COMPENSATOR DESIGN FOR STABILITY ENHANCEMENT WITH CO-LOCATED CONTROLLERS

Abstract

In this paper we present a stochastic-optimization based approach to the design of compensators for stability enhancement applicable to flexible multibody systems with co-located rate sensros/actuators—for example a truss with offset antennas at one or both ends. A continuum model—rather than a finite element model—is used, and an essential step in the Compensator Design theory is the formulation of the problem as a wave equation in a Hilbert space. In particular using white noise theory as opposed to the Wiener Process theory the fact that steady state covariances are not nuclear poses no difficulty. The optimal Compensator Design problem is formulated as a stochastic regulator problem. In particular it turns out that we can solve explicitly the infinite dimensional steady state Riccati equations characterizing the feedback control gain and the Kalman filter gain operators. We can also calculate in closed form the associated performance indices including the “mean square” control effort. We show that, as a first approximation, the Compensator Transfer Function can be realized as a bank of band-pass filters in parallel centered at the undamped mode frequencies. Numerical calculations for the gains and bandwidths for the COFS configuration are presented. We also evaluate the performance of the compensator when in fact in the truth model there is no acutator noise. The theoretical problem involved here is to show that the infinite dimensional stochastic process is asymptotically stationary. We are able to calculate the steady state covariance in closed form and thereby calculate performance indices of interest explicitly, facilitating the choice of optimal design paramters.