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