Two-Layer Linear MPC Approach Aimed at Walking Beam Billets Reheating Furnace Optimization

<table class="table-group" id="tab10"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left">Acronym</td><td class="align_center">Fuel<sub>5</sub></td><td class="align_center">Fuel<sub>4</sub></td><td class="align_center">Air<sub>5</sub></td><td class="align_center">Air<sub>4</sub></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">Temp<sub>5</sub></td><td class="align_center">1</td><td class="align_center">0</td><td class="align_center">0</td><td class="align_center">1</td></tr><tr><td class="align_left">Temp<sub>4</sub></td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">0</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Reduced Decoupling Matrix <svg height="11.8174pt" id="M282" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 16.2184 11.8174" width="16.2184pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.893,3.132)"><path d="M615 650H141L132 618C223 612 227 607 212 526L136 123C122 42 112 38 27 32L18 0H522C539 33 580 135 592 166L558 179C536 139 512 100 486 75C454 48 420 41 345 41C287 41 252 42 237 55C221 68 220 100 231 158L261 316H357C455 316 455 309 455 235H489L529 437H494C468 366 460 360 369 360H269L305 565C315 609 316 611 357 611H450C525 611 535 599 548 578C559 556 561 526 560 482L595 486L615 650Z" id="g50-70"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="639" vert-adv-y="639"></glyph.data></g></svg>.

Journal of Control Science and Engineering

tab10

Table 10

Table 10: Two-Layer Linear MPC Approach Aimed at Walking Beam Billets Reheating Furnace Optimization 