Second-Order Model Reduction Based on Gramians

<table>Frequency response on clamped beam model with size <svg height="10.8125" id="M314" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 50.724998 10.8125" width="50.724998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑛</tspan>
<tspan style="font-size: 12.50px; " x="9.6773224" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="21.71771" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="27.969212" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="34.220711" y="0">4</tspan>
</text>
</g>
</g>
</svg> and the reduced model of size <svg height="10.9125" id="M315" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 41.512501 10.9125" width="41.512501" 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,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="8.5645552" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="20.604944" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="26.856443" y="0">0</tspan>
</text>
</g>
</g>
</svg> by four different methods.</table>

Journal of Control Science and Engineering

Second-Order Model Reduction Based on Gramians

Figure 1