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

<div>Set of optimal and nearly optimal controllers nondominated in the neighborhood (<span class="nowrap"><svg height="13.3154pt" id="M288" style="vertical-align:-4.679501pt" version="1.1" viewbox="-0.0498162 -8.6359 20.6053 13.3154" width="20.6053pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.656,3.132)"><path d="M750 355C750 552 603 667 428 667C199 667 24 497 24 286C24 118 146 -4 316 -16L336 -29C480 -122 544 -145 582 -154C606 -159 666 -170 714 -172L722 -146C652 -117 562 -75 472 -15L454 -3C623 38 750 176 750 355ZM646 353C646 210 556 50 414 25L385 41L304 27C193 50 128 152 128 282C128 474 254 626 418 626C571 626 646 519 646 353Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.116,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,15.273,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg>)</span> obtained for the control design of the cooling system. Decision variables are shown using the LD visualization tool, using the 2-norm (<span class="nowrap"><svg height="12.4698pt" id="M289" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 24.5582 12.4698" width="24.5582pt" 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="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.248,0)"><path d="M170 255C170 288 146 313 114 313S58 288 58 255C58 221 82 198 114 198S170 221 170 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.118,0)"><path d="M162 -163V703H102V-163H162ZM309 -163V703H249V-163H309Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,19.461,3.132)"><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>).</span></div>

Complexity

fig8

Figure 8

Figure 8: Multivariable Controller Design for the Cooling System of a PEM Fuel Cell by considering Nearly Optimal Solutions in a Multiobjective Optimization Approach 

Figure 8 | Multivariable Controller Design for the Cooling System of a PEM Fuel Cell by considering Nearly Optimal Solutions in a Multiobjective Optimization Approach 