# Sensor fusion for active vibration isolation in precision equipment - My digital brain
Tags Sensor Fusion, Vibration Isolation Reference (Tjepkema {\it et al.}, 2012) Author(s) Tjepkema, D., Dijk, J. v., &amp; Soemers, H. Year 2012 Relative motion Control Control law: \(f = -G(x-w)\) \[ \frac{x}{w} = \frac{k+G}{ms^2 + k+G} \] \[ \frac{x}{F} = \frac{1}{ms^2 + k+G} \] Force Control Control law: \(f = -G F_a = -G \left(f-k(x-w)\right)\) \[ \frac{x}{w} = \frac{k}{(1+G)ms^2 + k} \] \[ \frac{x}{F} = \frac{1+G}{(1+G)ms^2 + k} \]
Author: — Thomas Dehaeze

# Sensor fusion for active vibration isolation in precision equipment

Tags
  Sensor Fusion, Vibration Isolation
Reference
  (Tjepkema {\it et al.}, 2012)
Author(s)
  Tjepkema, D., Dijk, J. v., & Soemers, H.
Year
  2012

## Relative motion Control

Control law: \(f = -G(x-w)\)

\[ \frac{x}{w} = \frac{k+G}{ms^2 + k+G} \] \[ \frac{x}{F} = \frac{1}{ms^2 + k+G} \]

## Force Control

Control law: \(f = -G F_a = -G \left(f-k(x-w)\right)\)

\[ \frac{x}{w} = \frac{k}{(1+G)ms^2 + k} \] \[ \frac{x}{F} = \frac{1+G}{(1+G)ms^2 + k} \]

## Inertial Control

Control law: \(f = -Gx\)

\[ \frac{x}{w} = \frac{k}{ms^2 + k+G} \] \[ \frac{x}{F} = \frac{1}{ms^2 + k+G} \]

## Design constraints and control bandwidth

Heavier sensor => lower noise but it is harder to maintain collocation with the actuator => that limits the bandwidth. There is a compromise between sensor noise and the influence of the sensor size on the system’s design and on the control bandwidth.

# Bibliography

Tjepkema, D., Dijk, J. v., & Soemers, H., Sensor fusion for active vibration isolation in precision equipment, Journal of Sound and Vibration, 331(4), 735–749 (2012). http://dx.doi.org/10.1016/j.jsv.2011.09.022 ↩