+++ title = "Review of active vibration isolation strategies" author = ["Dehaeze Thomas"] draft = false +++ 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., & 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, Christophe, Stef Janssens, and Kurt 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>