Mixed Skyhook and FxLMS Control of a Half-Car Model with Magnetorheological Dampers

<div>Comparison of vibration control quality for the front/rear Skyhook and mixed Skyhook-FxLMS algorithms: (a) the heave index for the front and rear excitation in phase and (b) the pitch index for the front and rear excitation in antiphase. Dashed lines—the average of <svg height="13.9769pt" id="M168" style="vertical-align:-5.341001pt" version="1.1" viewbox="-0.0498162 -8.6359 12.7601 13.9769" width="12.7601pt" 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="M429 650H175L169 622C251 614 259 612 244 532L174 152C163 91 152 37 135 -6C109 -72 67 -101 23 -113L33 -144C45 -143 73 -134 102 -119C186 -76 229 -1 254 133L327 532C341 609 347 613 423 622L429 650Z" id="g113-75"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,5.031,3.132)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g><g transform="matrix(.0065,0,0,-0.0065,9.099,5.233)"><path d="M363 392C363 416 330 454 273 454C246 454 189 439 146 400C110 367 97 335 97 309C97 248 143 215 199 179C254 144 264 123 264 101C264 77 242 42 196 42C156 42 112 77 90 109C83 119 76 123 55 112C40 104 25 89 25 66C25 31 88 -12 141 -12C238 -12 336 62 336 140C336 194 300 230 238 264C200 285 168 308 168 347C168 383 200 399 223 399C263 399 285 381 306 348C310 341 322 335 334 342C352 352 363 374 363 392Z" id="g176-116"></path><glyph.data ascent="3439" descent="-2858" horiz-adv-x="388" vert-adv-y="388"></glyph.data></g></svg> and <svg height="13.9769pt" id="M169" style="vertical-align:-5.341001pt" version="1.1" viewbox="-0.0498162 -8.6359 14.3677 13.9769" width="14.3677pt" 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="M429 650H175L169 622C251 614 259 612 244 532L174 152C163 91 152 37 135 -6C109 -72 67 -101 23 -113L33 -144C45 -143 73 -134 102 -119C186 -76 229 -1 254 133L327 532C341 609 347 613 423 622L429 650Z" id="g113-75"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="452" vert-adv-y="452"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,5.031,3.132)"><path d="M624 292C624 400 569 451 537 451C520 451 497 442 490 436L489 427C521 404 550 351 550 280C550 170 513 51 423 51C383 51 361 87 361 150C361 197 384 301 397 339L391 343L310 328C307 297 301 249 293 212C270 102 223 56 182 56C144 56 114 93 114 172C114 278 161 369 243 430L223 457C99 392 24 290 24 156C24 43 81 -12 141 -12C187 -12 247 32 286 88C295 31 325 -12 380 -12C431 -12 475 16 511 49C581 113 624 195 624 292Z" id="g50-246"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="648" vert-adv-y="648"></glyph.data></g><g transform="matrix(.0065,0,0,-0.0065,10.7,5.233)"><path d="M363 392C363 416 330 454 273 454C246 454 189 439 146 400C110 367 97 335 97 309C97 248 143 215 199 179C254 144 264 123 264 101C264 77 242 42 196 42C156 42 112 77 90 109C83 119 76 123 55 112C40 104 25 89 25 66C25 31 88 -12 141 -12C238 -12 336 62 336 140C336 194 300 230 238 264C200 285 168 308 168 347C168 383 200 399 223 399C263 399 285 381 306 348C310 341 322 335 334 342C352 352 363 374 363 392Z" id="g176-116"></path><glyph.data ascent="3439" descent="-2858" horiz-adv-x="388" vert-adv-y="388"></glyph.data></g></svg>.</div>

Advances in Acoustics and Vibration

fig7

Figure 7

Figure 7: Mixed Skyhook and FxLMS Control of a Half-Car Model with Magnetorheological Dampers 