COMPENSATOR DESIGN FOR STABILITY ENHANCEMENT WITH COLLOCATED CONTROLLERS

We present a stochastic optimization-based approach to the design of compensators for stability enhancement applicable to flexible multibody systems with collocated rate sensors/actuators. The controls are force and moments actuators at one or both ends, and the collocated sensors are rate gyros. A continuum model rather than a finite element model is used. The optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite-dimensional theory developed by the author despite the lack of exponential stabilizability. 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 also calculate in closed form the associated performance indexes 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 a typical configuration are presented. We also evaluate the performance of the compensator when in fact in the true model there is no actuator 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 indexes of interest explicitly, facilitating the choice of optimal design parameters.