Analytical Multiloop Control for Multivariable Systems with Time Delays

<table class="table-group" id="tab6"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Methods</td><td class="align_center" colspan="2"><span style="width: 24.473ptpx;"><svg height="12.0444pt" id="M115" style="vertical-align:-3.29106pt" version="1.1" viewbox="-0.0498162 -8.75334 24.473 12.0444" width="24.473pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z"></path></g><g transform="matrix(.013,0,0,-0.013,3.95,0)"><path d="M673 0V28C608 34 594 43 563 129C499 303 432 494 370 665L339 656L132 132C98 43 84 37 20 28V0H238V28C162 35 154 45 175 108C188 150 203 192 219 237H432C454 176 474 122 487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z"></path></g><g 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487 83S491 36 428 28V0H673ZM418 280H234C265 362 296 450 328 535H330L418 280Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.484,0)"><path d="M517 162C503 123 484 88 467 68C445 42 417 34 341 34C291 34 256 34 237 47C219 59 213 81 213 128V317H308C395 317 402 311 415 240H444V431H415C403 364 398 356 307 356H213V584C213 613 215 616 246 616H322C394 616 421 609 435 587C448 566 458 544 467 502L496 506C493 557 488 625 488 650H42V622C120 616 128 612 128 523V125C128 43 120 35 29 28V0H511C520 31 540 125 546 158L517 162Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.976,3.132)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z"></path></g></svg></span></td></tr><tr class="thead"><td class="align_center">Nominal</td><td class="align_center"><span style="width: 30.1509ptpx;"><svg height="8.85534pt" id="M117" style="vertical-align:-0.4673595pt" version="1.1" viewbox="-0.0498162 -8.38798 30.1509 8.85534" width="30.1509pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.631,0)"><path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z"></path></g><g transform="matrix(.013,0,0,-0.013,13.871,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 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302C133 302 122 403 122 454S133 605 193 605ZM567 351C465 351 421 250 421 169C421 90 465 -12 566 -12S710 90 710 170S667 351 567 351ZM566 322C628 322 637 221 637 169C637 121 628 18 567 18S494 119 494 170C494 223 506 322 566 322Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">Proposed</td><td class="align_center">234.4048</td><td class="align_center">219.1850</td><td class="align_center">16824.34</td><td class="align_center">14245.40</td></tr><tr><td class="align_left">He</td><td class="align_center">278.6150</td><td class="align_center">447.8400</td><td class="align_center">10393.18</td><td class="align_center">20731.42</td></tr><tr><td class="align_left">Shen</td><td class="align_center">316.1688</td><td class="align_center">323.3098</td><td class="align_center">25146.40</td><td class="align_center">22231.41</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Complexity

tab6

Table 6

Table 6: Analytical Multiloop Control for Multivariable Systems with Time Delays 