Control of an Automotive Semi-Active Suspension

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">  Component of the QoV</td><td align="center"> Value</td><td align="center"> Units</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left"> Sprung mass (<svg height="11.9625" id="M171" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 18.625 11.9625" width="18.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
q-97 56 -97 123q0 50 51 96q19 17 58 32.5t62 15.5q37 0 61 -18t24 -39z" id="x1D460"></path></g>
</svg>)</td><td align="center"> 522</td><td align="center"> Kg</td></tr><tr><td align="left"> Unsprung mass (<svg height="11.9625" id="M172" style="vertical-align:-3.39064pt" version="1.1" viewbox="0 0 24.8125 11.9625" width="24.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><use xlink:href="#x75"></use></g><g transform="matrix(.012,-0,0,-.012,19.758,11.762)"><use xlink:href="#x73"></use></g>
</svg>)</td><td align="center"> 50</td><td align="center"> Kg</td></tr><tr><td align="left"> Spring stiffness (<svg height="16.450001" id="M173" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 13.7625 16.450001" width="13.7625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D458"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.612,16.25)"><use xlink:href="#x1D460"></use></g>
</svg>)</td><td align="center"> 83</td><td align="center"> kN/m</td></tr><tr><td align="left"> Tire stiffness (<svg height="16.450001" id="M174" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 13.35 16.450001" width="13.35" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D458"></use></g>
<g transform="matrix(.012,-0,0,-.012,8.612,16.25)"><path d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" id="x1D461"></path></g>
</svg>)</td><td align="center"> 230</td><td align="center"> kN/m</td></tr><tr><td align="left"> Suspension stroke</td><td align="center"> [0.05, −0.07]</td><td align="center"> m</td></tr><tr><td align="left"> Suspension maximum velocity</td><td align="center"> [1.2, −1.5]</td><td align="center"> m/s</td></tr><tr><td align="left"> Motion ratio <svg height="12.175" id="M175" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 8.5249996 12.175" width="8.5249996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M471 401q0 -32 -14 -91l-83 -376q-30 -146 -21 -180l-7 -15q-22 0 -47.5 23.5t-25.5 40.5q0 49 53 271l53 224q4 18 6.5 31t3.5 22.5t1 15t-2 9t-4.5 4.5t-6.5 1q-31 0 -100.5 -63.5t-126.5 -145.5q-16 -53 -40 -163q-48 -11 -74 -21l-7 8l82 341q9 36 -4 36
q-8 0 -28.5 -14t-38.5 -32l-17 22q41 43 85 71t66 28q23 0 23 -39q0 -19 -10 -64l-24 -103h2q77 101 201 182q37 24 74 24q31 0 31 -47z" id="x1D702"></path></g>
</svg></td><td align="center"> 0.614</td><td align="center">—</td></tr><tr><td align="left"><svg height="11.9625" id="M176" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 18.625 11.9625" width="18.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><use xlink:href="#x1D460"></use></g>
</svg> resonance frequency (<svg height="19.262501" id="M177" style="vertical-align:-5.65108pt" version="1.1" viewbox="0 0 24.862499 19.262501" width="24.862499" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D453"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.975,16.25)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.008,-0,0,-.008,20.362,19.1)"><use xlink:href="#x1D460"></use></g>
</svg>)</td><td align="center">1.2</td><td align="center">Hz</td></tr><tr><td align="left"><svg height="11.9625" id="M178" style="vertical-align:-3.39064pt" version="1.1" viewbox="0 0 24.8125 11.9625" width="24.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.012,-0,0,-.012,13.475,11.762)"><use xlink:href="#x75"></use></g><g transform="matrix(.012,-0,0,-.012,19.758,11.762)"><use xlink:href="#x73"></use></g>
</svg> resonance frequency (<svg height="19.262501" id="M179" style="vertical-align:-5.65106pt" version="1.1" viewbox="0 0 29.275 19.262501" width="29.275" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><use xlink:href="#x1D453"></use></g>
<g transform="matrix(.012,-0,0,-.012,10.975,16.25)"><use xlink:href="#x1D45A"></use></g>
<g transform="matrix(.008,-0,0,-.008,20.362,19.1)"><use xlink:href="#x75"></use></g><g transform="matrix(.008,-0,0,-.008,24.858,19.1)"><use xlink:href="#x73"></use></g>
</svg>)</td><td align="center">11.5</td><td align="center">Hz</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab5

Table 5

Table 5: Control of an Automotive Semi-Active Suspension 