Instabilities due to instrumentation phase-lead and phase-lag in the feedback control of a simple vibrating system

Abstract

In many active vibration control systems, it is the high frequency dynamic behaviour of the system that limits controller gain. However, in the specific case of vibration isolation, the low frequency dynamics of the system have an important role in the performance of the system. The main problem is the phase advance due to the high-pass filters that are necessary in such a system to remove the DC signal in the feedback loop. To investigate this problem the active control of a simple vibrating system is considered in this paper. Displacement, velocity and acceleration feedback control are studied, and the effects of the high-pass filters on the system stability are investigated. A simple system is specifically chosen to facilitate physical insight. For comparison, the limit on stability due to the high frequency dynamics, is also quantified by assuming a fixed time delay in the feedback loop. Simple expressions that give the maximum control gain in each case are derived. These expressions give insight into how the physical parameters govern the limits on stability. It is shown that for velocity feedback control it is desirable to have a high natural frequency of the mechanical system compared to the corner frequency of the high-pass filter. For displacement control, when there is phase-lag in the system, it is desirable to have high damping, and this is also the case for acceleration feedback when there is phase-lead. Some experimental work is presented to support the theoretical results.