Identification, modeling, and control of flexible structures.

Abstract

Two important components in control design are the model development prior to control design and the performance analysis after the design is complete. Model development generally falls into two categories: (1) first principles modeling based on the physics of the individual components of a system; and (2) system identification based on experimental data. The problem of performance analysis can be quite broad, ranging from the step response of a system to the computation of system norms. In this dissertation we address problems from both of these fields of research. The modeling work presented in this dissertation includes both first principles and experimental modeling. We develop a first principles model of the dynamics of an M1/M1A1 tank as a motivational example and a simulation testbed on which we demonstrate the identification and control analysis tools developed in this dissertation. In the field of identification there are a number of methods available to engineers. Among these methods, the algorithms for solving the problem of identification in ${\cal H}\sb{\infty}$ have received much attention recently. The focus of the attention has been to develop the theoretical properties of the algorithms; however, less attention has been paid to the engineering applications of the algorithms. It is this practical application which is the primary focus of our work in system identification. This dissertation includes results on the key issues in engineering applications of the two-stage nonlinear algorithms, a step-by-step recipe for the selection of the design parameters, and heuristic rules for successful applications. In the area of performance analysis, we examine the computation of the worst-case and average ${\cal H}\sb2$ norm of a family of linear systems with constant real parametric uncertainty. It is shown that when the system matrices depend affinely on real uncertain parameters, any quadratic performance index will be a rational function of these parameters. Using this fact, in the case of a single real parameter, the computation of the worst-case ${\cal H}\sb2$ norm is quite similar to the computation of the ${\cal H}\sb{\infty}$ norm of an auxiliary system and the average performance becomes the integral of a rational function. Several examples are included to illustrate the utility of these results.