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

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Methods</td><td align="center">Gain <svg height="10.325" id="M261" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
</g>
</g>
</svg></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Proposed method</td><td align="center">1.7915</td></tr><tr><td align="left">Aizerman conjecture</td><td align="center">1.79</td></tr><tr><td align="left">Hirsch plot</td><td align="center">1.25</td></tr><tr><td align="left">Mee plot</td><td align="center">1.50</td></tr><tr><td align="left">Digital simulation</td><td align="center">1.787</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The gains <svg height="10.325" id="M260" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 13.2875 10.325" width="13.2875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
</g>
</g>
</svg> for just having a limit cycle.

Journal of Control Science and Engineering

tab2

Table 2

Table 2: Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags 