The vibration isolation problem

Isolation from environmental vibration is an important problem for structures or equipment that must be really precise.

We can consider the basic problem as schematized in the figure, where the equipment to be isolated is the mass me and the environmental disturbance is represented by the basement displacement xp.

The standard approach to this type of problem is to maintain the stiffness k of the mounting constant, changing its damping r. This is done in a passive way.

In the above figure is reported the response of the displacement x of the mass me with respect to the disturbance xp in the frequency domain.

It’s possible to see that, as the damping r rise, the response of the system, decrease in the resonance part (red circle) but increase in seismic part (green circle). So we have at the same time positive and negative effects.

To change this situation is possible to use an active isolation.

This active isolation is done by using a feedback control that gives to the system a force proportional to the velocity of the mass that must be isolated.

This type of feedback control is done as:

But being the reference velocity equal to zero (it must be isolated), the formulation becomes:

Choosing:

Is possible to obtain a really good result.

In this case with respect to the previous one in the resonance frequency region there is an attenuation and in the seismic region there’s no increase in the amplitude.

The problem of this solution is the ideal way in which the force is given to the system. In a real case this must be done by an actuator and this actuator should be a low cost actuator, as one of the inertial mass actuators found by the other members of OpenAdaptronik project.

See you soon.