Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

<table>(a) Root loci analyses of limit cycles of Example <a href="https://static.hindawi.com/articles/jcse/volume-2011/169848/figures/#ex2">2</a>. (b) <svg height="11.0375" id="M351" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 33.875 11.0375" width="33.875" xmlns="http://www.w3.org/2000/svg">
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<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜔</tspan>
</text>
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<tspan style="font-size: 8.75px; " x="0" y="0">m</tspan>
<tspan style="font-size: 8.75px; " x="6.8090558" y="0">a</tspan>
<tspan style="font-size: 8.75px; " x="10.694944" y="0">x</tspan>
</text>
</g>
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</svg> versus <svg height="14.75" id="M352" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 43.862499 14.75" width="43.862499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.75)">
<g transform="translate(72,-60.2)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
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<text transform="matrix(1,0,0,-1,-56.44,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">𝑎</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">3</tspan>
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</svg> of Example <a href="https://static.hindawi.com/articles/jcse/volume-2011/169848/figures/#ex2">2</a>.</table>

Journal of Control Science and Engineering

fig12

Figure 12

Figure 12: Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags 