjxd4/nNHP/n+ A8KxZmxq+/OQma4X/jxID/cU46XC3MNqnQFa4NNQriDpXD8mXXxtk7w3aG070CbYNnHZhF11mXQ0 JLZNYV3dA5jD+th4eg7be7+oAl3SmCzaqVQ5xIuF7ABV0InxZjDuLow/BaPQgPVRtNCqaF2dam+Z 8ODG68Q3jOIcHZS7OXf/b8by/Pie9LWgaJd8xkIcsx5L4uf+0vjksjMQ8HBvrHz/rNK+532lYrWk I1ph4mKzmD6Gdbo0j1typ3FAzTjCdwIVuw4MwNlPXwBYsORnOOadV7crP6qTne/cvOgLs/GEJSX3 1ZgJdf/QeD1O++m4TiUT0FVbAx82Xbe7Q8Kcwn1M+4Ns2ewC5kKYVxD4ZdQk2p/gG+kw6iYjzxXs ZPVy7zgLjp97w8N9cGXuV23f/9+5J8xvkfOnHk+pOc+jTZ898gfmrdTz7SShsVNXTIh1pBXm2Es9 S7lHXv3cB2HpN9ibkzu4T3+rJ4NLxzu+u6uXVR8Uk98hFHtf4qtWAVOnqO8VtnX7cqI5eRLrQ3hP lIml51PjV1I8HJ8f/25sJIrAp9y+6Vuvxt/A8T9UAH9MFhd/y1X3DeXlWeN3eN47cT8/RnH49B3/ 3Jc7f77O4KQXcHwZc6bv/Epeb0CEVVw36Y8rlMp1eI6oT+JtT+V9IqZ6BJ0OVStRo29D/UPOOp4T 6r7NksODY/GeQTtu7R7uX34iCfNePucl0imAlH9dDCT/9Yp1kQT7z3v9ofhIZKGV3MD8gUL+NzC/ 4eFUI1LZINx3abVBGdH5cRnTK6e3dVPkVqZ+KGfm1+T23I6Zpp6RXCSPrX02uC/PXHk+Dt3ToXqa cmW+yJZHFFD/fwPJikgv0gwAAA== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image048.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61WXWhcRRT+Zu7uuo1ps7nZxo0JurU/VBtLbBr0waUJavEhTcp1tS9SjDU0gfxX e/sQaKsFQRQiiA810AVFFIs+tCBoQLFQq9gSij8YfWhqaSk0GrVCxOB6zvxsprebErUHzj1nzsx8 c+53Zube706fPAwlO7EaPcqL7RBYBnh74+SjL8Yxfq5LVOFMcse2rQ8JNU4gqNcWOJrUKGy53YcF 6SRd5bTXEHiTB2Qf2baVR/OcOykeR0Q4QOu2EuBstO98DAfe9VBNbiUpL+8bn9evNX6GtM74xWKR 3wsp0irSXylQYdosy6UeX2naAemQ0HhP/k2THRmzFJDk0Yt+dGMPsuggG5INMEixLgxgKSLSRAfS gUhz6xYTzfzuY/Lt45gQEk/95uP73dPho5eOqT7JOdSOIfu5SE+0Etv1a/zJQ2OiLQEUxpvFkQf7 0LUBOGCS/IHah/7wkSOfrZWczcDBbD8OlcfAYaS5LRU5+5GlfPIdQsVY2WelWfjgBT2Wpek5oJHs Ky19GCdNOr4wtTLbhWuy/5m9urnWqZ+tQ9Gpg1ykDsL4/78OvsK6csVH9ebpkLm3UmXsKrwkvo3p XHh/MpM9Mz6m6keG7f7NfL1S7+W4nteWHhn+qn0AXOP8yrvuT+7+Kfzw7gthrRSEBhVvnWGkhfq+ RW1WzudlshdvK23TUj8z9NjT50M3/3cap8M5IUr5wqx/+r2PfjzKOMF0yO0tkTqMTG4Q0TpIh3tv 8TOgqHgWu4j9+/DfhU7pGJ/UGjRSnhu/nA9HCD/1mo7pPmifdJ+owadfzIfJRA3Wkj3H+5Xfx4y7 ET88/9QDdQrDWl7/eXoyPzD88NqFI3r9q7zPCDvFtyFZYfbpw7SO/2ZCYb968M9w++tzIe3pYsPP PpZ/1jmq89V52Ryj3J8jjCj3nsN9bHHub9K+v3ncrsN6DF32DacLe3X4jc7RfaSFmvzoUNyT92Dh 3PLchplOFZ8zez7KrZJffJzYeTW8TNqeEL4dW+qfCGTh0mYKBTI3W/FxIVOH9zfpsVyP6jLc99Do KPcxXPsdcGtyh+mz34uDcf2Zcu8r9/zkjVpZQZo17/fE499sETj1CcdfNLH2SGWKRrarGgTybCQf i58x660331oXf1AsDT83G8jZCA8Wv9neJWXyn5dLw28hPetgtjn/B1HMM97SMJsMpluvaI3GqUAX aTxznzbxlPH5HT2RVDW81V7qqJSr6X+I+yTdpWw3iozqEZL/IthbpkY3kP4lLxSdU6n/CXr7u/dk O7rDbDDY33X9KWTMewUMUrEMUumrtiQkUS4TfTPv6r3htazny3Lz/8X6nsOJRWTbKPT/TG2MGbX8 6je2mfM/2aaK2w11A1MrSgi2J6N6clOp0mq2p1n1tNAcG2lTkSaKXJvR9Zl46vkPIDumgQILAAA= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image049.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61Wa2gcVRT+7sxs3KxJk45rsjUx3RqNj7amxu0faTCNWEJI0xK3rYiEJDUkkaTN Q5z8KLhgQRCFiH9EAxuK+KCiPxSE0mKkoP6wEMQHvsDUklroxvGFBaHrOffemUwmu2GVHDhz7z3n 3u+e+c59fXPhk1chZQiNGJa11iMC5YB5LgJYOGWxjb9NZVV4oPzI/n0PCdlP4PCMKoFEuULhktuj WJFHSbcF2lYM2GUCyYf37+PePOY2skcQEjbQvG0E6IZ9Fy1k3jaxmaoVpFFSW9d5/hpdT5Bu0fV8 Ps//hWrSKtLfyBDTbZZKQ/Wv0O0e0nGh8B6/ToMDMuNRQJLGCMYwiCkk0U2lQ2UPjpOtH8dQiog4 A6UOiji3btDWxB82Ft74AGeFgb7fbXw7tOh0XH5f+gyOoWYGyU9F/GwbsV13u71wckbsLQPmZu8X 2T2jSG8HMjrI76l98i8bzVTn0pNm+R3tnxpWHEL7lx57WcxTjl558iWB8REi5xkkKZ50t4jzvKxc Z6VI8N6zkHaWQvG8uHsUs7vVqohiZa4U6RNPq+Ydgfx5ecgH8mAUyYN24SkcpUzch/8vtpz76lUb m1OLDnPvSZUut+F58bWlJ4yoNTecs/Fd3eSEt34TX96s1nJEjdsbn5z4vOsYrYxpipH+fehn58O7 Lzk1hiA02mhka8sx0kp+X6c2K8fzApVLtf4y9f3M0CMDF51g/G/tWHSuCeHHCz3/hdNnfniHcXoW HW5zn2AeJhe2i3AejAD3ZvE9sEHcr+anCXchfsWW/HjSQfFPvHbgxDTp3E3pE+MR07jH24QcJ/nr cwekfVZzF+ZHcrds43zvn84V0q4yYc/mlP2XZVXu+jhtzF1OCZhpY8CNNbi3bsG7LarvPPXlM4dt mczf0vaTDmCadA9pE+k8aUb4HKFPK61odyudD0HuG65vTYa5N4vkwSqeB2zMWbRxPHMOxymHzHNw 3a6HzWM97GsaO8yzlF9X59Dr683t5xBpo9WNvdlRt5LD+mWVQ7YF8zAs1p5FFlbfCcH8NGifd3dE y9SVFTy7gjlMa/U2TaW+Fznuw4e+elDgs4/Y95y2dYXyktdykOoDroXzoXg8/FqNf2cB/D5RGn6r eyrqFom/RbfbC+DnjNLwe92dwg3x7OG36/6dpMkQ/o9mafjNxMh0ALMz8BYJYx6ySsNMUeuL0HoI r4FGWgNL1H8TtePaXq3r/I+miMo1cqN3gaDCaKS3F/sMOpO5vFckpEcY/GLhWrnsXU/6j3EpH9j1 6v0xMjY4lewedJI9x8f61+5yxtwpoJHyBZD8G/ToyLpHuEIShSL5D+ON9XBQ+h+ZAW6CyDuEekPV WMysx7P6c29mfge2xG7RFA5kK30Ez1MrPa3Z6jVjWqSn1/eYvqddepqzUd/SKS2p7KZQrGtjNOX3 X6/3gyeQCwAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0192_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQEVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAABAD9 AA4AgAAAAP8AAAL/hHOmy+0Q0FvRxTqz3vzyD4ZQI4nmd5WHimCnlWSSOr62WNL3/tAuv9PFWECK sXeMFZfJGrPocz5NQqIU2mRYIZ6pV+ilaq/hTWqsaH2zzSoqBw7HtWdgqquszXuzvTht5Md1N7dF wpaHpCSYRsj4mEhHOKF2tcU4VkniiALYKIeYB+bX51kWqfFjl5gTmjoz1frZwUnpaui6mLs5mfpH WWurA3eHA8vXa2bKBbqMhkr2DPepeoO5+zesGCL71M3cvHd86AtuqRmEvRL9Mg7Nbptw3YHWUsek WuWDZy45SD4P2L1+dJYQcxaqmhOFJwbOUneqU8N33iKWCWgRYsZ4ERMJrtlYESQ3hiJLmjyJ0ksB ADs= ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0193.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Performance Contours of the LTI Sys= tem

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0193_image051.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC8zdefzNdf7///Nanq/lEEIZkSS7pCQyskSiDEmIqIjIIFmSlJFCipL0eY+UfR3V SCYJKVHZhiQpGUupKElJIeX3uLdN8/nO5x3d+uNXlyPxul3fr9d7Oee1PZ9n8z9fHZ/JBPbvmuwX yWgvY//MaullUvvDnmf7mThT4/s/069f2589qv/JHDt2LOP9+N9fPn76s8wv/u7/N//YqjyU+c/H sQ7/+dhx7Nz/85HRtpzI46ETeGT2/8rjpf/1eOj/ePz/6J9zj/3fj1/5QoX2azVf35eZzAWZyH4t G5XN+Pb9pT8pkXH2q+/pu02/y+Pr+1e/y+t/lqzM6nexpyVje5wafpGsyf60RPRz5Xv+j0sc9b0f P7I+bmVbIrH/HvGjn1bI/+HP/R+X/v572/9p6eDnpeV5Py8dfv/3+6364ePqb39Y0mX+8+P5Py4Z /rh1P6z1V8nGrGe/L2D/VzqIMm2OjT/W5tiBZH0ePfT7Hx6/NLQ2xe2/3/jFf/kJ/f7DXXV73343 9szcVs9+f1HebKkPX/ryts/s8cO6nJv55VqX844d+2/b6n5c0//cZi3x00f/b1X0Y+X+j8/Uv9V/ f4X+8zPjcv3MfJXZG3+VaZaZnNVDv//h8Z+fmej/2UJ9tO+/LP5//7r+8LGj/2Nb//s65bP/KxO4 /7pOv9zan/xfrs9PH8f7j++6KNfPQfL9x/N//Hgfx/+5rf/vx8jd2GjGBmgsMmMhNKaYMQkaI8wY Do1eZvSERmszWkKjthm1oFHajFLQyGNGCo0D0VeZzyNmbDHjbWgsM+NFaMw2YyY0RpvxADT6m9EP Gtea0Q4al5hRHxqVzKgAjYJmFIDGYfdV5mvHjB1mbIPGa2a8Ao25ZjwFjRwzHoHGIDPugEZnM26A RhMzLoNGVTPOhUZRM4pAI2PGdyEzPgq/ynwAjXVmrIXGs2bMh8bjZoyHxj1mDIFGdzO6QaOFGc2h UdOMGtAoaUYJaMRmOGjsC2w/N2DGJjM2QmOJGYugMc2MKdC434wR0OhtRi9otDGjNTTqmlEbGuXM KAONfGbkhcZB3/ZzfWZsNWMLNJabsQwac8yYDY0xZoyGxgAz+kPjejOuhcalZlwCjcpmVIJGYTMK QuOo91XmiMeM983YCY3VZqyExjwz5kJjnBk50BhsxiBodDGjMzSamtEEGtXMqAqNYmYUhYZvRgYa e7Sfm2HG69rPhcZCeyyAxiR7TIDGcHsMhUZP7edCo6X2c3/VUH2G/sdvZsvnJj7s740f9tmZ0If9 jWZsgMYiMxZCY4oZk6Axwozh0OhlRk9otDajJTRqm1ELGqXNKAWNPGak0DgQPeyzM6EP+1vMeBsa y8x4ERqzzZgJjdFmPACN/mb0g8a1ZrSDxiVm1IdGJTMqQKOgGQWgcdg97LMzoQ/7O8zYBo3XzHgF GnPNeAoaOWY8Ao1BZtwBjc5m3ACNJmZcBo2qZpwLjaJmFIFGxgx2JvRh/6PwYf8DaKwzYy00njVj PjQeN2M8NO4xYwg0upvRDRotzGgOjZpm1IBGSTNKQCM2w0FjX2D7uQEzNpmxERpLzFgEjWlmTIHG /WaMgEZvM3pBo40ZraFR14za0ChnRhlo5DMjLzQO+raf6zNjqxlboLHcjGXQmGPGbGiMMWM0NAaY 0R8a15txLTQuNeMSaFQ2oxI0CptREBpHvYd9dib0Yf99M3ZCY7UZK6Exz4y50BhnRg40BpsxCBpd zOgMjaZmNIFGNTOqQqOYGUWh4ZuRgcYe7edmmPG69nOhsdAeC6AxyR4ToDHcHkOh0VP7udBoqf3c EzoT+rCfm1gl3BtXCdmZ0CrhRjM2QGORGQuhMcWMSdAYYcZwaPQyoyc0WpvREhq1zagFjdJmlIJG HjNSaByIqoTsTGiVcIsZb0NjmRkvQmO2GTOhMdqMB6DR34x+0LjWjHbQuMSM+tCoZEYFaBQ0owA0 DrsqITsTWiXcYcY2aLxmxivQmGvGU9DIMeMRaAwy4w5odDbjBmg0MeMyaFQ141xoFDWjCDQyZrAz oVXCj8Iq4QfQWGfGWmg8a8Z8aDxuxnho3GPGEGh0N6MbNFqY0RwaNc2oAY2SZpSARmyGg8a+wPZz A2ZsMmMjNJaYsQga08yYAo37zRgBjd5m9IJGGzNaQ6OuGbWhUc6MMtDIZ0ZeaBz0bT/XZ8ZWM7ZA Y7kZy6Axx4zZ0BhjxmhoDDCjPzSuN+NaaFxqxiXQqGxGJWgUNqMgNI56VUJ2JrRK+L4ZO6Gx2oyV 0JhnxlxojDMjBxqDzRgEjS5mdIZGUzOaQKOaGVWhUcyMotDwzchAY4/2czPMeF37udBYaI8F0Jhk jwnQGG6PodDoqf1caLTUfu4JnQmtEuYmrnF74zWOnQld4zaasQEai8xYCI0pZkyCxggzhkOjlxk9 odHajJbQqG1GLWiUNqMUNPKYkULjQLTGsTOha9wWM96GxjIzXoTGbDNmQmO0GQ9Ao78Z/aBxrRnt oHGJGfWhUcmMCtAoaEYBaBx2axw7E7rG7TBjGzReM+MVaMw14ylo5JjxCDQGmXEHNDqbcQM0mphx GTSqmnEuNIqaUQQaGTPYmdA17qNwjfsAGuvMWAuNZ82YD43HzRgPjXvMGAKN7mZ0g0YLM5pDo6YZ NaBR0owS0IjNcNDYF9h+bsCMTWZshMYSMxZBY5oZU6BxvxkjoNHbjF7QaGNGa2jUNaM2NMqZUQYa +czIC42Dvu3n+szYasYWaCw3Yxk05pgxGxpjzBgNjQFm9IfG9WZcC41LzbgEGpXNqASNwmYUhMZR b41jZ0LXuPfN2AmN1WashMY8M+ZCY5wZOdAYbMYgaHQxozM0mprRBBrVzKgKjWJmFIWGb0YGGnu0 n5thxuvaz4XGQnssgMYke0yAxnB7DIVGT+3nQqOl9nNP6EzoGpeb2DXeG3eN2ZnQrvFGMzZAY5EZ C6ExxYxJ0BhhxnBo9DKjJzRam9ESGrXNqAWN0maUgkYeM1JoHIi6xuxMaNd4ixlvQ2OZGS9CY7YZ M6Ex2owHoNHfjH7QuNaMdtC4xIz60KhkRgVoFDSjADQOu64xOxPaNd5hxjZovGbGK9CYa8ZT0Mgx 4xFoDDLjDmh0NuMGaDQx4zJoVDXjXGgUNaMINDJmsDOhXeOPwq7xB9BYZ8ZaaDxrxnxoPG7GeGjc Y8YQaHQ3oxs0WpjRHBo1zagBjZJmlIBGbIaDxr7A9nMDZmwyYyM0lpixCBrTzJgCjfvNGAGN3mb0 gkYbM1pDo64ZtaFRzowy0MhnRl5oHPRtP9dnxlYztkBjuRnLoDHHjNnQGGPGaGgMMKM/NK4341po XGrGJdCobEYlaBQ2oyA0jnpdY3YmtGv8vhk7obHajJXQmGfGXGiMMyMHGoPNGASNLmZ0hkZTM5pA o5oZVaFRzIyi0PDNyEBjj/ZzM8x4Xfu50FhojwXQmGSPCdAYbo+h0Oip/VxotNR+7gmdCe0a5yYG 6d44SNmZ0CDdaMYGaCwyYyE0ppgxCRojzBgOjV5m9IRGazNaQqO2GbWgUdqMUtDIY0YKjQNRkLIz oUG6xYy3obHMjBehMduMmdAYbcYD0OhvRj9oXGtGO2hcYkZ9aFQyowI0CppRABqHXZCyM6FBusOM bdB4zYxXoDHXjKegkWPGI9AYZMYd0Ohsxg3QaGLGZdCoasa50ChqRhFoZMxgZ0KD9KMwSD+Axjoz 1kLjWTPmQ+NxM8ZD4x4zhkCjuxndoNHCjObQqGlGDWiUNKMENGIzHDT2BbafGzBjkxkbobHEjEXQ mGbGFGjcb8YIaPQ2oxc02pjRGhp1zagNjXJmlIFGPjPyQuOgb/u5PjO2mrEFGsvNWAaNOWbMhsYY M0ZDY4AZ/aFxvRnXQuNSMy6BRmUzKkGjsBkFoXHUC1J2JjRI3zdjJzRWm7ESGvPMmAuNcWbkQGOw GYOg0cWMztBoakYTaFQzoyo0iplRFBq+GRlo7NF+boYZr2s/FxoL7bEAGpPsMQEaw+0xFBo9tZ8L jZbazz2hM6FBmpuo96efnGVnQidnN5qxARqLzFgIjSlmTILGCDOGQ6OXGT2h0dqMltCobUYtaJQ2 oxQ08piRQuNANDnLzoROzm4x421oLDPjRWjMNmMmNEab8QA0+pvRDxrXmtEOGpeYUR8alcyoAI2C ZhSAxmE3OcvOhE7O7jBjGzReM+MVaMw14ylo5JjxCDQGmXEHNDqbcQM0mphxGTSqmnEuNIqaUQQa GTPYmdDJ2Y/CydkPoLHOjLXQeNaM+dB43Izx0LjHjCHQ6G5GN2i0MKM5NGqaUQMaJc0oAY3YDAeN fYHt5wbM2GTGRmgsMWMRNKaZMQUa95sxAhq9zegFjTZmtIZGXTNqQ6OcGWWgkc+MvNA46Nt+rs+M rWZsgcZyM5ZBY44Zs6ExxozR0BhgRn9oXG/GtdC41IxLoFHZjErQKGxGQWgc9SZn2ZnQydn3zdgJ jdVmrITGPDPmQmOcGTnQGGzGIGh0MaMzNJqa0QQa1cyoCo1iZhSFhm9GBhp7tJ+bYcbr2s+FxkJ7 LIDGJHtMgMZwewyFRk/t50KjpfZzT+hM6ORs7u9Gvzc+ZA+yVvm9vfHJHjPKW18RGhdb3wAa11jf Hhp9rb8VGqOsfxAaM6yfBY2l1r8Ejc3WvwON/dZ/AY3U3xvn8ZlRyvrS0KhlfW1oXGV9K2j0sP5m aAyz/l5oTLR+MjSes/55aLxu/RvQ2GP9J9DwA+sDZhSz/nRoVLO+OjSaWn8FNLpYfxM0Bls/BBrj rB8PjXnWz4fGauvXQuM963dB4xvrv4VG4XBvfGrIjMrfv+sjMy61vjE0rre+IzQGWD8QGmOsHwuN OdY/CY3l1r8Cja3Wb4PGQeu/hkY+tzcu4JhRzvoK0KhnfX1otLW+HTR6W98XGvdbPwoa06yfAY0l 1i+FxibrN0Njn/X7oRFHe+M0YkZJ60tBo6b1taDRwvqW0OhufU9oDLV+ODQmWD8JGgusXwiN9dZv gMZu6z+GRibeG/sxM4paXwwaVa2vBo0m1jeFRmfru0BjkPWDoZFj/ThozLV+HjRWWr8aGjutfx8a R6w/Co1Cyd74lIQZZ1t/DjQaWt8IGtdZ3wEat1l/OzRGWz8GGrOtnwONZdYvh8YW67dC44D1B6GR N90b50uZUcb6ctCoY309aFxtfVto3GJ9H2jcZ/1IaEy1fjo0Flv/AjTetP4taHxq/WfQiLJ74zjL jBLWl4RGDetrQqO59S2g0c367tC42/qh0HjM+gnHYfz76pTuws/96tTM6FCG3TOc35sZnewxo7z1 FaFxsfUNoHGN9e2h0df6W6ExyvoHoTHD+lnQWGr9S9DYbP070Nhv/RfQSP2ZUR6fGaWsLw2NWtbX hsZV1reCRg/rb4bGMOvvhcZE6ydD4znrn4fG69a/AY091n8CDT+wPmBGMetPh0Y166tDo6n1V0Cj i/U3QWOw9UOgMc768dCYZ/18aKy2fi003rN+FzS+sf5baBQOZ0anhsyobH0VaFxqfWNoXG99R2gM sH4gNMZYPxYac6x/EhrLrX8FGlut3waNg9Z/DY18bmZUAL7zbDnrK0CjnvX1odHW+nbQ6G19X2jc b/0oaEyzfgY0lli/FBqbrN8MjX3W74dGHM2M0ogZJa0vBY2a1teCRgvrW0Kju/U9oTHU+uHQmGD9 JGgssH4hNNZbvwEau63/GBqZeGbkw/evKWp9MWhUtb4aNJpY3xQana3vAo1B1g+GRo7146Ax1/p5 0Fhp/Wpo7LT+fWgcsf4oNAolM6NTEmacbf050GhofSNoXGd9B2jcZv3t0Bht/RhozLZ+DjSWWb8c Glus3wqNA9YfhEbedGaUD86kW8b6ctCoY309aFxtfVto3GJ9H2jcZ/1IaEy1fjo0Flv/AjTetP4t aHxq/WfQiLIzoxjOc1LC+pLQqGF9TWg0t74FNLpZ3x0ad1s/FBqPWT/hOIx/X52aGf3a1amO7pA9 2NWpju5kjxnlra8IjYutbwCNa6xvD42+1t8KjVHWPwiNGdbPgsZS61+Cxmbr34HGfuu/gEbqd3R5 fGaUsr40NGpZXxsaV1nfCho9rL8ZGsOsvxcaE62fDI3nrH8eGq9b/wY09lj/CTT8wPqAGcWsPx0a 1ayvDo2m1l8BjS7W3wSNwdYPgcY468dDY57186Gx2vq10HjP+l3Q+Mb6b6FROOzoTg2ZUdn6KtC4 1PrG0Lje+o7QGGD9QGiMsX4sNOZY/yQ0llv/CjS2Wr8NGget/xoa+VxHV8Axo5z1FaBRz/r60Ghr fTto9La+LzTut34UNKZZPwMaS6xfCo1N1m+Gxj7r90Mjjjq6NGJGSetLQaOm9bWg0cL6ltDobn1P aAy1fjg0Jlg/CRoLrF8IjfXWb4DGbus/hkYm7uj8mBlFrS8GjarWV4NGE+ubQqOz9V2gMcj6wdDI sX4cNOZaPw8aK61fDY2d1r8PjSPWH4VGoaSjOyVhxtnWnwONhtY3gsZ11neAxm3W3w6N0daPgcZs 6+dAY5n1y6Gxxfqt0Dhg/UFo5E07unwpM8pYXw4adayvB42rrW8LjVus7wON+6wfCY2p1k+HxmLr X4DGm9a/BY1Prf8MGlG2o4uzzChhfUlo1LC+JjSaW98CGt2s7w6Nu60fCo3HrJ9wHMa/r051dL92 dap4eMge7OpU8fBkjxnlra8IjYutbwCNa6xvD42+1t8KjVHWPwiNGdbPgsZS61+Cxmbr34HGfuu/ gEbqFw/z+MwoZX1paNSyvjY0rrK+FTR6WH8zNIZZfy80Jlo/GRrPWf88NF63/g1o7LH+E2j4gfUB M4pZfzo0qllfHRpNrb8CGl2svwkag60fAo1x1o+Hxjzr50NjtfVrofGe9bug8Y3130KjcFg8PDVk RmXrq0DjUusbQ+N66ztCY4D1A6Exxvqx0Jhj/ZPQWG79K9DYav02aBy0/mto5HPFwwKOGeWsrwCN etbXh0Zb69tBo7f1faFxv/WjoDHN+hnQWGL9Umhssn4zNPZZvx8acVQ8TCNmlLS+FDRqWl8LGi2s bwmN7tb3hMZQ64dDY4L1k6CxwPqF0Fhv/QZo7Lb+Y2hk4uKhHzOjqPXFoFHV+mrQaGJ9U2h0tr4L NAZZPxgaOdaPg8Zc6+dBY6X1q6Gx0/r3oXHE+qPQKJQUD09JmHG29edAo6H1jaBxnfUdoHGb9bdD Y7T1Y6Ax2/o50Fhm/XJobLF+KzQOWH8QGnnT4mG+lBllrC8HjTrW14PG1da3hcYt1veBxn3Wj4TG VOunQ2Ox9S9A403r34LGp9Z/Bo0oWzyMs8woYX1JaNSwviY0mlvfAhrdrO8OjbutHwqNx6yfcBzG v69OFQ9/7erUZv+QPdjVqc3+yR4zyltfERoXW98AGtdY3x4afa2/FRqjrH8QGjOsnwWNpda/BI3N 1r8Djf3WfwGN1N/s5/GZUcr60tCoZX1taFxlfSto9LD+ZmgMs/5eaEy0fjI0nrP+eWi8bv0b0Nhj /SfQ8APrA2YUs/50aFSzvjo0mlp/BTS6WH8TNAZbPwQa46wfD4151s+Hxmrr10LjPet3QeMb67+F RuFws39qyIzK1leBxqXWN4bG9dZ3hMYA6wdCY4z1Y6Exx/onobHc+legsdX6bdA4aP3X0MjnNvsF HDPKWV8BGvWsrw+Ntta3g0Zv6/tC437rR0FjmvUzoLHE+qXQ2GT9Zmjss34/NOJos59GzChpfSlo 1LS+FjRaWN8SGt2t7wmNodYPh8YE6ydBY4H1C6Gx3voN0Nht/cfQyMSbfT9mRlHri0GjqvXVoNHE +qbQ6Gx9F2gMsn4wNHKsHweNudbPg8ZK61dDY6f170PjiPVHoVEo2eyfkjDjbOvPgUZD6xtB4zrr O0DjNutvh8Zo68dAY7b1c6CxzPrl0Nhi/VZoHLD+IDTyppv9fCkzylhfDhp1rK8HjautbwuNW6zv A437rB8JjanWT4fGYutfgMab1r8FjU+t/wwaUXazH2eZUcL6ktCoYX1NaDS3vgU0ulnfHRp3Wz8U Go9ZP+E4jH9fndrs/9rVqbHeIXuwq1NjvZM9ZpS3viI0Lra+ATSusb49NPpafys0Rln/IDRmWD8L Gkutfwkam61/Bxr7rf8CGqk/1svjM6OU9aWhUcv62tC4yvpW0Ohh/c3QGGb9vdCYaP1kaDxn/fPQ eN36N6Cxx/pPoOEH1gfMKGb96dCoZn11aDS1/gpodLH+JmgMtn4INMZZPx4a86yfD43V1q+FxnvW 74LGN9Z/C43C4Vjv1JAZla2vAo1LrW8Mjeut7wiNAdYPhMYY68dCY471T0JjufWvQGOr9dugcdD6 r6GRz431CjhmlLO+AjTqWV8fGm2tbweN3tb3hcb91o+CxjTrZ0BjifVLobHJ+s3Q2Gf9fmjE0Vgv jZhR0vpS0KhpfS1otLC+JTS6W98TGkOtHw6NCdZPgsYC6xdCY731G6Cx2/qPoZGJx3p+zIyi1heD RlXrq0GjifVNodHZ+i7QGGT9YGjkWD8OGnOtnweNldavhsZO69+HxhHrj0KjUDLWOyVhxtnWnwON htY3gsZ11neAxm3W3w6N0daPgcZs6+dAY5n1y6Gxxfqt0Dhg/UFo5E3HevlSZpSxvhw06lhfDxpX W98WGrdY3wca91k/EhpTrZ8OjcXWvwCNN61/CxqfWv8ZNKLsWC/OMqOE9SWhUcP6mtBobn0LaHSz vjs07rZ+KDQes37CcRj/vjo11vu1q1PNMofswa5ONcuc7DGjvPUVoXGx9Q2gcY317aHR1/pboTHK +gehMcP6WdBYav1L0Nhs/TvQ2G/9F9BI/WaZPD4zSllfGhq1rK8NjausbwWNHtbfDI1h1t8LjYnW T4bGc9Y/D43XrX8DGnus/wQafmB9wIxi1p8OjWrWV4dGU+uvgEYX62+CxmDrh0BjnPXjoTHP+vnQ WG39Wmi8Z/0uaHxj/bfQKBw2sz9lRmXrq0DjUusbQ+N66ztCY4D1A6Exxvqx0Jhj/ZPQWG79K9DY av02aBy0/mto5HPNMgUcM8pZXwEa9ayvD4221reDRm/r+0LjfutHQWOa9TOgscT6pdDYZP1maOyz fj804qhZJo2YUdL6UtCoaX0taLSwviU0ulvfExpDrR8OjQnWT4LGAusXQmO99Rugsdv6j6GRiZtl /JgZRa0vBo2q1leDRhPrm0Kjs/VdoDHI+sHQyLF+HDTmWj8PGiutXw2Nnda/D40j1h+FRqGkWeaU hBlnW38ONBpa3wga11nfARq3WX87NEZbPwYas62fA41l1i+Hxhbrt0LjgPUHoZE3bZbJlzKjjPXl oFHH+nrQuNr6ttC4xfo+0LjP+pHQmGr9dGgstv4FaLxp/VvQ+NT6z6ARZZtl4iwzSlhfEho1rK8J jebWt4BGN+u7Q+Nu64dC4zHrJxyH8e+rU80yk7Oqj/hRxvYJ9c+PI6/c90vvNyX3q1d748nZvfEv mxNdaxlf/XwFjBgbf3U9nDbQ8+xX/e4cr6j9+t9c/W1hv2UyK1PcfveNP/nYD5+cL5V6oZ8p0LJb zxv7Zr68rZ79QYMke96HL31522f28L5f7tyfvwaSUn1qfX2EM52fqXyB3NzWdP+PX7tf2+qH/b3x w/7G3/TZ/2kLG/jHuYVVT2ALq8n9PbawSrg3rhKyLdwWHOcWnn8CW3i+3N9jC9e4vfEax7ZwoDvO Lax2AltYVe7vsYVd471x15ht4anxcW7hBSewhefJ/T22MEj3xkHKtvDj5Di3sPrxbqFnfyf399hC PcdPzrItvDd7nFtY4/i38LyM3N9jC/UKkt/bC7YwfzLoeF8tLjyRn0O5v88WzozyezOj376Fq6Pj 3sKaJ/JzKPf32cKOLr/X0f32LRzmnj3eLfzjifwcyv19trB4mP/n91f8LVtYLzzuLax1Ij+Hcn+f Ldzs5/95jt7fsoXf+Me9hRcd/xZWzcj9fbZwrJf/53Hev2ULF3jHvYW1j38Lz8/I/X22sNn396T9 9i3snTnuLaxz/FtYLSOXbOEPazcvmXi8e1x1j3/tumfk8rV7P3n9x7V79tfWrt7xr90tGbnHu3Y/ HF15uR5d1QtP+sXXeFgwLPg/1/PiE/ksyuWfxXzhlZl/fxZzXbv6x7923TJyT+Sz6HsC/uMY/Vjm P2ZH2W/SL7djfzw92zRz8H/tnZ7YmYX/beiVdfJxvKP1L9fzoV85l/C/P8bTdqw3N/zkhPbA/reh fmr4ITLUjwt3IkN9DjTU3xduRYb6u8K3kaF+ULgZGepvDzcho1X4anxFuAIZ6puELyNDfd1wKTLU 1wgXI0P9+eHzyFBfNvwHMtSfEc5DhvrTwr8jQ/1J4d+QoT4OZyFDvRdOR4b6g8EkZKj/LJiADPW7 g/HIUP+v4H+Qof7tYCwy1G8IHkKG+hXBSGSofym4DxnqFwbDkaH+iWAIMtTPDu5ChvpJwZ3IUD82 uA0Z6h8K+iND/fCgDzLUDwx6IkP9gKAHMtT3DG5ChvqOQSdkqO8ADfWtguvY/of1jYO2v2r8cHVN e79tbfncRGkXBS3RWqk/N7gCGeqrQEP9WcHlyFBfJGh4Ap/hhrZ8bqK0bFAPrZX6Y34tZKj/Dhrq P/erI0P9R/55yFD/ATTUv+1XYq/n1q/3yyND/Vq/LDLUv+ifiQz1z/klkKF+vl8cGepn+X9AhvpJ fmH2em79eL8gMtQ/6J+EDPX3+nmQoX6InyBD/a1+gAz1vXwPGeq7+d9FxFDf3j+MDPVX+4eQof5K /yAy1Df09yNDfT1/HzLUX+h/ggz1Z/sfIkN9eX8XMtSf4e9EhvpC/lZkqC/gv4sM9bG/GRnqj3hv IEP9IW8DMtTv8/6JDPU7vZXIUL/dew0Z6jd5y5GhfpW3FBnqX/NeQIb6Jd7zyFD/tPcPZKifCw31 07y5yFD/V+9v0fEfRfzNls9NlJZzHGJuRm9vfNTVy0GG+i7QUN/WewgZ6q/wRiFDfVNvJDLU1/OG s1dO62t49yBDfTVvCDLUl/fuZK+c1p/h3c5eOa0v5t2GDPX5vT7IUB97vdgrp/W+1xMZ6r/K3PSr xi+vfB7rcGJXaG+L9sY9oo9icoVWfYfofWSobxftRIb6q6LtyFDfKNqCDPV1o7eRob5W9BYy1J8T vYEM9WdF65ChvhQ01J8SrUKG+jR6BRnqk2gFMtR/65YhQ/1+twQZ6j91i5Gx0v09XuqeQIb6f7hZ yFD/jJuJDPUz3FRkqH/UTUSG+nFuAjLUP+AeRYb6u9z/IEP9nW4sMtT3c2OQob6rG4UM9R3dfchQ 396NQIb65u4eZKhv6O5ChvoGbjAy1NdwdyBDfUXXHxnqK0BDfQnXBxnqC7qbkaH+JNcDGeqd+zMy 1B8Ob0SG+s/DTshQvzfsiAz1O8JrkaF+U9gWGerfDNsgQ/1rYUtkqF8cNkeG+ufDK5Chfm7YBBnq p4aNkKF+QtgQGepzwgbIUH9fWAcZ6oeEtZChflD4R2So7x1WR4b6G8PzkKG+MzTUtwkrI0N9k7AC MtRfFpZHhvq6YWl2fGv9+WFJZKivHJZAhvqyYXFkqD8tLIIM9SeHhZGh/qSwEHvdt94L8yFD/cEg DzLUHwyy0MjGu4MIGer/FXjIUL8FGuo3BN9GxFC/IjiMDPUvBoeQoX5hcBAZ6p8IPkeG+qnBPmSo nxR8igz1Y4PdyFB/b7ALGeqHQ0P9wGAHMtT3DN5Fhvo/Q0N9x2AzMtS3CjYiQ/0VwQZkqG8crEOG +ouC1chQf37wGjLUVwleRYb6s4KXkaG+SPBCdHxz3ujKzAvRr90z+kKUDZ5Ha6X+O/9ZZKg/6v8D GZv9WdFafxoy1C/3JyND/Yv+JPaKZf18/zFkqJ/l55zAd0uOLZ/73Y450Xj/YbRW6h/0H0CG+pH+ KGSoH+Lfhwz1t/rDkKG+l38PMtR38+9Chvr2/p3IUH+Vfzsy1F/pD0CG+oZ+X2Sov9DvdQI/Pb1s +dzvOewVne3/Ga2V+jP8LshQX9y/ERnqC/k3IEN97F+HDPUZvx0y1B/x2iJD/T6vFTLU7/KuRIb6 ndBQv8n7EzLUr/IaI0P9SmioX+Jdggz1T3t1kaH+Sa8OMtRP82ohQ/1fvRrIUP+QVw0Z6kd6Vdkr uPV/8c5BhvpbvUrsFdz6Pl5FZKjv4pVFhvq23pnIUN8GGuqbeqcjQ3097w/IUF/bK4IM9dW8wshQ X94rgAz1Jb2TkKG+mJcHGerzezEy1DsvQIZ6Hxrqv8p8d0LzvOw4du4JzfMyxW9mRzxXZtjYrisz o/2rkaH+Qb9Nho0Pa2NHPNdn2Niu6zOD/I7IUH+rf2OGjQ+7MdPD744M9d38Hhk2PqyHHTX1zbDx YX0z1/j9kKH+Sn9gho0PG5i53P8LMtQ38u9CRml/rB3j5GTYmKqcTBH/cWSoL+RPzLBxWRPtGGdG ho2pmpGJ/JnIUH/EezLDxmU9mTnozUWG+n3e/AwblzU/84H3PDLU7/QWZ9jYrsV2nLQsw8ZlLcu8 6b2MDPWrvFUZNrZrVeYVbw0y1C/xNmTY2K4NmX94m5Ch/mnv7QwbH/Z2Zrq3HRnqp3k7Mmx82A47 XvsIGeof8fYgQ/1I7zNkqB/mHUCG+r94XyND/a3et2z/w/o+3jFkqO/iRd7xjf3TnmvkdfFyP4KM vLZefo+Nl8vvtfYKIEN9U+9Uj42XO9Vr5J2GDPX1vBIeG3NXwrvQOwsZ6qt5ZT025q6sV8GrjAz1 5b0qHhu3V8Ur5lX32Ji76vaVqYEM9fm9uh4bt1fXy+NdjAz1vn2nsnF7jez5pAky1H+VuYJ9r6d7 45rpHjTrhvrKKZvVVH3J9D1kqD89ZbOaqi+cbkeG+iR9Fxnqv0nYzKjqj0BD/WfJm2yWRuvfSzYg Q/3mZB0y1L8FDfWrktXIUP9KsorNQJS8GI9LlrBZgK1/KGGzvKofmbBZXtUPThYgQ33f5BlkqL85 YTPFqu+azEWG+nbJE8hQ3yyZjQz1TRI226z6+gmbbVZ99WQKMtRXSCYiQ335hM1Yq/70hM1Yq75A 8ldkfN8nY+PjPxKxZZPcRGmHYjZ/rfpP4lHIUL8zZvPXqt8ODfVvxGwOXPWvxncjQ/0LMZsDV/2i eDAy1D8V34EM9VPiAchQPz5m8+iqfyS+FRnqR8S9kaH+zvhmZKi/LWZz8arvFf+Zzd1nfae4KzLU t47ZXLzqW0JD/eVxB2SorxNfiwz158VtkaH+XGioL2NfGWKoLxq3QIb6k2I2k7D6vNBQn4mbIEP9 gagxMtR/EjVkr7fW744uYXPwW781uhgZ6tdHddh8u9avjNg8yOqXR39EhvoFUQ1kqJ8TnY8M9TMi Npey+onRuchQPyY6Gxnqh0UVkKF+SMTmdFY/ICrD5r63vkdUChnqO0RnsHnrrb8uYvNCq78qKoYM 9Y0iNi+0+lpR4RM4Iipsy+c+t1bh+JzoZLRW6ktFbJZo9UUiNku0+lOiLDLUp1GEDPXfOjbTtPov HZtpWv1+dwzN3ad+lzuKDPWbHZutWv0Gx2arVr/GfYUM9a+4L5ExyX0cPep2I0P9A+4DZKi/37GZ ptXf5dhM0+r7uW3IUN/VvRsd/zPju7Z87rNkvRu1d2zeafXN3ZvIUN/QsXmn1TdwryNDfQ3H5q5W X9GtQob6Mx2bu1p9CfcqMtQXdC8jQ71zLyJD/Xchm/9a/eFwCTLU7w0XIkP9jvBZZKh/N2RzaKt/ M5yHDPWvhX9n85Jbvzicgwz1C0M287b6ueEsNi+59VPD6chQnxNORob6R6Ch/r5wAjLUDwofRYb6 3mHOCbzq5djyuc8zlRN1DseitVLfJhyNDPXNQjY/uvom0FBfNxyBDPXnh8OQob5iyOZYV182ZHOs qz8t/Asy1J8U3oEM9XHI5mlX74Vsnnb1B4N+yFC/O7gFGep3BWyud/X/Cthc7+o3BN3YcZr1K4Iu yFC/LLgRGeoXBp3YK6f1TwTXI0P9pKA9O+a0fmLQDhnqxwZtkKF+eNAKGervCK5EhvqB0FDfM2iG DPUdgybIUN8maMxeb61vFTRChvrGwSXIUH9RUA8Z6i8I6iBDfZWgNjLUnxXURIb6IkF1ZKg/OaiG DPXZoCoy1H/nV2FHqtZ/7p+NDPX7/ErsXbis/8Avjwz1b/tlkKF+rX8mMtSvgYb6Ff4Z7PXFLxyN 9wtFbFRzoehBv0DERiQXiIb6JyFD/RBoqL/VTyM2IjmNuvkRfLfJKOroB+w1yvr2vg/fsdKPrvSP OTaa+Jhr6H+DDPV1/CPIUH+hfwgZ6s/2v0SG+jP8zx0b1fy5K+bvR4b6Qv6njo1q/tTF/seOjWr+ 2B3xPnJsRPJH7pD3ITLU7/Ped2xE8vtup7fDsdHEO9wmb6s7/jNMW2353McWb3WrvHccGxf8jlvi bXJsTO8mN8/biAz1T3tvODam9w03zVvn2Hjcde6v3hrHxuOucQ96q5ChfqS30rHxuCvdX7wVjo2l XeH6eMscGwe7zHX3XkSG+i7eC8hQ39Zb5Njo2UWuqfecYyNfn3ONvQXIUF/P+4djI1//4ap58xwb tTrPlfeecmzE6VOutPckMtQX8+awV07r83szHRtxOtP53jTHRotOcx401H+VmYSMx7LNMpOzLX51 DPwv51/KHDt2Qu82+VXmheBQZnFA5olS73vPIOP73puHDPX5vVm/avzwCq/P1CxbPvfvplnBad4E tFbqi3mPI0N9GW8sMtSX98YgQ/153v3IUF/NuxcZ6mt7dyFDfT1vEDLUN/b6I0N9U68PMtS39Hog Q31brysy1F/vdUKG+i7etchQ391riwz1fbyrkKG+v3cFMtT/xWuMDPV3ew2RoX6kVwcZ6h/0LkKG +r96FyBD/XjvfGSon+ZVQob6mV4FZKh/2jsTGeqf8c5AhvolXhFkqF/qnYIM9au8k5ChfrWXFxnq N3k+MtS/BQ31O73DPpvx+rD/vncIGep3e18iI/bf9RN7oPd6tr6QvwEZ6gtDQ/0Z/kpkqD/Tfw0Z 6s/2lyJDfWVoqL/QfxYZ6v/oz0eG+ob+E8hQ38ifgwz1V/pTkaH+Kn8yMtS398chQ30HPwcZ6rv5 o5Ghvqc/Chnqb/WHI0P9QP8eZKgf4g9Chvp7/duRof5Bvy8y1D/i90KG+vH+n5Ghfop/IzLUz/I7 IkP9XL8dMtTP99sgQ/0SvwUy1L/oX4EM9av9xshQv9aeldm7XzXy3/br+Md/hqmOLZ/7XQ91/A/8 C9Baqf/ArwaNav7nth+A3tXb+gN+JWSo/84/Cxnq/eBMZKjPBsWQob5AUAQZ6osEBZGhvkRwEjLU nxVkkaH+7CBge5rWVwl8ZKivFXzjEUP9RcERZKhvHHyBDPWXBZ8jQ32r4GNkqG8TfIQM9R3tWJW9 u+dOr2uwDRnqewbvIEN9/+BNZKgfGGxAhvphwWpkqB8erEKG+rHBMmSofyR4CRnqJwXPI0P99GAB MtQ/ETyDDPXzgyeRoX5hMAcZ6lcE05ChfkUwFRpTvQ3BY8hQvzF4FBnq/xWMRYb694PRyFC/OxiF DPUHguHIUH8wGIoM9V44CBnqg/AOZKg/KeyPDPWFwz7IUH9aeDMy1JcJb0KG+rJhV2SoPz/siAz1 1cPrkKG+bngNMtQ3DluyfTrrm4RXIUN9m/BPbH/M+mvCJshQ3zlsiAz1PcKLkaG+d1gHGeoHhRci Q/2gsAYyJodlvKlhaWSonx6exfZhrJ8blkCG+ufC05ChfnH4B2Sofy0siAz1a8ICyFD/ZpgXGeq3 hxEy1O+Ahvq9YQYZ6g+EP72XzG/c/7D+cHgEGeqd+xIZ6lN3ABnqC7rPkKG+hNuTOf6zmHts+dxn kNmTqeh2obVSX81tR4b6Gm4bMtQ3cG8jQ30TtwkZ6pu7jchQ396tQ4b6Tm4NMtR3dauQob6fW4EM 9QPdy8hQf5d7ERnqH3CLkaF+rHseGeofdc8hQ/0M9wwy1D/l5iJD/TPuKWSoX+r+hgz1q9xMZKhf 42YgQ/1mNxkZ6ne5x5Gh/kNoqN/vHkWG+m/dI8hQ76KH2V6A9Wk0hu0FWH9K9AAy1JeK7kOG+rLR CGSoPycajgz1taK7kaG+UTQYGeovi/6CDPVXRXciQ32H6HZkqO8R3YoM9b2jfshQPyDqiwz1w6Jb kKF+TNQTGeonRt1PYM+7uy2f+1zd3TNzopvQWqlfEHVBhvrlUWdkqF8f3YAM9W9GHZGhfmvUARnq d0fXIUP9gag9O/a1PhO3Q4b6vHFbZKgvGrdBhvoz46uRob4MNNSfF7dGhvo6cStkqL88bokM9a2h ob5TfBU7QrS+FzTU94HGeOunQEP9U9BQvwh+XdS/Cr/H1L8BDfXb4c+c+l3QUP8JfA5Sfwg+F37f J+w5WX2B5FpkqD89uR4Z6isk7PVWfUVoqK+edEKG+voJ2w9S3yxh+2Pq2yTdkaG+HTTUd01uZmft rO+b9EGG+jsTdhShfnDCjmbUj0zYUZX6cckgZKh/LGFHmeqnJ0OQof7phB25q1+QsDMI6l9IRiJD /apkNDtrZ/36hJ0dUv9Wws5SqX8vGY8M9R8m8Kyd9Z8l7Ayk+m+SmSdwxDzTls/9fbpnZpL0SbRW 6vOl7Hy1+sLpfGSoL5k+fwKfnedt+dzf1f35TOWUXd1Qf17KrrKor5m+hgz1F6fsypX6S1N2BU19 85RdDVTfIn0LGeqvS9nVUfXXp+wqrfru6UfIUN8z3YMM9bel+5GhfmDKrumrH5qy+xPU35uy+yTU P5QG6H4N9WNTdt+I+sfTfMhQPyll9+Ko/1vK7itSPydl9zepfzZl92qpXwAN9S+llZGhfllaBRnq V6fsHjr169I/IkP9ppTdl6h+S9oIGeq3pew+TfUfpeyeU/W7U3bvq/rPU3Yfr/oDaQd2z7r1R1J2 b7T6Yym7R1t9kGX3iqvPZtl97+rzZO9EhvpCWTaWQH2R7EhkqD8ty8ZWqC+VZeNE1JfOjkeG+rLZ iciok33Bq5dl46rUN8qycWbqL8uuZWMZrW+WZePu1LfK/voYwn8fVW2z5XMdHWlauywbHan+hux+ ZKi/Ifs5ND73bsqy0bPqb84GJzCOPvBvzvUzLK1flo1xVj8wW+QE1qqILZ/rnr1pd2XZSHT1w7Ns VL36e7NsdL/6kVk2y4D6Mdk6yFA/NlsfGepzsmw+CfWPZ9ncGOonZ9si46tMW+d77RybfbWdy+9d iwz1p3jXIUN9Me96ZKgv7XVERhPvJvcnexBDfVNoqG/r/RkZ6rt4PZChvo/XCxnq/+L1Rob6odBQ P9Lriwz1f/VuRYb6ad5tyFD/tHc7MtQv8e5Ahvol3p3QuNOt8v6CDPWbvLuQoX6ndzcy1O/zhiJD /ZfeMGSoP+INR4b62L8PGeoL+fcjQ/0Z/gPIUH+2P9od/x7eaFs+95kPR7sL/TFordQ39MciQ/2V fg4y1Lf3/4oM9Z38R5Ghvps/Hhnqb/UfR4b6If5EZKh/0J+MDPXj/WnIUP8YNNTP8mcgQ/18fxYy 1L/o/w0Z6tf6TyBD/Ub/SWSof9t/ChnqP/CfRob6z/1nkKH+O/8fyFCfDRYgQ30eaKgvEixEhvqz gueRob5KsBgZ6i8KliJDfYPgRWSobxy8hAz1rYKXkaG+Y7ACGep7Bq8iQ/3AYCUy1N8RrEKG+uHB GmSoHxv8ExnqJwXrkaH+iWADMtTPDzay1yjrFwZvIkP9imATMtRvCN5Ghvp/BVuQoX53sBUZ6j+G hvqDwTZkqPfCnchQf1L4HjLUnxZ+gAz1pcIPkaG+bPgRMtSfH+5Bhvrq4cfIuDbc7zqHXyBDfe/w S2SoHxR+hQz194WHkKF+THgEGepzoKF+avgtMtTPDY8hQ/3i0IvYXENe9FoYIEP9KmiofzN0yFC/ I4yRoX5vmEWG+sNhXmSo99xJyFDvXD5kqC/oCiBDfQlXEBnqK7rCyFBfwxVBhvqa0FDfwBVFhvrm rhgy1Ld3pyNDfVd3BjLU3+LORIb6ftBQf5crjQz1D7iyyFD/qCuPDPUzXEVkqJ/tKiFD/TPubGSo X+rOQYb6Ne48ZKjf7M5Hhvodrhp7jbJ+l7sAGer3uxrIUP+tq4kM9WlUCxnqT4nqIEN9EWioLxXV Q4b6c6L6yFBfK7oEGeobRZciQ/0VUWNkqL8qugwZ6jtETZChvkfUFBnqB9hnhM0ec0U0LLoSGerv hYb6MfaVYTPQXBVNjFojQ/2cqA0y1C+IrkGG+hejdshQvzxqjwz166PrkKF+q/3EwDlnot1RJ2So PxB1Rob6r6IbkaE+E3dFhvq8cTdkqC8ad0eG+jJxT2SoPyfuxV6jrD8vvgUZ6uvEfZChvnHcNzr+ uzAGRr3i3Gd+GRjdGQ9Ca6V+RDwYGeofiYcgQ/3E+B72DG39FGiofyoehgz1i+J7kaH+1fh+ZKh/ Ix6FDPVvQUP99vhBZKj/JH4IGeoPxQ8j4/s+eQQZ6vMlOchQXwAa6k9PHkWG+grJY8hQXz2ZgAz1 9ZNJyFB/aTIZGeqbJVORob5dMg0Z6rsmM9nZMuv7JrORoX5Q8jdkqB+czEGG+pHJk8hQPy6Ziwz1 05OnkaH+6WQ+MtQ/m/wDGepfSJ5FhvpVyXPsio71byXPs9co699LliBD/d7kBXZFx/rPoKH+m+Ql ZKhP0peRob5wugIZ6kumryJDfen0NWSor5yuRIb6mukadkXH+kvTf7LXKOtbpOuRob59uoFd0bH+ Omio755uRIb629JNyFA/NH0bGeofSrcgQ/0j6bvsWMz6x9OtyFD/t3RbxGYR2RY9m+5gr1HWL0vf i9jMG+9Fa9NdyFC/Lv0gYjNvfBBtST+K2KwZH0UfpXsiNuPFnuhA+gk7W2b9sXRfxGaJsD7LDPV5 sp9FbIaHz6Ii2S/YFR3rS2e/ZK9R1p+b/QoZ6mtlD7ErOtZfBA31l2UPR2xWhMNRq+w3yFB/TfYo MoZkg/jebBizcehhPDYbxWz8dxRPzia/amj5I36U8e2/mYeO/ThO233/9/uty31cdmP3beZi98vm hK/UWu97tZChPvJqIEN9fu8cZKgv4FVGhvqi3lnIUF/MK4UM9Wd5pyFDfXnvFGSor+wVQIb6Kl4+ ZNzjLQ6HeQtDYqgf6c1HhvrR3t+Rof6v3ixkqB/vTUeG+mneY8hQPx0a6p/yxiBD/dPeaGSoX+jd iwz1S7x7kKH+ZW8QMtSv8gYgQ/1arx8y1G/yeiBD/WavOzLU7/Q6IkP9Tq8DNDqEn3hXI0P9Pq8l MtR/5TVFhvoj3mXIUJ/xL0GG+tivjQz1efw/IkN9Ib8qMtSf4p+LDPVn+GV/1fjx6rftdZa15XOf 1aBsWNEvjtZK/dl+MWSov8AvhAz1F/r5kaG+rp8iQ31DP0SG+sv9YwEx1F/pH0aG+pb+QWSob+/v Q4b66/1PkKG+m/9ecPw/Pe/Z8rnPFPFe0M9/G62V+lv9zchQf5e/Dhnqh/hrkaH+fn8FMtQ/6C9D hvr/8RcjQ/14fwEy1E/25yFD/Sz/CWSof9KfhQz18/0pyFD/nD8BGepf9HOQof5lfywy1K/1RyJD /Tr/fmSof9u/Cxnq34GG+g/8/ifw7Nrfls99XpH+wX6/B1or9Z9DQ/1RvxMy1H/nd0SG+iRoiwz1 2eBqZKgvFFyBDPVFgj8hQ/0ZQUNkqD8rqI8M9ZWCi5ChvkpQExnqawTnI0O91oQY6hsEFZChvnFQ Bhnqr7DvEGKobxUUQ4b69sEpbP/X+o7BychQf1OQFxnqewYxMtT3C3y212z9wOBbnxjqBweHkfGv YJ7/YTAHGep3B7ORof5L29ckhvqDwSRkqPfCHP/49wJybPncZzvJ8U8KH0BrpT5/OAoZ6k8LhyFD ffHwHmSoLxveiQz1FcPbkaH+/LAvMtTXDHshQ33dsDsy1DcKb0SG+ibhDchQ3ypshwz1bcJrkKG+ U9gCGeo7h1ciQ33v8DJkqO8TNkaG+kHhxchQPySsgwz194U1kaH+obAaMtTnhOchQ/2ksBIy1E8N yyND/d/DM5Ghfi401C8OiyJD/dKwCDLUvxaejAz168KTkKH+zTBFhvptYYAM9TtCHxnq94ZHPWKo 3xd+gwz1h8MvkaH+WPg5MtQ79yky1BdwHyFDfUH3ITLUl3DbkaH+TLcNGeorureRob6qexMZ6mu4 DchQ38CtRob6S6ChvrlbgQz1rd1LyFDf3r2ADPVd3XPIUH+TW4AM9f3c08hQf4d7Ehnq73JzkKH+ ATcdGepHu2nIUP+om4gM9dPco8hQP8ONQ4b6Z9zDyFC/0I1GhvqlbhQy1K9xw5Gh/p/QUL/ZDUGG +vfdHchQvwsa6ve7/shQf8T1QYb6b11vZKhPox7IUF8wuontw1h/StQVGepLRTcgQ335qAN7Hov+ 6E2MaiJD/bSoBnsutH5OdAEy1C+IqiJD/fKoCjLUr4oqI0P9+uhsZKjfGlVAhvrdUVlkqD8QlUaG +oPRWchQn4lLIUN93vgMZKgvGp+ODPVl4uLIUH9efJp3/FcfTrPlc5+z6DSvTvwHtFbqL4+LIEN9 6/hUdhRhfaf4FGSo7xUXRob6O+NCyFA/AhrqH4kLIkP9FGiofwpui/pF0FD/Kvzaqn8DGuq3w+91 9Z9AQ/0h+LP/fZ+c2DNSmOQ+79FpXoGEPU+qPz0pgQz1FZKSyFBfPWGvgeprQEN9/YTtE6hvlrB9 E/XtErafpb49NNR3Tc5j54qs75uw/V/1AxO2H65+cMKOB9SPTOogQ/3DycXIUD8uaYAM9dOTxshQ /7ekCTLUP500Q4b6F5KWJ/Ds2tKWz30mpZbeqqQdO9Kxfn1yHTvSsf6thB1Nq9+RsDMD6t9LuiFD /WcJO1Oifn/Cztio/ya5HRnqjyXsDJb6JGVn49SflLKzguoLpyORof60lJ1pVV8yHYuM/ukH3m0p u5KnfkDKriiqvytlV0fVD03ZVVr196XsarH6h1J25Vv9mJRdgVc/LmV3E6h/PC2IDPWTU3Z3hfpZ KbtTRP3f0rOQof7vKbv7Rv2zabUTuNezmi2f+zxT1fwlKbtHSv2ytBEy1L+csnvG1K9K2T106tel 7F4+9etTdk+h+k0puz9S/ZaU3eup/l1oqN+Rsntf1X+Ysvt41X+UsvuJ1X+Ssvua1e9Pc5Ch/kD6 GDLUH0zZHezqj6Tsbnz1x9L5yFB/LP0HNKzPLkWG+jj7GjLU58muQ4b6vNkNyFB/cvZdZKg/JbsL GeqLZPcgQ33R7D5kqD89ewgZ6s/MspE46ktn2Ygg9WWzbGSS+gpZNspKfeUsGzGm/txsOWSoPy/L RtCpr5ZlowHVX5hlIxvV18qyUZrqL8o2ZqMSra+bZaNW1dfPshG46htm2Whi9Zdl2ahm9Zdle0Kj Z/CnbH9kqL8iy8aeq2+RZePo1bfKsjkB1LfK/g80/idok2VzJKi/Jsvme1B/bZbNXaG+Q5bNw6H+ hiybD0R9pyybl0T9jVk2x4r6m7Jsvhj1f86+hwz1PbJsNh31N2e/QIb6Xlk2u5D63lk2U5L6vlk2 65P6/lk2g5X627JsNi71A7NlkaF+YLY8NMqHd2bZfGfq/5Jlc7epvyvL5qFTf3f2T8jIyb4U5mRf hsbL4V+za9j8otaPy25Chvrx2e1sjlLrH8vuQYb6CdkDyFA/IXsUGkfDSdkIzYOrfnI2LzK+yjRx vtcEzvncxOX3/gTna/6TKwYN9eW9pnCO46aumtcMGerrec2Rob6p19KdwHVqWz43UVpbrw1aK/Vd oKG+j9cWGer/Ag31I71rkKH+r157ZKif5l2LDPVPedchQ/3T3vXIUL/E64AM9au8G5ChfpPXCRnq d3o3IkP9Pq8LMtQf8boiQ33s34QM9Xmhob6Q3w0Z6s/w/4wM9Wf73ZGh/kK/JzLUN/RvRob6K/1e yFDf3u+NDPXdoKG+OzTU3+r3RYb6IX4/ZKgf7t+KjKP+EPedPdgcgENcNrgbGeqLBPcgQ/1ZwVD2 LhbWVwyGIUN9lWA4MtRfFNyLDPWNgxHIUN8quB8Z6jsGI5GhvmcwChnqBwYPIEP98GA0MtTfBw31 Y4OHkKF+UjCGHSFa/0TwMDLULwweQYb6FcH/IEP9hiAHGer/FfwVGep3B4+ewJHZo7Z87jPxPeoO BuPRWqn3wseQof6kcAIy1J8WTkSG+rLhJGSoPz+cjAz1dcOpyFDfOJzGnuWtbwIN9W3C6chQ3zmc gQz1vcNZyFA/KJyNDPX3hXPYs7z1OdBQPzV8EhnqZ0FD/dzwKWSoXxz+HRnqXwufRob6N8N5yFC/ I3wGGer3hvORof5w+Cwy1Du3ABnqY2ioL+ieQ4b6Em4hMtRXdM+zowjra7hFyFDfwC1Ghvrmbgky 1Ld3S9nRv/Vd3YvIUP97GP3cMmSov8u9jAz1D7jlyFD/qFuBDPWT3SvIODXa4EpFbyBDfZloIzLU nxO9iQz1taChvlH0FjLUXxVtRob6DtE7yFDfI9qCDPUDoneRoX5otBUZ6odBQ/2YaBsy1E+MtiND /ZxoBzLUL4h2IkP98uh9ZKhfH+1Chvqt0QfIUL8r+hAZ6ndHHyFD/YFoNzLUZ+I9yFCfN/6YXdGx vmi8l71HsvVl4k/Za4P158X7kKG+TvwZMtTXj/cjQ/3l8efIUN86/gIZ6jvFB5Chvlf8JTLU3xl/ hQz1I+KvkaH+kfgQMtRPiY8gQ/1UaKh/Kv6G3TFg/aL4KDLUvxp/iwz1b8THkKF+e5yJ2AxCmeiT 2EOG+kOxjwz1fhIg4/s+CZGhvkDikKH+9CRChvoKSYwM9dWTFBnq6ydZZKhvluRBhvp2yUnIUN8R Guq7JvmQob5vkh8Z6gcnBZChfmRSEBnqxyWFkKF+elIYGeqfTk5BhvpFyanIODctFdVMz0KG+kvT MshQ3yItiwz116XlkKG+e1oeGepvSysiQ/3gtBL7ebF+KDTUP5SejQz1j6eVIzbLR+Xob2mViM2u USV6Nj0XGeqXpedFbB6L86J1adWIzR9RNdqSVovYvA3Vom3QUP9RekHE5ku4IDqQVo/YPAXVo2Pp hREb239hlCdbM2Jj6mtGRbJ/jNg49D9GpbO1IjZ2u1Z0brY2e22w/qJsnYiN760T1YaG+suydSM2 JrZu1CpbL2JjQOtFN2TrR2zMY/3o5myDiI3PaxANzDaM2DiwhtG90FA/NtsIGeonZBtHbJxP42jy cRha/ogfZfyM/tn/4xwN0fd/v9+63Gd2uyyM05/Gq0W/7dqs9VH6R2R836fnIkN9kJZFhno/LY4M 9V5aCBnqjyUpMtR/l/w0VvW3GeqPJgd/1fjxjjX77jtoy+c+T2S7YFPSFq2V+g3JFchQ/8+kITLU r0ouOoHPzkW2fO6zeV4UvJKcj9ZK/bKkAjLUv5CURIb6F5IzoHFGsDA5BRnq5yd5kaH+6SRGhvq/ Jz4y1M9ODvnEUD89+RwZ6qcl+5Ch/vFkFzLUj0v+hQz1Ocm7yFA/OtmADPUjk7XIUD8ieQ0Z6u9K liJD/eDkBWSoH5DMR4b6vslcZKjvlcxBhvquyVRkqL8xmYwM9e2SvyJD/TVJDjLUN0tG+cf/yjnK ls/9zPQov35yD1or9RdDQ3315A5kqK+a3I4M9RWSfshQXzLphQz1pyc9kaG+QHITMtRnkxuR8X2f dEKG+kPx9chQ/2ncDhnqP4GG+u1xG2SofyNuhQz1r8ZXIUP9orgFMtQ/Cw31T8VXIkP9FGiofwQa 6kdAQ/0g+DlVfyc01PeC32PqO8UtkaG+ddwaGeovj9siQ30d+Pyh/iJoqD8vvg4Z6svEHZGhvmjM Xl/UF4GG+rwxe61Un4l7IEP94YjtO6g/EPVGhvrdUX9kqN8esf0x9Vujgci4IlrmN4peRYb6SyN2 hKi+VrQOGeoviNgRs/pzoreQob5sxI7+1ZeKtiFDfZGInQ1Rf0r0ITLUp9G+Ezgy22fL5/6ewfv8 b93XaK3Uf+PYeS/1+90xZKj/1LFzeOp3uQQZ6rc7dk5T/WZ3MjLUb3Ds/Kz6Ne40ZKhf4di5ZvVL 3VnIUL/QsXPv6p9xlZGh/gnHriOon+GqI0P9RHcRMtQ/6uoiQ/3Djl3tUf+AuwwZ6oc7duVK/V3u KmSov92xq3Dq+7lrkaG+p+uEDPVdXVdkqO/keiBDfXvXBxnqr3b9kaG+ubsTGer/5O5ChvoG7l5k qK/n7keG+hruYWSov8CNRYb6im7CCVwtnmDL5z6SfEJwhpuF1kp9CTcbGeoLu3nIUF/QzUeG+tQt RoZ655YiQ/134Qp254X1h8NVyFD/ZbgOGer3hpuQof7j8G1kqN8R7kSG+u3he2yv2fpN4Sfs/hXr 3wz3IkP96vAgMtS/Fh5ChvqXQnaXkfrFYYjudlK/IGR3TKmfGxZAhvonQ3b3l/qp4a/fhfbvV4ri tnzu8/wUD8eF7N449TlheWSofzBk9/mpvy+8ABnqh4bsnkX1g8KLkaF+YMjuv1TfO2yKDPW9w2bQ aBZ2Da9GhvrO4TXI+DpYa89r65Gh/rNgEzLU7w7+hQz1HwbbkaF+W7AHGer/Za/hxFD/VnAAGeo3 BIeQof6fwVFkqF8R/PQeDMfzDB25FUHuc1RGtudZwKHXQOsX2p44Ovtk/fzgNGSofyIohQz1c4Kz kKF+SlAZGeonBeciQ/2jdgyKzmBZPzaogwz1DwUXI0P9vUETZKgfHvwJGeoHBy2RoX540AquRyv7 urSCX5dW9j3WGn6PtbafudbwZ661PX+0hs8frd1L8OuifkXQAhnqNwRXOvZKcaX7FzTU74aG+oPQ UO+FzFB/UtgcGepPC5shQ33ZsCky1J8fsucg9XVD9lyo/hJoqG8SXo4M9W2gob5zeBky1PcOGzt2 JNLYDQobOXZk1sjdF17q2FHmpS4nbOjYEXNDNzW8BBnq54YNHDuv0cAtDuuz/VPrXwvZ/of6NdBQ /2ZYz7Hzb/XcjrCuY+cj67q90FB/OGT7heqdq+3YOe/arqC7yLHz9xe5Eq6WY9ciarmK7o/IUF/D 1XTsilFN18Bd6NjVrwtdY2jscme7/fZgd72c7b51lRy7g6eSS6OKyFB/SlTBsfubKrhSUXnH7tUq 786Jyjl231k5Vysq69g9dGVdo6iMY/cDlnFXRaWRof66iB2rq+8ADfU9InbeQf2A6ExkqB8WlUSG +jHQUD8xOgMZ6udEJdh5GOsXRKcjQ/3yqDgy1K+PiiFD/daInR9Tvwsa6ndDQ/2BqKhj91cXdZn4 D47dK/4Hlzcu4tg960Vc0fhUx+6/P9WViU9xbBzAKe68mJ2DVV8nLuTY2IpC7vK4oGNjPAq61vHJ jo01Odl1itl5bfV/hob6XnF+x8bv5Hd3xvkcG0eUz42IT3JsTNRJ7hFoqJ8S52Xnxq1/Ks7j2Fi1 PG5RnHVs3F3WvRqnjo3/S90bceLYOMTEbY9jx8ZDxu4TaKj/PI6Qof4QNL7vE+fYeFnnCiShY2N/ Q3d6Ejg2BjlwFRLfsfHUvqueeI6NDfdc/STj2Dj3jGuWHENXQNW3S74L2UwC34WdoJFJvwgTexBD /ckpu0Ku/uR0OzS2hwVSdteB+gLpGmisMeNlaLwc5k8XIkN9/vTv0Ph7mC+djgz1+dLHoPGYGWOg MSY8Kb0XGerzpoOQoT5P2g8Z6vOk3aHRPcymHZGhPk3ZXUvqk7QpfA5qGmo2vl8z/nO2v5f8X84O uN+63GeQ+UPYNfnp3sTfOmt2obDLzzPT/TZD/Y0/z0znfuNMNseCzj/PTPcb31HS+k7JXmRcngwI Lk/6Q6N/0CjpgQz1DZJOyFBfP+mADPV1f57f7ze+86n1tX6e3+83vtOW9TV+nt/vN77LnvXVkwbI UF/15zkC3W+cy+eioPLPswL+NkN9heRsZKgv9/PMgr/NUH/mz7MC/jZD/elJUWSoP+3nmQV/47sN W1/o55kFf5uhvkCSIkN99ueZBd1vnNvI+uSoz96146i9kB1ChvpD8X5kqD8Y70OG+k/ij5Chfne8 Cxnqt8fbkaH+rfhdZKh/I34bGepfjTciQ/3SeAMy1C+K1yND/VPxWmSonxKvRob6R+JVyFA/Il6J DPV3QkN9L7gt6jvBz6n61vBrq/5y+D2mvj78XldfJ34DGerPi99Chvoy8TvIUH8mfB5TXzTehgz1 eeP3kaE+ga8N6jPxbvZ6a/2BiL1Wqv8CGup3R1+y10rrt0ds/0P91ugIMtSvjzy0P6b+nxHbp1O/ PEqQoX5JxPZx1S+I8iND/ZMR219XPyc6FRnqJ0YlkKH+8YgdA6kfE5VDhvoHInY8p35YVAUZ6u+K 2PGt+gHRhchQ3ydix+rqe0T1kKG+c8TOXajvEF2GDPVXR+w8jPqrohbIUN8kYueU1DeK2rNzbNbX idg5NvW1ohvZuS3rq0bsfKH6c6JbkKG+YtQXGRvcy8E6twIZ6te4lchQv8KtQ4b6pe5NZKhf5N5G hvpn3A5kqH/avYcM9TPdJ8hQP8Oxc/TqH3fsWoH6R90hZKh/2LHrHuofcCG6/qJ+hGPXcNTf5U5G hvrBjl2PUn+rK44M9f1cCWSo7+HKIkN9V1eJXZ+zvrM7Fxnq27sLkaG+nfsjMtRf6S5BhvrmriEy 1Dd2TZGhvoG7Chnq67qrkaG+huuADPXVXUdkqK/suiNDfUXXExnqS7t+yFBfwt2BDPXF3SBkqC/k 7kWG+oJuBDLUZ90YZKh3LgcZ6n33GDLUHw6n/6rx00wfL/nTbfncR9tNDz8P/47WSv3ecD4y1O8O FyJD/Y5wGTLUbw9fRob6zeEaZKh/M1yPDPXrw03IUP9auA0Z6l8NtyND/YvhHmSoXxx+igz1C8ID yFA/NzyKDPV/h4b6meFPd1X/xiMi66eGeZChfmJYABnqc8LT3PE/M55my+c+1v0092B4Flor9f9f a/cDbtWc73F877V+f9bv9Od2jSb10OXkT3V1OqkkUSLVdNT405AJ0xEayhNCIX9mKBn0lJoIHWlO KPpziqZblKuuuDEmIppcShHCSTF6ku76ZGjPPHef9r7v0WN4pvN6+3bO3muvvfZa63eXaYUa8mNN G9SQv8V0Qg35u8wJ8M9ygr0HziE/xbRFDfkZphw+asvtPNiQXwob8v8FHx/yq8yxlm3lj7Vr4WNd /n3YkN9mjrFsb+QYu8sciRrye+D2Q97aUsv2O0vtQfYIy/ahj7DNbXPL3lM0ty3toZYd9/L2D5a9 YsnPhA35BdZYdkzT2GU2a9nx2axdbfcadqx5r1mXPlLR3mrq/2LZ3oj8ZrsbNeRr02cuacjvsV+j hnxwO1FD/ieO7WnKN3ZfooZ8qatFDfky97lhn+98brq4bYZ9VrXN9HLsXYR8BWzIn+M+MuxzyI/M ILfFsM9Ut5hh7gN2nDj1o9xGwz7r3mhud+wdovwY2JCf6DYYdh7DBlPl1ht2TsZ6M9u9bdi5IW+b Re4t9k419UsdO4Igv8KtNey8n7XmNfc6O5KR+g2OHVGR3+peZUepUr/dsaND8jtgQz7jXzbsfL2X TX2/yrBzD1eZpn6lYedArjRHeXbUTr4VbMi3888bdm7q86arX2bYObLLTB//rGHn+z5rzvVLDDvv eImp9Oyorvxg/0fDzqH+oxnuFxl2LvciM9qzo9zy43wN+6w79ZP9PMPOsZ9npnp21F/+UT/HsOsF 5pg5frZh1y3MNkv8LMOun5hlXvSPsSPUqV/jq1FD/nXYkH/Pz2CfYKT+Uz/dsOuNpptv/DTDrp1K fcI+M5MPsCHfKJlq2HVxU81hyf2GXSd4v2mV/J69RqX++GQS+7w89Scm9xXxOWQPc0VS5x2Rkh7m 8oSdoSF/eVIOG+Xm1wk7c0Z+SHIovLL9UKMr5A/U+Psr8Cf83Xqytamre8v5ZPyUZyu2yT/pp7G1 PVP/hGfr2cnP9GxtPvkZnq0zKP+ovxk15Ks8W3dR/gHP1pCUn+wvQw35+zxbU1N+nD+/4LUKJ0Tn p19f9z7U+fFofyaaSv4Gz1ZPlR/uK1BDfrBnK8HKnwsb8n3gn0W+q++LGvKd4c9Fvp0/GzXkj/Ln oYb8EZ6tjCvf1LOVceX/BT6L5ev7S1FDPlPAVm3/lmBY+vV1H8EYFu9w16Gp5Lc7tr2W3+puQQ35 LY69fslvcONQQ/4dx16L5d9y96DGpW53fLFjq0HKD3IRupuS/PmOrQYpf45jq0HKn+XYapDyvd2h qCHfyzVHDflTHFtDUr6La4Ma8ic4toakfLlj6z/Kl7mTUEO+pWPrP8qXugrUkD/csTuYyR/i2J3U 5Bu7gagh38ixu8LJBzfUFP6qNzT9+ro/Wx5qso7dM09+j70RNeR3WXb/P/kvLbsPoXyt/R1qyH9i 2T0V5TfbB1FD/gPL7g8pv8Gy+1TKr7OzUUP+TcvuuSn/qmX3/pRfbZ9FDfkXLbuPqfxyy+6nKr/M voIa8ostuzes/ALLVqSVr7HsPrfysy273678AtiQXwgb8svsRviz3Zg+1jfCx/pG82f4c5FfZ9fD 7cf6dHv6DtyevmO2wce6fK19A76+vJG+3q6Br7drTOLY9kM+wIZ8Y/cS3LN6Kd3TfAHuab5gjoQN +TK3HO55L0/fiSyB70SWpO+IFsN3RIvTd2aL4DuzRek71Rr4TrXGXODY6778IDcHvnOfY4a5Wagh P8pVF7H3Xp1+fd1ny1WbMW46mkp+omN7ifKTYEO+yt2PGvKz3ST2Cp76+Y7tvcsvcuNRQ36FY+9E 5Fc79o5I/jU3FjXkN7jfsHcRqf/I3VzEs6ePGe3r/tymjxnne6Kp5Md7dqREfrLvbtina93No/5k wz5tPNnM9uzok/wc3x415Od6diRNfp5nRwXl53t2hFO+xrMjrfI1PsBGSBvsCLh8jf8KNr6KF/hP UUO+xm+Cc2xKG2/Dxttp40+w8ad4vl8Zs8fYynieXxqzx/rSeK6vidlzribWmSQHatj0n1E2m/7v /1XT7x4cPeEvM4em/7Y7en5vJtO6QesGOwWyJso06n/5lZeOyOwceUr6f1Q1LCn78PmdI79I/87u O/OlPPPDmTIqBZ0OE+m/cITNZjpm1K1rvtq/nWGT78/6/XQ3uduzBU7Xtpjp1OXTjffr7P7pejXo lX+68sKn65BRl093p/swKnC6dsVMpy6fbkTmpznTlWZLs3mnO67w6dpn1OXTVfmnkv3TXdXgqvzf u/bFTKcun+5l96QtcLoOxUynLp9up50dFThdx2KmU5dP92a0NmeLMjo7Ov/j7vjCpzsuoy6frkn2 6pytccNsw/zTdSpmOnX5dG0z1/v907mGrmHe6U4oZjp1+XR3Z3uU7J9uT7099fJO17mY6dTl03Wz bXIed081eCr/s+LEYqZTl0/3ku1mCpyuSzHTqcunO8ud5Quc7qRiplOXT/cXN7ikwOlOLmY6dfl0 H5sWOY+7xdnF+bcoXQ88XbJvujjTrqxjrDKf7/VoVLx/vmuy1+Sfr1tx86nM5zshW+b2z/dM+ivv fKcUN5/KfL6x2Z5h/3wD6g+on3e+7sXNpzKfb4B5IufZsaVkS0ne+U4tbj6V+Xz97UM5eytrG6zN /+w9rbj5VObzVdtnbIHz9ShuPpX5fF/b15IC5zu9uPlU5vMNib/Lma9JvSb59wp6FjqfyZSXdeqo Mp9vSnR2zvbFZm3+7V+v4uZT+Z/w+DOf5WyfX82+mn++3sXNpzKf72D7y5znR8v0V975flbcfCrz +dab65IC5+tT3Hwq8/luj6/OmW9Xya782+eKwp+/5WUdO6rM53s4XpXz830o+1D+x98Zxc2n8j9h +2c65Mx3Sfor73x9i5tPZT7fGHNszs/39Oj0KO98/YqbT2U+3xvxQFfg/unPi3l+HNdRZT7fueaL nPmWpb/yzndmcfOpXOh83x/JVeKHqw/r7ftP7C1q/d+Hw/3m4cDuyyv/YGD3GJafGti9juUfCOy+ zfL3B3YPavkpgd0LW35yYPf1lp8U2D3K5ScGdr91+QmBXVUsPyF0ho3OZnxgVybL3xvYlcnydwd2 ZbL8XYGtkyB/Z2BrPsiPCWz9Cvk7AluLQ/6OsBM2dsa/DWxtEvlbA1sjRf6WwNZ7kb8psLVr5G8I bB0e+ZHhOdSQHxmWwsbS+NpQgxry14TH2VpgqR8epqGG/LAwia0nlvqhYTxqyF8Rfoca8peF21BD /pJwPVsbLfWDAls/S/6iwNbxkr8wsPXE5H8Z2Npo8ucFuM5b6s8JbM06+bNDd9SQ/3lga/jJnxHY eoTyvQNbW1G+Z2iBGvI9AltrUv6UwNbelO8S2Dqi8p2DQw35ToGtqyp/XGDrzMq3CWzNXPk2YRts bItaBrYOsXyLwNZllj88vIka8s0DWy9bvmlYxdaHTn2TsBI1vkuqot3JVNSQ35VMQQ35L5N72NrO qf8iGYca8p8kt6OG/KbkhqjAe2iV741uSL++rqJq65PhaCr5t5IrUEN+TXIpasi/nFyIGvIvJQNR Q35ZcjZqyD+XnIka8k8nvVFDfn5yOmrIz0q6ooZ8dXIiashPSzqghvwDSTvUkJ+Q/DtqyN+dtEQN +d8kR6CG/K3Jv6GG/IjkENSQH5E0gY0m0ZDkX1FDvjJpgBryA5MS1JDvlxjUkO+bxKghf2qyN0sa 8scnu1FDvgNsyLdK/ooa8oclO1BD/qfJdtSQb5TUosY+n2xDDflv/CeoIf+p34oa8lv9R6gh/57/ EDXkX/ebUUP+Rf8BasgvgQ35OX4Tasg/Chvyk2FDfhz8fsiPhj9b+eGwIT8YPk7lz4fPF/lzYUO+ j/8YNeS7+k9RQ76d/xw15I/ybJssX+rZa4N8U89eo+Tr+69RQz7jd6GG/LeOve7L73B7UEN+q8ug fSn5DS4u4t1/rK+v80rpOHrNJWgq+RWuPmrIL3dsr1l+kWuEGvKzXWPUkJ/p2DsR+SrXDDXkJzr2 zkz+XsfeIcqPcUeihvwo1xo15Ec69q5bfphrixrylY4dhZAf5DqihvyF7njU6OAqojLXDzXkj3Hs aJl8qeuPGvKNHTvyJ38wbMgHdzFqyMeOHU2V/9Zejhry2y07uixfa69CDfnNdiRqyG+0N6CG/Dp7 K2rIr7HscwT51XYsasj/p2Wfq8gvs+PZkfLUL7DsMyL5GtiQn2mr2Ot+6mfY6aghP9XORA35ST9e rfz/PBcz9ffauWzfIfV32IWoIX+bXYQa8tfbZaghfy1syA+xq4p4B7Aq/fo6j1entQvsn9FU8gMt +9Ra/kz7DmrI97XsU3z50+wm1JDvZtkZCfKd7CeoIX+cZWdoyLe2O1FD/ijLzjaRb273sDMjUn+I ZWfOyB9k2Rk88vUsO5NI3tpGqCH/nWFnRcnvMk1RQ367YWd4yW8z7Ewz+S2GnfEm/75pgxry7xh2 9p78WtMJNeRfMexMRPlV5hTUkH/esDMz5ZeaPqgh/7RhZ5nKzzP9UUN+lmFnzMrPMBehhvw0w87+ lZ9ifo0a8hMNOxta/i4zAjXkxxp2Zrf8zeYW1JC/0bCz1OWvNuNQQ364YWfcy19iDnz1wP493knp 19d57nxaG2DYNQ3yA0wVbFTFfQ27PkO+wsxCDflTDbvWRL6beRo15DsZdt2MfHuzHDXkjzXsOiL5 o81/o4Z8qWHXRMk3M2+ihnwTw67vkm9gNqKGfH3DrlWTjwy7Zk4+a7ahhvxfY3YNofxX8TeoIf9Z zK6HlN8ax+i6TPlNMbu2U/7duCFqPBuXmSUxu+ZWfnHcHjXk58fsGmT5J+NuqCH/WMyup5Z/JK5A DfmHY3ZtuPykmF2jLn8fbMiPi9n19vJj48GoIX9LzO4dIH9juo+H9jRTf13M7oMgf2V8E2rID43Z PR3kK+M7TeF7q3emX1/nJ71p7byY3fFC/hfxZNSQ7xc/hBryvePpqCHfI65GDfmT4jmoId8lnosa 8u3ixagh3zZeghryLeMXUEO+RbwKNeSbx6tRQ75JvBY15BvHb6KGfL34PdSQL4k3ooZ8FH+MGvLf RZ+jhvyuaAdqyG+PdqOGfG30LWrIfxg5SxryW6IENeTfjRqhhvzbUWPUkF8bNUMN+VeiUtSQXx21 QA35F6I2qCG/PCpHDfn/iDqhhvzC6GTUkJ8fdUcN+cejClv4XlFF+vV1FVWrivqjqeQfjAaghvzv o4tQQ/7B6Fdwjl+l3zHWkF8IG/LLo0HwkT8o3RIMgluCQelWrRJu1SrTLXQl3EJX2u3RxZa9Yl1s v4MN+ZJ4sGV7EoNtE9iQbwEb8m1hQ/4k2JDvHbOfi/wvYEO+Ejbkr4QN+RthQ34sbMhPgg35R2BD /knYkF8MG/IrYUN+DWzIvwsb8v8DG/VMpW1g2HZdvhlsyB8NG/LtYUO+G2zIV8CG/ADYkL8ENuSv hg35m2FD/i7YkJ8CG/IzYEN+HmzIL4UN+VWwIb8WNuTfhw35bbAhvws25K1lDfmDYEO+OWzIt4YN +U6wIX8abMifCRvyF8CG/BDYkL8WNuRvgw35e2FDfipsyM+EDfkFsCG/DDbkV8OG/DrYkN8MG/K1 sCG/Bzbkg2MN+cawIV8KG/JlsCHfBTbke8GG/DmwIT8INuSHwYb8KNiQHwMb8hNhQ74KNuRnw4b8 ItiQXwEb8q/BhvwG2JDfChvyO2BD/lvYaOUrbTvPGvJdYUO+D2zInwsb8oNhQ344bMiPhg35cbAh Pxk25B+FDfk5sCG/BDbkX4QN+ddhQ/492JD/FDbkv4GNfT5hDflGsCF/GGzIt4IN+eNhQ/5U2JDv BxvyA2FDfghsyI+ADflbYUP+btiQfwA25KthQ34+bMg/BxvyL8OG/FuwIb8JNuS/gA353bAhnwTW kD8YNuQPhw35NrAh3xk25HvChvzZsCF/EWzID4UN+ZGwIX8HbMhPgA35h2FD/onAztuSfyL0h43+ aaMCNirSRnfY6G4fD+xsQ/nHQxvYaGMfC+wMTvnHQjPYaGZnBnZmrfzM4GDD2erAzlaWrw47YGNH 2vgMNaaH5eaRwK52kK8K7KoL+apQDRvVZlpgV8PIaz3bAzW+XzlXK/LmX+N3YnR42L/G7+p6q/Os EX9akm+Nc5ezxq/ft8ZvNtMuo25d89X+beXfulcgbhW1LmiF+HS6nxUznbp8ukZmVs768HOzc/NP 16eY6Rod4Lr83Onky7JN6/wZj7Kbc+bUX3nnrChmTnX5d3GUjXyB051R3HSRL+67WPczZYVZkfNM WViysCTvnH2LmVPdQuf8YQXs6PtvVJS7hrbWzK5rq/F1pl9mekm/TF3rbh9wS1yyzRfSyLNmd6bu Nbu/Tt4oyab//sN/7UhfHfdM/y5mW/mPjY5+ctzRP3PAxvdzZn786x+/s6p/m/7+3r17f/zdH/4U 8Y8Vl/7zaHf0vp9PvK/zv2KrIm7wWAQA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0194.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Response Amplitude of the LTI System=

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0194_image052.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+XddbhUZfc38H2v2HvP0CCd0iAdgiCIdLeEpAhId0l3tzQcQQREugURRCQkD0iI ICINgrRICb/vHDw88OijeG6u6/3jhetzzpyZPetee92xp+e7PdumOQ7jf7xo290xxsG/snWME8CZ Ews6jufsDp3llIDfcF6qiL8ePXrkmD9+Py3yPOepy6L2D9frG/HzT/8E8lAoZ8fJ67j4md5N7xDa Dp2TwlH8JBPKJHQqGoX2LXQqOm1xY0cLnfJMaEsPEsh2N160yC3cJ9ciQ39s8YDMU+1mxRY+ft8j NzIdenw+/bF1xH5T5Nb8ZOtQPPNka4m4/Bqu9bjd0KWPt1Tn2fbojy3lj717nPU2N2k0XM+Jjb/S suvMejTl91mPrrgJo4eETj/2dIxQNsnw+z4le7qcEc1Ve79jpyatna5FQpUPBtOe23Sr61V4nEsO 5+msM5hHj/5qX/WPTJ/d59AWka3/1bXcP66l/6NS/4n6nx56tjL6t5UpbM5rYVPeuRAMCZ1+7NnK uH/aw1BrEd1Cf92vj9t2/8e+/nVOMfFXOta/zOnpvY2M/3Q+T7fzn1Hn/m0N/Ij2yIls69l9/XMb fx/jvIZytYkRuv6LyCO0P/+v9+VF5VHY7LXMozw0+cc8nl0Vs5nEjvOXYyZ06UtUyU1nHq8Vs/5Y gm+FrmqEnNjVm7du0tG5FbFWtIsZ/Omv1wqNiBR4MoNeVoPLQnH/LtNrf8yAf9rrrHxes7Jd5bJy eWgSpR6MrNJL/JxVOvn8VcrphOK+iCol0/OaTO2qlEzLg12VWJ+zSqeev0q5nFDcF1GlaN55jebZ VSmaVx7sqnTDfc4qnX7+KuV2QnFfRJXu+Of1jm9XpTt+ebCr0gn/Oat05vmrlMcJxX0RVXp8hNtr eZQMHa3tqhQefM4qnX3+KuV1QnFfRJVCx72axv62RHgUj+GPqxR0HzjPWaVz/+YYF4r7Yqq0XWqC XZW2S3gwajEeV+mS9H3eKp3/5yr5EVUSJ0e2HHlDkV9MneZzTbCr03wOD0YtxuM67eYVz1unC89b J0adcnIo8oup0zCqCXZ1GkbhwajFeFynxfTc4+nivxlPOfOGIr+YOrU0NcGuTi1NeDBqMR7XaYx5 7vH0878ZT7lMKPKLqVN5p6blPaDQsS48ivcIH9epnfPc4+nSvxlPufKGIr+oOv3/du/7P4+hPfu4 xaP/elTHfeY+6CW9HCznFDK7I1pr7FwPnNObcBvuwD34HR4BBc+pggcBiA44UGsciAcJIBEkheSQ ClJDWsgAmSELZIeckAdehfxQEApBESgGJaAUlIFyUBEqQzV4C2rB21APGkAjaAzvQXNoBW2gHXSE ztANekAv6Av9YSAMgWEwEkbDOPgAJsEUmAZhMAtmw1z4BBbAIlgCy2ElrIF1sB42wCbYDFthO+yE 3RAO++EgHIYjcAx+hJ/gNJyFf3qM6u/68r5/Th+Cg75jUPAgCNEhFsSBlyAhJIakkAJSQRpIBxkh M2SF7JAT8kA+eA1eh8LwJhSDElAaykIFqAxVoTrUhNpQF+rDO/AuNIVm0BJaQ1voAJ2hK3SHntAH +sEAGAxDYQSMhrEwHibCZJgGM2AmfARzYB58CgthMSyDlbAa1sLn8AV8CV/BFtgGO2A37IV9cAAO wRE4CsfhBJyCM3AOLsJluAKheWXTly76MQDRISbEgXiQABJBEkgOKSE1pIMMkAmyQDbICbnhVcgP BaEQFIGiUBxKQVkoD5WgClSDGlAL6kA9aAjvQhN4D1pAK2gL7aETdIH3oQf0hr7QHwbBUBgOo2AM jIMJMAmmwnT4EGbBxzAX5sMCWAxLYQWsgjWwFj6HDbAJNsNW2A47YTfshf1wAA7D93AMjsNPcArO wnn4GS7DVbgOt+A23IHQvLLpy7jeaY0PCSExJIOUkArSQDrIAJkhC2SHnJAH8sFrUNA7o4WhCBSD ElAaykIFqARVoDrUgNpQF+rDO/AuNIFm0AJaQ1voAJ2gK7wPPaE39IMBMBiGwggYBWNgPEyEyTAN ZsCH8BF87J3VeTAfFsISWAYrYDV8Bp/DF/AlfAVbYBvsgF2wB/bBATgER+Ao/AAn4CScgXNwES7B FbgGN+FXuAP34HcPxzKgUB+Ca9mXyd0jmhJSQ1r3e00PmSALZIOc7lHNDXkhPxRwj2kheAOKQgko 5f6gZaA8VIQqUA1qQC33uNaBetAQGkFj90d9D1pAK2gL7d0T2hG6QDfoAb3cn7QvDIBBMASGw0gY 457UcTABJsFUmA5hMMs9pbNhLsyHBbAYlsJyWAVrYB2sh42wCb6Gre5p/QZ2wh4Ih2/hIHwH38Mx +BFOwmk4BxfgZ/gFrsINuAW/wT14AA/BYOwzuOBDNIgBsSE0r2z6MqNu1Vcgq27THLpdc0Ee/Ubz 6Q59DV6HN3SnvgnFdZeWhNK6W8tBBd2jlaEqvKV7tSa8DXWhgYbrO9AYmkJzaAltoB10gM66T7tC d+gFfaAfDITBMAxGwCgYA+N1v06AyTAVZsCH8BF8DPNgPiyExbAUVsBq/VY/g8/hC9gIX8HXsA2+ gV2wVw+glQM4dUAPwXdwFH6AE3pQT8IZwC0YvQCX4BdseQ1uwq9wB+7BA3gExj2sAi4EIBrEdL/T 2BAP4kMiSIK5FJpXNn2ZS+pqXqmn+aGA1NdC8IY00KJQXBpqSXlHy0A5aaQV5V2tIo21GrwlTbSW NNW35T2tBw2kmTaS5tpYWuh70lKbSyttJa21jbTR9tJWO0o77SLttZt00B7SUXtJZ+0jXbS/dNWB 0k2HyPs6XLrrSOmpY6SXjpPe+oH00UnST6dIf50uAzRMBuosGayzZYjOlWH6iQzXBTJCF8lIXSqj dbmM0VUyTtfIeF0nH+h6maAbZJJuksm6WaboVpmm38h03SlhugfCZabul1l6UGbrYflYv5c5ekzm 6o/yif4k8/W0fKpnZYFekIX6syzWX2SJXpWlekOW6S1Zrr/JCr0rq/S+rNaHskYNRgzrWnV1nfoY OUFdrzEwemJBXN2gL2EUJdQvNYlu0mQYTSl0s76MEZUG0usWDc0rm74szCnlTU4vxTiLlOTcUppf k3JcRCpwSanMFaQqV5XqXFtqcgOpzU2kLreSBtxB3uFu0ph7S1MeJM14hLTkcdKaJ0s7/lA68Bzp zAukKy+V7rxaevJ66c2bpB9vk4G8SwbzfhnGh2UE/yCj+aSM5XMyni/JRL4qk/mWTOO7Esa/y0wm /YhdncNBnccx9VOOqws5gS7hJLqMk+tKfllXc1pdyxn0c86sGzirfsk5dDPn1i2cV7dzft3BBXQX F9S9XEj38Rt6gN/Uw1xMj3AJPcYl9TiX0hNcRk9xWT3D5fQ8l9eLXEEvc0W9wpX0OlfWm1xFb3NV /Q3ucTV9AI+4uhqpriJvqQu+1NBoEANiS02NB/GlliaCJJAMUkptfRnSytuaHjLBK1JHs0EOzKnQ vLLpy7I0icrTTKpEn1AVWkrVaA3VoI1Um7ZSHdpF9Wk/NaTvqBEdp8Z0mprSBWpOv1BLuk5t6Da1 p3vUkX6nzmS4Gwl3J597UTTuQzG5P8XmgRSXh1B8HkYJeSQl5tGUlMdRMv6AUvAkSsVTKDVPpzQc Rml5JqXn2ZSB51Am/oQy8wJ6hRdRVl5K2Xg5ZeeVlJPXUG5eS3l5Pb3KGyg/b6ICvJkK8lYqzNup CO+gorybinM4leL9VIYPUnk+TJX4e6rKx6g6H6da/BPV4VNUn89SI75ATfhnasaXqRVfpXZ8nTrx LerGt6kn36W+fJ8G8UMazg6PZuYPWHkKexzGQZ7NMXg+x+LFHJdX8Eu8lhPwRk7MX3NS3sEpOJxT 8SFOw8c4PZ/kjHyeM/MvnJVvcna+y7n4EedhV/JxdHmN48rrnFhC88qmL6ubmlTTlKbaJj/VNRmp vklIDY1H75rbpqk5a5qZA6al2Wxam+WmnZllOpixppPpa7qatuZ908D0NJVNH1PE9DM5zQCTxgw2 8c1Q45kR5r4zylxxxprTznhzxJlo9jiTzRZnmlnvzDArnQ/NQucjM9eZY2Y688w051Mz0VloxjtL zBhnmRnlrDAjnNVmuPMZfn9uRjob4Ev4yox2tmCbbdh2B66zy0xx9poZzj7zkXPAzHMOIe4Rs9w5 aj5zfjAbnRNmm3PK7HXOmMPOeXPCuWguOJfMdecK8rtm1Nw0scyvJom5Y9Ka+yaH+d0UNI9MSUNU 1Qiq4VELE6AuJjr1NzFptIlDU008mmfi0wqTiDaapLTTJKfDJhWdMqnpiklH90wGcikTxaUslJyy 4VROyoP/b9CrVJbyU3UqSA2oEGZEEcyCotSDStAgKkWjKDSvotKXiSL6MugUNuupiFlJxcwiKmlm U2kzhcqakVTB9KVKphP2qCmF+vtfvWam79+/ZiYyh8hHuq4HtsqNwNf/6pmT/96P3wPL5FFgsVBw gWhwnnjBORIIzpLowQ8lZnC6xAlOlXjByVFqIxjRBjvpg6MkA2SCqMRJEhEnmlM4+IEUCU6QYsFJ UgI5lQpOkzLBGVIuOFMqBmdLZeReLThfqgcXWuXbMLhBGgU3wpdRivNSRBzfaR08IG2CB6Vd8Ih0 DB6XzsFT0i14XnoEL0nP4DWrHAcHRYdEcNWm/8cHk+gHwaQ6KZhSpwTT6LRgBg0LvqKzgtl0djCX zg3mgbxRaiNynK4JvqHrwCbPXchhN3IJR077g9n1YDCLHg5m1CPBdHos+LL+GEyhJ7AfNnne91vL A79VlPolVUSMmE70QF2JFXhb4gRqy0uBWpIwUFMSB2pIUkgBqSANpMP5GXF5Zmz3Cra3yfv1QDMp FGhhNVbLBnpJhUBfqRwYJFUDw6R6YLTUDIyX2oHJ8nZgmlV+7waWSGOsM1GJETcihue0xlrXNrBD OgTCpXPgkHQNHJXugZ/gtFVuAwK/ycDAPas1dEwgho4NxNLxgXg6MZBQJweS6rRACp0ReFlnBtLo R4F0+nEgg9rM988QY20gra5DPJt+3h6IozsCMXV3IKh7A6r7AkYPBB7IocAd+S5wy6qWp9AfpwM/ Wq1rvwR2yRX0c+jYZpOL68cV349jdbxJ7seWlIiRGrHS+S9JBj+BZPITSRY/qWTzU0hO/2XJ7aeV PH4Gq1yL+AXkTb+Q1fwo51eW8n5VqeTXkip+fanmN5Yafgup6bex6o8G/gBpGGGQVX7N/GnSwv9Q WvlzpK2/UNr7y6WTvxbWWdWup79Xevn7rObvEP+MDPXPynD/ZxnlX5Ex/g0Z5/8qE/w7Msm/L1P9 BzLNf2hVxyX+XVmKeMv836zW6fXIc4N/Wjb5P8pm/6hs9Q/Jduz/Tn+n7PK/sarlQX+VHEK/2OR3 wg+Tn/wZcsqfLGf98XLeHyU/+8PkMsbPVb+vVX5xvV38kreHbfJL7R3nNN6PnM47xRm8c5zZu8RZ vGuc3fuVc3j32Sa/17xYUsCLazVPinoZpBiU8LJJaS+vlPUKSQWvOJS0Gn/VvDpSPUK9KMWJHRHH dep4HaQu1Pe6yztef3nXGy6NvfFWubXyPpHW3qewwKp2nbwvpav3tbzv7ZCeXrj09g5KP++I9Pd+ sMpvgndBJsIksBl7c5HLPO87me99Kwu9vbLE+0aWId8V3gZZ6X1uleN6b6584c2Bj61quMUbLdvQ pzu8AbLL6yV7vC6yz2sHba3m7vfe2/K9V8uqfqe8EnLGKyrnMCcuevnlkpdbrnjZ5Zr3itzwMlrl 5/gJhfz4VjGSu905hduLbeZXenc8Z3IncRY3jLO5czinu5Bzucut1qX87jZ+zd1hlVcR90cu6p7m Eu4lLuXe4jLu7/DQKq9Kbjyp7CaIUs0j36dUw31Farm5pI5bUOq5xaWBW86qD5u4DaSp28hqnLZx u0pbt5u0d3tLR3eQdHGHSzd3jPRwP4CJVvmNcmfKGLCZ42HuaJmFnGYjt7luH5nvdpcFbidZ5Laz WoNWunVllfs21LY6xnzhlpCNbhHZ5L4mX6Nvt6KPt7vpreoW7saRfW4sq3793r3Hx9xf+Uf3Gp/E PDjtnudzmBMXMDcuuset5sJv7h6+5+5im/rH9HZybAjdTrLJJaP24Yzan23mZTadwjk0jHPpJ5xH l3NeXWuVUwHdywV1n1VORfQcv6kXuLje5JL6kEupZzXey2syqaApIKXVGlZV88pbWkhqail5WytD dbvHL7W5vKMtoJXV/aLm2lda6kBpo8OknY6SDjpWOut46aoTpDv0gj76gVWuw7WfjEA7I7S31Zrx AfZ5gjaVyVpfpmoNmaEVoZxVbrPRLx9rHsht1b+fanJZqAllscaUpSqyXH+3mgufYQyv1bNWx/MN Gs4bMae+0m38tW7kbbqGt+syq7zCdTrvw7y3WWOP6AA+qn35B+3BJ7QLn9T2fEZb8zltzhe0qdX6 eFfr8D14ADbHz5huE47tNuV4bnOO77bmRG57TuJ25tDtP5v65ZJMnEuyRClG9IgY4uSXolxAKnAh qc2FpZFVPsWkKxeT7lZrbmkZy2VkHJeT6VxR5nFlsRtjb8lWriHfWPVfPTnODeQ0N5KL3Fiu8nty i5vLHW4pdvf/e8lD7i0PrOblcOQ0Us7wGPmRx8l3/IHs44my0yqvGbKKw2SFVV4fSxjPlan8Cfpy gQzlRdKXF0svq7xWSTNeJU2s8lovVXiDlONNUpw3SyHeKvl4u+SyWif2SQreL8kgKds8F3RCgvyT BPi0eHxWlC+I8M/wC1yFGzjvlrj8m/h8F9velxgQ0yp3T1OxHyGN1RyJo/k4LrykhTmhluAkWoGT aXWoaZVfam3JabCep9E2VmOnMK/kwrzGam0qyru5GJTkI1yaT3NZvmyVU2UmjEaxus1VhxNKXWjA ieUdaMyJpCnHx0yJKy05prRmX9oyW90X6sxXuAtfsqpdDz7MPflb7s3buR+v5/682qp2g3kmD+Ew q2PfCEQYzT14LLfhcdzUKp+JXIUnckWrfKbxa9ijLNizlDyLE1nlM4eJ5/Ijsrodyj/TQj5FS/gw LeNdsINsclrNK2kNLyer+/o8nTbwNPqSx9FmHkZbuB9t455Wee3lZhTOTaIUI0VEjBjOD1ydjnM1 OsFV6BRXojNwHi7CZbiC86/j8pv8Ft3mWlDHKmcjbYmkvVUtAzKIoslQiiFjKbZMoXgyC+aSzXqd WD6nJPIFbLAaeynlW3pZjlJaOUvp5RrctKrXKziuZpFoVnMqh7zModvcNjHK0hAqS8OjtC8JImIE nMo0k6pANZpHNWgR1aYVVIfWUH1aRw3pC9hgVav2iNWBVpHN7YGeNIt6Icc+NJX603gaSCOw5wOh n1Vuo6k1jaEWVuN+Er1FU6giTaeSFEaFkeWrkNcqr08oFc2nFFb9uowCtJx8WkmEHnho1tJds55+ NRvoutlEV8xX9IuxmZsH6YI5HOGisenb03TfnEV+F4jpZ+R8mWLTVUoISazWjl8pB92OkMtq7XhA pekhVSCHaxJzI2hm1bce9yKf+5LNsT0GT6RYPJPi8iKKx2us8knAuykhh1vVKAmfpaSQgm9RKmZO xa7VupaWk3I6TmF1+ycj5+HMXISzciV4y+p+Q05uwbm4FbS2yikvD+B8PAy3zKZwQf7Yqkah1/dW N29ZjaNa5o0nrwevZ1JYzbcGxo94PXlDo1Y5NTZXn7wevZnZa2xq1MqsNa3MGqt17unXwtvk0tW0 MN3Me8bqfo+p8szr8PuZHFY5DTRJzCCT0CqnYYaeeQ/AWHPSsbrvY3Y5k8wOx+aY/FfvO5hvJjk2 42CdGRnx/oT1ZniU4iSLiBPd2W66OTtMF2eX6ezsNZ2cffh9AH8fMl2dI+Z956jp6fxg+jonzEAY bJXzBez3RTMdwqzqedUsd66hpjfNeudXs9W5Y8Jhv1U//27Ow0XHZq0geuQIBbHqJMDqk8pqLkSn V010ym9s8olDFU08rKbxqQW0tconCQ0ySWioVT4pKMykorkmNa0yaWijVT4Z6IDJQIet8slMl00W 3P7MRo9MDophdbslD6XBrez0Vsea/FQQ/4tTIdwDeoPqWh3/iuNeTgnqBJ2t9iv03p7CZp3V7bES Zs4z7wsqbwZY5VTZtKHKptU/xnjms37/9AnFf/1ZNpGPV18PrNKbgdV6G+7AvcAa/R0eAQXXqIIH AYgOMSFO8LMovb8xdUSbsZxciJEHXoX8UDC4WgtBESgGJaBUcJWWgXJQESoHV2pVsGm3Y3C5doZu wWXaA3pBX+gPA2EIDIORMBrGwQcwAWzaXYM218F62ACbYDNsDa7Q7bATdkM49m8/HITDEVZZtXvf H6QPwQkMVAYFD4IQHWJBHHgJEkJiSArJwKbd1wNDtDC8CcUCQ7UElIaygWFaASoHhmtVqA41AyO0 NtQNjNR6gVFW7fYMTNQ+0C8wSQcEJutgGBqYoiMCU3V0YJqOhfGB6ToxMEMnB8J0GswIfAgzrdpd H5ivX8CXgU/1q8AC3QLbAgt1R2CR7oa9gcW6L7BED8ChwFI9ElimR+FYIGrjKvLxStevrQG/jkb3 62pMv77G8RtoPL+hJvAbaSL/XU3iN9HkflNN6TfT1H5zaGG1n2/472sRKOp31+J+Ty3l99Kyfm8t 7/fRSn5freL302r+AK3hD9RaUAdjr54/GIbY9as/RntDX+jvj9VBMBSGwyh/nI6BcTABJsFUmA5h EJV2I9fGDf4o3QSb/ZG6FbbDTn+E7oa9/nDdDwfgMHzvD9NjcNwfatVmXK+8xoeEkBiSQUpI5ZXT NJAOMnhlNTNk8cpodsjplbaqb2WviFbx3tDqUMMrrLWhrldI63uv6zvwrldQm0Azr4C2gNbQFtpB VNpNG9FubGec96qOh4kwGabBDPgQPvLy6ccwD+Z7+XUhLIFl3mu6IkIBq33e772pB+CQV1SPeMX0 qFdcf/BK6AmvpJ70SukZ1PQcansRdb6E+l/xKug1ryJUsurf5O6nkhJSuwskLaSHTO5CyeIukmzu YskJud0lktddKvndZVLAXS6vuyui9B70yPs+tdwtUsfdKvXc7dLQ3SGN3J3S2N0t77nh0sLdJ63c A9LWPSTt3e/giFVbw9yrMhxGutdljHtLxrm3ZYJ7Vya5D2Sq+1Cmu0bDXNZZrgue2rS11k2h62C9 +7JudNPoJjedfu1m0K1uJv3GzaI73Wy6x82h4W4u3e/mseq3X9zietUtoTfcknoLfnNL6T23tD5w y+hDt6wajBPG3HTBh2gYM9EhKm1Gvi4qo74rr2gzyaqtJIe2l1zaWfLo+5JPe0t+7Sc272UvqzOk nIZJBZ0llXWOVNVP5C1dIDV1ibyty6SurpT6ukZsatZVd0l33S29dI/00b3ST8NloO6TwTAMRuh+ GQVjYDxMgElg0+Ya/UY+0+3yuW6TL3SLbNSv5SvdLF/rV7JNN8k3ulF26QbZq1/IPl0v3+rnckDX ic1ackMXy034VRfJHV0o9+ABavkIDOa6gAsBiObOl5gQG+JCVNqNfK9iLjnNeeUk55cTXECOcyE5 xm/IES4qh7m4HOSS8i2XkX1cVvayze2MxrKO35O13FzWcCtZxW1kJbeX5dxRlnEXWcrdZAn3kMXc SxZxH1nI/cGmvdmINxc+QewFaGMR2lqKNpej7VXIYQ1yWSef83r5gjfIRt4oX0apvcjnbA6iZofl KH+PGh6Tn/hHOcM/yXk+LZf4rFzl83LDKv4diSV34b7Ek4eSUIwmE9ZU4mo68TWTBDSL2KwTibWM JIFkWlFSaBV5WWtIGn1b0msDCa0hNrELcwx6k+NQMY5PJTkJleYUVI7TUAXOSBX5lSh9nkbkc1B1 uAzV5bLUgCvTO1yTGnM9asqN6b0nz/VolB4368BDqDOPpq48ibpzGPXkuTDPKuZg3kbDeA+N4EM0 mo/TWD4L56xiTmWXp0EYx+SZnIA/4hT8Madjm5iLuQQv4VK8jCvySq7Bq7k+f8ZN2KafNvMA3sJD eTuP4R08iXfxDN7Ls+Fjq3lxjL/i4/w1n+Bv+BTv5jO8n8/zIb7IR/gy/wDH2eZYIJi3Lvhyk6NB DLnFsSEeTseHRLgsCSST65xSrvHLmOtp5EqU2ox8DKgsXTLl6ZapRA9NFfKpCkW3GiN1KAvVp9zU kApSIypKjakMlCOb40YHakEdoTO1oW7UgbrjVC+c6kM9qD/1pIHUm4bgr6HUl2z6dw5a+YTa0gJq RYuoOS2lJrQce7ESe7SG3qbPqBbZrE3bUZMdlI92oz7hlJ32U2Y6SOnpMKWm7588jx+1Gl0ipstk 6Cr68To9MLforrlNv5m76Nv7dMM8pOvG4auGOfL5/Ki1kwYx0vM1k5FvmMx8y2Tl30x2vmty8QOT hx+ZfEz0GisVYC9K+xP5mOvTn0NV2+SzilXfJHjyGVbvml+NTaz3zMEnn4HVyqy0itXejH/ynGEX nLKZx//7Ob+o5TbYxHryuV0jzVXHZk2YYPb+6fO+wswSx+b+wCIz7m8+G2yw86Xp72wyva3aOGY6 Oj/ACdPFOWW6OWdMD+e86eNcNAOcS2aIcwVtXTGjrWpz3yxyfjfLnUdmnUO0yRHaAbutYsagy05M iEO3nXj0yIlPQROfoluNr+SU1aSi3CY1FTbpqAxUsIqXhdqYbNTZ5KS+Jg+NgNFW8QrSElOI1pgi 9JUpSrthr1W8//7stFJmhtUaVMH0ePKZa9VMnX+M9d/fM2f+9nvm6nDsp769YRAP4r/+9oaeEpz2 19/e4P7pO3jI6dkzFPfvMr32x7M8f//dErn/lN0X9D+ym/682Rmnm5P7hWRnnr92M/5N7cy/yO55 vktwkXvkub7/DXmG/XOekd9k0il79YjIz5vp4+funv0W2ac/C/Cpb/l0/vyNppFR/vNts4/32HH+ DwkoudlAdwAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0219.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Root Locus

•Provide the exact stability bounds of the control gains for time invariant linear systems •Visualize the effect of the optimal feedback gains for time invariant li= near systems with time delay

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0195.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Root Locus of the LTI System
- With respect to ki whil= e kp is f= ixed at an optimal value

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0195_image053.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+zcB1SU5773/fu+5r6ue2Yk9hrQWGIvEMWuKGLBhh1LTNBYomIFC4gFsWDB2Ati wYIFC4oaRaOiiC2KbjVGYzTG2IMVxYLI8x2Tfc7ez7OffbIzWet913rf7fpYEIaZq/z//58nZ74/ c2yZpln4USzXaescXeN/rbvomo0PFrplaKZW5P3HHD+/5GMzHH/QcnJyNP33X//R3z+m/cPfOfc/ HuP3X//l3/5vj/////n/HX824Ckc50rTamqKn8upcprgfDg+UkKT/Cx0x2lx/C6XcJw/x+9cxElr 4VyO35m64zNNFDZOW4vl+vtnqP/6KqGL3z/jrdB///6O71uVz7Dy6xuh/v60xG8fF79/9vvnKf7+ 2Zb/+mzH4+n/9dnG+79/wlf99n0df/vbZ0rtn7+f+P0zjd9f3W/P+ltriVw6v8/Lnz62KG1mzrKc mTkZVt3FwfH73/zjYziejRu/Zgm3f1zW99+uU2jwyH5DtDGN+b2HtB+5k/x8zGP89lw8tH981uX1 nJx/9Vrl78/0n1+z4zP+/t3/1Vep379K/l9W6r8f9b936J9XRv7blamgp5sVdD/tvN3B8fvf/PPK qP/jFTq+2/ttEf96X3/73ur/8lr/9XPKzZ/KWuS/fE7/+Gr//vj/+Hz+8fv896lT/3YNrO+/n9D+ /r3++bX+n9/j3z9Guul4rs48huPr/4rn4Xg9/0+/lr/qeVTQLzj5PPzQ/398Hv9cFavpxTTtX54Z x98WFJ2tyb/Xitjfi/Bzx5fqhtDydh44pF+w9vx9rbhl2rV/XSvk+0eyvb9BjudaSlq0qp94aI5H /nfP9cnvd+B/et0LLOnmAotza7fA4of+f2oP/75OPpY/uE76/7xO5vt1ElrVmo7H/StWKVumm9nS uVXKln5wbpVuyT+4SuKPrpKuOc7SLflXrNIAa7o5wOrcKg2w+sG5VWpn/YOrZPnjq1RTczzuX7FK v1XvC052AEcncm6VYu1/cJWMP37jPvFwPO5fsUqOmu6tO98nk/5kf/ptlfJYx//R+i3/g/rt6WE6 HvmvWaeXyhvOrdNLlWT/c4/x2zp9aP7hdVL/wTrV8FCOR/5r1snCOlmcXCcL62RxYp3Kqz+8TuZ/ sE7VPZTjkf+adcorveHcOuWVSfY/9xi/rVMN+YfXyfofzU3S8ch/zTq5Gd5wbp3cjCT7n3uM39ap sXHnj66T7T+ZCByP+9esUkWLN5xbpYqWJPufe4zfVqmNZfcfXSX7f9LrHI/716ySp/CGc6vkKZLs f+4xflulbuIPr1KuP75K1T0cj/vXrJL3+x/OrZK3nmT/c4/x2yr10//wKrn88VWq4eF43L9mlfw0 byfztGO6TPqT/77w2yqN0P7wKn3wx1fJ08PxuH/VKv1/7V9y/vvfY//538By/rd/IVT/9O8ZT8xL 9rZ8/en3362vlmUdZOq2QaaEHXlQEMVQAmVQDhVQFdVRGw1sgaY3mqM12qMLuiMAfTHQNtgcgiCE YBwmYSqmYRbmYpFtiLkMq7AOm7ANO7EXB3DENtQ8jtM4h0u4ihu4hbu4j8fIsA0zXyEbwj7MNOGC fCgMV5S0DzfLohLc4Ym68IIPfNESbdEB/uiBAPSzjzAHYSiCEYLxiEAkojAPi+1BZgxiEYd4bEEC diEJB3HEHmyewBn8T//e+e/2spIZYLqbvUxP1IUXfOCLtuiIruhm9jZ7wvGjPwIxHKMQiomYYn5h TsdszMdSLMdqrMdmbDf7mDuxG/twCEdxEmm4gMu4ZvY1b+Iu0vEEmciCZu1rGrAhN/KgAIqiuLWf WRrlUQWfoBbqozGaoZW1v9kOndEdn6MPBiAQgxFk/dIcgzCEYypmYg4WIhorrQPMtdiIrUjEHuxH MlJxHKesA82zuIgruI6buIeHeIpM7pTjXv2ZvTz1fi/7aK1lF7M9uqAHAqS/2RcDMRTBCMF4RCAS UbKrOReLEI1lWIV12IitSMRefIPDOIZvZTfzHL7DD/gJt3Afj5Ahu5uvkA2hupsmXJAXheGqepgf 4WNUhDtqoA4aoglaqE/NNugAf3yKXuiHQRimepojEYoJmIxIRGE+liBGfWbGIg7xSMAuJOEgUnAC Z3Ae3+NH9bn5M+7gVzzBC7xBDizcGRtyIz+KwA2lURaOO+XMnRxraWNOxBTMwFdYgKWWtuYKrMEG bMEOJGI39iEZqTiJNFzAZYufeQ03cRfpeIpMvEEODMPPtCG30c4sgKJwQ2mURXlUgQdqoj4aGe3N pmgJP3RCN3yGL/AlBmOE0cEcjTCEYypmYCbmYCGisRJrsQFbkGh0NPdgP5KRilM4i4u4gutGJ/MX 3MU9PMQzvMRb6LKTqZBLdjbzohA+RAmUQUVUQ3XU5s40gDeaoDkcd+rP7OWJ93v5hXZE722m4Jje y/xW/9w8jb/pn5nf4Qe9p/mT/ql5W+9h3te7m+l4pHN38ErvamYhG0L4m6boYrogn+hsFoar6GSW RCmUFR3NSnCHp+hg1kUDNIQPfEV7sy06wF+0M3siAL3QFwOFnzkUwQjBeESItmYkojAPi7AYMYhF nGhjxiMBO5GEg0jBcZzGeVzCVdzAbTzAY9HafI7XeAeLpbVpxQfIjyJwQymUQ2V4oCZ3oB684IOW 8ENHdEVP9EZ/BGI4RsFxn/7MHh57v4e9tfNiPa9nPa9rPa8vjtcZZ+5DEnYiQaxjLdaxJutYm7Ws 0VpzCRZjnljDGq5hLdewpmtY2zVmqFjNOq9mvVez7rGsfyz7EMt+rGJfVrE/q9inlezXSvZtBfu3 gn1czn4uZ2+Xs8cx7HUMe76MvV/GGYjmLERzJpZyNpZyRpZwVhZzZhZzdhZxhhZxnhaaL/QFnK0F nLH55gN9HmduHmdvLmdwDmdxDmfyK85mlHlGn8U5ncWZnWmm6jPMIzikTzcP6JHmXn0appo79SmY bG7TI8zNeri5SZ9obtAnmLH6SIw2V+tBCMFwc40+1lyrDzXX6WEYYsbp4zDY3KgP4usGmVv0ATzO AHO73p/H7Gd+rffle/Qxv8EB/QvTcYecqafRxk5qzE5qzU5qzk7qz07q0E5zHMIwGiOMRGpVIjUr kdqVSA1LpJYlUtMSqW2J1LhEat0Oat4Oat8OauAOauEOauIOauMOauQOauUOauZ2aud2auh2aul2 aup2aut2aux2au12am4CtTeBGpxALU6gJidQmxOo0Qnmd7hg2Ubd3kb93kYd32Yewj7sxg5swXqs wQrLVnrCVnrDVnrEVjMKMzAFEzHWsoXzv4V7sIX7sIV7sYX7sYV7spn7spl7s5n7s9lsjZbwgZcl njsWz12L587Fc/fiuYObuIubuJObuJubzALIjw8sG7m3G7m/G7nHG7nPG7nXG7nfG7nnG7jvG8xb uIGruMT9cdwlZ/ZykDpA/z/AHPAN88A3Zjf4owPaoAWaoCHqoAaqqf3MGPuZNfYzc+xn9thvFkJe uMCEQLbcz8yy38xEBh7hvtzHXLOP+WYfc84+5p19zD37mH/2MQftYx7ax1yUxHyUxJyUxLyUxNyU xPyUxByVxEyVxGyVZC7EXLmXeWsvc9de5q+9zGF7mcf2MpftZT7by5y2l3ltD3PbHua3Pcxxe5jn 9tCD9tCL9tCX9tCf9tCn9pg15df0rK/pXV/Tw76ml31NT/ua3vY1Pe5ret3X9Lyv6X276YG76YW7 6Ym76Y276ZG76ZW76Zu76Z+76aO7zcu4iLM4hVRjFz13F713Fz14F714Fz15F715Fz16F716l+m4 V87Mq42tx5jLjzGfH2NOP8a8foy5/RjzeypzfCrzfCpzfSrzfSqzfiozfyqzfyoZIJUskEomOEo2 OEpGOEpWOEpmOEp2OEqGOEqWOEqmOPr+xyEzhayRQuZIIX+kkENSyCMp5JIU8kkKOSWFvHKE3HKE /HKEHHPEjMBEhGIUhiMQ/dHbPEwWOkwuOkw+OkxOOkxeOkxuOkx+OkyOOkyeOkyuOswseJiZ8DCz 4WGzBNzMZObFZObGZObHZObIZObJZObKZObLZObMZObNZObOQ8yfh5hDDzGPHmIuPcR8eog59RDz Kq8IB9VBcz+SsAsJiEccYhGDJZiPKO5MJCZjAkIxEsPguFPO7GM+expZOY3MnEZ2TiNDp5Gl08jU aWTrNDJ2Gnk7jdydRv5OI4enkcfTyOVp5PM0cvoZ8voZcvsZ8vsZcvwZ8vwZcv0Z8v0Zcv4Z8v4Z cv9p8v9pcxqmYhLGIQRBGIKB6IsA27dmd3RBe7RGc3ijAWqjOqraTpkVUAYl4IpiKIg8sENCR5b1 JDntJHntJLntJPntJDnuJHnuJLnuJPnuJDnvJHnvBNnvBBnwBFnwBJnwhLkLidiKjViLlYi2HidP HidXHidfHjenIRxhGIMgDMEA9MHn6I7OaMddaYtWaAbHffoz+9jx/T6W187Yz5snkIKDSMIuJCDe /jczDrGIwWLMQxQiEYHxCEGw/Zw5FIPQDwHoAX90QFv4wsd+1vRCXXjCHZVQFiXhisJwnC9neka2 dYvSbVuUhB15UBDFUAJlbFtVBVRFddRGA3ijuW2baoXWaI8u6I4A9MVAW4IagiCEYBwmYRpmYS4W YQmWYRXW2barTdiGndiLAziC47Yd6jTO4RKu4gZu4Q7u47EtUWXgFbIh7InKhAvy2XeqwnBFSZRF JbjDE7Xtu1RdeMEHvmiLDvBHDwTYd6t+GIShCEYIxiMCkfav1XREYR4WIwaxiEM8ErALSTiII/Y9 6gTOwJm9dDdXKU/UhRdVzge+aAWSieqIruiJ3uZq1R+BGI5RCMVETDHXqOmYjXmYj6VYjtVYb65V m7Edu7EPh3AUJ5GGC7hsrlPXcBN3kY4nyEQWlVizxikDNuRBARRFcet6VRKlUR5V8AlqoT4aWzeo ZmiFduiM7vgcfawb1QAMxGAEYQzCEI6p1k1qJuZgIaKxEmuxEVuRiJ3YY41X+5GMVJzCWVzEFetm dR03cQ8P8RSZyILjXjmzlwPlfBWIoQhGCMbLBSoCkYjCXCxCtFyoVmEdNmIrtiERe/GNXKQO4xi+ xTl8hx/kYvUTbuE+HuEZMvAK2RBqsTLhopaovCgMV3yEj1FRLVXuqIHaqIOGaIIWaKOiVQf441P0 Qj8MUsvUMIxEKMIwAZMRiSgVo+ZjCRw/YhGHeCSo5WoXknAQyUjBCZxRK9R5fI8f8TPu4Fc8wQu8 QY5aqSzmSiVhQ27kRxG4oTR3qCwqwXGvnJkBlloi1QqswQZswQ7sxj4kI9UyXZ1EGi7gMq7hJu4i HU+RaZmh3iAHhjFD2ZAbBVAUbihtzFTlUQUeqIn6aISmaInW8EMndMNnxiz1Bb7EYIzAaIQh3IhS UzETc7AQSxGNlVhrzFYbsAWJ2IP9SEaq8ZU6hbO4iCu4jhv4BfeMOeohnuEl3kKXc5RCLjlX5UUh fIgSKINyqIhqqI7aaCDnKW80R2u0Rxf04N4EoC8cd8qZfXyhr1Ov9DUqW49VQqxUpliurHARMSqP WKbyobBYqorAVSxRJcViVQplxSJVSSxUleEOT7FA1RHzVV00FPOUD1qIucoXbdFBzFH+6Ca+Uj3R C33FbDUQQ0SUGopghIhZajwiEClmqhmIwjwsRgxixQwVh3gkYDt2iukqCQeRguM4LSLVeVzCVdzA bTzAYzzHazFNZeMdLJZpyooPkB9F4IZSKIfK8EBN1IMXfNASfuiIruiJ3uiPQAzHKIzFOEzEFO7H DHyFBXDcJ2f+3bGe5WdVBzXhgcqWGzznGzz3G7yGG7yWG7ymG7y2n3iNP/Faf+I1X+f1X2cdrqun 4hprco21ucYaXWOtfmTNfmTtflQXxFXW8SrreZV1/YH1/YF1/oH1/oF1v8IeXGEvLrMnl9UaxCIG i8X37Nv3ajaixCX28xL7+h37+50aixAEi4vs/QXOwQXOw3nOxd84H39Tn8JfnOPcnOX8OKRxltI4 V2eUNxqK05y1b1UteIpTnMGTnMWTnMkTnM0TqrQ4zlk9zplNVR+isDiq8osUzvMRzvZhznmyUuIQ Z/6g0sQBzv836q2+n7uQpF7oe1SG/rV6pu9WT/Rd6rG+Qz16L0E91Lfx6xbE8/FN/P1GPm89nx+n HHfJmf6o5FPqxFPqxRPqxhPqxxPqyBPqyRPqyhNqzBNqzWNqzmNqz2N1GqeQimTsNx5Rpx5Rrx5R tx5Rvx5Rxx5Rzx5R1x5S4x5S6x5S8x6qaZiKcIRhNEZgML400qmb6dTPdOpoOvU0nbqaTo39lVr7 q2qCRqiPmvBAFZQ3HlCnH1CvH1C3H1C/H1DHH1DP71PX7ysLciz3qfX3qfn3qf336AH36AX36An3 6A336BH36BV36Rl36R136SF31SHss9yht9yhx9yh19xR67EGK7AUCy23uUe3uU+3uVe3uV+3uWe3 uXO3uHu3uIO3uIu3uJO/qD7ojZ7oio7ws9zkHt/kPt/kXt9UjvvkzF7+qLLp19n07bf077f08bf0 87f09rf0+Lf0+rf0/Cx6fxYzQBazQBZTQBazQRYzQpaahyhE0tknYwJCMRLDMAj91Gtmj9fMIK+Z RV4zk7xmNnnNjPJa+aAJGqIOaqCaesVs84oZ5xWzzitmnleqEPLCBaZ6yWz0khnpJbPSS5WJDDzC fdySmcxWmcxYmcxamcxcmcxemcxgmcxiL5jJXjCbvWBGe8G89kLFYyPWYRWi5XNmu+fMeM+Z9Z4z 8z1n9nvODPicWTCDmTCD2TCDnpZBb8ugx2XQ6zLoeRn0vgx6YAa9MIOe+Ize+Iwe+Yxe+Yye+Yze +Yw++ox++pS++pT++pQ++5R++1Q57pUzPXKr1UqGt5LhrWR4kwxvkuFNMrxJhjfJ8CYZ3iTDm2R4 ZY5EEIZgAPrgc3RHZ7RDKzRDY9S3SrMWPkEVlEdpFEdRq2EWQB7YYEBDlmmYmXhiWsx03MVNXMNl XMA5pOGkKcyjOIR92I3t2Iz1WG3q5nIsxXzMxnRMwURTM0MxCsMRiP7ojZ7oauaQwXLIYjnkshzy WQ45LYe8lkNuy2HOzFHVUAllURpu5jtm0nfMpu+YUd8xq75jbn3H/PqOU53NPJvNXJvNfJvNnJvN vJutbsBxp5zZxzB7fjMEwRiKQeiHAPSAPzqgrT2f6QsfeKEuPOGOSihrz2uWRkm4ojDywQUmBLJt ec1XtjxmBh7jPm7hBq7iEs7ZcpuncQrHcQQHsBc7sQ2bsM72gbkKy7AIczEL0zAJ42wuZgiCMAQD 0RcB6I4uaI/WaA5vWy6zAWqjOqqiAsqgBNxQzGY3CyIP7JDQkWW1m5l4iodWm3kPN3EdV3ARZ3EK x7kvqUjGfuxBIhz36c/sY4X3+5hfO2MvaJ5ACg4iyV7A3IUExCMOsYjBYsxDFPsaiQiMh+MsOHOW pO2JtNueyjwoiGIogTKoYHsmq6I6aqMBvG0Zsjlaoz26oDsCbM9lXwzEIAxBEEIwDpMwDbNsL+Rc LMIyrMI6bLBlyk3Yhp3YiwM4guO2l/I0zuESruIGbtleyTu4j8fIwCtkQ9hfSxMuyIfCcEVJ+xtZ FuVQCe7wRF14wQe+aGvPkh3gjx4IQD98iUEYan8rgxGC8YhAJKLs2XIeFiMGsYhDvP2d3IwE7EIS DuIITuCMPUc606d9zBuyKXzNn2VbdERX9ERv9Ecghps35SiMQSgmYgqmm7/I2ZiPpViO1eYtuR6b sR273/9flG7LQziKk0jDBfOOvIxr+Ak3cRfp5l35BJnIgma9Kw3YkMd6TxZAIRRFcZRGeet9WQWf oBbqozGaWR/IVmiNduiM7vjc+qvsgwEYjCCMsabLMIQjAlMxE3OsD+VCRGMl1mIjtlofyUTsQRL2 IxmpOIWzuGh9LK/gOm7iHh5an8inyEAmsqBznxx3ypk7GSnTZBTmYgEWIVqelauwDhuxVZ6TidiL b3AYKTgm/ya/xTl8hx/kefkTbuE+HuGZvCAz8ArZEOqCNNVF6YK8KAxXfMR0VAofoyLcUQN10BBN 1CXZAm3QAf7qe/kpeqEfBmGYuixHIhQTEI7JiFRXZBTmYwlimMZiEYd4JGCHuip3IQkHkYITOIPz +F79KH/Ez7iJO/hVXZNP8AJvkAOLeV1S2WVu5EcBFIGb+ZMsjbKoBHd4cofqwguOO+XMPqZaDsqT SMMFXLYcktdwE3dxD+l4iky8QY4lWRpGsrQhNwqgKNxQ2jgsy6MK3OGBmqiPRsYR2RQt4YdO6IbP 8AW+NFJkIAZjBEYjDOGYahyVMzEHCxGNlUaqXI212IAtSMQe45jcj2Sk4hTOGsflRVzBdfxinJD3 8BDP8BJvocsTUsqTUiEX8qIQPkQJeUqWQUVUQ3XU4iTXRgN4ozlay9OyPbqgBwLQV56R/TAQQxGM EO7MeETAcZ+c2cceIl12ETdxCzdwR/qLe7j+X792Ew/wo/xUXJU9xQ/yM3FZ9hLfyy/EJdlXXJT9 MFBckIMwVPxNjhDnZDBCRJoMxXhMEmdkBCLFt3IWosQpOQ+LxUm5BDHihIxFnDgu48UxmYCdIlV+ jSRxVB5EikiRx/EtTuO8OCIv4SpuiMPyNu7gAR7juUiWr/EOFs6fFR8gL/KjCNxQivNbDpXhgZqo By/4oCX8LAdkR3RFT/RGfwRiOEZhLCZiCmbgKyzAUqzgMdZgA7ZgB3ZjH5LhuE9/Zh+Pvt/HXtpl y0dk8o/I5CXI5CXI5CXI5MXJ5MXJ5MXJ5MXJ5G5kcjcyuRuZ3JVM7komdyWTu5LJPySTf0gm/5BM XoxMXoxMXkyNxHAEWoqSy4uSyYuSyYuobuiKjvCzFCaXFyaXFyKXFyKXF1Q14YHKlgKqPMqhFNws +VUR5LfkU/nwAayWvMqCdyKPysZrPBe51WPxgfoVD3AbN4SLuipyqUs4L+zqtLCp40gRVnVQmCpJ KLUTiUKqBMQLQ60XFhWHWCFUjNDVYqGp+ZgncjiD7+QMRIpszuZbzmgWZ/WNHIsQ8Zoz/IrznCmH YKB4Lgegr3gm+6CXeMI9eMR9eCgdd8iZOzhXfkLW/kTNkB7kbQ/ytgd524O87UHe9iBvu5O33cnb 7uRtd/K2O3m7muqE9miN5vBGA1mVzF2VzF2VzF2VzF2VzF2FzF2FzF2FzF2FzF2FzF2FzF1F6Xhr VFYv8QwP8QD38ItRSV3HFVzEWZwyKqpUJGM/9rxXQSViCzZgLVYa5VU0FmIOZmKaUU5NRTjCMBoj MBhf4gujrPoM3dAVneBnfKxaoikaob5RRtWEB6qgMsobpVVpuKEoChilVG7YYEBDjqWkeoNMPEU6 d+UubuIafoDjDjkzp/Y2G6ue6IqOaAtf+JiNyNuNyNuNyNuNyNuNyNqNyNqNyNqNyNpeZG0vsrYX WduLrO1F1vYiazckazckazckazckazckazcgazcgZzdQ3+M8zuCEqq9ScBBJ2IUExKt6Kg5rEIsY LMF8VVdFIRKTMQGhGKnqqGEYhAHoh174FP7ogDaqtmqBJmiIOqihail3VENFfIyP4IpCqqbKCxeY EMiWnuoVMpGBR7iPW0xhP+GH99NYDXUO3+KYrK4O4xC+wV4kYis2Yh1WcYeisQiOO+XMnaxqa6cq oIzNT5VAMRREHrjADmlrq3RkWduqTDzFQ9yztlE3cR1XcBFncQqp1tYqGfuxB4nYio1Yi5WItrZS CzEHMzEN4QiztlRjEIQhGIA++Nzqq7qjM9qhFVqiGRpbW6j6qIVPUAXlURrFrc1VURRAHthhgwHN 2kxlmc1UJp4gHXdxE9dw2WyqLiANp3ESR3EI+0wftRvbsRnrsRrLzSZqKeZjDmZjOqZgoumtQjEK wxGI/nDcqT+zj7ve72M37Yy9hzqBFBxEkr27+hq7kIB4xCEWMVhs76bmIQqRiMB4hCAYQxGIQeiH AHtX1QP+6IC28IUPvOz+qi484Y5KKIsyKAlXexdVGPngAhMC2bbO6hUy8Bj3cQs3cNXWSV3COZzG cRzBAey1dVQ7sQ2bsA6rsAyLbB3UXMzCNEzCOIQgCEMwEH1t7VUAuqML2qM1mnMXvNEAtVEdjjvi zMxitzWSeVAABVEMJWyNZRlUQFVUR200gLfNWzZHa7RHF3S3NZEB6IuBGGLzkUEIwThMwjRbUzkL c7EIy7DK1kyuxTpswjbstDWXe3EAR3Acp3EOl3DV1kLewC3cx2Nk2HzlK2RD2H2lCRd7S5kPheGK kihrbyUrwR2eqAsve2vpA1+0RQf4o4e9jQxAPwzCUAQjBGEYjwh7WxmJKMzDYsQg1u4n4xCPBOzC HiThoL2dPIITOANnel1bs7zsaFaQXdETvc2Ksj8GIhDDzUpyFEIx0awsp2A6ZmG2WUXOx1Isx2qz qlyPzdiG7diNfWY1eQhHcdJ0l2n4Gy7gsukhr+Em7iLd/EQ+QSayzOpSs1aXBmzIY60hC6AoXFEc pVHe6imr4BPUQn1rTdkY3miGVmhnrSU7ozs+Rx9rbTkAAzEYQdY6cgzCEI6p1rpyJuZgPhYiGiux 1lpPbsRWJGKPtb7cj2Sk4pS1gTyLi7iC67hpbSjv4B4e4ikyrV4yC7rNS0o47pEz/78UtaUghwrZ EN5oLi1kUQtZ1CCLGtIfPRBAwu2LgaTcoRiOYIRIkzxqygxS7yuZT2ZDqHzSVPmlDS7Ii8KqgHTF R6qg/BgV4Y4aTKV10BCNVGHZBC3QRhWRHeCPHqqo/BS90E8Vk4MwDCOZakcjFBMwGZHKVUZhPhZg iXKTMYhFnCou45HARLwdu5CEg+ojmYITOKNKyvP4Hj/iZ1VK3sGveKJKyxd4gxwma4tZRtpgR27z Y5kfReBmlpWlURYVzHKyEtzhibrcHS/4wBeOu+TM/k20PDGmWB4bM/AVFmApVmCN5ZGxAVuwA7ux D8lIxUmk4QIu4xpu4i4eIB1PeZxMvEEODOOxYUNuFDCeGEXhhtIoj8rGU6MKPFAT9dEITY1nRkv4 oRP8jQyjGz7DF/jSeG4MxgiMNl4YYxGGcEzFTMwxMo2FiMZK46WxFhuwxXhlJGIP9huvjWSkGm+M UziLC0aWcRFXcB2/4J7x1niIx3iGl0Y2P2cbunxnKNiQC3lljlEIH0pNlkAZVJS6rIbqcNwfZ/rg KEsjOdziJQMtDeVA9Lc0kL0t9eVn6Imulnqyk6Wu7Ag/Sx3Z0lJb+lhqyUaWmtIL9SzUL0sNWRMe luqymuUTWdniIctZ3GUpSzX5kaWqdENRS2VZBPktFeUHlvLSBVZLOWmxlJE5opR8hyxRUr4WJeQr vBCu8rn4UGbgqSgqn4jC8rEoiPzIizx8LDd/58Ln2PlcG19j5WsVj6HkW2HwmBapWQTfQ5fKovH9 NL7vO+MD5LdkGwUsb40ilizDDaUsb4xyltd4ZVTGv/qYh+WlUcOSadREPcsLwwtNLM8NH7SEnyXD 6Igu6Gp5ZvREb/S3PDUCMQzDuS+jMBaOu+PMf9OToybKbLzBCzzBr2oC9WICdWMC9WMCdWSC/A7n SfVncAIpOKjGUXvGUYPGUY/GUZfCqE9h1Kkw6tVY6tZYathYatlYOUOFUtdCqW+h1LlQ6l0ItS+E GhhCLQyhJobIvuiFT9UYauYYaucYauhoauloaupoautoauxoau0oau4oWQ0V1Uhq8Uhq8khq80hZ SAVTq4Op2cHU7yDqeBD1PEi6GB2kzaAjIMfSTr7BK4ufzMRTpFvayru4ZWkjb+IaLltayws4jzRL K3kSqZaWMhmHsM/iK3dbWsgdSLA0l1uwHmsszWQsVliayqVYYPGR8/CVpYmcgSkWbzkZEy2N5Vju juP+OLOH+60L6MUL6MkL5A5sxUbrfPr1fPr2fPr3fPr4fHr6PHr7PDkN4QjDGARhiHUuc8Fc5oO5 zAlzmRfmMDfMkR3RDq3QDI2tXzFnfMW88RVzx1fMH7OZQ2bLMiiN4ihqjWJeiWJuiWJ+iWKOiWKe mcVcM4v5ZhZzzizmnZnMPTOZf2YyB81kHprJXDSTGWmGPIWTOIpD2GdOZ56azlw1nRlrOrPWdGau SLkKy7EU8zHbnMaMNo1ZbRoz2zRmt6nMcFOZ5aYy001lvpvCnDeFeW8Kc98U5r8p9K4pso05mT42 mX42mb42mf4WQZ+LoN9F0Pci6IGTZBmUhhuKIL8ZTr8Mp3eG00PDpeMeOZPXx9vXMB+vYU5ew7y8 hrl5DfPzGvkFAtDDvprZejUz9mpm7dXM3KuZvVczg8cyi8cyk8cym8cyo8fK8iiLknBFYeSDC0z7 Kub8Vcz7q5j7VzH/ryIHrJIPcd+2kmywkoywkqywksywkuywggyxgiyxgkyxgmyxgoyxQu7CTmzD JttycshyMslysslyMspysspyMksM2SWGDBMjx2McQhBkW0bOWUbeWUbuWUb+WUYOiiYPRZOLoslH 0dIXzeFtW0p2WkqGWkqWWkqmWkq2WkLGWkLWWkLmWkL2WkIOW8IcuYR5cjFz5WLmy8XMmYuZNxcz dy5i/lzELLpI/ozruIKL1oXMqwuZWxcyvy5kjl0oHXfpz+xjuff7mI+8Hkc+iZMpOGhfR25ZR4ZZ R5ZZR6ZZR7ZZR8ZZS9ZZS+ZZS/ZZSwZaSxZaSyZaIx3nwJlck2VN03RbmiZhRx4URDGUQBnbGa0c KqAqqqM2GsAbzdEa7W2ntS7ojgD0xUAMQRBCMA6TbN9qUzENszAXi7AMq7AOm7ANO7EXB3DEdko7 jtM4h0u4ihu4hbu4j8fIsJ3UXiEbwn5SM+GCfCgMV5S0n9DKohLc4Ym68IIPfNESbdHBflzzRw8E oB8GYSiCEYLx9mNaBCIRhXlYjBjEIg7x2GJP1RKwC0k4iCM4gTNw7n1ULmvu8ERdeMHH/F7zRVt0 RFd0Q0/0Rn8EYjhGIRQTMcW8pE3HbMzHUizHaqzHZmw3v9N2Yjf24RCO4iTScAGXcc28qN3EXaTj CTKRBc16UTOsFzQbciMPCqAoiqM0yqMKPrGe12qhPhqjGVqhHTqjOz63/k3rgwEIxGAEYQzCEI6p mIk5WIhorLSe09ZiI7YiEXuwH8lIxXGcsp7VzuIiruA6buIeHuIpMrlTjnvl3Puo/KK1Rxf0QIC8 qfXFQAxFMEIwHhGIRJT8WZsLqpYWjWVYhXXYiK1IlDe0vfgGh3EM3+IcvsMP+En+pN3CfTxCBl4h G0L9pJnquuaCvCgMV3yEj1ER7qiBOmiIJmihrmlt0AH++BS90A+DMEz9qI1EKCZgMiIRhflYghh1 VYtFHOKRgF1IwkGk4IT6QTuD8/geP+Jn3MGveKKuaC/wBjmwmFc0G3IjP4rAjXtTGmXhuFPOvY/K r+TVX7UpmIGvsABLsQJrsAFbsAOJ2I19lgdaMlJxEmm4gMu4hpu4i3Q8RSbeIAeG8UCzIbdxXyuA onBDaZRFeVSBB2qiPhoZ97SmaAk/dEI3fIYv8CUGY4RxVxuNMIRjKmZgJuZgIaKx0rijrcUGbEEi 9mA/kpGKU8Zt7Swu4gqu4xfcxT08xDO8NG5pb6HLW5pCLuRFIXyIEiiDiqiG6qjNnWkAbzRBczju lHPvo/K9loJj+mXtW/2Kdhp/03/QvtOvaj/oP2o/6de02/p17T7Sde4OMvQb2iv9Zy0L2RDipmaK XzQX5BO3tMJwRUlxWyuFsqgk7mju8ERdcVdrgIbwga+4p7VFB/iL+1pPBKAX+mKgeKANRTBCMB4R iEQU5mGR+FVbjBjEIg7xSMBOJOEgUkS6dhyncR6XcBU3cBsP8BjP8RrvYLGka1Z8gPwoAjeUQjlU hgdqoh684IOW8ENHdEVP9EZ/BGI4d2IUHPfpz+zhkfd7GMDrWMDrWcDrWsDrW8DrXKDtEwt5zQt5 7QtZg4WsxSLWZBFrs4g1WqQtEYtZr8Ws3WLWcDFruYQ1XcLaLtFCxVLWeSnrvZR1j2b9o9mHaPZj GfuyjP1Zxj4tY79i2LcY9m85+7ic/VzB3q5gj1ey1yvZ81Xs/SrOQCxnIZYzEcvZWM0ZWc1ZWcOZ WcvZWcsZWsd5itNe6Os5W+s5Y+u1B/oGztwGzt5GzuAmzmI8Z3IzZ3OLdkbfyjndyplN0FJxRN+u HdJ3aAf0RG2vvlPbqe/Wtul7tM16krZJ36dt0PdrsfpRHNFW66lIxgltjX5IW0t3WqcfxLdanH4A 32ob9TN8XZq2RT/H45zTtut/4zHPa1/rF3j8i9o3+nd8r0vv745z758yjdoyjRozjVozjbozjfoz TRuHMIzGCCOSGhVJrYqkZkVSuyKpYZHUskhqWiS1LZIaF0mti6TmRVL7IqmB06mF06mJ06mN06mR 06mV06mZ06md06mh06mlM6ipM6itM6ixM6i1M6i5M6i9M6jBM6jFM6nJM6nNM7XvcAFpOIlUHLLM op7Poq7PosbPotbP0tZjDVZYougFUfSEKHpDlBaFGZiCiRhrmc25n835n809mM19mM29mM39mM09 mc19mc29+UprjZbwgRfqoaZlDndtDnduDndvDndwDndxDndyrlYA+fEBrLBY5nF/53GP53Gf53Gv 53G/53PP52u3cANXcYn74rhDzr1/yjj6/jj6/zjmgHFaN/ijA9qghRrPzDCe2WE8M8R4ZonxWjVU xMf4CK5qglYIeeECEwLZcgKzygQtExl4hPtyIvPMROaaicw3E5lzJjLvTGTumcj8M5E5aCLzUDhz UTjzUThzUjjzUjhzUzjzUzizVDgzVbi2EHPlJOasScxbk5i7JjF/TWIOm8Q8Nom5bBLz2STmtEnM a5OY2yYxv01ijptE74mgB0XQjyLoSxH0pwitJqqjGiqiDErIyfS0yfS2yfS4yfS6yfS8yfS+yfTA yfTCyfTEKfTGKfTIKfTLKfTNKfTPKdplXMRZnEKqMZVeO5WeO5XeO5UePJVePJWePJXePJUePfX9 vXLu/VOCmceDmcuDmc+DmdODmdeDmdtHMr+PZI4fyTw/krl+JDP+SGb9kcz8I5n9R5IBRpIFRpIJ RpINRpIRRpIVRpIZRpEdRpEhRpElRpEpRpEtRpExRpE1RpE7RpE/RpFDRpNHRpNLRpNPRpNTRpNX RpNbRpNfRmsRmIhQcwzZZgwZZwxZZwyZZwzZZwwZaAx5aAy5aAz5aAw5KYS8FEJuCiE/hZCjQshT IcyAIcyCIcyEIVoJuJmhzImhzIuhzI2hzI+hzJGhzJOhzJWhzJehzJmhzJtjmTvHMn+OZQ4dyzw6 lrl0LPPpWObUscyrY5lbx2r7kYRdSEA84lQYs24YM28Ys28YM3AYs3AYM3EYs3EYM3IYs3IYM/M4 Zudx7++Uc++fMoiMPIisPIjMPIjsPIgMHUiWDiRTB5KtA8nZgeTtQHJ3IPk7kBweSB4PJJcHks8H k9MHk9cHk9sHk98Hk+MHk+cHk+sHk+8Hk/MHk/eHkPuHkP+HaFMxCeMQgiAMwUD0RYBtqNYdXdAe rdEc3miA2qiOqqiAMigBVxRDQdswLQ/skNCRZR1GPhtGThtGXhtGbhtGfhtOjhtOnhtOrhtOvhtO zhtO5htO9htOBhxOFhyu7bKOIBeOIB+OICeOIC+OIDeOID+OIEeOIE+OIFeO0KYh3BpE3gwidwaR P4O0IRiAPvgc3dEZ7bgrbdEKzeC4T869f8qX2gmk4CCSsAsJiLcP0OIQixgsxjxEIRIRGI8QBGMo BqEfAtDDPlDzRwe0hS984IW68IQ7KnF+yqIkXFEYjvPl3PunzNZ122xdwo48tii9IIqhBMqgAqqi OmqjAbzR3DZLb4XWaI8u6I4A9MVA20x9CIIQgnGYhGmYhbm2GfoiLMEyrMI6bMI27LRN1/fiAI7g OE7jHC7hqi1Sv4FbuIP7eIwMvEI2hH2absIF+VAYriiJsqgEd3iiNurap+pe8IEv2qID/NEDAfYp ej8MwlAEIwTjEYFI+2R9OqIwD4sRg1jEIR4J9gh9F5JwEEdwAmfg3PunROueqAsv+MAXrdAWHdEV PdHbXKr3RyCGYxRCMRFTzCX6dMzGPMzHUizHaqw3F+ubsR27sQ+HcNRcpJ9EGi7gMq7hJu6aC/V0 PEEmsqBZF+oGbNYFeh4UQFEUR0mURnlUwSeohfpobJ2vN0MrtENndMfn6GOdpw/AQAxGEMYgDOGY ap2rz8QcLEQ0VmItNlrn6FuRiJ3Yg/1IRipOWb/Sz+IiruA6buIeHnKPniITWXDcK+feP2W9Hoih CEYIxiMCkYiScfpcLEI0VmEdNmIrtiERe/GNXKcfxjF8i3P4Dj/ItfpPuIX7eIRnyMArZMs1ulBr dBMuyIvCcFWr9Y/wMSrCHTVQG3XQUMXqTdACbdAB/vhUrdJ7oR8GYRhGIhRhmIDJiESUWqnPxxLE IBZxiEeCWqHvQhIOIhkpOIEzarl+Ht/jR/yMO/gVT1SM/gJvkAOLGaNL2JDbXKbnRxG4oTTKohIc 98q5909J1FdgDTZgC3ZgN/YhGamWHfpJpOECLuMabuIu0vEUmZbt+hvkwDC26zbkRgEUhRtKGwl6 eVSBB2qiPhqhKVoa2/TW8EMndMNn+AJfYrCxVR+B0QhDOKZiJuZgobFFX4porMRabMAWJGIP9iMZ qcZm/RTO4iKu4Dpu4BfcM+L1h3iGl3gLXcbrCrnkJj0vCuFDlEAZlENFuVGvhuqojQbwRnO0lhv0 9uiCHghAXzjulHPvn7JIf6Uv0bP1aF2IGN0UK3QrXMRKPY9YpedDYRGrFxGrdVeUFGv1Uigr1umV RJxeGe7wFOv1OqgrNugN4SM26i3EJt0XbdFBxOv+6CY26z3RC33FFn0ghmAogsVWPQTjxTY9ApGY gSiRoM/DYsQgVmzX4xCPBGzHTrFDT8JBpOA4TotE/Twu4Spu4DYe4DGe4zWy8Q4WzqwVHyA/isAN pVAOleGBmqgHL/igJfzQEV3RE73RH4EYjlEYi3GYiCmYga+wAI775Mx/51TP4q/XQU1LV55jV55r V55zV557N15DN15LN15TN15bd15jd15rd15zD15/D9ahh/4Uj/EAt8WnrNWnrFlP1q6nfgHncVp8 xrp+xvp+xjp/znp/zroHsAcB7EUv9qSXvgaxojf71Jv96s2+faHPRhQiRR/2tQ/721cfixAEi37s fX/OQX/Ow5eciy85HwP0T+GPDmIg52cQ5yiQMzVY90ZDMYRzNkSvJYZy7oZy/oZxDodzHodzLkfo pUUQ5zSI8xqsf4jCYpSeX4zmLI/mXIdwxkN1JcZy3sN0Ddn6eP2tPoF7EK6/0CfpGXqE/kyfrD/R p+mP9Uj9kT4dM/SH+ix+nY05fHwOfz+Pz1vA5y/UHffIufdOaUGNaEGt8KVm+FI7fKkhvtQSX2qK L/XFlzrjS73xpe746qeNltSgltSiltSkltSmltSoltSqltSsltSuVtSwVtSyVtS0VtS3VtS5VtS7 1vo0TEU4wjAaIzAYXxptqJltqJ1tqKFtqKVtqKltqK9tqbNt9SZohPqoCQ9UQXnDjxrtR632o2b7 Ubv9qOF+1HI/arqfbkGOxY86345634663476344+0I5+0J6+0J7+0J4+0Z5+0Z6+0Z7+0UE/hH3Y jR3YYumor8carMBSLLR04g514i514k514m514o514r515t515v515h525j521vugN3paunBXu3Bn u3B3u3CHu3CX/bnT/rrjLjn33in16dX16dn16d316eH16eX16esN6O8N6PMN6PcN6PsN6P8NmAMa MA80ZC5oyHzQUJ+HKERiMiYgVHkxV3gxX3gxZ3gxb3gxd3gxf3gxh3gxjzRiLmnEfNJI90ETNEQd 1EA11Zi5pjHzTWPmnMbMO431QsgLF5jKm7nIm/nImznJW89EBh7hPm7hJ/yA73BONmHuasL81YQ5 rAnzWBPmsibMZ02Y1Xz0eGzEOqxCNBZhLqJkU+a9psx9TZn/mjIHNmUebMpc2JR+1oy+1oz+1ow+ 14x+14y+14z+14w+2Ix+2Jy+2Jz+2Jw+2Zx+2Zy+2Zwe2pxe2oKe2oLe2oIe24Je20J33Cvn3jvF gxnag1nag5nag9nagxnbg1nbg5n7E30awhGGMRiJIAzBAPSxVmeGr84sX52ZvjqzfXVm/OrM+tWZ +asz+9cgA9QgC9QgE9QgG9QgI9QgL9QgN3iSHzzJEZ7kCU9yhSf5wpOc4Une8CR31CR/1CSH1CSP 1CSX1CSf1CSn1NTPIQ0ncRSHsA+7zVpknFpknVpknlpkn1pkoFpkoVpkolrko9rkpNrkpdrkptrk p9rkqNrkqdrkqjrkqzrkrDrkrTrkrjrkrzrksDpksjpks7pktLpktbpktrrMmHX1aqiEsigNN7Me 82g95tJ6zKf1mFPrMbPWY3atxwxbn1m2PjNtfWbb+sy49Zl16+s34LhTzr13SlkybTmybTkybjmy bjkybzmybzkycDmycDkycTmycXkycnmycnkyc3myc3lydHnydHlydXnydQW9NErCFYWRDy4wIZBt q0BWr0Bmr0B2r0CGr0Cer0iur0i+r0jOr0jer0jur6ifwnEcwQFbJX0vdmIbNmEdVmEZFmGurbI+ C9MwCeMQgiAMwUBbFb0vAtAdXdAerdEc3raqegPURnVURQWUQQm4oZitml4QeWCHhI4sazWyYDUy YTWyoTsZ0Z2s6E5mdCc7upMh3cmS7mRKd/04UpGM/diDRO6M4z45994pH+snkIKDSMIuJCAecexz LGKwGPMQhUhEYDwcZ8G5905pIezIg4IohhIogwq25qIqqqM2GsDb1kw0R2u0Rxd0R4CtqeiLgRiE IQhCCMbZfMQkTMMszMUiLLM1EauwDhuwCduwE3tt3uIAjuA4TuMcLuEqbuCWrbG4g/t4jAy8QjaE vZEw4YJ8KAxXlLR7ibIoh0pwhyfqwsveUPjAF23RAf7oYW8gAtAPX2IQhiIYIRhvry8iEIkozMNi xCAWcYi31xObkYBdSMJBHMEJnLHXFc69d0o30RS+ZlfRFh3RFT3R2/QX/RGI4RiFMQg1u4iJmILp mI35ZmexFMuxGuuxGduxG/vMTuIQjuIk0nDB7Cgu4xp+wk3cRbrZQTxBJrKgWTsIw9pe2JAHBVAI RVHc2k6URnlUwSeoZfUT9dEYzdAKrdHO2lZ0Rnd8jj4YgMEIwhhrGxGGcERgKmZijrW1WIhorMRa bMRWayuRiD1Iwn4kI9XaUpzCWVzEFVzHTauvuIeHeIoMZCLL2kLo3BvHnXLuvVMGiSjMlQPFAixC NFZhnRwgNmIrErEX38gvxWGk4Bi+xTnZX3yHH/ATbuE+HuGZ7Ccy8ArZEKqfMFVf4YK8KAxXfKT6 iFL4GBXhjhqoo74QDdEELdBG9RYd4I9P0Qv9VC8xCMMwEqGYgHBMRqQKEFGYjyWIUZ+LWMQhHgnY oT4Tu5CEg0jBCdVTnMF5fI8f8bP6VNzEHfyKJ3iBN6qHyIHF7CFsyI38KIAicDO7i9Ioi0pwhyd3 qC684LhTzr13Sqg4iTRcwGVcw03cxT2k4yky8QY5lhBhGCHChtwogKJwQ2ljjCiPKnCHB2qiPhoZ o0VTtIQfOqEbPjNGiS/wJQIxGCMw2hgpwhCOqZiJOUawWIhorMRqrMUGbEEi9hhBYj+SkYpTOGuM EBdxBdfxizFc3MNDPMNLvDWGCV0OExIKuZAXheRQ8SFKoAwqyiGiGqqjFmqjAbzRHK3lYNEeXdAD AegrA0U/DMRQBCOE+zMeEXDcJ+feO6WN6CL80Rnd0JE/tUcPtHv/azfhh0/58ZnoKT7n51786C2+ QF/RR/TDQH4ehKGivxghvhTBYoAI4aOhGM/fTBKBIgKRYoiYhSjM47MXi2FiCWLEcBGLOL46XgSJ BOzkUb5GEg6KkSIFx8Uo8S1O4zwuidHiKm6IMeI27uABHuM5z+A13sHC+bPiA+RFfhSBG0qhHCrD wzJW1EQ9eMEHLeGHjuiKnuiN/gjEcIzCWEzEFMzAV1iApViBNdiALdiB3diHZL6v4z45994pxbiH xbiPH3IvP+TxPhSHLK48vivfx5Xv58r3dRXrLW48DzeejxvPy00stBTnORbnuRbnORfnuZfgNZTg tZTgNX0kRmI4Ai0leb0led0lef2lRDd0RUf4oaWlNGtVmjUrw9qVYQ3LsJYfs6Yfi/KWsqxvWda5 LOtdjnUvx/qXF/nwAayWCuxPBfapgsjGa1GRvavIHlYSv4rK7Gdl9rYye1yFva7Knldl76txBqpx Htw5Fx6cDw/OySecmeoiUdTg/NTgHHmK9YhDrKjJGavFeast5os6nL26nMF6YgYiESEacEaZd0RD wc5zYhpx6hpzQptwUptwin040cyBojmnvTnn35d70Ir70Fo47pAz/w3iXGnSE00xQ1q5z1butZX7 beWeW7nvVu69lftvpRZYqQk2aoONGmETndAerdFc2qkjduqJnbpip8bYqTW5qDm5qD25qEG5qEW5 qEku1CYXapQLtcqFuuVC/fqAOvYB9ewD6toH4gHu4RcjNzUvN7UvNzUwN7UwNzUxD7UxDzUyD7Uy DzUzD7UzDzU0D7U0LzU1L/U1L3U2L/U2H3U3H/U3n5iGqQhHmJGfGp2fWp2fmp2f+p2fOl6Ael6A ul5AdEUn+BkFqfkFqf0F6QEF6QWF6AmF6A2F6BOFRGWUR2m4GYXpJYXpKYXpLYXpMUXoNUWEhhxL EfpPEfpQUfpRUfpSUXpUUXpVMXpWMfEDHPfHufdNeUnWfknWfknWfkXWfkXWfkXWfkXWfkXWfk3W fk3Wfk3Ofk3Ofk3Ofk3OfkPOfkPOfkPOfkPOfkPOfkPOziJnZ5Gzs8jZWeTsLHL2W3L2WzL2W/17 nMcZnEAKDiJJZeu7kIB4xOG3d11/p8dgCeYjCpGYrHL0CQjFSAzDIKWJAeiHXvgU/uiANkpnLtKZ j3TmJJ15SWduEsxPQlRDRXyMj+CKQsgLF2VhDrMwj1mYyyzMZxaRiQw8kgbzm8EcZzDPGcx1BvOd ZM6TzHuSuU8yA0pxCN9IxVyomA8Vc6JiXlTMjYr50WSONJknTeG4T869b8oDsvYDsvYDsvYDcvYD cvav5OxfdRfYIaEjy/orWTudrJ1O1k4na6eTtdPJ2ulk7XSy9kOy9kOy9kNy9kNy9kNy9kNy9iNy 9iNy9iN9I9ZiJaKtj/WFmIOZmIZwhFmf6GMQhCEYgD74HN3RGe2sT/VWaIlmaIz6qIVPUMX6TC+P 0iiOoiiAPNYM3Q4bDGjIMjP0TDwxn+vpuIubuIbL5gv9AtJwGidxFIewz8zUd2M7NmM9VmM592Ip 5mMOZmM6pmAiQjEKwxGI/nDcKefeN+Un/QRScBBJ+Bq7kIB4+w09DrGIwWLMQxQiEWH/WR+PEARj KAIxCP0QYL+p94A/OqAtfOEDL/svel14wh2VUBZlUBKu9lt6YeSDC0wIZNtu6a+Qgce4b7ut38IN XMUlnMNpHLfd0Y/gAPZiJ7Zhk+2uvg6rsAyLMBezMM12T5+EcQhBEIZgIPra7usB6I4uaI/WaM75 90YD1EZ1OO6Ic++b8kbkQQEURDGUsL0WZVABVVEdtW2vRAN4ozla216K9uiC7ghAX1umGIghCEII xmESptleiFmYi0VYhlW252It1mETtmGnLUPsxQEcwXGctj0T53AJV3EDt2xPxX38r/bOA87K6ty7 M2fv/Z5zRtRobLkYNSiCXpVojF0UEcSCCgpIkQEcDfaCRgy22DDSe5NepIgo2LAQBLuxXGOPGiVG xAYGwYLItwaTmERucr+cZESzkt9yGJh533fW/9l7P88Ah6WwHD6G1cVluVzFslweasEmsAXUhu2g bgWdDDSAPWFfaFjxfq4xNIPm0AJaQ7uK93KVcDKcBmdBt4p3c92hB1wCV0BP6A0DKt7JDYVRMA4m w3SYVfF27la4A+bCPFgAD8PjUNrrpmwSWkKb/HdCB+gMp+Q3DqfC6XAOXAAXwWX5jcJVcC30gj75 DcNAGA7Xw/h8rTAFZsBNcHN+g3Ab3AW/zFeE++EReAL+J18Mv4YX4BVYBIvh3XwhLIOVsCqfD2WF fIhQhI0LWfgubAW14ftQp5BCPdgFdi/EsBfsDwdDI2hSCOEIOAaOh7bQEU4q5EJXOBXOgPMK5eFC 6AGXw9WFsnAd9IOBMBhGFNbkxsBEmAozC5/nZsMdcDfML6zOPQCPwpPwTOGz3IvwKiyCN+EteA8+ gJWFVblVUF5clUtQvY5Ke92UvcIBcGD6cWgETeHItGc4FlpBa2gHlelHoQpOTXuEs+Ac6Abd0+7h Elie6oePYTXksvohn9ULRagF34Etsh1Dbdg2qxt2gJ2gQbZD+BHsk20fDoSD4BA4LKsTjoIW0Bra ZT8I7aETnJxtF06Ds+H8bNvwU7gILoUrs21CT+idfT8MhEEwDEZlW4dxMBmmw6ysdrgZboW5MC/7 r7AQHobHs++Fp+F5eDnbKrwOb8I72ZZhGayAT7MtwhoI+c1DESpgI9gUtoSt85uFOlAX6ue/G3aG BrAn7JvfNDSExtCMNVS9lkp73ZRm4Sr4BfQNh4dBMBxGwwS4AW6EW+A2uAvmwwPwCDwBv4YX4BVY BIvhbXgXPoCV8CmsgRibhSJsBN+FrWBrqBMPC/Xgv2EX+CH8GPaPTcNBcCgcDkfDcdA6NgknwInQ BX4SDw1nwLnw08jUDT3gcrgarouHhH4wGEbERmEMTIQb4sHhRpgNd8Dd8aAwHx6IDcOj8CT8Oh4Y noEX4VX4XTwgvAXvxf3DUvgDfASfxf1CedovZFCEDeA7ad+wOfxX2idsA9vDTmnvsBvswbqpXj+l /N2lC8KnzNermK8/y50Kp0DnsDp3YvicOftzZuw1ueNCWWgJR4dyEsiFxiGEg0IMDWG/kMJeIQs/ hh+GfNgtFMJ/h2LYEX4QNgjbhlpha9gqbBS2hE3DxmHDsAk/swkf+V2utDl32JI7bcVTfC98kqsd PoYVue+HD3PbhOW5bcMHTO7LctuHpbm6UA924v3/5ud35dcb8HEN+Pgf8nl78Pl78BX8iOvtyRP/ mOvvzZPtw7324Z77ce/9eIb9ufP+PM8BPNuBPGdDnvcgOJhnP3idP/fD0Cj8CNiluMIh/Gpj/tuY /x+Kk0Nx0wRHTUIraBOahg7QGU6B08Nh4Ww4By6An7FWqtdNKTPCmmxubjV8Ciuyu3LL4B14E17P 7s69DM/Ds/B0dk/ucXgYFsK87N7cXLgVZq1lXm46TIZxMAqGwcDsl7ne8AvoCVfCpdn83EVwPpyd 3Zc7DU6GKugE7bMFzGoLmNUWMKstZFZbyKy2MHcQHAj7ZPczr93PrHY/s9r9zGr3M6s9wKz2ALPa A8xqDzKrPcis9iCz2oPMag/lasW3mKeXME8vYZZewiz9du5jWAkfhHeYp99hnn439wYsglfCe8zT 7+d+DU/DE1TMI/AAVTMffgl3UT23wS3hD7lZcCOVNAUmUE3jYDQVNRwGhZW5AdAXfhE+yl1FlV0J l8HPqLbq9VPa66ZM5iyezJk8JXcLzISpMBHGwIjCDbnB0A+ug2sKU3OXQw+4EM6DMwvTcl3hJOgI bQvTc8dDSzgGjoAmcHBhRm5/2At2h12gHmwPdQo35r4PW8F3YWMoFmbmIpTBqvzM3Mr8Tbll8C4s hkX5WblX4AX4NTyRvzn3KDwC98Mv4a78Lbnb4GaYAVNgPIyF62F4fnZuIPSBa+Gq/JzcZXARXADn 5G/NnQ6nQGfokL8t1wZaQnM4Kn97rhk0hoawb/6O3J7QAHaGurA91IGt83fmtoRNYSMo5ufmAlSv pdJeN2UI/fEQ+uSh9MtD6ZuH0j8PzXWBSmhXMYzeehg99jB67WH03MPovYfRgw+nFx9OTz6c3nw4 PfrwXD2oC9tBbdgCNqkYQV8/gv5+BH3+CPr9EfT9I+n/RzIHjMy9B0vgDXgNflMcxcwwitlhFDPE KGaJUcwU1zNbXM+McX3uVpgDN8G04mjmkNHMJKOZTUYzo4xmVhnNzDKG2WUMM8yY3CVwMXSH8+BM OLU4lrlnLPPPWOagscxDY5mLxjIfjcs1g6bQCA6AvWGP4nhmqvHMVuOZscYza41n5prA7DWBOWwC feQE+smJ9JUT6S8n0mdOpN+cSN85if5zEr3opNzr8Cq8CM+wZp6ER+EBmA/Va6m0100ZxHwyKLcQ 5sFcuBVmVQxmphnMbDOYGWcws85gZp7BzD5DmIGGMAsNYSYakquug1LmmlQ8KlTAxrAZfA+2ge2L R4b6sBPsCnvA3nBA8YjQCJrCkXBs8fDQClpDW6iEqmKzcCqcCedBd7i4eFj4OVwN10Av6F9sGobA SBgLk2Aa3ARz4PZik3An3AsL4CH4VfHQ8BQ8B7+B1+CNYuOwBN6GpbAcPobVxUNCruKQkIdasAls AbUrGoXtoC7sDA1gz4qDw77QEBpDM2gOLaA1nADtKg4KlXAynAZnQTfoXtEwXAJXQE/oDQNgUMWB YSiMgnEwGabDrIoDwq0wF+bBAngYHodS9vU2+VOYTU9mNj2Z2fRk5tKTwxlwTr6K2bSK2bSK2fQk ZtOTQk+4Nt+F2bQLs2kXZtPOzKadmU07h4n5TsynnZhPOzGbVjKbVjKbVjKbVob5cD88ku/IfNqR 2bQjs+mJzKYnhldhUb4D82kH5tMOzKftmU/bM5+2D59DWaEdM2o7ZtR2zKjtmFHbMqO2ZT5tG7aB OlCvcAIz6gnMqCcwo7ZhRm3DjNqG+bQN82lr5tPWzKetmU9bMZ+2Yj5txXzaitn0eGbT45lNj2c2 PY7Z9Dhm0+PCtXAd9IPBhZbMpi3DGJgIUwstwky4CWbDHXB34dgwHx6ARwvHhCfhGXgRXi0cHRbB W/AefFBoHlbCKvgcyovNQ4JSvkf0VBoQnk39w3PwUuoXfpv6hkXwRuoTlqTe4X1Ymnoxe/Zi9uwV PkvXMX9ex/z5C+bPa0MF1Mp6Mn/2ZP68JmwFtbOrmUGvZga9KtSDnaBBdiVz6BVhb9gHDsx+zhx6 OXPo5cyhlzGHXsYcemloA+2hU3YJc+jFoSucBmdnPZhFezCH/iz8DC6FK7OLmEW7M4t2Zxbtzhx6 IXPohcyhP2UO/Slz6AXMoReEOdn5zKHnM4d2Yw7txhx6HnPoecyh5zGHnsscei5z6DnhFXgd3oR3 srOZRc8Oy7OzmEfPYh49i3n0TObRM5lHz2AePYN59Azm0TOYR09nHj09/ADqQN38acyjpzGPnso8 eirzaFfm0a7Mo12ZR3/CPPqT0JK1U71+SplrTkifhFbp43Bs+igcmVaGZmlFaAqHpOWhERyQ/gAf MD8tC3ulpcxS74fdYbf0btglvcOM9Xaon5aEHdJbzFyLww/Sm8xfvwtbp0XMYq+FrdKrYYv0MrzE fPYCPB82S8/B0/z4f+Apfu0J+BUf+yif8zCf+yDXuB8Whu1g+zQ/7Jjmca97w67pbu59N88wl2e5 k2e6g2e7PeyfbuM5bw0HpTk89+zQJN3C13FzOCLN4uuaxdc3k69zRmgN7dL0cGKaFiqhKt0QTk1T whlpcjgrTQrd0sTQPU0IPdL4cAlckcaFq9LY0DONCb2hTxod+sOQNCqMSCPD2DQiTErDw9Q0LEyD mTA7DQ1z0pBwJ9yTBod5aVC4Dx5MA8OjrJXHoHrN/DO53bM2tw7Vf4c97pV+HvdIl8XdYbd0SdwV dko94o7porh96h63SxfEbdL50C1unc6N/5XOiVulM+MW6XQ4LW6euq5ls/QTOIkfd+bnK+FEPq49 H9+Wz2vD57eKP0jHcc2WcYfUItZPx3CfY+IuqTn3bc79j+Q5juR5Do97wwHpsHhIahqbpkNjMzgy NY7HpkaxVTo4ngDt0kGxMjWMnaEqHRi7pgPiqWn/eFbaL56T9onnpr14u2c8O+3Bz/0wnpF2i6en XfiYnfnY+vEnacd4StohnpzqwHZcYxuozY+/B1vwa5vzMd/lYzfhczaGjfj8DbnOBlyvCAWunece iXsF3pbzc2uog9WhK1Slz0LntIr6WEWtfBqq10gp3/sZlt0XB2bzY29gPozMh/HSbF78GVyU3RvP h7Oze+Jp0BVOhk7Z3bF9dldsA62hRTY3HpXdGQ+DQ7I74oGwT3Z73Bt+BLtlt8WdsltjPdgBts3m xNrZ7LgVbJ7dEr8DtbKbYwXkIZfNiqvTTfEz+DjNjMthaboxvg9L0oz4RpoeF8Fv4aU0LT6XpsZn 4al0Q3wsTYmPwoNwX5oc56VJ8R64M02Mc2B2mhBnpvFxWhoXp8KkNDaOTWPiiDQ6DoH+aVTsA73T yNgzjYhXpeHxCrgkDYs9oHsaGrulIWQyiMwGkd9A8h1AzfSLJ0K71De2Tn2op97UVS/q6xfxCGia ro1NUs/YKF0TD0pXU4dXxf3TlbF6rZSS316F1+PuhdfiLlAP6hR+G7eB78NW8N3Cq3FjKEIsvBLL 4PP8K3EVrMy/zPVeju/C4vxv4iJ4FV6BF+DX+ZfiE/AI3J9/Mc6HX8JdcFv+hXgzzIAp+efjRBgP 18Pw/HNxIPTJPxuvhZ5wFVwGF+WfiRfAOXBG/tfxdDgFOuefjh2gDbTM/09sDs3yT8XG0BD2zT8Z 94QGsHP+iVgX6uQfjz+ArWFL2DT/q7gRVOQfi0UIsCZ7NH4KK7JH4nJYBu/Am9nD8XV4BV6G57OH 4tPwePZgfBgWZg/EeTA3uz/emi2Mc2AWTIfJ2YI4DkaxdqrXTyk95tLih/FtWAJvwGvwG3gOnoJf wUPF5XEB3At3wu0wp/iHeBNMg0kwFkYWP4hDoD/0gmvgavh5cVm8GLrDeXBmcWk8FaqgEtpC6+L7 sRUcC0dCU2gEB8DexffiHrAr7AT1YXvYpvhu/B5sBhtDRfGdmKAcPi+8E1fBysLb8QN4D96CRYUl 8VV4EZ6BJwtvxUfhAZgPd8MdhcVxNtwEM2EqTCy8GcfACBgM/Qq/j9fBtXANXF54I/aAC+E8OLPw u9gVToKOhUWxLRwPx8AR0IR1czDsD9Vr6J/JsGpthj9k5vwsPgwLYR7MrVgVb4VZMB0mwzgYBUNh EAyo+DT2hp5wBVwC3aFbxSfxLDgNToZKaAcnVHwcW0MLaA7NoDE0rPgo7gt7QgPYGerCdhUrY23Y AjaBWpCvWBFzsLq4In4My6G6/kr5vsnKQntybk/mHci+AzXQgVroQE10oDY6UCMdqJUO1MyJ1M+J 1NGJ1NOJcT84ABpBUzgSji12pAY7Uo8dqcuO1GdH6rQj9dqRuu1I/Xakjiup50pqu5Iar6TWK6n5 Smq/kjVQyVqoZE1UsjYqWSOVrJdK1k0l66cT66gT66kT66oT66sT66wT660T664T668TLjrhpDNu OsfPYDXkKjrjrTP+OuORHgRqw3ZQF3au6IL3LvjvQg5dyKMLuXQhny7k1IW8upBbFzLsQpYnkelJ ZHsSGZ8Uz4Vu0B0ugSugJ/SGATAURlVUUTtV1FAVtVRFTVVRW1XUWBW1VhUXwMPwOJT051XyR7K3 HsUeexR77VHsuUex9zZnD27OXtycPbl5bA1toAN0zh/Nvn00+/fR7OVHs6cfw95+DHv8MfFKuAqu hT75YzkLjuVMOJaz4VjOiBacFy04N1pwfrSIc+A2uCvfkrOlJedMS86blpw7LTl/juMcOo7z6DjO puM4o47jrDqOZz+Os+s4zrDjOc+O51w7nvPteM654znvWnHuteL8axW3hTpQD3aB3QutWeutWfOt Wfut2QNasxe0YU9ow97Qhj2iTewAHeEk6Fo4IZ4B58GF0AMuh6vhukJb9qC27EVt2ZPasje1ZY9q y17Vlj2rLftXW/axtuxn7djX2rG/tWOfa8d+1459rx37Xzv2wfbsh+3ZF9uzP7Znn2wfq9dTSX+H jR53Gj3uVJhEnzspNYnj6HPHpkPiGPrc6+lxx9DbjqW3nURvewNMpb+dCbPhTvrce+A+eBAeg6fg WXgJfgtvwBJ4H5bzOR/Dashl+9O/7U8fdwD93AH0dQfELaA2bJsdSO93IH3ggbEB/ChrSI/YkF6x IT3jQfSOB9FDHkQveRA95cH0lwfTZx5Mv3kwvWcjetBG9KKNYne4CC7NDqFXPYSe9RB618b0sI05 ixvHkdmhnMuHcj4fyjl9KOd1E87tJpzhTTjLm8R7s6ac600535tyzjflvG/Kud+U8/8w+oDD4mvw OryZNaNPaEa/0IzeoRk9xOH0EofTUxweMyjCRvkj6DmOoPc4gh7kSPqRI+lLjqQ/OTJWr6dScmyW v5r1d3VsBA1h3/xVrM2rWKNXcf0r405QF+rkr+DeV/AMP4+bwaawUf5ynu9ynvUynvmy+Dl8ml3K 13EpX8+lfF2XxLfhTXg9u5iv+2K+/h546IGPn+HlZ/H+7CIcXYSri/DWHX/d42yYlV2I0wtx+1Mc X4DrC/B+Pv7Pj/2zbmTRjUzOI5vz4uXZueR0LnmdS3bnxHPh7Oxs8jybXM+KXbIzyfhM6uLkuD1s m1VRKyfFLWHzrAv10zluCLWyTtRVpxiySmqsklrrGD9hDvwYlqcOcRnz4PupHTXZNi6GN+C3zIav wkupNfNBK+q3FXV8XHwCHoOHmBUfhPvSsXE+8+I96eg4l3nxTpjDvDgbbmItVa+nUr7/9FFhDGt6 DGt7DGt8DGt9DGt+NGt/NHvAaPaC0ewJo9kbRsdH4IHC9ewX17NvXM/+cT37yCj2k1HsK6PYX0bF sTAGRhRGsveMZA8ayV40gh5oBHvTCPaoEexVw9mzhtMDDWcPG85eNow9bRj72zD2uWHxWDgGjigM ZQ8cyl44lD1xKHvjEPbIIeyVQ9gzB7N3DmYfHcx+Oph9dRD76yD22UHstwPZdwey/w5kHx7A1zyA fXlAfAsWwyJ4Jd+fvbs/e3h/9vJ+7On92Nv7scf3Za/vy57fl/2/D+dAH86D3pwLvTkfenNO9OK8 6BX7Qh+4Nn8dZ8l1nCvXcb5cxznzi9gNzoHT89dyBl3LWXQtZ1LP2A7aQMv8NZxZ18TqNVTKGpxX MZNzdibn7UzO3ZmcvzM5h2dyHt/IuXwj5/ONcQgMgN7QE66ASypmcKbP4GyfwTk/g/N+Buf+DM7/ GfQB0+kHptMXTI9HQ3NoBo2hIewLe0ID2LliGj3GNHqNafQc0+g9ptGDTKMXmRo3gDzkYHVxKj3L VHqXqfQwN9DL3EBPcwO9zQ30ODfQ69xAzzOF3mcKPdAUeqEp9ERT6I2m0CNNpleaTM80md5pMj3U ZHqpSfRUk+JA6A+94Br4OVxcnEgfNpF+bCJ92UT6s4n0aRPp1ybG9tC2OIEebgK93AR6ugn0dhPo 8cbT642n7xtP/zeePnA8/eC4WA+2h23ge7AZbFwcSw85ll5yLD3lWHrLMbF6Df0zOdZam2OkP7+J Hmkm/fnMWJ1paf3uK2EVlBdfCQkqYGPYrPhy+B5sA9tDfdgV9oC9YT84ABpBUzgSji3+JrSCtlAJ VXAqnAnnQXe4uPhS+DlcA72gPwyBkTAWJsG04ovhJpgDd8K9sAAegl/BU/Ac/Kb4QngN3oAlsBSW w8fwGayGXMULIQ+1YJOK58MWUBu2g7qwMzSAPWFfaAiNoVnFc6E5tIDW0A4q4WQ4Dc6Cc6EbdIdL 4AroCb1hAAyFURXPhnEwGabDLLgV5sI8WAAPw+NQWr/7fmiQfy/sCftCQ2icfzc0g+bQElrn3wlt oAN0hlPg9Pzb4Ry4AC6Cy+DK/JJwFVwLfWAgDIfrYXz+rTAFZsDNMAdug7vyi8Mv4X54BJ6AX+ff DC/AK7AIFsO7+d+HZbASVkFZ4fchFt4IRdgYvgtbwfdh28LvQh2oB7vA7rAX7A8HQxNg9g3MwIFZ ODAThw7AfBxOgq6F18MZcB5cCD3gcrgariu8FvrBYBgBY2AiTC38NsyE2XAH3A3z4QF4tPBqeBKe gRfhVVgEb8F78AHrqHo9ldbvLg3T0gdhKkxKy+HDMC6tCGPTyjAmfRSuT5/wdhXvr+LXPgs3pNV8 7OowM30eZsOdcA/cBw+mNeExeAqehZfgt/z8G7AE3ofl8DGshly2OuShAmrBd2CL7LNQG7aFHWCn bFVoAD+CfeBAOCT7NBwGR0ELaJ19EtpDJzg5+zicBmfD+dlHoTtcBJfCldnK0BN6w0AYlq0II2EU jIPJMD37MMyCW2Eu3JstD/NgITwMj2d/CE/D8/AyvJZ9EF6HN+EdWJYtCyvgU1gDIb80ZFCEjWBT 2BK2Zv3UgbqwM1Svp9L63dmsv9mhUX4Oa3EOa3IOa/NW1uitXP+2sBPUhTr527n37TzDHWEz2BQ2 gmL+Tp71Tp55bvgcPoUV2V18PXfxdd0d3oY34fXsHr7ue/j678XDvfi4Fy/zwv2wEOZlv8TbfPzN D7NhVnYfTu/D7QIcL8T1QrwvxP/9oT/0zh4gkwfI5sFwOVyaPUReD5Hdw+FcODt7hDwfIddHQxfo BDtkz4TtYdvsWWrlubAlbA7fyZ4PG2bsvZDPXgwhe4kae4la+034JL1M3b1M/b0SlqVXqcVXqcnf hsXpNerzNep0UXgVXoLn0u+o3zeo49+HJ9Kb1PSb4aH0FvX9FnW+JMyHe9I7YS7cmd4Nc9L7rIX3 w02sper1VFq/O4I1PYK1PYI1PpK1PpI1P5K1P5I9YBR7wSj2hFHsDaPCI0C/y35xPfvG9ewf17OP jGY/Gc2+Mpr9ZXQYC2NgRGEMe88Y9qAx7EVjwjVweWEse9RY9qqx7Fljw5mFcexh49jLxrGnjWN/ G88+Nz4cC8fAEYUJ7IET2AsnsCdOYG+cyB45kb1yInvmJPbOSeyjk9hPJ7GvTmJ/ncw+O5n9djL7 7mT23ynsw1PYj6ewL98Q3oLFsAheyU9l757KHj6VvXwae/o09vZp7PHT2euns+dPZ/+fzjkwg/Ng BufCDM6HGzknbuS8mBn6Qh+4Fq7K38S5chPny02cM7NCNzgHTs/fzBl0M2fRzZxJN4d2+Vs4n27h rLqFM2t2qF5DpfW7vThne3He9uLc7cX524tzuBfncS/O5V6cz73CEBhQ0Zszuzdnd2/O8N6c5b05 03tztvfmnO/Ded+Hc78P538f+oA+9AN96Av6hKMr+tIj9KVX6EvP0JfeoS89RF96ib70FH3pLfrR Y/Sj1+hHz9GP3qMfPUg/epH+YQPIQw5WF/vTs/Snd+lPDzOAXmYAPc0AepsB9DgD6HUG0PMMoPcZ QA80gF5oID3RQHqjgfRIA+mVBtIzDaJ3GkQPNYheahA91aAwEPpDr+Jg+q3B9F2D6b8G04cNph8b Ql82hP5sCH3aEPq1IaE9tC0OpYcbSi83lJ5uKL3dUHq8YfR6w+j7htH/DaMPHEY/OCzUg+1hm+Jw esXh9IzD6R2H00MOp5ccQU85gt5yRKheQ6X1u9fRI/UKC6E60390rQJvP81lZRvwdk1Z2R///FO2 9teX8Xl/ea/HCttsUM6PC2vvlSsbmPaI0/88I2f/p+f922tM5xoDS7zGytyWacOwWyrlGhuGLdPK XGnXWF98LC6fnq0pX5CVco01XGNxidfQhz708c3z0SK3KHXNfVrSXtiVa7Qo8RrWh/XxTfBR/Sr0 s8p75ku5xqy1r2Rf2jVcL64X14u5uG5dt65b163znD7Wp3VrLvr4JvjwfHG+dd26bl233651ax/k erE+rA/3U8996/TfX6euF+cG69Q6tU6tD+vD76+bi7mYi7mYi7mYi7mYi7mYi7mYi7mYi7mYi7n4 51D0oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33ow9fZtE71 4Z8/9c+fmou5mIu5mIu5mIu5mIu5mIu5mIu5mIu5mIvfL9SHPvShD33oQx/60Ic+9KEPfehDH/rQ hz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+ 9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfejD1y02F3MxF3PRhz708a/yYS76 0Ic+vul9kLnoQx/60Ic+9PHv91GVVoQeqVZJ1+jBNapKvMbK3JZpw7BbKuUaG4Yt08pcaddYX3Jp kVuUuuY+Lelr6co1WpR4DX1Yp9apPvz+uvVhfVgf/6n1YS6uW+vD+rA+rA996EMf+tCHPvShD33o Qx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf +tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996MPXUTQXczEXczEXczEXczEXczEXczEXczEX czEXczEXczEXczEXczEXc1l/cvHfFfX3b78JPqrSrrFHOrTEfy9611hV4jXMRR/60Ic+9KEPfehD H/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/6 0Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33o41/jY315fTpz0Yc+9KEPffw7fPh6n/rQhz70 8e2aG8zF1xvXhz70oQ/PfevD+rA+rA/rQx+uF+vD+rA+rA/rw/qwPvw+rrmYi7mYi3OlPr4uH/57 nuZiLvrw3DcXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXc/H3PfShD33oQx/60Ic+9KEP fehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33o Qx/60Ic+/Huv/r1XczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEX czEXczEXczEXczEXczEXczEXczEX/xy9PvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCH PvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPr5tPhaXT8/WlC/ISrnGGq6xuMRrWB/r p4/15e+LmYt/j+/vXaMq7Rp7pENLukYPrlFV4jX0oQ/3D3NxX9fHv2cfWxF6pFolrpcVoarEa1gf +tCHPvShD33oQx/60Ic+/L6DuZiLuZiLuZiLuZiLuZiLuZiLuThn60Mf+tCHPvShD33oQx/60Ic+ 9KEPfehDH/rQhz70oQ996EMf+tCHv49sLuZiLuaiD+vUOtWHPtzH3MesU33oQx/60Ic+9KEPfehD H/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/6 0Ic+vp3/nvj68fcrzUUf1qm5mIv7h3VqLuZiLuZiLuZiLr6Oka9jZJ3WVJ2uCD1SrRLrdEWoKvEa 7uuuF3Nx3Vof1of1YX3Yn+rjCx9Lw/SUL9HH0jCwxGu4j1kf1ofnnPXxbasPv09nfVgf5mIuzi/6 8PvJfp/fXMzFXMzFXMzFXMzFXMzFXMzFXMzFXMzFXMzFXP6zc/H72taHubhurQ/rw/rQh+vF+rA+ rA/rw1xct65b68P6sD6sD+tDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70 oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEP fehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33o Qx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf +tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQ hz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+ 9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+vl4fVWlF6JFqlfgcK0JVidcYmJaG6Slf Yi5Lw8ASr6EPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf +tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQ hz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+ 9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvSh D33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ99 6EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehD H/rQhz70oQ996EMf+tCHPvShD33oQx815WNlriJsGOqEUq6xYagIK3OlXcP6sD6sD+vD+vjX1Ie5 uG6tD+vD+rA+rA99uF6sD+vDXFy31ofr1lzMxVzMxVzMxVzMxVzMxVzMxVzMxVzMxVzMxVzMxVzM xd/P1sf648PfnzMXczEXz9t/VX3sGnukQ0v0sWusKvEa1sf62n/sEaenw0vMZY84sMRrWB/Wh/Xh /OJ5++06b83Ffcz6sD4858zFdWt92J/6/UJz0Yf7qbmYi7mYi7mYi7nYB1mn5mIu7h/WqXVqnepD H/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/6 0Ic+9KEPfehDH/rQhz58HSNzsU71oQ/3MXPRh3VqLuZiLu7r+tCHPvShD33oQx/60Ic+9KEPfehD H/rQhz70oQ996EMf+tCHPvTh7yObi7mYi7mYi7mYi7mYi7mYi7mYi3O2PvShD33oQx/60Ic+9KGP b86/471r7JEOLXGe2zVWlXgN60Mfft9BH/rQh/v6f46PFrmGua65VrlSrtGVa7Qo8RrrSy760Mff u8bi8gvL15T3LS/lGmu4xuISr2F96EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf +tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996GN99uHfJzQXczEXczEXczEXczEXczEXczEX czEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXczEXc/HP0etDH/rQhz70 oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEP fehDH/rQhz70oQ99+Pde/Xuv5mIu5mIu5mIu5mIu5mIu5mIu5mIu5mIu5mIu5mIu5mIu/r7H+uej Kq0IPVKtkr6WHlyjqsRrmIu5uH/ow3Pfc99czMVc3NetD+vD+rA+rA/rQx+uF+vD+rA+rA/rw/qw PuzH9KEPffh9XM85fehDH/r49vpYXH5h+ZryvuWlXGMN11hc4jX0oQ996MO54V8zN5iLPvShD33o Qx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf +tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPv4dPvz3PK3Tb4IPX3d0/czF1z03 F3MxF3MxF3MxF3MxF3MxF3MxF3MxF3MxF3MxF3MxF3MxF3MxF3//Vh/60Ic+9KEPfehDH/rQhz70 oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEP fehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Me/woevx2Z9WB++jqK5uG6tD+vjP7U+9LF++vDf 0bRO//6/B7xr7JEOLfHfA941VpV4DevUOv171xhePrtsVvnDZaVcYxbXGF7iNfShD33oQx/fLh/r y3xrLvrQhz6+6T7MRR/60Mc33Ye/72Eu5mIu7uv60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvSh D33oQx/60Ic+9KEPfehDH/rQhz70oQ996EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ99 6EMf+tCHPvShD33oQx/60Ic+9KEPfehDH/rQhz70oQ99+LrF5mIu5mIu5mIu5mIu5mIu5mIu5mIu 5mIu5mIu+tDHv8pHi1zDXNdcq1wp1+jKNVqUeA1z0Yc+9KEPfehDH/rQhz70oQ996EMf+tCHPvSh D33oQx/60Ic+9KEPfehDH/rQhz70oQ///Kl//tRczMVczMVczMVczMVczMVczMVczMVczMVc/H7h 1+PD+lg/68M6tU6tU+vUOrU+/h314etM2K9bH+5jrhfXi+vFvtA+yHXrvu560Yf7h6+j+O3Lxf1D H65b6/Sb7sP6cM52vbherA/rw/rQh+vF+tDH+utjZa4ibBjqhFKusWGoCCtzpV2jJn1Uf/ynuaws V1b9vzV/XOdp7a8v4/P+8h7L8s9VNOez/nSP+uVbx6crto5/+Tnrukfiba68nP+u64mrf3Wz3C2F AWlrfrQqN27N2kcp+7D6E8pjruw7x5965sndyj688GB+4vhixR5vzv/wwqVQvvbjfvjnWaD6SsXq LyRX5D8/SKms5cn1u+1UVn3tv/eMy/7o50/Puts/eNZr44ZlXz7r1eHq8L8+64/+7896+JnVz1p9 7f/rs/51dmV/tUcv4/P/Xn0ckd4o2zm9+Q/nqOrP/uyLG/Dfv66OP310bp3V8qc7fof3dgjZ2rv9 d/qgrJgW8+PfrH3/yyfI/c1X/dUnWLNmzZ+fIPz5a1y3g3V/7Rut/drTOp/kH9Xw33O5JF5T9gn8 o2usy2X2v7hMf9flJ2vv2KOsdqp+O+CP71/zNy6z/y+X2T/lcl1PUorL49O08vppRnnNuay+W/10 e3mWbuTt2PIv3v/TE9Sky3U9SSkuX4+HlX8CNVmX1Xc8oLx2qn7bsvyTv3qCmq3Lrz5JKS47pjNy 9dNZuZqsy7O440W5LJ3N25NyX7z/pyeo2br86pOU4vLxuHGuPG1cgy6r71aeUq7O2re1c1+8v/HX 4HJdT1JaXf441E37hZpzWX23HVOTENOBYYfUYO3dv3yCmnS5ricpxeUpKUv1Uy7V5BrPpXppQ+5b nnZKH8fq9798gppd4199klJczo3tuVbnGnRZfbcstearOCmldHr64v3OX4PLdT1JKS5bpydS3fR4 qsk1/jh3fCHF9Ku0Y1qQvnj/8fR1rPGvPkkpLmfFHbPP4y5Zzbmsvtua+INs27RbtjruvfbuXz5B Tbpc15OU4rJ96p/VTwOzmtwvB3LH0VmWBvG2Z/bF+wOzr2O//OqTlOLysbg0K0/Ls5rsiZZzx8VZ nfRhVpY+z754f3n2dfREX32SUlx2Tsfn60JN7pfVd6zMx7VvD8/X/asnqNn98qtPUorLO+LLuY/i SzXYq1ff7aP4ZG6r9CJvf5/74v2XvoZefV1PUorLsmLtuKDw/VhzLqvvtqBQP44vbMPbTeMX7//p CWrS5bqepBSXq3O1Y/tQuwZdVt+tfdgkXrz2bb34xfu1vwaX63qS0r7n9mk4Ia2qgRly07Uu82XV dzs+ZXGftDS0Tx9w98/WPsGXT1GTPtf1NKX4bJsOjq2h5mqz+m5t05Fxr3REPC7ttfbuXz5BTbpc 15OU4nJ+9nD8MHu8Bl1W321FtiBunn8yLs+eX3v3L5+gJl2u60lKcbkw3poP6Y4a7IvW3i3dmN8h zeXOC9be/csnqEmX63qSUlxOz34a3s3OrsHvu1Xf7Z2sKmyUPyO8l/1s7d2/fIKadLmuJynFZbf8 dXGH/FU1uMar77Z9vl8M+Su480Vr7/7lE9Sky3U9SSkuH8qaxLL8ETXosvpu5fmDYp1887gma7X2 7l8+QU26XNeTlLRfZn8IKb+sBtd49d1S/vdhx/xS3n4Wvnh/2dewxtf1JCV9bz0/K9TP316DLqvv tnP+vlDMzw318jPW3v3LJ6jR7xWt40n+kYcv7lP25//97Z/t+IunLFv3n8uovgqrs2zHbMe1TxvW Xuf/AYboL3FAyAkA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0196.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Root Locus of the LTI System
– Zoomed View

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0196_image054.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+3dDZyOZcI28Os6z/O6rvu+iSHVY31kLWnykWZnx3pESNRjSRoiIa2kJoRCtXaS byk7v3rnnZSQlKxfVl4SUrPWQ6h8pmZnbT4q8pGlScJ6j3sktY9lOPw877vPsfu7KnL853Dc53W7 5x7Vpvf+c6LnWfx/VWJ1bILv4X/PZvpeHN+Zud15kXcs+V3FfzyI7xt6/FvHjnn+d3/+4XXi+7wf /L3/d/937EfXsR9933nQ/+Hn/v/bt3/4fQ5XukmeE8/7hRfij1eEV3gGj3fye6p6Af5o/OSjn/yr UiZ5npJ/Vdq8G1uRSP5V5Cd/ZITrUrc6tipx4keE36eMb777EUeM/93HT37cuvgRMfz5WxOeqGWO f7/57kcX9zQnfrT9/kcnPf/7H+2K//4+pI5/3OTfPf4jA+/HH8989yPddz+7461XxdYnfPx1Cr5V w4Zep2MTj3U6diD2Qanklfzr49cPjWSbyvjzYVP5h7MWf7hbHx744N19vMFN8dd/K5O44bN3vhr8 Ja7jXep7P2xdyz927FQ/1+C7pj/+OSd/xImPfqpU+F0q+CdLnVRPPkI/XiY47TJfe7ujr7223pRE 8kr+9fHrx8uE/+VnmPxoxQ+LOfXjevxjh//k53rqTmXwrZo2OGWnH/5sT/g/7HPi4/g/OnXhaTeI FX88893H+yL68c/1v36M0xvrYawljYUwFpDGVBiTSWMMjFGk0Q9GH9LoCCOTNBrDaEQaNWBUJ41S MOKksT/82tsXckYBjI9IIx/G26QxA8bLpDEBxpOkMQjGg6TRFUYX0mgBozlp1IaRShrlYaSQxqHg a+9gwBmfwNhMGsthLCON12DMIo1cGM+QxlAYj5JGTxh3kUZrGDeRRhqM+qRREcZlpOHB+LvjjM/d 196npPE+jNWkMQ/GXNJ4HsZE0hgOYxhp3AejN2m0h9GONBrCaEAa1WBUJY0IRkAaey1e51rO2Ahj PWkshrGQNKbBmEoa42CMIY3+MPqRRicYHUnjOhiNSaMWjJqkUQZGadIoMl97BwxnFMIoII2lMPJJ YyaMGaSRA2MCaQyBMYg0usPoShotYbQgjbowapNGBRjlSeOwj9e5Pmdsg7GFNFbCWEEac2DMJo08 GLmkkQ1jKGn0gtGTNNrAaE0a6TDSSKMSjIqkYWB4pLEz+TrX44w1yde5pLEA13zSmIxrEmmMwjWC NPrgyiKNzOTr3DMayfTlyW+YtvjxpxPrmN1RHcO9E1rHrIexljQWwlhAGlNhTCaNMTBGkUY/GH1I oyOMTNJoDKMRadSAUZ00SsGIk8b+sI7h3gmtYwpgfEQa+TDeJo0ZMF4mjQkwniSNQTAeJI2uMLqQ RgsYzUmjNoxU0igPI4U0DgV1DPdOaB3zCYzNpLEcxjLSeA3GLNLIhfEMaQyF8Shp9IRxF2m0hnET aaTBqE8aFWFcRhoeDO6d0Drmc1fHfEoa78NYTRrzYMwljedhTCSN4TCGkcZ9MHqTRnsY7UijIYwG pFENRlXSiGAEpLHX4nWu5YyNMNaTxmIYC0ljGoyppDEOxhjS6A+jH2l0gtGRNK6D0Zg0asGoSRpl YJQmjSJTx3DvhNYxhTAKSGMpjHzSmAljBmnkwJhAGkNgDCKN7jC6kkZLGC1Ioy6M2qRRAUZ50jjs 43WuzxnbYGwhjZUwVpDGHBizSSMPRi5pZMMYShq9YPQkjTYwWpNGOow00qgEoyJpGBgeaexMvs71 OGNN8nUuaSzANZ80JuOaRBqjcI0gjT64skgjM/k696zeCa1jTif2sLujHpZ7J7SHXQ9jLWkshLGA NKbCmEwaY2CMIo1+MPqQRkcYmaTRGEYj0qgBozpplIIRJ439YQ/LvRPawxbA+Ig08mG8TRozYLxM GhNgPEkag2A8SBpdYXQhjRYwmpNGbRippFEeRgppHAp6WO6d0B72ExibSWM5jGWk8RqMWaSRC+MZ 0hgK41HS6AnjLtJoDeMm0kiDUZ80KsK4jDQ8GNw7oT3s566H/ZQ03oexmjTmwZhLGs/DmEgaw2EM I437YPQmjfYw2pFGQxgNSKMajKqkEcEISGOvxetcyxkbYawnjcUwFpLGNBhTSWMcjDGk0R9GP9Lo BKMjaVwHozFp1IJRkzTKwChNGkWmh+XeCe1hC2EUkMZSGPmkMRPGDNLIgTGBNIbAGEQa3WF0JY2W MFqQRl0YtUmjAozypHHYx+tcnzO2wdhCGithrCCNOTBmk0YejFzSyIYxlDR6wehJGm1gtCaNdBhp pFEJRkXSMDA80tiZfJ3rccaa5Otc0liAaz5pTMY1iTRG4RpBGn1wZZFGZvJ17lm9E9rDnk7Mdbuj XMe9E5rr1sNYSxoLYSwgjakwJpPGGBijSKMfjD6k0RFGJmk0htGINGrAqE4apWDESWN/mOu4d0Jz XQGMj0gjH8bbpDEDxsukMQHGk6QxCMaDpNEVRhfSaAGjOWnUhpFKGuVhpJDGoSDXce+E5rpPYGwm jeUwlpHGazBmkUYujGdIYyiMR0mjJ4y7SKM1jJtIIw1GfdKoCOMy0vBgcO+E5rrPXa77lDTeh7Ga NObBmEsaz8OYSBrDYQwjjftg9CaN9jDakUZDGA1IoxqMqqQRwQhIY6/F61zLGRthrCeNxTAWksY0 GFNJYxyMMaTRH0Y/0ugEoyNpXAejMWnUglGTNMrAKE0aRSbXce+E5rpCGAWksRRGPmnMhDGDNHJg TCCNITAGkUZ3GF1JoyWMFqRRF0Zt0qgAozxpHPbxOtfnjG0wtpDGShgrSGMOjNmkkQcjlzSyYQwl jV4wepJGGxitSSMdRhppVIJRkTQMDI80diZf53qcsSb5Opc0FuCaTxqTcU0ijVG4RpBGH1xZpJGZ fJ17Vu+E5rrTiauC3dGqgHsndFWwHsZa0lgIYwFpTIUxmTTGwBhFGv1g9CGNjjAySaMxjEakUQNG ddIoBSNOGvvDVQH3TuiqoADGR6SRD+Nt0pgB42XSmADjSdIYBONB0ugKowtptIDRnDRqw0gljfIw UkjjULAq4N4JXRV8AmMzaSyHsYw0XoMxizRyYTxDGkNhPEoaPWHcRRqtYdxEGmkw6pNGRRiXkYYH g3sndFXwuVsVfEoa78NYTRrzYMwljedhTCSN4TCGkcZ9MHqTRnsY7UijIYwGpFENRlXSiGAEpLHX 4nWu5YyNMNaTxmIYC0ljGoyppDEOxhjS6A+jH2l0gtGRNK6D0Zg0asGoSRplYJQmjSKzKuDeCV0V FMIoII2lMPJJYyaMGaSRA2MCaQyBMYg0usPoShotYbQgjbowapNGBRjlSeOwj9e5Pmdsg7GFNFbC WEEac2DMJo08GLmkkQ1jKGn0gtGTNNrAaE0a6TDSSKMSjIqkYWB4pLEz+TrX44w1yde5pLEA13zS mIxrEmmMwjWCNPrgyiKNzOTr3LN6J3RVcDrRi3ZHXsS9E+pF62GsJY2FMBaQxlQYk0ljDIxRpNEP Rh/S6AgjkzQaw2hEGjVgVCeNUjDipLE/9CLunVAvKoDxEWnkw3ibNGbAeJk0JsB4kjQGwXiQNLrC 6EIaLWA0J43aMFJJozyMFNI4FHgR906oF30CYzNpLIexjDRegzGLNHJhPEMaQ2E8Sho9YdxFGq1h 3EQaaTDqk0ZFGJeRhgeDeyfUiz53XvQpabwPYzVpzIMxlzSehzGRNIbDGEYa98HoTRrtYbQjjYYw GpBGNRhVSQMvG6KANPZavM61nLERxnrSWAxjIWlMgzGVNMbBGEMa/WH0I41OMDqSxnUwGpNGLRg1 SaMMjNKkUWS8iHsn1IsKYRSQxlIY+aQxE8YM0siBMYE0hsAYRBrdYXQljZYwWpBGXRi1SaMCjPKk cRjf5N4J9aJt+OYW0liJb64gjTn45mzSyMM3c0kjG98cShq98M2epNEG32xNGun4ZhppVMI3K5KG SX6TNHYmX+d6nLEm+TqXNBbgmk8ak3FNIo1RuEaQRh9cWaSRmXyde1bvhHrR6cSM2O4oI8a9E5oR Ww9jLWkshLGANKbCmEwaY2CMIo1+MPqQRkcYmaTRGEYj0qgBozpplIIRJ439YUaMeyc0I1YA4yPS yIfxNmnMgPEyaUyA8SRpDILxIGl0hdGFNFrAaE4atWGkkkZ5GCmkcSjIiHHvhGbEPoGxmTSWw1hG Gq/BmEUauTCeIY2hMB4ljZ4w7iKN1jBuIo00GPVJoyKMy0jDg8G9E5oR+9xlxD4ljfdhrCaNeTDm ksbzMCaSxnAYw0jjPhi9SaM9jHak0RBGA9KoBqMqaUQwAtLYa/E613LGRhjrSWMxjIWkMQ3GVNIY B2MMafSH0Y80OsHoSBrXwWhMGrVg1CSNMjBKk0aRyYhx74RmxAphFJDGUhj5pDETxgzSyIExgTSG wBhEGt1hdCWNljBakEZdGLVJowKM8qRx2MfrXJ8ztsHYQhorYawgjTkwZpNGHoxc0siGMZQ0esHo SRptYLQmjXQYaaRRCUZF0jAwPNLYmXyd63HGmuTrXNJYgGs+aUzGNYk0RuEaQRp9cGWRRmbyde5Z vROaETudmBXfHWXFuXdCs+LrYawljYUwFpDGVBiTSWMMjFGk0Q9GH9LoCCOTNBrDaEQaNWBUJ41S MOKksT/MinPvhGbFC2B8RBr5MN4mjRkwXiaNCTCeJI1BMB4kja4wupBGCxjNSaM2jFTSKA8jhTQO BVlx7p3QrPgnMDaTxnIYy0jjNRizSCMXxjOkMRTGo6TRE8ZdpNEaxk2kkQajPmlUhHEZaXgwuHdC s+Kfu6z4p6TxPozVpDEPxlzSeB7GRNIYDmMYadwHozdptIfRjjQawmhAGtVgVCWNCEZAGnstXuda ztgIYz1pLIaxkDSmwZhKGuNgjCGN/jD6kUYnGB1J4zoYjUmjFoyapFEGRmnSKDJZce6d0Kx4IYwC 0lgKI580ZsKYQRo5MCaQxhAYg0ijO4yupNESRgvSqAujNmlUgFGeNA77eJ3rc8Y2GFtIYyWMFaQx B8Zs0siDkUsa2TCGkkYvGD1Jow2M1qSRDiONNCrBqEgaBoZHGjuTr3M9zliTfJ1LGgtwzSeNybgm kcYoXCNIow+uLNLITL7OPat3QrPipxOnJHZHUxLcO6FTEuthrCWNhTAWkMZUGJNJYwyMUaTRD0Yf 0ugII5M0GsNoRBo1YFQnjVIw4qSxP5yS4N4JnZIogPERaeTDeJs0ZsB4mTQmwHiSNAbBeJA0usLo QhotYDQnjdowUkmjPIwU0jgUTElw74ROSXwCYzNpLIexjDRegzGLNHJhPEMaQ2E8Sho9YdxFGq1h 3EQaaTDqk0ZFGJeRhgeDeyd0SuJzNyXxKWm8D2M1acyDMZc0nocxkTSGwxhGGvfB6E0a7WG0I42G MBqQRjUYVUkjghGQxl6L17mWMzbCWE8ai2EsJI1pMKaSxjgYY0ijP4x+pNEJRkfSuA5GY9KoBaMm aZSBUZo0isyUBPdO6JREIYwC0lgKI580ZsKYQRo5MCaQxhAYg0ijO4yupNESRgvSqAujNmlUgFGe NA77eJ3rc8Y2GFtIYyWMFaQxB8Zs0siDkUsa2TCGkkYvGD1Jow2M1qSRDiONNCrBqEgaBoZHGjuT r3M9zliTfJ1LGgtwzSeNybgmkcYoXCNIow+uLNLITL7OPat3QqckTid+7e2OvsHFtCrr747K+Zxx JfJXkUYz5K8njduRv4M0BiL/EGmMR/4p0piO/CuksQT5d0hjE/Ifk8Y+5PeTRtzsjkoZzqiOfA3S aIR8Y9K4FfkOpHE/8n1JYyTyo0njBeSnkMYbyL9JGmuQX0caO5HfRRrGIm85oxLyVUgjHfkM0miD /M2k0Qv53qSRjfww0shDfiJpzEF+LmmsRH41aWxFfjtpHEb+KGlUcLujSx1n1EX+atJoifyNpNEd +R6kMQT5R0gjB/mnSWMm8rNIYynyy0ijEPnNpFGE/EHSKBPsjlICzqiFfCppNEW+OWl0Rr4LafRH fiBpjEN+PGlMQ346aSxGfglpbER+E2nsRX4faUTh7igeckY15KuTRkPkG5FGe+QzSSML+T6kMQL5 UaQxCfnJpDEf+QWk8QHya0ljB/JfkEbyv09iIs6oiHwl0khDPp00WiPfhjR6It+LNIYin00aucjn kcZs5OeQxgrkV5LGFuS3kca3yB8hjYtju6NLYpxRB/l6pHED8q1Ioxvyd5LGYOQfJo0JyOeQxgzk Z5JGPvJLSaMA+ULSOIB8EWmUju+OysQ5oybytUijCfJNSeM25DuTxgPIDyCNscg/QRovIv8SaSxC /i3S2ID8h6SxB/kvSSNM7I6iBGdURb4aaTRAviFptEO+PWnci3wWaTyO/AjSeA75SSUwTn51Kvm7 8E//1amD4Te4uK9OHQzL+ZxxJfJXkUYz5K8njduRv4M0BiL/EGmMR/4p0piO/CuksQT5d0hjE/If k8Y+5PeTRtwcDEsZzqiOfA3SaIR8Y9K4FfkOpHE/8n1JYyTyo0njBeSnkMYbyL9JGmuQX0caO5Hf RRrGIm85oxLyVUgjHfkM0miD/M2k0Qv53qSRjfww0shDfiJpzEF+LmmsRH41aWxFfjtpHEb+KGlU cAfDSx1n1EX+atJoifyNpNEd+R6kMQT5R0gjB/mnSWMm8rNIYynyy0ijEPnNpFGE/EHSKBMcDFMC zqiFfCppNEW+OWl0Rr4LafRHfiBpjEN+PGlMQ346aSxGfglpbER+E2nsRX4faUThwTAeckY15KuT RkPkG5FGe+QzSSML+T6kMQL5UaQxCfnJpDEf+QWk8QHya0ljB/JfkIYXHQxNxBkVka9EGmnIp5NG a+TbkEZP5HuRxlDks0kjF/k80piN/BzSWIH8StLYgvw20vgW+SOkcXHsYHhJjDPqIF+PNG5AvhVp dEP+TtIYjPzDpDEB+RzSmIH8TNLIR34paRQgX0gaB5AvIo3S8YNhmThn1ES+Fmk0Qb4padyGfGfS eAD5AaQxFvknSONF5F8ijUXIv0UaG5D/kDT2IP8laYSJg2GU4IyqyFcjjQbINySNdsi3J417kc8i jceRH0EazyE/qQTGya9OHQzP9NUpG36Di/vqlA3L+Zb86pQNryKNZshfTxq3I38HaQxE/iHSGI/8 U6QxHflXSGMJ8u+QxibkPyaNfcjvJ424sWEpY8mvTtmwBmk0Qr4xadyKfAfSuB/5vqQxEvnRpPEC 8lNI4w3k3ySNNcivI42dyO8iDWORt5b86pQNq5BGOvIZpNEG+ZtJoxfyvUkjG/lhpJGH/ETSmIP8 XNJYifxq0tiK/HbSOIz8UdKo4Gx4qbPkV6dseDVptET+RtLojnwP0hiC/COkkYP806QxE/lZpLEU +WWkUYj8ZtIoQv4gaZQJbJgSWPKrUzZMJY2myDcnjc7IdyGN/sgPJI1xyI8njWnITyeNxcgvIY2N yG8ijb3I7yONKLRhPLTkV6dsWJ00GiLfiDTaI59JGlnI9yGNEciPIo1JyE8mjfnILyCND5BfSxo7 kP+CNLzIhiay5FenbFiJNNKQTyeN1si3IY2eyPcijaHIZ5NGLvJ5pDEb+TmksQL5laSxBfltpPEt 8kdI4+KYDS+JWfKrUzasRxo3IN+KNLohfydpDEb+YdKYgHwOacxAfiZp5CO/lDQKkC8kjQPIF5FG 6bgNy8Qt+dUpG9YijSbINyWN25DvTBoPID+ANMYi/wRpvIj8S6SxCPm3SGMD8h+Sxh7kvySNMGHD KGHJr07ZsBppNEC+IWm0Q749adyLfBZpPI78CNJ4DvlJJTBOfnXKnvGrUynBN7i4r06lBOV8zrgS +atIoxny15PG7cjfQRoDkX+INMYj/xRpTEf+FdJYgvw7pLEJ+Y9JYx/y+0kjblKCUoYzqiNfgzQa Id+YNG5FvgNp3I98X9IYifxo0ngB+Smk8Qbyb5LGGuTXkcZO5HeRhrHIW86ohHwV0khHPoM02iB/ M2n0Qr43aWQjP4w08pCfSBpzkJ9LGiuRX00aW5HfThqHkT9KGhVcSnCp44y6yF9NGi2Rv5E0uiPf gzSGIP8IaeQg/zRpzER+FmksRX4ZaRQiv5k0ipA/SBplgpTi/3NfnUoJUkmjKfLNSaMz8l1Ioz/y A0ljHPLjSWMa8tNJYzHyS0hjI/KbSGMv8vtIIwpTgnjIGdWQr04aDZFvRBrtkc8kjSzk+5DGCORH kcYk5CeTxnzkF5DGB8ivJY0dyH9BGl6UEpiIMyoiX4k00pBPJ43WyLchjZ7I9yKNochnk0Yu8nmk MRv5OaSxAvmVpLEF+W2k8S3yR0jj4lhKcEmMM+ogX480bkC+FWl0Q/5O0hiM/MOkMQH5HNKYgfxM 0shHfilpFCBfSBoHkC8ijdLxlKBMnDNqIl+LNJog35Q0bkO+M2k8gPwA0hiL/BOk8SLyL5HGIuTf Io0NyH9IGnuQ/5I0wkRKECU4oyry1UijAfINSaMd8u1J417ks0jjceRHkMZzyE8qgXHyq1MpwZm+ OlXZfYOL++pUZVfO54wrkb+KNJohfz1p3I78HaQxEPmHSGM88k+RxnTkXyGNJci/QxqbkP+YNPYh v5804qayK2U4ozryNUijEfKNSeNW5DuQxv3I9yWNkciPJo0XkJ9CGm8g/yZprEF+HWnsRH4XaRiL vOWMSshXIY105DNIow3yN5NGL+R7k0Y28sNIIw/5iaQxB/m5pLES+dWksRX57aRxGPmjpFHBVXaX Os6oi/zVpNES+RtJozvyPUhjCPKPkEYO8k+TxkzkZ5HGUuSXkUYh8ptJowj5g6RRJqjsUgLOqIV8 Kmk0Rb45aXRGvgtp9Ed+IGmMQ348aUxDfjppLEZ+CWlsRH4TaexFfh9pRGFlFw85oxry1UmjIfKN SKM98pmkkYV8H9IYgfwo0piE/GTSmI/8AtL4APm1pLED+S9Iw4sqOxNxRkXkK5FGGvLppNEa+Tak 0RP5XqQxFPls0shFPo80ZiM/hzRWIL+SNLYgv400vkX+CGlcHKvsLolxRh3k65HGDci3Io1uyN9J GoORf5g0JiCfQxozkJ9JGvnILyWNAuQLSeMA8kWkUTpe2ZWJc0ZN5GuRRhPkm5LGbch3Jo0HkB9A GmORf4I0XkT+JdJYhPxbpLEB+Q9JYw/yX5JGmKjsogRnVEW+Gmk0QL4habRDvj1p3It8Fmk8jvwI 0ngO+UklME5+daqyO9NXp1LtN7i4r06l2nI+Z1yJ/FWk0Qz560njduTvII2ByD9EGuORf4o0piP/ CmksQf4d0tiE/MeksQ/5/aQRN6m2lOGM6sjXII1GyDcmjVuR70Aa9yPflzRGIj+aNF5AfgppvIH8 m6SxBvl1pLET+V2kYSzyljMqIV+FNNKRzyCNNsjfTBq9kO9NGtnIDyONPOQnksYc5OeSxkrkV5PG VuS3k8Zh5I+SRgWXai91nFEX+atJoyXyN5JGd+R7kMYQ5B8hjRzknyaNmcjPIo2lyC8jjULkN5NG EfIHSaNMkGpTAs6ohXwqaTRFvjlpdEa+C2n0R34gaYxDfjxpTEN+OmksRn4JaWxEfhNp7EV+H2lE YaqNh5xRDfnqpNEQ+Uak0R75TNLIQr4PaYxAfhRpTEJ+MmnMR34BaXyA/FrS2IH8F6ThRanWRJxR EflKpJGGfDpptEa+DWn0RL4XaQxFPps0cpHPI43ZyM8hjRXIrySNLchvI41vkT9CGhfHUu0lMc6o g3w90rgB+Vak0Q35O0ljMPIPk8YE5HNIYwbyM0kjH/mlpFGAfCFpHEC+iDRKx1NtmThn1ES+Fmk0 Qb4padyGfGfSeAD5AaQxFvknSONF5F8ijUXIv0UaG5D/kDT2IP8laYSJVBslOKMq8tVIowHyDUmj HfLtSeNe5LNI43HkR5DGc8hPKoFx8qtTqfZMX51KN9/g4r46lW7K+ZxxJfJXkUYz5K8njduRv4M0 BiL/EGmMR/4p0piO/CuksQT5d0hjE/Ifk8Y+5PeTRtykm1KGM6ojX4M0GiHfmDRuRb4DadyPfF/S GIn8aNJ4AfkppPEG8m+Sxhrk15HGTuR3kYaxyFvOqIR8FdJIRz6DNNogfzNp9EK+N2lkIz+MNPKQ n0gac5CfSxorkV9NGluR304ah5E/ShoVXLq51HFGXeSvJo2WyN9IGt2R70EaQ5B/hDRykH+aNGYi P4s0liK/jDQKkd9MGkXIHySNMkG6SQk4oxbyqaTRFPnmpNEZ+S6k0R/5gaQxDvnxpDEN+emksRj5 JaSxEflNpLEX+X2kEYXpJh5yRjXkq5NGQ+QbkUZ75DNJIwv5PqQxAvlRpDEJ+cmkMR/5BaTxAfJr SWMH8l+QhhelGxNxRkXkK5FGGvLppNEa+Tak0RP5XqQxFPls0shFPo80ZiM/hzRWIL+SNLYgv400 vkX+CGlcHEs3l8Q4ow7y9UjjBuRbkUY35O8kjcHIP0waE5DPIY0ZyM8kjXzkl5JGAfKFpHEA+SLS KB1PN2XinFET+Vqk0QT5pqRxG/KdSeMB5AeQxljknyCNF5F/iTQWIf8WaWxA/kPS2IP8l6QRJtJN lOCMqshXI40GyDckjXbItyeNe5HPIo3HkR9BGs8hP6kExsmvTqWbM311qpn/DS7uq1PN/HI+Z1yJ /FWk0Qz560njduTvII2ByD9EGuORf4o0piP/CmksQf4d0tiE/MeksQ/5/aQRN838UoYzqiNfgzQa Id+YNG5FvgNp3I98X9IYifxo0ngB+Smk8Qbyb5LGGuTXkcZO5HeRhrHIW86ohHwV0khHPoM02iB/ M2n0Qr43aWQjP4w08pCfSBpzkJ9LGiuRX00aW5HfThqHkT9KGhVcM/9Sxxl1kb+aNFoifyNpdEe+ B2kMQf4R0shB/mnSmIn8LNJYivwy0ihEfjNpFCF/kDTKBMn/qiln1EI+lTSaIt+cNDoj34U0+iM/ kDTGIT+eNKYhP500FiO/hDQ2Ir+JNPYiv480orCZHw85oxry1UmjIfKNSKM98pmkkYV8H9IYgfwo 0piE/GTSmI/8AtL4APm1pLED+S9Iw4ua+SbijIrIVyKNNOTTSaM18m1IoyfyvUhjKPLZpJGLfB5p zEZ+DmmsQH4laWxBfhtpfIv8EdK4ONbMvyTGGXWQr0caNyDfijS6IX8naQxG/mHSmIB8DmnMQH4m aeQjv5Q0CpAvJI0DyBeRRul4M79MnDNqIl+LNJog35Q0bkO+M2k8gPwA0hiL/BOk8SLyL5HGIuTf Io0NyH9IGnuQ/5I0wkQzP0pwRlXkq5FGA+QbkkY75NuTxr3IZ5HG48iPII3nkJ9UAuPkV6ea+Wf6 6lRb7xtc3Fen2nrlfM64EvmrSKMZ8teTxu3I30EaA5F/iDTGI/8UaUxH/hXSWIL8O6SxCfmPSWMf 8vtJI27aeqUMZ1RHvgZpNEK+MWncinwH0rgf+b6kMRL50aTxAvJTSOMN5N8kjTXIryONncjvIg1j kbecUQn5KqSRjnwGabRB/mbS6IV8b9LIRn4YaeQhP5E05iA/lzRWIr+aNLYiv500DiN/lDQquLb4 Xs6oi/zVpNES+RtJozvyPUhjCPKPkEYO8k+TxkzkZ5HGUuSXkUYh8ptJowj5g6RRJmjrpQScUQv5 VNJoinxz0uiMfBfS6I/8QNIYh/x40piG/HTSWIz8EtLYiPwm0tiL/D7SiMK2XjzkjGrIVyeNhsg3 Io32yGeSRhbyfUhjBPKjSGMS8pNJYz7yC0jjA+TXksYO5L8gDS9q65mIMyoiX4k00pBPJ43WyLch jZ7I9yKNochnk0Yu8nmkMRv5OaSxAvmVpLEF+W2k8S3yR0jj4lhb75IYZ9RBvh5p3IB8K9Lohvyd pDEY+YdJYwLyOaQxA/mZpJGP/FLSKEC+kDQOIF9EGqXjbb0ycc6oiXwt0miCfFPSuA35zqTxAPID SGMs8k+QxovIv0Qai5B/izQ2IP8haexB/kvSCBNtvSjBGVWRr0YaDZBvSBrtkG9PGvcin0UajyM/ gjSeQ35SCYyTX51q601JJNPfmtDDa8Lk/777J6+C4h+9D8qZvno15fuPGJxT66+93dGUxO6IMZL5 89Hja++//+dyvnp87a0ne7TF1euMPYLkofF9/DH5V/X8ivjjqdzk361gMmOveJXxV4fNlGPHD9xX yajvjJeSeW+fuwd6Xw1uiu+ok5Ko9dk7Xw3+Epdf/OPqf3+uk1I8eVxN8iP8NDBe3bSke7qm+767 H874Os/sjuoYbrk6uK/qmF7n9AieWGm+X8KVrjzzSrHilZxX95p6v0jK52OnHnZ31MNyO/WwbXFx O5WzJdwp9SxO0zVJ93yslOt2R7mOWynXtcXFrVTNlXClq87iNNVPnqZq7nzstCrYHa0KuJ1WBW1x cTu9HpRwp9olPU0+/l7SPR8redHuyIu4lZLv+3gRt9IfwxKuVKekp8l6OExeUj4fO2XEdkcZMW6n DHwulxHjdqoSK+FOdUt+mq7xku75WCkrvjvKinMrZeEziaw4t1KdeAlXqlfy03RN8WmqEz8fOx1/ bbmefH2afJ3M7TQ6UcKdri75aUrzku75WCn5irOsz7+KH32Or56Pr1Q2NrSkry7rn8XrgV8m3fOz 0sGwrH8w5FY6GI5OnJtxfKWfRCVe6ZqzWCkj6Z6flSxWsuRKFitZYqVaYYlXSjuLldKT7vlZKSUo 66cE3EopwejEuRnHV/p5UOKVfn42n88l3fOzUmVX1q/suJUqu9GJczOOr9TUzSvpSuln88oy6Z6f lVJt2e//u83nulKqHZ04N+P4Sr+yJV7pF2fza1zSPT8rpZuy3//3A851pXQzOnFuxvGVOpkSr5RR 8pXSvaR7flZq5pf9/t9jc64rNfNHJ87NOL7S3X6JV2pQ8pUyvKR7flZqW/z79tlXlaPP8V3P4yv1 90q80i9LvtIvvaR7vlb6n/b+8vH3U5ODnnif/pj5Taygyo/fpz/2o39D2j54P/zY+6KXEm28Im9F 8ce+y3vEvuo/bV/y8+w0//d2sv8n+6z/n7j+Yp/xi+wE/2tcF7kn/CvcKD8V13VumN/J/cbv6h71 +7sh/lg30H/GDfBfdP38RS7Lf8/19je4e/zd7td+EHT340E3v2pwu98guM1vGWT67YJb/XuCm/3H gtb+KFzPBjf6rwct/BVBM38Vrm1BY/9I8O/+RWED/5Iww68X/txvFV7tdwjr+neGdfwhYaqfE9b0 J4c/82eG1f2l4eV+YVjZ3xP+xD8QVvRLR5f6NaOL/WujFL8Jro7RRX6/KOGPiSJ/QhT6UyPnL4x8 f130d297dNTbFR3xXOyQVyX2NT6rP+A1xtU29jfvntheLzu2y8uL7fT+EPvMeze23dsa2+J9E/ur dxhXhXihVzde4LWMb/K6xDd63XANjq/zfhdf470af9/Lj6/yCuLvegfiy71SiWVejcQfvatwXZt4 x+uQWOL1TSzGHbrQ+9+JN3GGFpzVV3f+8THcY963X5k/2SNmkf27WWCtnWPj9hV7kZ1kE/ZpfN84 exTXp2aY3Woes6vNI3aRGWTnmgftRNPX5pj77TBzr73X/Nr2xnWLucNebzrbX5qO9qfmZnu5aWsj 08oac4Pd6zexn/mN7Eb/F3a1n2YX+3XsfLw+mOZXs1P9y3FaLrFP+BfbbL+UHeAb2x9XT/8bc7u/ 13T295hb/O3mP/w/mxv8taaZv9w09f9krvPfMk38ufjzTHx7WvG/EesGPxc/bjx+/HDkHja/9vuZ vv7dZoB/l3nU72LG+O3NE347k+ffaKb5zcyrfhOzGL8Cr/Frm43+leYz/6dmr1/FHPUvM5G52Fxq LjKXm7ipb6z5JW6iX5lv/VvMN/695m/+MLPTH2s+9yearWiwGU3+7K82G/z3cH1q3vP3m5X+381y /zL7jv9vuK62C/1m+FnfaOf5Pexs/347y0/eR+fyGK4sfgx/7Q0z7cJ7zY3hLea68FemSfhL0yC8 xqSHl5t64aWmdhiZmuFR/6fhXv8n4Wf+ZeFGv2y4BnfJYt/hsuGr/rfBNP/rIM/fFzzhfx6M8T8L HvULgwH+h0Fff33wa//doLP/dnCLPy/4D//3wQ3+i7jbng2a+rnBdf6EoIk/En/+Db79IL5/AP5+ b/y4bvjxmcj9Cndw66Cn3yzojzt5gJ8RZPt18XGuCCb4Pwum+j/Bx64YzMfnHIv9i4L3/DDY6Nvg M/+I2+t/64w54CLzN3e52el+iuuXZqu73vzV3WIKXW+z0d2La5j5wOWYVW6iedfNNUvdIvNHt9q8 5baaBe5T84Y7al5zf8eVsC+5i+xzLm5znLWj8X2PuSNmqPvKDHR7zH3uM9MDP767+8Tc5gpMG/eh aeHWmX93a0x99765AtfF+Os4vu+Y/dAU2QKzy35ituLeKLCfmY9s8l5iHscu8V9HLeN3RnXj3aIK 8Tuiw7HO0Te4tsZui96NZUZ/iN0S5cVujrJjv4ruif1H1DbWKmocuyHKiLWIqsSaRy52XbQrujba HjWK1kUNo4VRg2hqlB5NiK6JxuDqF9WLOka1oybRlfhRV0Y18f/SUfXoQHh5tCesGuG5MFoa/ls0 M7w0mhxWiHLC8tGQsGx0Z1g66hCWilqFsaheGESXhCa6KPSjI8Hfw23B4XBVcDBcgev14ED4bLAv HBXsCR/DdU+wM2wXfBq2DLaFDYItYdXgL2E8KAgDXLvdh+EGty58z60NF7n3wxfdu+Ezbnk41i0L +7v8sKt7K+zkFofXuQVhqpsbXoHrIvda+LV9NSzC9Rf7Uvifdkr4Jzs5/L2dGObZ3PBp+7/CR+zv wvvt+LCHHRfeaEeEzezw8Gr72/Df7MPhZXZI+HczINxv+oWfmqzwPXN3uBrXXNMtnGm6hBPNbeFY c0uYvJ/O5XG8ovhxLIfn5GHR/048Fo1O/Dbqm/hN1CHxSHRtYkh0VWJQVANXqcTA6EC8f1QQ7xfl x++PXo3fF/0u3jsaHL876oYzkDwHJf1q+zHzVVhQ5XSnaoNLDd52PwsWuerBi65S8Lz7STDWVQh+ 41KC/q500M2FQSfngubuiLvOHXZXugPuCrfflXM73UXuc3fU/tXhrLsv7Ua3065y++0f8e18/D2I bgF+7BvIzXOd3FzX373uxro57kVci9wf3AZcu3EFwR9cVVwNgjmuHa57gtfdY8Fc9yyu14P/41YF 89y2YL47ErzhyoYL3CW46oVvulbhQndnuNgNCd9yOeESNzN82y0N891H4R9dIa4D4VJXOvqTqxn9 p2sSLXcdo3ddv2ilGx2tcmNwTY3ecwuj9926aI3bFa11LrbeVYltcNfENroMXG1jm9w9sY9cdqzA 5cX+7P4QK3Tvxja7gthf3VZch2NbXIX4Vlc3vt21jH/qusU/d4PjO9yY+E73O1yvxne5/PhuVxDf 4w7E97pSiX2uRuJv7t8TB9y1uDokvnJ9E0X4PP9rNyXxjTuXUzW++HFskfw9FeHoRBj2TbjwvoQN OyT88NrEsaBG4khQKvFtEMN1IH4wKIgXBfnx/cHv4/uCV+NfBr+L7wkGx78I0D24Jf5ZgJ9HUDe+ NagQ/2twOFYYbI0VBO/GPgz+ENsQvBpbH+TF1gTZsfeDe2Irg9tj7wZtY8uDjNifgiqx/KBs7O3A xd4KdkULg3XRG8HyaF6wMJob5ISjg7HhyGBIODy4M/xtcEv4m6BV+EhQL3woqBT2Dy7BdTS4P9gR 9A62B/cEq4K7gjeCbsHrQdfg2aBTMCbIDB4L2uPvtMH3tA7aBa2CBkHzIC1oFlQNrg0S+FYQZAS7 Xf1gu6sbJM90ye+Q6/0z3SFl7dvuErvIXWpfdFXs8+5yO9bVtL9xqba/q2u7uTTbyf3cNneN7HXu Wnulu8Fe4Vracu5me5G7xR61nW2R7Wa/tL+2O+39dr8dhG8Pxt8baqu7x/BjH0NuOIyR8EbCHoWP Mxofb7TdgGu3G2ODYLStiqsBrnbBKHsPrseCkfZZXK8HI+yqYLjdFjxujwTDbNnwMXtJmG3rhb+1 rXDdGf4Gz2yP2hw8+80Mh9il4WD7UTjIFuI6ED5kS0cDbc1ogG0S9bcdo362X9TXjo7ut2NwTY2y 7MLoPrsu6m13Rb2si91tq8R62mtiv7YZsbts21gPe0+su82OdbN5sa72D7Eu9t3Y7bYg1tluxXU4 dputEO9g68Yzbcv4rbZb/BY7ON7OjonfbH8Xb2tfjbex+fFf2YJ4a3sgfpMtlbjR1ki0tP+euMFe i6tDooXtm2hu8Xm5nZJoark75GozOpFm+ibSzX24OiQyzLWJhqZGopEplWhiYrgOxJuZgvj1Jj/e 0vw+fqN5Fdfv4q3N4Hgb0y3eztwSb2/w8zB14x1NhXhnczjWxWyNdTPvxnqYP8R6mldjd5u82D0m O3afuSfWx9we62faxvqbjNiDpkpssCkbe9i42CNmV/Rbsy4aZpZHw83CaKTJCV83Y/ErzZBwvrkz XIRfZd4yrcK38QrtT6ZSuNxcEq4wR4P3zI5grdkerDOrgk3mjeDP5vWg0DwbbDFjgu3mseAzc0+w y3QN9pp2wd9Mg+CgSQu+MVWDoyYRGJwhi7MUt9tdKZs802fa8sTnfqWSn/md5e/R2mHnu2P2Peod 0GMwdpCGeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiH eqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiH eqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqiHeqjHv1KPQ2a4LWcnUv/t 73J2uD1kOEOPi3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qo h3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3qoh3r8a/5zfC+4cnae4/45vhfcITNPj4t6qId6 qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6 qId6qId6qId6qId6qId6qId6qId66J9r1B7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7q oR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7q oR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoR7qoX+vpP69ktpDe2gP9fin52O4LWcnWu58DLeH DGfocVEP9VAP9VAPvQ7SHtpDe2gP7aE9tIf20Psw6qEe6qEe6qEe6qEe6qEe6qEe6qEe+jxbe2gP PS56XNRD51TnQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz3UQz30dVM9Lnpc tIceF+2hPbSH9tAe+nVO/z42nVPtoXOqx0WPix6Xf8X3x7LsMfu45Xpk2R2koftFj4uex/S46HWy Hhc9LnrfQT10TrWH9tAe2kN7aA/toT20h/bQHtpDe2gPfZ6tc6pzqsdF7xfqfOhx0eOix0V76Jzq cdHjosdFj4v20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2h PbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQ HtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3to D+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20 h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7a Q3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/t oT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf2 0B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe1y4PQ6Z4bacnWi5HsPtIcMZO2yWPWYft9zj kmV3kIb20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH 9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpD e2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2h PbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQ HtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3to D+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20 h/bQHtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe2gP7aE9tIf20B7a Q3toD+2hPbSH9tAe2kN7aA/toT20h/bQHtpDe1yoPfS46HHR46LHRXvonOpx0eOix0U9dD70uGgP nVM9LtpDe2gP7aE9tIf20B7aQ3toD+2hPbSH9tDjoj20h/Y4H3scMi+4cnae43q84A4ZztDj8o97 zHfH7HuO22O+20Eaelz0uOh5Xc+n2kO/7utx0etTnVM9LtpD7wfpfGgP7aE9tId+fdHjoj10TvW4 qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qIe+TqgeOqd6XPS4aA/toed1 9VAP9VAP9VAP9VAP9VAP9VAP9dDn2dpDe2gP7aE9tIf20B7aQz3UQz3UQz3UQ/9+Sz0ueh2kPbSH 9tCvc+qhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqh HuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqhHuqh HuqhHuqhHvr3jurfK6l/r6R6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6 qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId6qId66J9r1PlQD/VQD/VQD/VQ D/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQD/VQ D/VQD/VQD/VQD/VQjzP/83MvuHJ2nuP++bkX3CHDGXpc1EM91EM91EM91EM91EM91EM91EM91EM9 1EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM9 1EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM91EM9 1EM91EM91EM91EM91EM9/vV6lC42nDfNXRZMdZcHz7mawdOuVsBYyfw4OCPgPQ6XsZL5Ea4svBh6 hWSvED+/GH6eZYNpZC/tpb20l/bSXtpLe2kv7aW9tJf20l7aS3tpL+2lvbSX9tJe2kt7aS/tpb20 l/bSXtpLe2kv7aW9zsYqDCq7gqCm2xDUdquCuo6xkvmlcN6CtxAuYyXzbwUV4JVBr9Jkr9L4+ZXB z7OCKyR76XxpL+2lvbSX9tJe2kt7aS/tpb20l/bSXtpLe2kv7aW9tJf20vv3ev9e50vnS+frn1t/ xt4f4zysP0/n649wFp+n87UY5+GP5+l8rYfzMbw/63zp+UvPX3q9qvtR96POl15P/De/ntD9qPtR 96Ne3+v1l15/6flez196/tL9qPtR96Ner+p86XzpfOl86XzpfOl86Xzp9b3eX9Xnj/r8Ub8+6n7U /aj7Ufej7kfdj7ofdT/qfOnzRz1/6flLryd0P+p+1P2o1xM6X3q+1/O97kfdj7ofdT/qftTrL50v PX/pfOn5S89fev7S85fOl/bS870+f9Tzl56/9Pyl5y89f+n3k+t86ddHff6o86XnL50vPX/p+UvP X3r+0vnS+dL50q+P+vVR50vnS+dLvz7q9wPoftTzvc6XzpfOl86XXk/o8209f+n5S+dL50vnS78+ 6vNt3Y+6H3W+9Pyl1/e6H3U/6n7U/aj7UfejXt/r9b2ev3S+dL50vvTro16v6n7U873Ol86Xnu/1 fK/7Uc/3Ol86Xzpf+v0Aer9Q96Oe73W+dL50vnS+9HpCryd0P+p+1PnS+dL50vnS+dL50vnS+dLX 0/T1NN2Per7X+dL50vnS+dL50vuren9V96PuRz3f63zpfP1rvz9R3U51V9nnXH37tEuz3K9DaXYc nBHwHofL/fpYHU5FeBejVzmyVzn8/C7Gz7OinUb20v2o+1HP9zpfOl/6/FGfP+p86flLz186Xzpf /1PPl/bS/ajfP6H37/V8r+cvnS+dL32+rc+39fyl5y+dL50vnS+dL33+qM8f9fyl5y+dL50vnS+d L329Q+/n6PWXnr/0/KVfH3W+dL50vnS+tJfuR92POl86XzpfOl86Xzpf/++eL+2l+1H3o86XzpfO l86X9tL9qPtR50vnS+dL50vnS68ndD/qftT50vnS+dL50vnS+dL5+p/2+3317xPV/aj7Uc/3Ol86 XzpfOl86X/r3uev1l56/9Pyl86XzpfOl86WvP+r9L73+0vnS872e73W+dL70ekJ7aS89f+n9Qr1f qF8f9fyl86V/v5z+ewG6H/V8r/Ol86Xzpdf3ej9az196/tL50vnS+dL50vnS6y+9v6r7UfejzpfO l86XzpfOl86XzpfOl37/hN5f1f2o53udL50vnS+9/6X3v3Q/6n7U+dL50vnS+dL50vnS+dLrVb1e 1f2o53udL50vPd/rfOn5S89fev7S85fOl56/9Pyl86Xfb6L3J/T8pecvnS+dL50v/fqoz4d0P+p+ 1P2o+1H3o+5Hff6o86XnLz1/6flLryd0P+p+1PnS+dL50u8H0Ot73Y+6H3W+dL50vnS+9HpCn2/r fOl86Xzp10f9+qjzpfOl86VfH/Xro56/9Pyl5y89f+l86flLz186X/r9OXq+1/2o+1H3o+5H3Y+6 H3U/6nzp9b2ev/T8pecvPX/p+UvnS89f+nxI96PuR92Puh91P+p+1Ot7nS893+v5Xvej7kc93+v9 HD1/6flLz1+6H3U/6n7U/aj7Ufejzpeev/T8pecvvZ7Q+xM6XzpfOl86XzpfOl86XzpfOl/6fEif D+l+/J9zP2ovPX/p+UvPX3q9qvOl86Xzpa+n6etpev2l86XPh7SX7kfdj3r9pdf3ev7S85fOl86X zpder2ov7aW9tJf20l7aS3tpL+2lvbSX9tJe2kt7aS/tpfdX9f6q7kftpb20l/bSXtpLe2kv7aW9 tJf20l7aS3tpL+2lvbSX9tJe2kt7aS/tpb20l/bSXtpLe2kv7fWvuldSuRzfOGYqu5f3xPCtb03o GS/5v2Pm+I8Oi3/0Pig//Mj7opcSbbwiL1b8kY33tVfZTUmc+B1B4T/9iAH+bHwffzzVzyP5dyuY ObE7g8r4q8NmyrHiKt5XyYDvjJeSeW+fuwd6Xw1uiu/IujSR+tk7Xw3+Epdf/OPqeyd+xkkpnvyJ mDj+8NMg8NrffeXAVC9pn67jvu/WOtG13hm6jnEXeSe7jrQj7T/telXJu97UJ9k1aZ9d14qn7brV fnaqXQ26tr/14T539bvfO9G19pm7RsVdfW+wl3RL2vOft6vgaofH280706Nep+Tt6ntJl2+31bYP S3gm65a8XTUv6fLtrrebS/rI1jubRzbp8u0estVL+sheXfJ213hJ93xsd1NJH9n6Z/PIJl2+3WhT WNJH9pqzeWSTLt/uTVOtpI9sWsnbpXlJ93xs16qkj+zPz+aRTbp8u6Neie/Z9LN5ZJMu3+5q/2cl fWR/UfJ2P/eS7vnY7j9K+shmnM0jm3RL2u7Hr5Y888PXWvuQP1X7E6+WBvpV3XpcJXl9duT4B8Af f/x67MSPNqd8fXbiI6bgWzVs6K0v/ogXu6LiP6e69T9qYP7hdcZ/bXDs2LHvG9jvf47/bINTNSlT /HMPTtnkXF7zntiye1TVlYou5Jalij9iqvsiTP75YlfqRw0u5JanasJsuc4YV2j22Au3ZfKjrTM7 7E7zvv3M/M0mv32ywYXc8lRNmC3XmJ+7zebWC3gukx9th2nrdpkH3AZzW/FHP9ngQm55qibMlreY 7vYK0/4CnsvkR/uZucOGppW9Clfy2ycbXMgtT9WE2bKL2eTqmU8v4LlMfrRrzJeujNnraps/F3/0 kw0u5JanasJsWdeN9B9wD/sXbsvkR+vr+vo5bqA/wI0o/ugnG1zILU/VhNnyp+71MMvlhxduy+RH 6+vmh+Pd8vBet6r4o59scCG3PFUTZstO0dMmiKaYC7dl8qNF0e/Np+F046Lc4o9+ssGF3PJUTZgt XwwftX8OB13AX3uSH60gvN8eDgfawnBY8Uc/2eBCbnmqJsyWr4TvuL+Ef7yAv/YkP9rm8A13FH/+ S/he8Uc/2eBCbnmqJsyWPaMZgY2eDS7clsmP5kfTgm3hM0EQTSj+6CcbXMgtT9XkXLY8/m5CRTcj VpJ3E+qkJBqd+t2E8AfvJpQqfjch4TUf0KPvr3tXu/6aakn/dO32fbfZmR7xKvFV9tr4hAv4TJT8 aGnxcbZ1vL9tGX+m+KOfbHAhH/FTNTnTDsc/jvf9//7x61k/aPn93w1+tFNSCfHnK8IritvaYuf/ AmJ1tha+yAkA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0197.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

Tracking Performance of the= LTI System

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0197_image055.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC+XdB5RURR7v8b6/quoEKCIiyYAioiAZEQkCggqCCLIoIkgQBAQVQQmKIooRFZSc c8455zTkjOQcBSRn5H17YFzddXfHuZzz3jkPzmcYurv+Vfdf4d6+3X1788rF3QMBw98UyZYEf/AC /KlU1QtEuHFKwUAgFFgRuylQGhe47YH4/12/fj3g3fz3jxJuC/zhPv9/iNE6/mcg4Wfsj0U+xdoe COQPBPmZJZglINoQu+XegOOnvFiLYr8lU2wbY78l18JgNFnst5AXe2QIaeySYIpkCY8I/l5Knm4+ 4qq8P9T7GI8I8+9lBROaoxu36+aj47dfCY82vz86Fs/7/dE2/v6TlLpRb+zeG490gT/Xp5uPtDe3 7karFwfvShZ7REr+l9kEA92vd73W/fqJ4B3JY2K/3/DHGLHWZOTfK8r4xyTHV/dSiyZN6zQKNCvG 7/eniW47OPdss19xoy25An9s9cPe9et/ta3uZkv/vM2xRyTU/lelgjdLuf+QqX9G/WcP/Tkz7r9m 5gnvkHvCKxvYG42J/X7DnzMT/LctjNUW3y366369UXfwP2zrX7fpNv73kHF/2aY/bm1C/D+254/1 /HPUBf9rDsLx9SmQUNeft/Xf6/jvMQ65WFv9xIiVvxXtiG3P/+1tuVXteMJb5bMdZVHnf7bjz6ti Di9dIPCXYyZ2b2qVD97n3Vgr+t5ceM/GinpWgZSV6jeq0yRwNn6teDh59Je/XitcfKTI7zMok/O4 Lxb3v7X05M0Z8L+2eoMOuQ3yl7kNKos6SerBhCzNUCKzdCzxWcodiMW9FVlqbA+5xtZflhrbsvCX pVdsIrN0PPFZyhOIxb0VWUoRPORSBP1lKUWwLPxl6axLZJZOJD5LeQOxuLciS8NCh9ywkL8sDQuV hb8stQ8lMku/Jj5L+QKxuLciS6Uih1ypiL8slYqUhb8sZY8kMksnE5+l/IFY3FuRpRvHAat8HkvE jmn8ZSkumsgsnUp8lh4PxOLeiizFjg4qeP6PuOKSeKRzI0vR4PlAIrN0+u8cCcTi3pospSdL6X1m KT1ZSu8jS4Vdy8Rm6cz/zlI4Pks2kCtHrvyxyLcmT+VsBfjLUzkbF01ajBt5eteOTGyeziY2T4Y8 5baxyLcmT5+YCvCXp09MXDRpMW7kaYBJ9Hg693fGU+78sci3Jk/jVQH+8jRecdGkxbiRp01K9Hg6 /3fGU574yLcmTwe8CvCXpwNeXDRpMW7kKaJEj6cLf2c85ckfi3xr8pSOPKXzmad05CmdjzwV8RI9 ni7+nfGU14tFvjV5Khuo4PO8Q+zYKS6J52FuruOBRI+nS39nPOXNH4t8q/L0/9s5r3+euf7z2cLr /3IuNfinMz+/uIPR5wMFvBXxtb0RSM2KnAZpkR4ZcS/uxwPIjCx4BNnwGHIiN/IiPwqgIAqhCJ5C cTyNkngWpfE8yqE8KuAl/AMvowqqohpeRy3URl3UQwM0xNt4F++hKT5Ac7TER/gYn6IN2uJLfI1v 8R1+QAf8hE7ogm7ogV7oi34YiMEYiuEYidEYi/GYiMmYiumYiTmYiwVYhMU393jLsRKrsRbrsRGb sQXbsBO7ft87ukSNnH/ty2cj41UGz+MFvIiKqITKeAWv4jVURw3Uwhuoi/pogEZ4B43RBO+jGVrg Q7TCJ/gUn6EtvsLXaIfv0R4/oiM6oyu6oyd6oy/6YyCGYChGYBRGYxwmYBKmYBpmYBbmYB4WYDGW IA4rsBJrsA4bsAk/Yyu2Yyd2Yy8O4CAO4xccw684hTM4hwu4hCu4huvw6CcDhxCiSIbbkBKpkNpn X34UZiyjNdrgc3yBr/AN2uEHtMdP6ITO6IYe6IU+6IcBGIQhGIYRGI0xGIsJmIgpmIYZmIU5mIcF WIQliMNyrMRqrMN6bMLP2Irt2Ind2Iv9OIjDOIpjOIFTOI1zuIBLuIJruA6PXBs4hBBBMqRAStyB 1EiDtEiPjLgX9+MBZEYWZMWjyI6cyI28yI8CKIhCKIKnUBxPoxRi88pPX44JMZ4xAZMwBdMxA7Mx F/OxEIuxFMuwAquwBuuwAZuwBVuxA7uwB/twAIdwBL/gOH7FKZzBOVzEJVzFbwiQZ8EiiDCiSI7b kBKpkBp3Iy0y4B7ch0x4EA/hYTyCbHgMOZEbefE4nsCTKIyiKIYSKIln8BzKoCxeQAVUxD/wMqqg KqrhddREbdTBm6iPt9AI76IxmuIDNEdLxOaVn77cH2Qs4zCO4hhO4CRO4yzO4yIu4yquI0CuDRxC iCAZUuD20ATdgTtxF+5GOmTAPbgXmfAgHsLDeATZ8BhyIjfyIj8KoCAKoyjxi6EESuIZPIcyKIsX 8CIqohJexiuoimqojpqojTp4E/XxFhrhHTRGE3yAZmiJj9AKrdEGn+MLfIVv0A7foz1+RCd0Rlf0 QE/0QT8MwCAMwTCMwCjE5pWfvrw7OFbpkAH34D5kQmY8hKx4FNmRIzhOuZAH+fA4nsCTKIyiKIan UQrPoDSeRzmURwW8hH/gZVRBVVTH66iJN1AH9RgzDdAQb+NdvIem+ADN0RKt8DFa4zN8ji/xNb7F d/gBHfATOqELuqEHeqEP+mMABmMohmMkRmMsxmMiJmMqpmMmZmMe5mMRliAOy7ESq7EW67ERm7EF 27ADu7EHsXnlpy/LuskqhxdR0U1SJVTGK3gVr7mJqo4aqIU6qIt6boLeQkO8g8ZogvfRzHHMgw/R Cp/gU3yGtvgSX+MbfIcf3Dh1wE/ohC7ohh7ohT7ohwEYhKFurIZhJEZjLMZjIiZjKqZjJmZjLuZj IZZgKZZjJVZjLdZjIzZjC7ZhB3ZhD/bhIA7hKI7hBE7iNM7iPC7iMq7iNwSYA4JDEBEkQwrcjjtw J+5CbF756ctP7CJ9is/sYrXFl/ga3+I7tEcHdERnu0Rd0R090Rt90R8DuX8whmI4RmIMxmICJmEK pmEG9c3CHMzDAizCEsRhOVbZhVqNddiATXaBfsZWbMdO7LbztRf7cRCH7TwdxXGcsHN1CmdwFhfs HF3CFVzDdXhujoybLYcQIm6WkiMFUiKVm6k7kQZpkd7NUEbci/vxgJuuzMiCrG6asiE7ciC3m6q8 yI8CKIhCKIKn3BQVx9MohWeZR6URm1d++nKCqabJ5nVNMTU03dTSTPOGZps6mmve1HxTTwtNAy02 DbXUvK1l5h2tMI21yjTRGtNU68wH2miaa5NpoS3mQ23DdtNKu8wn2mNaa59powPmMx0ybXXEfKFf zFc6br7Rr+ZbnTLtdNZ8j/Y6bzrokvlJl01HXTOddN10kWe7ythucraHQranIraXktk+SmH76nbb T6lsf91pB+guO0hp7WCls0OU0Q7VvXaY7rfD9YAdocx2pLLYUcpqR+tRO0bZLfsJy37CjlceO0H5 UMBOVEE7SYXsZBWxU/SUnarieNpOUyk7Xc+itJ2h5+1MlUN5O0sV7Wy9hMqMh1fwKl5jvFRHDcZR LbzB2KqLeoy5BmiItxmTjfEe3me8NkMLfIhWiM0rP315SH10RN31izrpuDroV7XTKX2lM/pc59Ra F/ShLquFrqiprqmxAvSpR/9a+jpoaivMGIgyHpKbV3WbeVkpTSWlMhWU2pRXGlNWaU0ZpTfPKaMp pfvM08pkiutB85QeMkX0sCmsR8yTymYK6jFTQDnN48pt8iuvyav8Jo8KmNx60uRSIRQ1OVXM5FAJ 85hK4hmTXc+hDMqabHoBL6IiKqEyquBV7q+G11GTcrVRhzhvoj4x3yJ2I7xDXY2pswl1v2/yqTnt aEF7PsLH5gm1po1taOvnppC+oN1f0f5v2I52ppi+NyXUnm370ZRUR/OMuphn1dWUVg+2vRc56GPK qR/5GGBe1CBTUUPMSxpm/qERprJGmVc0htyNM68pNq/89GUG1Xf3qLa7j71iJvaSD7LXzMJsz8rs f5TVILuedDmUz+XSYy6PHnb5WF0eVzr3BCvQk0rmCsu6orpqi+ucLcHKVkqH7LPaZUtrs31ea2w5 LbXlNddW0FT7ksbZf2iYfZmVuQqrdVVW8Gr6ytZQa1tTzW1tvWPr6E37pl639Rn1bzELGjEz3lFR 21iP2ybMqvf1kG3GDGyh1PZDJbcfM3s/0RVWgDPmcx1l9u9l9m9l9q9l5scx8+cx86eaH8lWRw01 ndXXdCXT3cl+L3qkN73Uj14bQE8OoneHqJYZpqpmBCNiFKNkjEqZcSpiJuhxM4nRNkVZzTRGJCuu maU7zVylMPMZ1Qt0XYt1SUt1Wst0TCt0UKu0W2u0Veu0gb+rtElx+lkLtE2ztV1TtVMTtEejtVfD dEADFZtXfvqy/M3Xjl/CP/AyqqAqquF11ERt1MWbaICGeBvv4j00xQdojpb4CB+jNdqgLb7A1/gW 7fADOuAndEIXdEMP9EIf9PMOuoEYhKEYjhEYjbEYj4mY7B1wUzEdM739bjbmevvcAiz09rrFiPP2 uGXebrfS2+VWezvdWm+HW+9tcxu9rW6zt8Vt8Ta7bd4mt8Pb4HZ569web43b561yB7wV7rC3zB3x lrpj3iJ3wpvvTnpz3WlvpjvrTXfnvcnuojfBXfbGuqveSPebN8wFOEoTR2yWo7cQR3JhjuqSqb1L oXbudo7+7lAbd6c+dnepububo8Z0etvF5lVS+jJjfF8mjz/7+yQKoyiKoQRK4lk8h+dRDuX/7jtJ W//3d5ImtCXhTHTqaG+lifb5W6/YJcTIHB8jZSBbdLAeQ07kjg5R3uhQ5Y8OU4HocBWMjlCh6EgV wVPRUSoeHa2no2NUMjpWz+K56Lgk1R2Nr9sEqkWn6/V4M5IUJ2t8nFSBJtH5aooPogvUPLpQLaOL 9BE+ji7Wp2gTXaK20aX6El9H4/RtdJm+ww/R5eqAn+KtSFIbEvpiaHSNhsNPX8yNrtUCLMJixGE5 VhJ3NdZiPTZic3S1tmAbdkZXaRf8tP/ZyGqVhp/2V4ssUnXUiCxUrch8vRGZp7qRuaofmaMGkdlq FJmldyIz1TgyQ00i0/V+ZJqaRaaqRWSKWsLPWPo+MkrtIyPVAUmJkyU+zh2BQZEBGoKhkf4aEemn UZG+Go1xkT6agEmR3poS6aVpmBHpqVmYE+mheVgQ6a6F8LMdWyJdtBXb4WdOnI501RmcwwVcinTT FVzDdXjRbjLR7nIIRXsoimTRnroNKaO9lCpeb19j6qPwaLUKj/U1pjqEp+un8Ax1Cs9U5/AsdQvP Vo/wHPUKz1Wf8Dz1Cy/QgPBCDQov0pDwYg0LL9GI8FKNDsdhma++mBderwXxNvgaUz+Ht2krtoe3 ayd2h3doL/aHd+ogDuMojoV36QRO4XR4t87hAi7CTz/cFtmllPDTD1ki25Q1slWPIntki3JGflZu 5I1sVn4UiGxSwchGFYpsUJHIej0VWafikbV6GqUia3y1f0xoucaGktaXD8THuD2wIDRLC0MztTg0 XUtD07QsNFUrQpO1KjRJa0ITbp6/H6dNobHaEhqtraFR2hEaqZ2hkb7G0OlQP50J9dVZ+BlDkXA3 RcNdlRy3hbsoJVKFOys17kbacCdlwD24D5nwIB4Kd9TDeAR+tqMo9RVDcer3sx2Vw731MqqE+6gq qoX76vVwP9UM91ft8ADVCQ/Um2GO+PFWeLAahYfo3fBQNQ4PU9PwcIzwNZb2B7fqQHC7r7lwMXhY l4NHdDV4VNeDvygQOiYTOi4XOqFQ6KQioVNKhhSh07o9dEZ3hM7qztA53RU6jwu++uGR0DVlQ3b4 6YcSod9UEs/gOZQhXlm8gBdRMXRVlfBy6IpeQdXQZVVD9dAl1QxdVC342Y4PyFOz0K9qTs78zOtv Q/vVLrRP34f2qH1ot34M7VSn0A51Dm1X19BW9QhtUc/QZvUJbVK/0EYNCK3XoNBaDYafcXR3cLnS Bv2tSY8EZ+rR4AxlD05TjuBU5QpOVp7gJOUL8qw2OP7m6xdjVTg4WkWDo1QsOFJPB0eoVHC4r9xX CfZXVbwGP2PovWBfNcUHaB7sp5ZohY+J2xqfBQfoc3wZHKiv8W1wkL7DD8HB6hAcoh+DQ5NUf/L4 +m1gEPkZjKHxr4lM8NUX04NzNBOzg3M1Lzhf84MLtCi4SEuCixUXXKLlwTitpL9X0+9rgyu1Prha G4MciwfX+uqLsi6/KeceNy+4AsZPX9RyT5k6qOuKmXp4yxU3DfEOGrsSpgneRzO0wIdohU/wKY9p Az/b0dkVNl1cIdMNfvphhMttRrpcZrTLaca6HGa8y24mukfNZPeImeoeNtNdFjPTZTaz3QNmrstk 5rv7zEJ3j1nkMho/83mjS2E2u2RJinFvfIwUgYPuqg65KzrqLuqYO68T7qxOutM67U7qrDuh8+4X XXRHdNkd0lV3QNfcfl9jJ3lwo1IEN+i24Hpfa9kn9rxa23O+9ok/2kPqaA+os92vrnafutu96mn3 qLfdrb52l/rbnRqIwXaHhmK43a6RdpvGYCz85GExsZZgKXH9jL0dtH0ndtuD2sv27LeHddAe0WF7 VEftMR23x3XC/qpT9qTO2FM6a8/ogj2ri+TPT/sjzprk8VySxt/98XFuC2R0d5p7XWpzv0tjHnB3 m8wuncniMpiszI1s7l6T3d1vcjBncrsHTV7mUH7m0uMuq695/5zLZ0qjDOuYnzE4wZwwk+Bn/i0z B8wKs9+sMvvMGrPHrDO7zUaz02wyO8wWs42/W8x2s9ns4pY9ZgOPWuerzafNPHPWzElSjPTxMWJv LB1lPDvSGDvcODvEhOxAE7H9TDLb26Sw3c3ttqtJZTviR19tvde2NvfbVkmKkTY+RjSQzTYw2W19 k8PWNblsbZPH1jD57GumgK1iCtrKppCtaIrY8v7Gky1sSttCpox90ldeK9us5hX7kHnVPmBes/eb 6jajqWHTm1r2bvOGTW3q2lSmnr3d1LcpfLW3ub2mFvaqWtorvtbgQxpvjmicr2OAKxpkrmmgCZiB xjMDjDX9TRBh089EkRy3ISVSITXSIC2PSY8M8JOLnGaEyY08ZqSvY4CSZop5xkw1z5lppoyZYcqa meYFM9u8yFyryJyrZBaYymahqWIWm1fNElPNxJnXzTIs99X+d83PpjHeM1t99UNb1qEv8JU5aL4x h0w7c9h8b46Y9uao+REdzS+mC7qaY6aHOW56oQ/6sf4NwMAkroMJYymDvnEZ9ZVLSozU8THCgSxq 6rKqsXtUDV121XM5VNvlUnWXR1VcXlV2fvJcSMVdYRVD0STFSRUfJxQopWzuWT3sSiuTe14ZXDnd 5corpXtRyZ2f/L3MXv0V9u5+2laDo4ia2m5ra5OtozX2TcXZ+lpoG2iu9dO2xhph3+MIyk/bWugn +6G+tx/rK/uJPrNt1Mp+rma2rZr6als7vW6/UzXrZ9x1UmnbWc/Yripuu6uQ7aXHbW/ltv2UHY/6 at9wpbEjdGeSYqSJjxEJTNR1M0nXzBRdMtN0zszUSTNLx81cHTHzdcAs0F5fa9BqrTZrtAorkxQn 4ao2OzXD7NE0s1dTzAFNMrH9i5/clU/C55//dV2sdwte1/aT24TXuvvDz3OdqZS/8Rr4ATcbc739 bgEWevvcYsR5e90yrPT2uNXebrfW2+XWezvdRm+H2+xt97U2HfHWuF+81c7PsdFlb7a76s10v3nT XECTnTTRWY1zIY12YY1wyTTUpdBADPCV77Rq79Lpe3zna5sTXnP/XzH+dPWnf7tm1V9/ziphbN6K z1kl5X0FCfXfis9ZJaX+hNcLu96Cz1lNS2IbEs7nbb0Fn7VKyOezkYkqg+fxAl5ERVRCZbyCV/Fa ZIKqowZq4Q3URb3IBF/1f035dvge7fEjOqIzuqI7eqI3+qI/BmIIhmJ4EutP6M8VlF+JNViHpHzW 6njEX3/eis9bJeTzo/A4fYzWaIPP8QW+wjdohx/QHj+hEzqjGxI+b+Wn/qR93mqCtmI7dob99ed1 ynv0o4FDCBEkQwqkxB1IjTRIi/TIiHtxPzIlcUwl9GcJ5svTKIXY/PKTzzGhcRqHCZiEKaGxmo4Z mI25mI+FWIylWIYVWIXVobG+6j8VGqMzOIeLuISr+A2B8BgJFkGEEUVy3IaUSBW730f9eSn/OJ7A kyiMoiiGEiiJZ/AcyqAsXkAFVAyPVaXwWF99+QHzojlaIja3/GzL/uAsHcRhHMUxnMBJnMZZnMdF XMbV4ExdRyA0UwYOfuZG5tB0PYSH8Qiy4bHQNOVEbuRFfhRAwdBUFUZRFEMJlEQp+MlB3dAkvYn6 eAuN8A4ahyaqCT5AM7TER2gVmqDWaIPP8UUoaXMz4Xh/CHNoGEZgFGLzy8/23B0cpHTIgHuCg3Uf MgWHKDMeCg5VVjwaHKbsyBEcrlzIg3zBEXo83khf9VcOcjyEKqiK6sEJeh018UZwouqgHhoEJ6kh 3g5O1rt4D02DU/RBcIqv+rsEZ6gbeqAX+qA/BjBuB2MohmMkRmMsxmMi43sypiAp9aeMrz8Y2EL5 bdiB3diD/UmMmfC8pazrr3Kun150fVXR9VElVHa99Qpedb30muup6qjheqgW6rjuqot6rpvegp98 fuM68iygo35wP6kDfkIndEE39EAv9EE/DMAgDMUwjICv4yHXWSux2nXRWqzHRtdVm7EF29i+HdiF PdjHdh/EIfJwFMfi9UxSGxLOuyQL9lcK3B4coDtwZ3Cg7kJsrvnp109s1HyKz2zEtMWXNmy+xrc2 ZL6zQdMeHawzHa01na0xXdHdyvS0numFpNSd8JrTDHtas+xJzcE8e0IL7HEtsse0xB5VHJbbw1pl D2m1PaB1dr822H3aZPcmaXsTzg+ftmt1xq7RWbtKF+xKXbLLdQXXbJyu26Xy3BIZt0jOLVTILVDE zVdyN1cp3Bxfec7mxiq7G6McbrRyu1HK60YqvxuhAm64CrphKuSGqogboqfcYBV3g/Q0SrmBetYN UGnXP0l1J5x3mmDKa7KpqCmmsqabVzXTVNdsU0tzTR3NN/W1wDRMUvyEcwIbzFfaiE2mnbaYH7TN /KjtprN2GeaD6al9po8OmAEYKD/vnz9v5uiSmafLZqGumcW6buLk0XeGvnT0a8iuV8RuUjL7M7b4 GicPMCYzIwtjNKs9q0fteWW3F5TDXlQue1l57BXls9dUwP6mgva6CtmAKcJ8KMLc8LPWvWaTm+qo gVp4A3VRDw3QEG+jMd7D+2iGFjaZ+RCtmMtJqT/hHOohRXVETr8ooOO64v2qC94pnfbO6IR3Vse8 pMROeI3VmTVe0Kzywma5FzVLveRmsXebWeilNPO8VGaOl9rM8tKYGV5aM81Lb6Z6GeBnzj1pxnmF UNSM94qhhJnglTQTvWfMJO85M9krY6Z4ZanrBTPde9HM9CpSfyXaUZn2VDbzPT9jtaHZ6jXCO2aH 19js9pqYfd775oDX3BzxWphfvI/Mr97H5rTX2pzD+STVlfDaanuTSj+a1Opo7lYXk0Fdzb3qYR5Q L5NFfcwj6mceQ84kzYeE82jjTFnF1hE/xyUZOHq4h9XsPpVwmVjxHmQFzKw8zk/Mx5TK5VBKl0th l0cBl08XbX6dsn5iFtFaW5Q9T3H2RiXYQ5XSRIzzFbOs2tty+sGWV1tbQR/Zl9QE7/iK+arK26oq Z6vpaVtDT9qarEw1ldP6eS7wpm639RW2b+k300hnzds6Yfy0salWmve1wjRjT9NCU82HGo1Rxk8b 26id+VxfmC/0EXud98zXaugrXnuVZY9VwnRUQfZaOZHN1zb3UjLTW1HTTx57vYsapF81mBXVTxtH aZnGaIHGaYYmaLwmabivuThL32iu2mi+PiTq+1qsRnjL1zHqaj2vNSqjdSqpDSqiTSqgn5Vb25TN 19pzUMkV2y/52a/eis9R+qn/VnyO0s/+aK23za33trqN3s9us7fJbfE2um3eOrfDW+N2eavcHm+F 2+fFuQPeEnfYW+j8HG9e8oa4y94gd9Xr537zermAujrxrM3yDC6kb/C1rzU/lRq4O1Xf3aXa7m6e eabjmWhs3/L/7Gczf79uX+I+mxm7ImuVv3lF1n+N0ZLyPXzGmEX5nT5jXKd8JvmLUYLytXzG+Jzy g3zGWEz5wz5jRMx4PWr8xShL+UY+Y3xP+bE+Y6yl/GmfMe6043ke5S9GZco38xmjK+Wn+4yxjfJX fca4143XU85fjBqUb+MzRn/KL/AZ4wDlg0F/MR6mfGmfMRrcvF6WnxijKL/KZ4xfKX9HyF+M3Dev 5+YnRtOb12TzE2My5X/2GSN2rcL0YX8xCt+8ZqCfGLFrcfb1GWMu5ff4jKGb17T0E6PUzeu9+okR u97rMJ8xlt18H4CfGCmi45Uj6i9G+ZvvdfETI3ZN4Qk+Y2yg/N5ExPjXb/fy/uu3e9U00T9cvbut aWv+49W7ryb+6t3NszZ9JBY5sVfvTsz3kI0MrkvstyJdS/z12JvmrPRILHJiW3rjqDzwp2+g/OO7 vP7wDYGBf/1eQ/N7lH9+U+WNLQ4E/g/bxRtyhHMAAH== ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0198.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" PID Control of Linear Time Delay Systems

University of Delaware

Mechanical Engineering

The System

Parameters

Periodic System with PID Control
- Example 2

------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0198_image056.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC91bfXBU1RU/973dzSZAgA2kRD4MSPhKwGzCQETSREWkRQGZoPmDdoEEJRIwEXQz itO1KkX/SICqEz8yMjVoO7WOVmZ0KE6dgpU6VjFW6owfqLExfqCL4jRRxvTc++7dffvevXk3L9Dp 9M3cvLv33vO753fOuZ+7+eff//oQsKfM3AvXs9zxGgLZAOZFFwCMhPwxtIz+nREaDdMKr71q6WWE tSPw5Lf0bdA/hQCleZjKaTlAI6SfmSbAHtvnL1cCrB+FIpdftZS2pjLthPbleIKYAgDVWJd01n0U gMTvTBgLllwYU4Tnaf/5PD8BUwHPDwwMUF5ACY3GdAoLcvhn+rSGrfZCj9WYmoiFt/YHFLY9u4UJ 8KmBBtgCG2EbGmEFvuP4Xg03Ytl62Ao6TyPc9W0EfoY5+hYP/Ry8acNN6+s2w0/GXQ0b1/6aUJPU fB1hHZdMX8PKDlWjtSdOjxy7aze5JASw75Fy8ujiRlhWDJDgSr6z2OpjtqOP2exvBMwfN0KHxYnV 34a4R9Bv7TfsIbB9/c1gw5jlwADLTTCrbA3TWaXPw/MsfcI8AfPJiYH6W6yPRTb/CT8MOPLCJ4bE J4eMdH74PiGBxISbm3dFSIDBYgC2vDkenj82HpYizk2ItwxxG6EJSjDfhCW0N9rfUogym1ZET8ep aNMXEViC7+ovLL8txvcHN9/S/E2QXEKx0cwQ4rxFW/r0YZ72Sdu981OL8z8+j8AhTHMW98dp/iFM gvaqpIU/SjDg73FYPgfft3eu2FFoDVU4jXJPY2pu7I5XBKdl+ITKOX1i2Gxvqm3P/m6HOrR+FPw/ cr+2kDxor5lhDsevVF7g0Pdu+nb4FXz6dcx9RSbsxgR5UIq2nffKmfgRUY5lNFk+sfK0/xf/diZu t32LxPamYgwE1POSzQ/lMJxnBCkmUwcaIJ+MMYROVBfYsxB7qmDpjpfXYsF8Arb4WXcyAvWYGjGN KV1IEgPzyb5PsA3KdWE9TfkE+KxtG3WwkAyQKmBtYaGFibLrAm2EKpCo3ktCfP6+rq0Ojk2tYJgU v+OetUyO5lm5zSZV+KZlNHEbwY6ri8kfehpg1xO3MYPZ/ZAl8UPAZvugwvbkrM0//x9+nYGrRdOn EeZXgdOJss0Pr9zRgmlfXs2OpqBp2G3/Ku3DYfugwg8hrTEwnLkoPaZLTg5hTIfyoAjfCaYDckMM XVtRjPTjttUc29xObTXp5EpW3nfSmodoWoL5yGMRMzW+vorA4Z+fjn+K6coQiYi2S76y6oVudj98 IPFDyGb7LC3blw0rTs+jHDE9SNLrwDqecIwkz8dxVcjbUp+IeZjakPop8fKZeMdLZ+IHMAnM3qIC 9q4oLoDS6RUktBRtgnO4kwv1J10nxP7mt9imHdNybH/FJafjol86Fx3B8gO2OvpZtd5s+hLrwla/ R2z92m0Pkvkny2b7sNr2Z2n+OfexLZsHzlZsgyS26VxWmcx5bfesAniqzGo7CX0x1rUnHfiF0/Zh hx9k5SHbOp1IJDLa2Ndv+5wm/JmtXk/O0jy2EX2P+8d/WTapf7AvTn0armazPjyN5bvQr/U9Edhz R398H9ajHQa24+dfHj0T78W6Mdj2A2xL44fmqa8ewfpZPXLMQI+F+TyrT2MelWCWcUxGFt/0TFbd k/Y59fWttUEWh1S/VQ9YWIco9l9W7hB7YIFn96chGUvZDr+dLX/azzAyTKKIo4CPcpkOhqI8MMha KmufpSgPK+KXnqN7z+l+COeDbpxju62zD83v7U6ffZb1Wmccmp7/JALzHesOlaPz9bv47vskkioL j++P9+Gb2uFFfL/KMV/Ht8D8uJu274tTuYANc36ZlUbyM5WBUUvlAeWuH7tyxw34vhffFMeKcEun 4o8j0MmxqzF/am1fvKY3E9sevwFJ/OYo/KlT/r8Qd1mKsWjHd+47pog9Kr+rKSrNHKMDg+hWwxN9 FmDKxbSGj8dr1rxVReDon9m1kmmVXenajVvPKnZGC7L1zX4+E/hU/4Wc0zUO/Mswf1IDvyhZQZYP Yk/RVy7nUiDh0qXJ5b2kCfsdPhL4BRx/moRLnOjhb+dnWpn+Uzl+iUT/rzTx309eTfY74kTgU+wK TEsxXevAj5p6+JXJALt7VI2FGZgm0fMUl50iMGztRvD+S2wxeB1Yd6IUozvYHM5iqRzz5fa+ErNs GPY5WHDs5GP7j3zus3N8EIOwJeTNsRS16LJhXsjn80rixnxhrB5mlO8BBWY7x3xcgtn9I109gxmY ndy/lHuthPthUwcTXNwrOPdaCXc9zI9ynNwrOPdaCXcdzCjMJV2OOBT4cR5POzHtcuD/gHbNJd74 VRjkHypibCfHv4/n7fgnsvTw58PFOV2KcUpxN2Hah+lXDvxnwnr4q5KNOQcG2a/V8DNjJ+fykoQL jZlcfr+p6ovibMO9zFZ4PGc/n9u6HHO14HWU93Vc0tehEXq8yuCdDLvZ5+fjHP+EBL91pB7+dqjJ bnGsxQL/a+4XCuL0S1muHv6K5N3ZKr9nEQs/X4K/ZbQefnHyuWxV3E4mln2Kids+z43RtX+vUv9i rv9Cif73jNWN2wDoxO3FnMs6CZfmiF7c1uF+exs8HD7AY3a/Im7reF/Nkr6OjdO12+thVdw2c/xb Jfi/Ga8btyQjbsOO+fY6Pt/ulMy3OvilUM78PpF/P7gJHf9k0L3ep65cEpnr/QKb3PowKNd0gf/I KH/4VE4H/+l8f/hUTge/t8AfPpXTwad2/Lfhz/5ULx37+8EXftOxvx984Tcd+/vBF37Tsf+loIf/ VLb1W4HVefbfCqTvYkr5FSD93t/pK8pBx1e6ujh9pYNPbe4HX/hYx1d+8IWPdXxFx9S5HIt+x7pu rPmNZV37+LX/pQCe57PhnhEPc0XeIukz4s7zmsMbJtJUjnn1GdHr/uNtYvHpIe4z9+8n6t5/fBjs 0rif6OF9nZL0dfsk3fuJgPJ+4hTH/4647yemTda9n9gTUN1P9HN8+gMQp/4PTda9nzgc2D/IHWvq 3siw+soz3GfEqil6fVUlvw98OIhfhhqH+fxydbaRjsPLC5vDDefTVI75od1VVBrWHcByw30H0DZV 9w7gOdN+tt7EMW+RYEam62J2Z2DezzEfk2AenKGLOSrQ5eBewbnXSrjr3StcFHByr+DcayXc9TDr A07uFZx7rYS7HuZMotr7LzKsvfkyw703XzdVb2++GcLmAcfdtsC/wqDnc5Q33GeyudMA3gVv/AZY ZC5X6L+B698k0f+FC3T136zUfyvX/1aJ/vdO19O/CTrMBxT6t3H9OyT6b5yhq/9yUOnfwfV/QqJ/ 2Uw9/evRiw/Y1utXCv3tN6iczn5m5gX+8KmcDv7rRf7wqZwOfnyWP3wqp4NP7ehnPyb8pmN/P/jC bzr294Mv/KZjfz/4wm869vezXxV+07G/H3zhNx37+8EXftOxvx984Tcd+/s5Tw1lfPkdv7rx4zc+ de3j1/7/jfPUn/g+9jXbPnb87ObwKZbKMe//PPUG37efkJwRFs3RPU+5v0OQnUdO8L4+k/Q1slj3 PDWXqM5Tn3H8bwz3eeqZYt3z1OfBFsUZp5/jh0333nJvie4ZJ5DxPZX9+4rRprV3nWS6v+99d64e /obkFDissD/FXcD/n8Vp/0fn6Z4HAxn37iD5XcOSUjw7Y3v6/f448bsmnqf6mCTM/DbCEP8kM9LY C2UmrTMIYW3mkQmshhj0v15oLpu1puPme+PjAdsvBq3/YWnYsnFb4YqN8cLVN25Z7/5FDsWcy3/3 nG0MgD2XiZn+Lww9TCKTt37zVtcw6A/eLHlDqQljJ5DKvZFMlzwZEpOAEmdojIKDyZd5y4dk8kPg kZXCyfwc5Jam31GJmrTthQ0kNhwC93CqLz99iyjNlAUHH9PzsxOZuEpMl8+dLUKukiyHjU76jLNs R9+qz+eSb8jhL9M2x9g9WMJ/J54f2AsLTAD5DCJ6pbN5Wc4qPim1QG5qjFs1K/Gz9QvKoERDIZ3L 2ryH67fQWdQUsJrtEHbJTGU176dkgqmaBaymEmdgp9Xo3dZ3hhXeaT1y2LxehLNxPdZcw1Ib5ttS 7TO9afWYRDkRJVbP06GT9VyKfETJhSxSoraSdpLZZrVLajWXspe0p3AEJ6smAXEmXQWjHdokYCer mZ+SCaZq7mM1q5C3e4yO5G062bfT2xq2ooXDiJH2nkA5ylDKUviBVM1xh9fCqZqvWc0KiU5ZjGGx hMdkktlPWqaYePO4mFAedTduw5Jc5OLmUUdUPJpJJo+0TmkvUrxxRhS2ZEZLIh1d7DfQhoktnPEj ZHs9ZXuVsncSL9k7iUr2oKfsQYVszJNvVMk35sk3quQb8+QbVfKNefKNKvm2evKNKfm2evKNKfm2 evKNKfm2evKNKfmaGvF8UBlX3rHhP65iw/BRq0R2qGvES7i2vclSG+bbpH6Tr5FvE7FGqlfCHqJa CU8R1UrYT8RK6N7RiDYBQ6wS7r69GM80DJjAUhvm2zxXwUrDuQpucpXcbzhXuEpXySZXSVrKOVMv YjWbUWexo7Jq7oQrWE0DBF0yG5QyTaymCXJcMm1KmQ5WUw/pUVBqeI2gUkM1gmo9ZWuVsnd7yt6t lH3WU/ZZQzVyvfhGlXxjnnyjSr4xT75RJd+YJ9+okm+rJ9+Ykm+rJ9+Ykm+rJ9+Ykm+rJ9+Ykq+p Ec/PKuOq1LedYxp29u+jVonsUFeEF3BufJWlNswPZUV4w/BeEU4YqhXhMyNzRUjP9v1G5pkgnKoZ zf7fdgOMcvUzycxcRcR5x30eZH/gPzrB8rqIRgAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0198_image057.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61WXUhUQRT+5u5qVpZ12zbLqLUf6Z+2jHpoUwmlBzO1rSAiMltyY9VVo9tDD0JC EAWKEVFCPkQUCT0UBCH0UFQPBRH90A+lFUagZX8URN3OmTtjt6uFRAfOnZlzZr458535uQ9vXz8O KSWYiSpZC2wSGAn4yvz0wV4f2/ibk5qBntRNa4tWC9lPIHzEKYFrqQ4Kl9xO4JfkkWa72kdHAIsJ L1S4toh785gpZPfDIymOMZ8A+72+F340nvVhPFXTSdNITVXn+YOqnkk6WdVt2+Z1YRxpBul7MoxS bZYxhtM/XbXLSZPCwdvygwa7pFlTQBJFHNWIoQEhYjEGi8py1JKtAjUYjogATY1ZZSLArRHKmvnR xJ3TF9EpDGz7YOLRzm5rzesL0sf9m4PNCN0Qgc58YjtrlnmnqVkUEJftbUvFyZUJVMwHGlWQT6jd 9NlEhOpcaonIrwnfqoTEhPJ3bW4VHV3AsV0tAnsq6mPJhniitgbREhHgeVm5zkqR4Px+SDvLUPEc XpZAG2meylWamitMumOP05ztyp/Og+3Kg/HnPMjQd6OSMhHGv4sp5+7tNTE+t9ti7rVkqDIbB8UD v5owxdlzVX0mHmfV16XovN2bKLcuf3hcQaC+7lZxjdzf0YkzlqftfGldmvvKChqC0Jx9n9/HSL/y e4rarBzPISp7Jg1s0wE/M7R++wvLHf+ZBd3WVyEG4oWa//a5y087GKe82+J2yJMH235ue/NguLj3 /Zl7/J8zAKyh+OpOrNu3l7R9QnRfMsVnzNOHjOMg/9S+ddLeprjxrp8lB3OQfGPizdZPlpuvv2Hz WI39VWE3Nn6xilOF2UWNKt3xnYmrhMvY7NN99dzb1q8Q7a9zybRCRPqFyb5pP6aHkm9NtBZSPKSD ube/e7n34fe7yJ2Tacqn76wWv3NVus9MVKk+HOnqDuZ4Nm64nydw8wr7DihbsScXtpJSqpf2x3HR hRlUmDlDYJaJ4WFG+p073b1ejR92vRshD/4zY3j4YeL/rodDL28dxFsP9R/Lb56yj1N1PpM+kSZ5 Ha0PO9KNmbS72WfQGeNykciUHmHw68K1kbL3VNJvxivbdVKctyJeHWsIlcSsUHltdcXgk8GYCwUU kj00knPbVcb/etU5SGKo8Rh+JIZrTRqRywXCeaeCfmZE8+NEzG/sklFT1JJLiX9tCUpLhFjW6NoT lp4wxnrmGzyP/B3BT6ZJ4gq4CAAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0198_image058.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61WXWhUVxD+zr27MW6jidc1XZugK2oI1RY1Kfjg1kRR8xBXTbe1FGkTNWhkYxIV byiCCxVKSwspfZE2kDyIKBV9qH0pQgWhlVJBpCr9eUjEJgomrloxUHWdOT/Xu9eNxpKBueecmTkz c745P/fqhZ+/gaSNmI+dshfZLDAVsFeHgRBWhVjG36qiUnxcvHn92tVC2gmk1qkWeL9YeeGWx2k8 pXrieb7x+SnAEhuIr1m/lq15zhyShxEgFlDcOnKYDequhZA5bmMGdUuIObyj+xy/XPdjxLN1P5fL 8bpQRlxKfIcEET1mmmYp+xI9biLuFMrflsc02Uc9BgKiFNrQjlbsRRxJal1qm9BBshbsxkRIRCk0 FmwSUR5N0dLYPQcXj57GGWGh+a6DP3YMug3D30sd2/eU9yD+i4ieqSO0KxY4Fw/1iPoioL+3RvSt SKNlEZDRSf5F40P3HSSoz62hhPw6sN9OS5/Q+oEPvhanqUaHd30lsL01va+F6kX5pJIiynGZuc9M meDUJ5BypkL5fPlWGr3EK3Wt9HZBLfH2/Wq40Fc/U4ecrw7WOHXQKuzDNqrEUvx/cmTsW7cczKgd dBl7Q6W6nYfPxZWQDhhWe27niIM/K/Z0mf0b+32W2sthNa8+uqfrt8bdtDO6KUe1vmaaM/Sqt/W8 +Lzqd7Zec42km+zQ/gM+o0nHqMXAo4PBrL8gm48u/+Py/GOLB90xIbx8oeNf+O7Hv09wzKZBl8fx QB3oKBwM1sHyYW+PfwYmCft8fKpQjehNJ8+igfLv+nbDgW7i/pmpA51h23rdHELOk/SVIxukvHfE 8eR+fJiOjDo49+G/7k3ixiLhsC3TjVHV1mG56B+uFbCXi2Q2cq+hYjZOLlO2Z8mW7xyWZTIPpGxA B+omXiFzB84SZ4SHEZo1E9LZuXQ/+LF/QOAHsbd92IfGxx6Tc/9MHrZct06qG2NrfB95gW+ea3yP ad9BbCXdzq/bmJdHoG7UJrKRhUtqntatclTVjWV+7G8XwD6E/HfAX5M5Wmfei1Mh9Uz57yv/+Ulp Ngdlun4LOe/33r28UuD8T6z7VMsaA3XJadpI/WQW1qVAPsZ/TPuvLuC/Q0zMfyKr3lk/DsZ/je8t jwf8P7Qm5p/v+ksBbIN4/kpBh8iecYpqeZnucz62KJZ4v2IuYJRY8+nfhXUW3XvcviliUiMsfvG5 N1VaVxL/Z13P+U6Qer/b2lv3xpOtbrypo73l2RPDPt8Q0J5yBTx5L9C2tudegcqTKJTJS8y3Cs3H xFdi+zAxHrldLNS/R3mIETX4qhWbzPn/aVnkNQ1dsm+658FoYlKT6CvzohlNjdTU0pz8+M/GteX3 CR2ceaWcCgAA ------=_NextPart_01C60EF7.14366D20 Content-Location: file:///C:/9EC85B93/DelayedLinSys_files/slide0198_image059.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC61WW2yUVRD+zv/v1qWWtvxd69Y2ughtiFaytpj0wQ00aMNDb5ZVXgxQSyNNegXl 70OTUiUxGk1WY4ipTdoEYjASfaC8GBIIGG8RQgiXcHmgjUBIQOstqaG6zpzLcvhpyapMMv/MmTNn zvzfnNu541+PQtJGLMNWqYU2CCwC3B1h0tEdYht/q/KKcCKyoalhrZB+ApMDSgL7IyoKS2534za1 EC+12sspeMIF4s83NbA3j3mM7GEEiA007xoKOBPsmw5h56culpBaQMzTe1rn+Uu1HiMu03omk+H/ QjFxEfEvZMjXbabFjvIv0O024n6h4r38Nw22KG0gIEqhCz3oxHbE0UzSJ9mGPrK1oxe5kIg6jMsL IsqtB7Q19puHk59M4pBwsPlXD+dfnfLXXTsg+9g/XZpG/BsRPbSG0C5f7p3clRb1ecDEWK0Yf7Yb 7U8CO3WSF6m96w8PSdJZGkqaDKyYjZOQefSOIsptR4IzjDjlk2oW0sbMOjONwhdvKl+mxOtANcn3 nunGGHHE0lfrWunlggTxlh2qWWnVz9QhY9XBWaAOQuv/vw6ejHXjhoclq6Z8xt5QkZZL8Y44G1K5 8PpkJLfe9HChfNuAWb+x0w+ptRxW4+qj2wZ+aOzFIPkx8xybSV59OLv0svPzX69/Zdo3FvZHz0G8 TYP2kcTlv4aDWb9LPpvOXPF5/L7qKX9WiGy+0PMf/+zLS/t5zrYpn9vsY9eBtsKtYB0cC3t34T0g oXgNHYT+0/jvVOkiTYwSVFOeK7+f87/ivfmhsjGr6ZQ+KEpw5Ls5P5JXgkqSl3m98v/IGPfGh8d/ lKpyOYaRdLq5b9CX8YHGh+dOjKr5G3idUexiPg1JCr1On6PY3h7P5djvj/zpt+6e9QnLTMVPHhYf bRlS+aq8TI6J2rIg9oeD2LsW9qGFsb9P6/7+YVuFFei/7kFhqmgv+Qx83DI0SDxRkhrqD7vOE7i9 b3lsxc0WaZ/V+yOIraSfPRzb+Lt/nbgxT3jG1/S3Pl4nJq6tIlOdSM7kf7CuvAyf1yhfrgffFWwL YD8cxD6EO+8BuyaP6j5zX4yE1TVln1f2/klpNlRIHNf/99KLZ1YLfHuY7W9pW2MA34ymVlUD51Qg HxM/pudboe9aO36fyC1+ckbdszYOJn6tOUvmyX/OyS1+DfEpK2a99T4Ixjzh5hYzoWPa9QrWaIwK dJX8Gfuothdrnf/RFRFZwwfNoY4CZxm9h7jPoXOA5UoRkz3C4VcEa4ukdwXxLefHjLUr1Zugq6dz e7y504+39fW0370LOeZTAjpSZp5I2Vstp0hivkzUydzRdc9jWY13