Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" colspan="2" rowspan="2"> </td><td class="align_center" colspan="3">Differentiators</td></tr><tr class="thead"><td class="align_center">HG1</td><td class="align_center">HG2</td><td class="align_center">ST</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left" rowspan="2">Error <svg height="12.2872pt" id="M218" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.0808 6.86362 12.2872 " width="6.86362pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,6.864,-3.549)"><path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z" id="g117-11"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path></g></svg></td><td class="align_left">Norm 2</td><td class="align_center">1.4167</td><td class="align_center">1.1556</td><td class="align_center">1.349</td></tr><tr><td class="align_left">Norm inf</td><td class="align_center">24.9879</td><td class="align_center">25.0273</td><td class="align_center">10.0679</td></tr><tr><td class="align_left" rowspan="2">Error <svg height="15.184pt" id="M219" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.7546 7.82272 15.184 " width="7.82272pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,7.823,-3.223)"><path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z" id="g117-11"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z" id="g113-243"></path></g></svg></td><td class="align_left">Norm 2</td><td class="align_center">.3888</td><td class="align_center">.1292</td><td class="align_center">.0634</td></tr><tr><td class="align_left">Norm inf</td><td class="align_center">.8410</td><td class="align_center">3.2624</td><td class="align_center">.5597</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Proportional Retarded Controller to Stabilize Underactuated Systems with Measurement Delays: Furuta Pendulum Case Study 