3.3 KiB
+++ title = "Review of active vibration isolation strategies" author = ["Dehaeze Thomas"] draft = false +++
- Tags
- [Vibration Isolation]({{< relref "vibration_isolation.md" >}})
- Reference
- (Collette, Janssens, and Artoos 2011)
- Author(s)
- Collette, C., Janssens, S., & Artoos, K.
- Year
- 2011
Background and Motivations
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
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.
| 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="<span class="figure-number">Figure 1: Comparison of Active Vibration Isolation Strategies" >}}