Comparative Analysis of Neural-Network and Fuzzy Auto-Tuning Sliding Mode Controls for Overhead Cranes under Payload and Cable Variations

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:5.65em"/><col style="width:4.11em"/><col style="width:5.20em"/><col style="width:6.66em"/><col style="width:3.67em"/><col style="width:3.35em"/><col style="width:5.86em"/><col style="width:5.89em"/></colgroup><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td class="align_left">Parameter:</td><td class="align_center"><svg height="9.35641pt" id="M188" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -6.0653 15.4068 9.35641" width="15.4068pt" 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="M801 97L785 128C766 109 732 86 722 86C717 86 712 92 717 114L759 300C790 439 749 454 720 454C700 454 681 447 653 434C628 422 565 377 487 276H485L490 301C520 439 483 454 451 454C427 454 404 445 375 429C353 417 294 378 208 268H206L223 335C243 412 241 454 204 454C161 454 89 411 21 347L36 314C51 331 92 357 103 357C112 357 110 348 106 331C80 211 56 108 24 -2L33 -12C64 -4 113 6 152 9C165 74 180 143 198 196C231 251 330 364 363 364C379 364 379 333 367 275C349 188 325 94 298 -4L307 -12C339 -4 385 6 430 9C440 73 452 131 468 194C510 259 602 364 637 364C647 364 651 342 641 301L590 88C571 8 590 -12 623 -12C657 -12 732 23 801 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.726,3.132)"><path d="M425 395C425 436 373 457 323 457C255 457 183 422 140 386C62 321 22 236 22 147C22 51 67 -12 165 -12C232 -12 320 30 393 106L370 142C347 119 282 74 238 74C190 74 164 107 164 186C164 255 179 301 203 355C216 384 236 400 256 400C290 400 320 375 350 329C356 320 367 317 375 322C412 343 425 373 425 395Z"></path></g></svg>[kg]</td><td class="align_center"><svg height="12.0314pt" id="M189" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 12.9928 12.0314" width="12.9928pt" 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="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.281,3.132)"><path d="M425 395C425 436 373 457 323 457C255 457 183 422 140 386C62 321 22 236 22 147C22 51 67 -12 165 -12C232 -12 320 30 393 106L370 142C347 119 282 74 238 74C190 74 164 107 164 186C164 255 179 301 203 355C216 384 236 400 256 400C290 400 320 375 350 329C356 320 367 317 375 322C412 343 425 373 425 395Z"></path></g></svg>[Ns/m]</td><td class="align_center"><svg height="14.114pt" id="M190" style="vertical-align:-5.3737pt" version="1.1" viewbox="-0.0498162 -8.7403 14.6552 14.114" width="14.6552pt" 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="M401 353C473 367 557 406 557 502C557 551 535 592 498 616C460 640 410 650 333 650H41V615C112 608 121 602 121 516V134C121 49 112 42 35 35V0H289C372 0 449 14 500 43C556 74 593 126 593 193C593 288 517 335 401 349V353ZM253 363V553C253 574 255 589 262 596C268 602 284 609 307 609C361 609 415 575 415 484C415 401 372 363 276 363H253ZM253 323H273C386 323 445 276 445 182C445 84 382 43 326 42C273 41 253 62 253 136V323Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.281,3.132)"><path d="M607 293C607 404 553 457 443 457C407 457 387 456 348 448L366 523L354 532C314 517 252 484 228 458L217 419C184 408 144 391 110 369L122 333C146 345 173 356 204 366L106 -115C94 -173 75 -187 17 -196L9 -237L300 -224L308 -184L291 -183C235 -180 221 -171 232 -117L255 -3C278 -10 292 -12 315 -12C385 4 443 33 516 102C579 162 607 239 607 293ZM467 292C467 184 389 41 325 41C312 41 283 58 272 72L335 392C347 395 361 398 381 398C425 398 467 380 467 292Z"></path></g></svg>[Nms/rad]</td><td class="align_center"><svg height="11.4129pt" id="M191" style="vertical-align:-5.37372pt" version="1.1" viewbox="-0.0498162 -6.03918 11.6148 11.4129" width="11.6148pt" 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="M220 349V455C158 436 98 425 38 417V389C85 378 92 374 92 323V104C92 43 83 38 28 32V0H302V32C225 38 220 43 220 104V291C237 330 257 343 276 343C292 343 305 336 322 322C329 316 339 313 353 318C379 328 402 356 402 392C402 426 374 454 335 454C297 454 259 411 222 349H220Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.252,3.132)"><path d="M607 293C607 404 553 457 443 457C407 457 387 456 348 448L366 523L354 532C314 517 252 484 228 458L217 419C184 408 144 391 110 369L122 333C146 345 173 356 204 366L106 -115C94 -173 75 -187 17 -196L9 -237L300 -224L308 -184L291 -183C235 -180 221 -171 232 -117L255 -3C278 -10 292 -12 315 -12C385 4 443 33 516 102C579 162 607 239 607 293ZM467 292C467 184 389 41 325 41C312 41 283 58 272 72L335 392C347 395 361 398 381 398C425 398 467 380 467 292Z"></path></g></svg>[m]</td><td class="align_center">R[Ω]</td><td class="align_center"><svg height="12.0314pt" id="M192" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 17.4254 12.0314" width="17.4254pt" 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="M699 0V35C659 41 632 57 591 109C519 200 445 301 381 397C426 443 468 491 527 545C582 597 623 609 685 615V650H425V615L443 613C490 607 492 592 468 561C435 516 395 467 328 399C298 368 273 352 252 346V516C252 602 260 608 331 615V650H37V615C112 608 121 602 121 516V134C121 48 111 42 39 35V0H338V35C261 42 252 48 252 134V314C267 316 280 310 301 280C372 176 455 59 498 0H699Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.139,3.132)"><path d="M816 97L798 134C780 118 744 92 734 92C731 92 726 98 731 120C731 120 771 304 772 304C803 443 760 457 729 457C709 457 690 450 661 438C636 428 575 384 496 283H494L499 307C530 442 488 457 456 457C433 457 408 450 379 433C357 420 301 382 216 277H214L228 335C247 413 246 457 206 457C164 457 93 416 22 349L38 314C53 329 93 354 104 354C113 354 112 346 108 330C82 213 58 110 25 0L35 -12C68 -4 117 6 158 11C171 76 187 141 203 192C234 249 333 361 369 361C383 361 383 326 374 284L304 -2L311 -12C346 -4 394 6 438 11C449 74 462 131 476 190C517 258 609 361 645 361C656 361 657 337 648 300L599 93C579 8 600 -12 636 -12S749 25 816 97Z"></path></g></svg>[Nm/A]</td><td class="align_center"><svg height="11.9218pt" id="M193" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7403 15.5986 11.9218" width="15.5986pt" 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="M699 0V35C659 41 632 57 591 109C519 200 445 301 381 397C426 443 468 491 527 545C582 597 623 609 685 615V650H425V615L443 613C490 607 492 592 468 561C435 516 395 467 328 399C298 368 273 352 252 346V516C252 602 260 608 331 615V650H37V615C112 608 121 602 121 516V134C121 48 111 42 39 35V0H338V35C261 42 252 48 252 134V314C267 316 280 310 301 280C372 176 455 59 498 0H699Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.139,3.132)"><path d="M628 650H133L125 606C212 600 216 590 204 522L128 125C115 57 109 47 24 42L17 0H537C554 41 586 126 598 162L556 180C534 136 509 105 483 79C460 58 429 50 362 50C310 50 285 55 274 75C264 94 266 122 274 161L301 311H375C467 311 461 307 457 225H504L542 439H496C470 373 471 367 376 367H311L344 551C353 598 358 600 401 600H451C511 600 529 593 540 577C558 559 562 523 565 478L612 481L628 650Z"></path></g></svg>[V/rad/s</td></tr><tr><td class="align_left" colspan="8"><hr/></td></tr><tr><td class="align_left">Value:</td><td class="align_center">25</td><td class="align_center">0.25</td><td class="align_center">0.1</td><td class="align_center">0.07</td><td class="align_center">3.35</td><td class="align_center">0.24</td><td class="align_center">0.24</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Numerical values for the simulation model parameters.</div>

Journal of Control Science and Engineering

tab3

Table 3

Table 3: Comparative Analysis of Neural-Network and Fuzzy Auto-Tuning Sliding Mode Controls for Overhead Cranes under Payload and Cable Variations 