Application of Quadratic Linearization for the Control of Permanent Magnet Synchronous Motor

<table>Time response of <svg height="10.9125" id="M261" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 13.975 10.9125" width="13.975" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,66.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
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<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
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</svg> for the linearized system in closed loop when <svg height="16.6" id="M262" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 49.125 16.6" width="49.125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.6)">
<g transform="translate(72,-58.72)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑣</tspan>
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<text transform="matrix(1,0,0,-1,-65.62,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑞</tspan>
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<text transform="matrix(1,0,0,-1,-57.29,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">0</tspan>
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</g>
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</svg> unit; <svg height="16.7875" id="M263" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 49.587502 16.7875" width="49.587502" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,16.7875)">
<g transform="translate(72,-58.57)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
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<text transform="matrix(1,0,0,-1,-65.17,60.22)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑝</tspan>
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<text transform="matrix(1,0,0,-1,-56.92,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="18.279387" y="0">0</tspan>
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</g>
</g>
</svg>; <svg height="14.7125" id="M264" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 39.825001 14.7125" width="39.825001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.7125)">
<g transform="translate(72,-60.23)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.17,60.37)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑖</tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.48,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="12.027886" y="0">2</tspan>
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</svg> after tuning.</table>

Advances in Power Electronics

fig17

Figure 17

Figure 17: Application of Quadratic Linearization for the Control of Permanent Magnet Synchronous Motor 