digital-brain/content/paper/collette11_review_activ_vibrat_isolat_strat.md

+++ title = "Review of active vibration isolation strategies" author = ["Thomas Dehaeze"] draft = false +++

Tags

[Vibration Isolation]({{< relref "vibration_isolation" >}})

Reference

^{(Christophe Collette {\it et al.}, 2011)}

Author(s)

Collette, C., Janssens, S., & Artoos, K.

Year

2011

Background and Motivations

Passive Isolation Tradeoffs

\[ X(s) = \underbrace{\frac{cs + k}{ms^2 + cs + k}}_{T_{wx}(s)} W(s) + \underbrace{\frac{1}{ms^2 + cs + k}}_{T_{Fx}(s)} F(s) \]

• \(T_{wx}(s)\) 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

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.

Table 1: Active isolation techniques

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

Sensor Limitations

Conclusions

{{< figure src="/ox-hugo/collette11_comp_isolation_strategies.png" caption="Figure 1: Comparison of Active Vibration Isolation Strategies" >}}

Bibliography

Collette, C., Janssens, S., & Artoos, K., Review of active vibration isolation strategies, Recent Patents on Mechanical Engineeringe, 4(3), 212–219 (2011). http://dx.doi.org/10.2174/2212797611104030212 ↩