Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

<div>Time history of FOPF states (controller in action at<svg height="8.55521pt" id="M134" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.34882 36.3576 8.55521" width="36.3576pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,4.358,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341" xpluscharwidth="8.791"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.423,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587" xpluscharwidth="20.054000000000002"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,23.686,0)"><path d="M447 623H65C61 580 56 530 47 475H76C100 541 106 550 172 550H388C308 376 196 170 91 -1L98 -12L172 -2C268 204 360 408 455 611L447 623Z" id="g113-56"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480" xpluscharwidth="29.926000000000002"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,29.928,0)"><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" xpluscharwidth="36.168"></glyph.data></g></svg> s).</div>

Shock and Vibration

fig10

Figure 10

Figure 10: Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control 