# Review of active vibration isolation strategies - My digital brain
Tags Vibration Isolation Reference (Christophe Collette {\it et al.}, 2011) Author(s) Collette, C., Janssens, S., &amp; 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.
Author: — Thomas Dehaeze

# Review of active vibration isolation strategies

Tags
  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 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 ↩