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content/article/spanos95_soft_activ_vibrat_isolat.md

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+title = "A soft 6-axis active vibration isolator"
+author = ["Dehaeze Thomas"]
+draft = false
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+
+Tags
+: [Stewart Platforms]({{< relref "stewart_platforms.md" >}}), [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Spanos, Rahman, and Blackwood 1995</a>)
+
+Author(s)
+: Spanos, J., Rahman, Z., &amp; Blackwood, G.
+
+Year
+: 1995
+
+**Stewart Platform** ([Figure 1](#figure--fig:spanos95-stewart-platform)):
+
+-   Voice Coil
+-   Flexible joints (cross-blades)
+-   Force Sensors
+-   Cubic Configuration
+
+<a id="figure--fig:spanos95-stewart-platform"></a>
+
+{{< figure src="/ox-hugo/spanos95_stewart_platform.png" caption="<span class='figure-number'>Figure 1: </span>Stewart Platform" >}}
+
+Total mass of the paylaod: 30kg
+Center of gravity is 9cm above the geometry center of the mount (cube's center?).
+
+Limitation of the **Decentralized Force Feedback**:
+
+-   high frequency pole due to internal resonances of the struts
+-   low frequency zero due to the rotational stiffness of the flexible joints
+
+After redesign of the struts:
+
+-   high frequency pole at 4.7kHz
+-   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.
+
+<a id="figure--fig:spanos95-iff-plant"></a>
+
+{{< figure src="/ox-hugo/spanos95_iff_plant.png" caption="<span class='figure-number'>Figure 2: </span>Experimentally measured transfer function from voice coil drive voltage to collocated load cell output voltage" >}}
+
+The controller used consisted of:
+
+-   second order low pass filter to gain stabilize the plant at high frequencies and provide steep roll-off
+-   first order lead filter to provide adequate phase margin at the high frequency crossover
+-   first order lag filter to provide adequate phase margin at the low frequency crossover
+-   a first order high pass filter to attenuate the excess gain resulting from the low frequency zero
+
+The results in terms of transmissibility are shown in [Figure 3](#figure--fig:spanos95-results).
+
+<a id="figure--fig:spanos95-results"></a>
+
+{{< figure src="/ox-hugo/spanos95_results.png" caption="<span class='figure-number'>Figure 3: </span>Experimentally measured Frobenius norm of the 6-axis transmissibility" >}}
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Spanos, J., Z. Rahman, and G. Blackwood. 1995. “A Soft 6-Axis Active Vibration Isolator.” In <i>Proceedings of 1995 American Control Conference - ACC’95</i>. doi:<a href="https://doi.org/10.1109/acc.1995.529280">10.1109/acc.1995.529280</a>.</div>
+</div>