Designing a Kalman–Bucy State Estimator for a Full Vertical Car Model

<div>Time responses of the parameters of <span class="nowrap"><svg height="15.1709pt" id="M63" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.7415 138.689 15.1709" width="138.689pt" 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="M574 193C552 131 535 101 511 78C482 51 412 45 334 45C271 45 243 47 210 51C335 250 459 440 584 635L576 650H170C138 650 127 652 112 675H86C84 623 78 553 75 476L108 475C119 522 135 552 147 570C163 594 182 605 284 605H410C286 412 157 211 29 17L40 0H571C581 35 599 136 607 185L574 193Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.077,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,20.025,-3.21)"><path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 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101 511 78C482 51 412 45 334 45C271 45 243 47 210 51C335 250 459 440 584 635L576 650H170C138 650 127 652 112 675H86C84 623 78 553 75 476L108 475C119 522 135 552 147 570C163 594 182 605 284 605H410C286 412 157 211 29 17L40 0H571C581 35 599 136 607 185L574 193Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,128.473,3.132)"><path d="M528 97L513 125C484 95 440 68 431 68C425 68 421 76 427 107C449 227 476 342 505 451H495L418 424L385 278C338 191 220 62 157 62C145 62 133 76 145 130L200 368C215 434 210 451 183 451C157 451 92 418 24 352L37 324C78 356 106 377 115 377C123 377 122 364 116 340L64 115C58 89 56 68 56 52C56 2 78 -12 103 -12C127 -12 159 -4 190 18C247 59 309 113 366 187H368L351 108C328 1 348 -12 368 -12C403 -12 472 33 528 97Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,133.496,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g></svg>.</span> (a) Displacement of sprung mass <span class="nowrap"><svg height="9.01194pt" id="M64" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.96212 9.12937 9.01194" width="9.12937pt" 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="M669 636L663 650H260C230 650 221 652 208 675H186C177 621 162 548 144 481L173 479C195 534 211 560 226 578C248 604 266 615 373 615H544C460 511 114 112 23 16L31 0H561C577 34 611 135 622 170L594 182C566 125 544 88 515 65C481 38 416 35 319 35C249 35 197 37 152 41C270 184 542 501 669 636Z"></path></g></svg>;</span> (b) Displacement velocity of the sprung mass <span class="nowrap"><svg height="11.8044pt" id="M65" style="vertical-align:-0.04980087pt" version="1.1" viewbox="-0.0498162 -11.7546 9.12937 11.8044" width="9.12937pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g 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Mathematical Problems in Engineering

fig8

Figure 8

Figure 8: Designing a Kalman–Bucy State Estimator for a Full Vertical Car Model 