Mobility analysis of active isolation systems

A frequency-domain formulation is used to analyze the stability and performance of an active vibration isolation system which uses feedback control. The active mount is modelled as a single-axis force actuator in parallel with a passive spring and damper. The feedback sensor measures either the absolute velocity of the equipment to be isolated at one end of the mount, or the integral of the transmitted force through the mount. The plant response, from force actuator input to sensor output, is derived for these two cases in terms of the mechanical mobilities of the two structures connected by the active mount. The limits of the phase of the plant response are derived for the two feedback strategies and these are used to explain the stability and performance of several specific examples of active isolation systems. It is shown that, in the absence of actuator and sensor dynamics, the integrated force feedback system is unconditionally stable. The stability of the absolute velocity feedback system is, however, threatened if the vibrating base structure becomes very mobile, with a small effective mass, at the same frequency as the equipment structure becomes very stiff. By quantifying the conditions under which velocity feedback systems can become unstable, these conditions can be avoided. If the stability of an absolute velocity feedback system can be assured, it is shown to be more effective at controlling resonances caused by equipment dynamics than integrated force feedback.