An Embedded Linear Model Three-Dimensional Fuzzy PID Control System for a Bionic AUV under Wave Disturbance

<div>Membership function <svg height="12.5794pt" id="M162" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 27.2563 12.5794" width="27.2563pt" 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="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.748,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 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604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> corresponding to the fuzzy set <svg height="14.5316pt" id="M163" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 120.324 14.5316" width="120.324pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,2.33939e-05)"><path d="M321 -265V-236C237 -225 227 -181 227 -132C227 -64 244 49 244 143C244 202 220 254 159 269V273C221 287 244 339 244 397C244 489 227 585 227 676C227 723 237 765 321 776V805C259 805 168 790 168 663C168 574 176 471 176 380C176 342 173 292 73 286V255C173 249 176 199 176 162C176 74 168 -28 168 -127C168 -252 259 -265 321 -265Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.986,-.718)"><path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 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104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.748,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.833,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,15.331,0)"><path d="M536 404C536 423 520 448 491 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Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: An Embedded Linear Model Three-Dimensional Fuzzy PID Control System for a Bionic AUV under Wave Disturbance 