Analysis and Synthesis of Global Nonlinear <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.458401pt" id="M1" height="16.7905pt" version="1.1" viewBox="0 -12.3321 30.3484 16.7905" width="30.3484pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><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(.013,0,0,-0.013,17.831,4.308)"><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> Controller for Robot Manipulators

<div>Simulation output responses (a) and input torques (b) of the perturbed closed-loop system under <svg height="11.9224pt" id="M208" style="vertical-align:-2.303181pt" version="1.1" viewbox="0 -9.61922 43.4323 11.9224" width="43.4323pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M542 56L520 58C483 62 478 72 478 124V449C455 445 422 441 387 438C351 435 316 432 287 431V402L318 395C345 389 350 383 350 336V93C328 71 306 65 279 65C245 65 211 88 211 153V298C211 356 211 407 214 449C187 445 151 441 118 438C84 435 53 432 28 431V402L51 395C77 388 83 383 83 337V130C83 42 131 -12 214 -12C245 -12 272 -1 300 18C322 31 333 41 350 55V-5L359 -12C389 -5 420 2 452 8C485 15 513 20 542 24V56Z" id="g13-115"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,7.519,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,12.207,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,16.827,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,25.3,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,37.038,0)"><path d="M252 635C85 635 28 460 28 311C28 167 82 -12 250 -12C419 -12 472 166 472 312C472 457 419 635 252 635ZM248 594C314 594 335 455 335 314C335 174 318 29 252 29S165 180 165 315S181 594 248 594Z" id="g13-46"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Analysis and Synthesis of Global Nonlinear <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-4.458401pt" id="M1" height="16.7905pt" version="1.1" viewBox="0 -12.3321 30.3484 16.7905" width="30.3484pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><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(.013,0,0,-0.013,17.831,4.308)"><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> Controller for Robot Manipulators 

Mathematical Problems in Engineering

Analysis and Synthesis of Global Nonlinear Controller for Robot Manipulators

Figure 4