+++
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., &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, 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>