Model-Based Control Design of Series Resonant Converter Based on the Discrete Time Domain Modelling Approach for DC Wind Turbine

<div>Illustration of magnitude asymptote of desired loop gain <svg height="14.776193pt" id="M85" style="vertical-align:-5.487858pt" version="1.1" viewbox="-0.049816 -9.288335 47.711417 14.776193" width="47.711417pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.312,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,12.827,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.72,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.235,0)"><path d="M162 -163V703H101V-163H162Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,25.667,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,28.572,3.132)"><path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.591,3.132)"><path d="M185 344V453C137 433 92 421 41 413V386C100 378 104 375 104 310V106C104 41 97 35 33 30V0H268V30C190 35 185 41 185 107V283C206 340 240 371 267 371C282 371 296 364 310 351C316 344 325 343 336 348C357 357 369 378 369 399C369 424 345 451 310 451C262 451 219 397 187 344H185Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.988,3.132)"><path d="M472 439C432 432 382 428 334 425C303 442 271 451 236 451H235C158 451 54 398 54 285C54 216 97 171 140 152C124 133 93 105 53 90C52 81 55 63 64 48C77 27 102 5 137 -6C115 -22 77 -53 57 -73C40 -88 32 -107 32 -130C32 -189 96 -253 208 -253C340 -253 461 -159 461 -56C461 44 378 63 314 63C281 63 246 62 207 62C163 62 145 80 145 99C145 114 160 130 175 141C191 138 210 136 226 136C314 136 405 188 405 294C405 329 393 359 376 382L433 378C448 387 469 415 477 430L472 439ZM226 417C282 417 320 364 320 288S281 172 236 171C180 171 142 224 142 300S182 417 226 417ZM248 -9C291 -9 319 -11 346 -22S390 -57 390 -90C390 -151 339 -199 246 -199C171 -199 114 -159 114 -106C114 -79 132 -53 159 -30C178 -15 200 -9 248 -9Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,40.3,3.132)"><path d="M384 109C349 76 310 59 268 59C197 59 123 113 120 245C240 248 367 259 384 262C403 266 407 275 407 296C407 376 338 451 254 451H253C201 451 148 425 105 378C65 334 39 272 39 203C39 88 112 -12 235 -12C266 -12 339 5 402 84L384 109ZM230 411C285 411 319 365 319 313C319 298 313 293 294 293C236 291 180 290 125 290C141 370 185 411 230 411Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,44.264,3.132)"><path d="M303 37L293 66C280 59 256 49 231 49S173 63 173 143V396H281C294 404 298 428 287 439H173V575L158 577L92 509V439H46L17 408L22 396H92V107C92 27 128 -12 192 -12C203 -12 218 -9 237 2L303 37Z"></path></g></svg> (target curve of loop gain) [<a href="/journals/jre/2018/7898679/#B11">11</a>].</div>

Journal of Renewable Energy

fig8

Figure 8

Figure 8: Model-Based Control Design of Series Resonant Converter Based on the Discrete Time Domain Modelling Approach for DC Wind Turbine 