Adaptive Terminal Sliding Mode Fault-Tolerant Control of Spacecraft Based on the Left Attitude Error Function of SO(3)

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Parameters</td><td class="align_center">Case 1</td><td class="align_center">Case 2</td><td class="align_center">Case 3</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><span style="width: 7.47216ptpx;"><svg height="12.3916pt" id="M85" style="vertical-align:-3.42948pt" version="1.1" viewbox="-0.0498162 -8.96212 7.47216 12.3916" width="7.47216pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g></svg></span></td><td class="align_center">7.7730<span class="nowrap"><svg height="6.1673pt" id="M86" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.50181 6.1673" width="5.50181pt" 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="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g></svg>-</span>05</td><td class="align_center">0.0686</td><td class="align_center">7.7724<span class="nowrap"><svg height="6.1673pt" id="M87" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.50181 6.1673" width="5.50181pt" 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="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g></svg>-</span>05</td></tr><tr><td class="align_left"><span style="width: 22.4701ptpx;"><svg height="14.5054pt" id="M88" style="vertical-align:-3.9253pt" version="1.1" viewbox="-0.0498162 -10.5801 22.4701 14.5054" width="22.4701pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-6.668)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-3.066)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,.535)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,4.136)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.363,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.68,3.132)"><path d="M636 22C611 29 589 38 560 74C536 104 518 134 495 173L430 300C518 328 592 392 592 492C592 555 563 594 528 618C491 643 435 650 377 650H140L131 618C222 610 223 601 208 518L137 136C121 43 116 40 27 32L18 0H295L300 32C212 40 206 42 223 138L248 279H296C334 279 350 272 369 230C393 174 413 140 441 94C482 24 523 1 626 -8L636 22ZM497 480C497 422 468 374 417 343C387 324 353 315 304 315H255L298 556C303 583 309 598 319 603C331 610 348 613 367 613C448 613 497 573 497 480Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.988,-6.668)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.988,-3.066)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.988,.535)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,16.988,4.136)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g></svg></span></td><td class="align_center">0.0088</td><td class="align_center">0.2597</td><td class="align_center">0.0088</td></tr><tr><td class="align_left"><span style="width: 23.6758ptpx;"><svg height="14.5054pt" id="M89" style="vertical-align:-3.9253pt" version="1.1" viewbox="-0.0498162 -10.5801 23.6758 14.5054" width="23.6758pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-6.668)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-3.066)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,.535)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,4.136)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.363,0)"><path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.68,3.132)"><path d="M727 145L694 147C669 79 660 74 614 74H536C582 128 696 227 696 364C696 547 564 666 388 666C215 666 78 544 78 361C78 224 189 126 240 74H155C117 74 102 83 79 147L48 145L64 0H313L320 21C290 72 182 208 182 360C182 527 261 628 387 628S593 523 593 362C593 199 488 69 456 21L461 0H709L727 145Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.193,-6.668)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.193,-3.066)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.193,.535)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.193,4.136)"><path d="M162 0V316H102V0H162ZM309 0V316H249V0H309Z"></path></g></svg></span></td><td class="align_center">0.0554</td><td class="align_center">0.0627</td><td class="align_center">0.0554</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Error situation table for three cases at 50 s.</div>

International Journal of Aerospace Engineering

tab2

Table 2

Table 2: Adaptive Terminal Sliding Mode Fault-Tolerant Control of Spacecraft Based on the Left Attitude Error Function of SO(3) 