Integral Sliding Modes with Nonlinear <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3443pt" id="M1" height="16.2432pt" version="1.1" viewBox="-0.0657574 -11.8989 30.4769 16.2432" width="30.4769pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g198-9" d="M714 664L702 678C677 661 651 638 627 626C588 607 568 607 547 607C524 607 496 619 461 638C391 673 360 687 319 687C215 687 144 611 144 536S191 410 271 410C339 410 379 452 412 517L394 526C361 473 326 440 273 440C209 440 185 482 185 534S237 635 301 635C329 635 366 621 403 601C456 572 487 557 527 557C532 557 540 557 547 558C427 454 384 369 336 292C189 231 53 149 53 45C53 9 77 -15 110 -15C127 -15 146 -11 166 -4C260 31 369 152 443 298L550 339C495 254 446 155 446 77C446 21 481 -12 533 -12C594 -12 659 42 735 134L714 147C642 63 586 18 547 18C528 18 513 32 513 53C513 111 593 253 687 387C835 446 991 527 991 637C991 673 965 687 934 687C874 687 752 597 612 422L579 379C540 364 503 356 464 340C536 484 606 581 696 650L714 664ZM958 635C958 559 851 493 720 434C805 554 896 657 934 657C950 657 958 650 958 635ZM307 241C253 147 171 15 110 15C98 18 86 24 86 44C86 120 179 182 307 241Z"/></g><g transform="matrix(.012,0,0,-0.012,17.109,4.134)"><path id="g50-30" d="M1000 227C1000 351 905 451 780 451C658 451 590 380 530 279C465 385 388 451 261 451C168 451 38 376 38 210C38 98 121 -12 261 -12C381 -12 448 59 508 160C573 53 652 -12 780 -12C879 -12 1000 64 1000 227ZM485 199C434 109 370 25 271 25C188 25 133 117 133 241C133 355 189 414 249 414C357 414 426 302 485 199ZM903 204C903 70 852 25 790 25C681 25 611 136 552 240C603 330 669 414 768 414C855 414 903 321 903 204Z"/></g></svg>-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

<div>First simulation. Link position error <svg height="12.6786pt" id="M329" style="vertical-align:-3.42939pt" version="1.1" viewbox="-0.0498162 -9.24921 6.50656 12.6786" width="6.50656pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.137,-.222)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z" id="g119-25"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z" id="g113-114"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="491" vert-adv-y="491"></glyph.data></g></svg> and joint position error <svg height="12.783pt" id="M330" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.5766 6.59789 12.783" width="6.59789pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.183,-3.549)"><path d="M470 619L451 641C422 610 391 595 348 595C316 595 288 601 248 612C197 628 172 633 138 633C97 633 43 615 0 555L19 532C54 562 86 578 130 578C166 578 189 571 222 562C267 549 301 540 337 540C381 540 434 557 470 619Z" id="g119-25"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="470" vert-adv-y="470"></glyph.data></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><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g></svg> corresponding to the iSMH controller and the Cao-Xu controller, respectively, using the link reference signal (<a href="https://static.hindawi.com/articles/mpe/volume-2017/4876019/figures/#EEq61">64</a>).</div>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Integral Sliding Modes with Nonlinear <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.3443pt" id="M1" height="16.2432pt" version="1.1" viewBox="-0.0657574 -11.8989 30.4769 16.2432" width="30.4769pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g198-9" d="M714 664L702 678C677 661 651 638 627 626C588 607 568 607 547 607C524 607 496 619 461 638C391 673 360 687 319 687C215 687 144 611 144 536S191 410 271 410C339 410 379 452 412 517L394 526C361 473 326 440 273 440C209 440 185 482 185 534S237 635 301 635C329 635 366 621 403 601C456 572 487 557 527 557C532 557 540 557 547 558C427 454 384 369 336 292C189 231 53 149 53 45C53 9 77 -15 110 -15C127 -15 146 -11 166 -4C260 31 369 152 443 298L550 339C495 254 446 155 446 77C446 21 481 -12 533 -12C594 -12 659 42 735 134L714 147C642 63 586 18 547 18C528 18 513 32 513 53C513 111 593 253 687 387C835 446 991 527 991 637C991 673 965 687 934 687C874 687 752 597 612 422L579 379C540 364 503 356 464 340C536 484 606 581 696 650L714 664ZM958 635C958 559 851 493 720 434C805 554 896 657 934 657C950 657 958 650 958 635ZM307 241C253 147 171 15 110 15C98 18 86 24 86 44C86 120 179 182 307 241Z"/></g><g transform="matrix(.012,0,0,-0.012,17.109,4.134)"><path id="g50-30" d="M1000 227C1000 351 905 451 780 451C658 451 590 380 530 279C465 385 388 451 261 451C168 451 38 376 38 210C38 98 121 -12 261 -12C381 -12 448 59 508 160C573 53 652 -12 780 -12C879 -12 1000 64 1000 227ZM485 199C434 109 370 25 271 25C188 25 133 117 133 241C133 355 189 414 249 414C357 414 426 302 485 199ZM903 204C903 70 852 25 790 25C681 25 611 136 552 240C603 330 669 414 768 414C855 414 903 321 903 204Z"/></g></svg>-Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances 

Mathematical Problems in Engineering

Integral Sliding Modes with Nonlinear -Control for Time-Varying Minimum-Phase Underactuated Systems with Unmatched Disturbances

Figure 3