Multivariable Controller Design for the Cooling System of a PEM Fuel Cell by considering Nearly Optimal Solutions in a Multiobjective Optimization Approach

<div>Response of <svg height="11.8559pt" id="M467" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.8061 17.5102 11.8559" width="17.5102pt" 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="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.29,-5.741)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.464,-5.741)"><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"></path></g></svg> (optimal) and <svg height="11.8559pt" id="M468" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.8061 17.5102 11.8559" width="17.5102pt" 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="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.29,-5.741)"><path d="M625 186C574 85 512 32 429 32C293 32 194 153 194 337C194 485 274 621 419 621C496 621 573 586 606 468L643 475C636 537 629 583 620 638C593 644 519 665 438 665C199 665 42 523 42 317C42 158 152 -15 418 -15C486 -15 578 5 604 11C621 46 647 122 660 171L625 186Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.464,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g></svg> (nearly optimal) controllers. Both responses are significantly different, although it has similar performance.</div>

Complexity

fig13

Figure 13

Figure 13: Multivariable Controller Design for the Cooling System of a PEM Fuel Cell by considering Nearly Optimal Solutions in a Multiobjective Optimization Approach 

Figure 13 | Multivariable Controller Design for the Cooling System of a PEM Fuel Cell by considering Nearly Optimal Solutions in a Multiobjective Optimization Approach 