Finite-Time Reentry Attitude Control Using Time-Varying Sliding Mode and Disturbance Observer

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/262753/figures/262753.fig.006a.svgz" name="262753.fig.006a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Comparison between <svg height="6.53193pt" id="M341" style="vertical-align:-0.24019pt" version="1.1" viewbox="-0.0498162 -6.29174 5.30805 6.53193" width="5.30805pt" 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="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z" id="g13-113"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="383" vert-adv-y="383"></glyph.data></g></svg> and <svg height="9.71953pt" id="M342" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.29174 11.2852 9.71953" width="11.2852pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z" id="g13-120"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="445" vert-adv-y="445"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.029,3.264)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> under BTVSMC/DO</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/262753/figures/262753.fig.006b.svgz" name="262753.fig.006b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Comparison between <svg height="6.53193pt" id="M343" style="vertical-align:-0.24019pt" version="1.1" viewbox="-0.0498162 -6.29174 5.30805 6.53193" width="5.30805pt" 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="M338 322C336 342 324 413 314 436C291 446 264 454 218 454C113 453 50 390 50 312C50 226 131 187 178 164C239 135 253 110 253 81C253 51 231 27 199 27C138 27 91 96 69 159L40 156C40 108 49 38 55 22C76 7 128 -12 181 -12C265 -12 360 37 360 136C360 214 306 249 225 284C174 307 151 330 151 361C151 393 176 415 202 415C249 415 281 374 308 313L338 322Z" id="g13-113"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="383" vert-adv-y="383"></glyph.data></g></svg> and <svg height="9.71953pt" id="M344" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.29174 11.2852 9.71953" width="11.2852pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z" id="g13-120"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="445" vert-adv-y="445"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,6.029,3.264)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> under SOTVSMC/DO</td></tr></table>

<div>The estimations of sliding surface by BTVSMC/DO and SOTVSMC/DO.</div>

Mathematical Problems in Engineering

fig6

Figure 6

Figure 6: Finite-Time Reentry Attitude Control Using Time-Varying Sliding Mode and Disturbance Observer 