Evolutionary Tuning Method for PID Controller Parameters of a Cruise Control System Using Metamodeling

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Process</td><td align="center" colspan="2">Metamodel</td><td align="center" colspan="2">Actual</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left">Model type</td><td align="center">Nonlinear</td><td align="center">Linear</td><td align="center">Nonlinear</td><td align="center">Linear</td></tr><tr><td align="center" colspan="5"><hr/></td></tr><tr><td align="left"><span style="width: 23.475px;"><svg height="16.237499" id="M83" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 23.475 16.237499" width="23.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.2375)">
<g transform="translate(72,-59.01)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑝</tspan>
<tspan style="font-size: 8.75px; " x="4.2797279" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">1.5</td><td align="center">1.5</td><td align="center">1.5</td><td align="center">1.5</td></tr><tr><td align="left"><span style="width: 21.525px;"><svg height="14.3625" id="M84" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 21.525 14.3625" width="21.525" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.3625)">
<g transform="translate(72,-60.51)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑖</tspan>
<tspan style="font-size: 8.75px; " x="2.7218721" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">0.23</td><td align="center">0.22</td><td align="center">0.3</td><td align="center">0.09</td></tr><tr><td align="left"><span style="width: 23.950001px;"><svg height="14.375" id="M85" style="vertical-align:-3.24037pt" version="1.1" viewbox="0 0 23.950001 14.375" width="23.950001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.375)">
<g transform="translate(72,-60.5)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.42,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑑</tspan>
<tspan style="font-size: 8.75px; " x="4.656064" y="0">1</tspan>
</text>
</g>
</g>
</svg></span></td><td align="center">0.75</td><td align="center">0.65</td><td align="center">0.75</td><td align="center">0.55</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Best gains for the cruise control system.

Modelling and Simulation in Engineering

tab3

Table 3

Table 3: Evolutionary Tuning Method for PID Controller Parameters of a Cruise Control System Using Metamodeling 