Time-Delay LPV System Control and Its Application in Chatter Suppression of the Milling Process

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/307149/figures/307149.fig.005a.svgz" name="307149.fig.005a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Without control</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/307149/figures/307149.fig.005b.svgz" name="307149.fig.005b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>With control</td></tr></table>

<div>Machined surface quality. Workpiece: 302; tool: YT15; cutting parameters: <svg height="8.91176pt" id="M179" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 28.3129 8.91176" width="28.3129pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0136,0,0,-0.0136,0,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,9.895,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g 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-171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,12.489,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,24.227,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z" id="g113-49"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,30.73,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z" id="g113-47"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data></g><g transform="matrix(.0135,0,0,-0.0135,33.819,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg> mm/r.</div>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Time-Delay LPV System Control and Its Application in Chatter Suppression of the Milling Process 