Identification of parametric uncertainty for the control of flexible structures

Modern robust control techniques require a description of the uncertainty in the plant to be controlled. For lightly damped structures, the most appropriate description of the uncertainty is in terms of interval ranges for parameters such as natural frequencies and damping ratios. What is desired is an algorithm which can determine such interval ranges from noisy transfer function measurements using set membership identification techniques. We begin with a parameterization of the structural model which is numerically stable. However, because the parameterization is nonlinear, this will result in a set of nonlinear optimization problems. Our approach is to embed these problems into a set of convex optimization problems. The added conservatism of the embedding can be made arbitrarily small for a one mode system by partitioning the parameter space into a finite number of regions. For a multiple mode system, an overbound on the level of conservatism can be easily measured. We then investigate the situation when the compensator designed for our uncertain system does not achieve the desired robust performance goal. The philosophy pursued is to determine a new input to apply to the open loop system in order to reduce the uncertainty. A new approach based upon sensitivity analysis is presented. Using the standard upper bound to the structured singular value as our measure of performance, we calculate the sensitivity of the performance to the size of the parametric uncertainty, and estimate the effect of the inputs on this uncertainty. This information is combined to determine the input with the largest expected improvement in the performance. Several examples demonstrate the ability of this procedure to achieve the desired performance using only a small number of data points. Thesis Supervisor: Michael Athans Title: Professor of Electrical Engineering