Introduction

Abstract

Many control design tools exist for discretized ordinary differential equation models of vibration and noise systems (e.g. observer-based state feedback [83] and H ^∞ control [46]). A substantial difficulty in the design of these controllers is the choice of the discretization order. Reduction of the infinite dimensional continuum model to a finite dimensional (N ^th order) discrete model means that an infinite number of motions are neglected. Typically, modal analysis motivates the model reduction. With sufficient system damping, higher order modes can be neglected if the controller rolls off (i.e. the controller gain drops sharply) at high frequency. Choice of N too small results in spillover instability that occurs when the controller, designed for the finite dimensional model, senses and actuates higher order modes, driving them unstable [4]. Reduction of the control gain to eliminate spillover often results in poor performance. Choice of N too large results in a high order compensator that can be difficult and costly to implement.