Feedback Control of Flow Separation Using Plasma Actuator and FBG Sensor

<div>(a) Flowchart for the closed-loop control of flow separation. (b) <svg height="9.49473pt" id="M138" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.59789 9.49473" width="6.59789pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g></svg> time-series, running <svg height="15.2701pt" id="M139" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.4361 13.9414 15.2701" width="13.9414pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.174,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="361" vert-adv-y="361"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.784)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z" id="g50-67"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="622" vert-adv-y="622"></glyph.data></g></svg>, <svg height="8.68572pt" id="M140" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 7.31558 8.68572" width="7.31558pt" 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="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data></g></svg>, and <svg height="8.68572pt" id="M141" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.095 8.68572" width="10.095pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g></svg> fluctuations for 10 s. The running <svg height="15.2701pt" id="M142" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.4361 13.9414 15.2701" width="13.9414pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.174,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="361" vert-adv-y="361"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.784)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z" id="g50-67"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="622" vert-adv-y="622"></glyph.data></g></svg> at a given time was evaluated using the past 50 values for <svg height="12.4698pt" id="M143" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 13.9414 12.4698" width="13.9414pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.132)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z" id="g50-67"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="622" vert-adv-y="622"></glyph.data></g></svg>. Flow separation occurs in the region of <svg height="11.9165pt" id="M144" style="vertical-align:-1.119801pt" version="1.1" viewbox="-0.0498162 -10.7967 31.7994 11.9165" width="31.7994pt" 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="M475 507C475 612 440 712 326 712C139 712 23 420 23 215C23 96 58 -12 180 -12C369 -12 475 293 475 507ZM391 522C391 486 387 448 379 394H126C155 538 222 677 310 677C386 677 391 571 391 522ZM373 346C344 193 283 22 189 22C126 22 106 114 106 196C106 243 111 293 118 346H373Z" id="g113-230"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="498" vert-adv-y="498"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,10.107,0)"><path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z" id="g117-93"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,21.37,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,27.61,-5.741)"><path d="M339 262C339 340 273 403 193 403S48 340 48 262S113 121 193 121S339 184 339 262ZM283 262C283 210 242 168 193 168S104 210 104 262S144 356 193 356S283 314 283 262Z" id="g54-73"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="385" vert-adv-y="385"></glyph.data></g></svg> when the running <svg height="15.2701pt" id="M145" style="vertical-align:-3.834pt" version="1.1" viewbox="-0.0498162 -11.4361 13.9414 15.2701" width="13.9414pt" 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="M529 97L508 118C475 75 449 58 438 58C428 58 421 66 415 104C393 234 374 403 364 496C345 670 307 712 254 712C220 712 174 691 153 669L161 645C176 653 194 658 206 658C237 658 261 640 278 562C287 522 290 483 293 434C223 269 110 105 23 9L32 -12C59 -6 85 0 108 7C152 64 251 252 300 366C307 297 315 221 337 82C346 24 363 -12 393 -12C425 -12 475 13 529 97Z" id="g113-233"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="552" vert-adv-y="552"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.174,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="361" vert-adv-y="361"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.761,3.784)"><path d="M598 511C598 627 497 650 401 650H141L131 618C219 611 222 606 210 538L130 119C117 43 108 39 25 32L18 0H236C324 0 396 5 456 30C531 59 585 119 585 193C585 285 520 331 428 351V353C529 373 598 423 598 511ZM502 508C502 418 431 368 330 368H263L298 559C303 584 308 595 317 600C329 608 345 612 369 612C428 612 502 595 502 508ZM483 197C483 95 404 39 309 39C225 39 206 58 219 139L256 330H317C395 330 483 301 483 197Z" id="g50-67"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="622" vert-adv-y="622"></glyph.data></g></svg> is larger than <svg height="11.7782pt" id="M146" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 55.8524 11.7782" width="55.8524pt" 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="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z" id="g113-225"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="501" 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International Journal of Aerospace Engineering

fig12

Figure 12

Figure 12: Feedback Control of Flow Separation Using Plasma Actuator and FBG Sensor 