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content/article/collette11_review_activ_vibrat_isolat_strat.md

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+title = "Review of active vibration isolation strategies"
+author = ["Dehaeze Thomas"]
+draft = false
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+
+Tags
+: [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
+
+Reference
+: (<a href="#citeproc_bib_item_1">Collette, Janssens, and Artoos 2011</a>)
+
+Author(s)
+: Collette, C., Janssens, S., &amp; Artoos, K.
+
+Year
+: 2011
+
+
+## Background and Motivations {#background-and-motivations}
+
+
+### Passive Isolation Tradeoffs {#passive-isolation-tradeoffs}
+
+1DoF Equations:
+
+\begin{equation}
+\boxed{X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}\_{T\_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}\_{T\_{Fx}(s)} F(s)}
+\end{equation}
+
+-   \\(T\_{wx}(s)\\) is called the **transmissibility** of the isolator. It characterize the way seismic vibrations \\(w\\) are transmitted to the equipment.
+-   \\(T\_{Fx}(s)\\) is called the **compliance**. It characterize the capacity of disturbing forces \\(F\\) to create motion \\(x\\) of the equipment.
+
+In order to minimize the vibrations of a sensitive equipment, a general objective to design a good isolator is to minimize both \\(\abs{T\_{wx}}\\) and \\(\abs{T\_{Fx}}\\) in the frequency range of interest.
+
+To decrease the amplitude of the overshoot at the resonance frequency, **damping** can be increased.
+The price to pay is degradation of the isolation at high frequency (the roll off becomes \\(-1\\) instead of \\(-2\\)).
+
+**First Trade-off**: Trade-off between damping and isolation.
+
+To improve the transmissibility, the resonance frequency can be decreased.
+However, the systems becomes more sensitive to external force \\(F\\) applied on the equipment.
+
+**Second trade-off**: Trade-off between isolation and robustness to external force
+
+
+### Active Isolation {#active-isolation}
+
+We apply a feedback control.
+The general expression of the force delivered by the actuator is \\(f = g\_a \ddot{x} + g\_v \dot{x} + g\_p x\\). \\(g\_a\\), \\(g\_v\\) and \\(g\_p\\) are constant gains.
+
+<a id="table--table:active-isolation"></a>
+<div class="table-caption">
+  <span class="table-number"><a href="#table--table:active-isolation">Table 1</a>:</span>
+  Active isolation techniques
+</div>
+
+| **Feedback Signal** | **Effect**                               | **Applications** |
+|---------------------|------------------------------------------|------------------|
+| Acceleration        | Add virtual mass                         | Few              |
+| Velocity            | Add virtual dashpot connected to the sky | Sky-Hook Damping |
+| Position            | Add virtual spring connected to the sky  | Sky-Hook Spring  |
+
+
+## Practical Realizations {#practical-realizations}
+
+
+## Sensor Limitations {#sensor-limitations}
+
+
+## Conclusions {#conclusions}
+
+<a id="figure--fig:collette11-comp-isolation-strategies"></a>
+
+{{< figure src="/ox-hugo/collette11_comp_isolation_strategies.png" caption="<span class='figure-number'>Figure 1: </span>Comparison of Active Vibration Isolation Strategies" >}}
+
+
+## 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>Collette, C., S. Janssens, and K. Artoos. 2011. “Review of Active Vibration Isolation Strategies.” <i>Recent Patents on Mechanical Engineeringe</i> 4 (3): 212–19. doi:<a href="https://doi.org/10.2174/2212797611104030212">10.2174/2212797611104030212</a>.</div>
+</div>