On an Optimal Control Applied in MEMS Oscillator with Chaotic Behavior including Fractional Order

<div>Deviation of the desired trajectory with the proposed control with parametric errors in feedback control and feedforward: (a) deviation of the desired trajectory <svg height="13.8999pt" id="M220" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 81.2537 13.8999" width="81.2537pt" 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" id="g113-102"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.317,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g 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472 33 528 97Z" id="g50-118"></path></g><g transform="matrix(.0091,0,0,-0.0091,68.878,3.784)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,73.31,3.784)"><path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path></g><g transform="matrix(.013,0,0,-0.013,77.578,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path></g></svg> and (b) deviation of the desired trajectory <span class="nowrap"><svg height="13.8999pt" id="M221" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 81.2537 13.8999" width="81.2537pt" xmlns="http://www.w3.org/2000/svg" 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Complexity

fig10

Figure 10

Figure 10: On an Optimal Control Applied in MEMS Oscillator with Chaotic Behavior including Fractional Order 