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Thomas Dehaeze
" /><meta name="description" content="Tags Stewart Platforms, Vibration Isolation Reference (Spanos {\it et al.}, 1995) Author(s) Spanos, J., Rahman, Z., &amp;amp; Blackwood, G. Year 1995 Stewart Platform (Figure 1):
Voice Coil Flexible joints (cross-blades) Force Sensors Cubic Configuration
Figure 1: Stewart Platform
Total mass of the paylaod: 30kg Center of gravity is 9cm above the geometry center of the mount (cube&amp;rsquo;s center?).
Limitation of the Decentralized Force Feedback:" />
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<h1 class="post-title">A soft 6-axis active vibration isolator</h1>
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<h2 class="post-toc-title">Contents</h2>
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<dl>
<dt>Tags</dt>
<dd><a href="/zettels/stewart_platforms/">Stewart Platforms</a>, <a href="/zettels/vibration_isolation/">Vibration Isolation</a></dd>
<dt>Reference</dt>
<dd><sup id="a48f6708d087625a42ca2375407a2bc4"><a href="#spanos95_soft_activ_vibrat_isolat" title="Spanos, Rahman \&amp; Blackwood, A Soft 6-axis Active Vibration Isolator, nil, in in: {Proceedings of 1995 American Control Conference - ACC'95}, edited by (1995)">(Spanos {\it et al.}, 1995)</a></sup></dd>
<dt>Author(s)</dt>
<dd>Spanos, J., Rahman, Z., &amp; Blackwood, G.</dd>
<dt>Year</dt>
<dd>1995</dd>
</dl>
<p><strong>Stewart Platform</strong> (Figure <a href="#org4317d08">1</a>):</p>
<ul>
<li>Voice Coil</li>
<li>Flexible joints (cross-blades)</li>
<li>Force Sensors</li>
<li>Cubic Configuration</li>
</ul>
<p><a id="org4317d08"></a></p>
<figure>
<img src="/ox-hugo/spanos95_stewart_platform.png"
alt="Figure 1: Stewart Platform"/> <figcaption>
<p>Figure 1: Stewart Platform</p>
</figcaption>
</figure>
<p>Total mass of the paylaod: 30kg
Center of gravity is 9cm above the geometry center of the mount (cube&rsquo;s center?).</p>
<p>Limitation of the <strong>Decentralized Force Feedback</strong>:</p>
<ul>
<li>high frequency pole due to internal resonances of the struts</li>
<li>low frequency zero due to the rotational stiffness of the flexible joints</li>
</ul>
<p>After redesign of the struts:</p>
<ul>
<li>high frequency pole at 4.7kHz</li>
<li>low frequency zero at 2.6Hz but non-minimum phase (not explained).
Small viscous damping material in the cross blade flexures made the zero minimum phase again.</li>
</ul>
<p><a id="org67e505c"></a></p>
<figure>
<img src="/ox-hugo/spanos95_iff_plant.png"
alt="Figure 2: Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage"/> <figcaption>
<p>Figure 2: Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage</p>
</figcaption>
</figure>
<p>The controller used consisted of:</p>
<ul>
<li>second order low pass filter to gain stabilize the plant at high frequencies and provide steep roll-off</li>
<li>first order lead filter to provide adequate phase margin at the high frequency crossover</li>
<li>first order lag filter to provide adequate phase margin at the low frequency crossover</li>
<li>a first order high pass filter to attenuate the excess gain resulting from the low frequency zero</li>
</ul>
<p>The results in terms of transmissibility are shown in Figure <a href="#orgf128817">3</a>.</p>
<p><a id="orgf128817"></a></p>
<figure>
<img src="/ox-hugo/spanos95_results.png"
alt="Figure 3: Experimentally measured Frobenius norm of the 6-axis transmissibility"/> <figcaption>
<p>Figure 3: Experimentally measured Frobenius norm of the 6-axis transmissibility</p>
</figcaption>
</figure>
<h1 id="bibliography">Bibliography</h1>
<p><a id="spanos95_soft_activ_vibrat_isolat"></a>Spanos, J., Rahman, Z., &amp; Blackwood, G., <em>A soft 6-axis active vibration isolator</em>, In , Proceedings of 1995 American Control Conference - ACC'95 (pp. ) (1995). : . <a href="#a48f6708d087625a42ca2375407a2bc4">↩</a></p>
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