H∞ optimal control : general solution by interpolation and design with multiple objective functions

• Main Author: Pokrud, Boonyarit
• Published: University of Surrey 1989
• Subjects: 629.8; Control systems & control theory
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235319

A new method for solving Hinfinity control problems is developed. The method makes use of the Youla parametrization to characterize the set of all stabilizing controllers K(s) in terms of a stable function Q(s). and also to transform the Hinfinity control problem into a model-matching problem with an objective function E(s) being linear in Q(s). The model-matching problem is then solved by using the interpolation results of Hung. In the general case (i.e. problems of the 3rd kind) closed-form state-space characterizations of optimal and suboptimal solutions for Q(s) and E(s) are given. Furthermore, the solutions generally only require to solve two standard algebraic Riccati equations of smaller size than the McMillan degree of the (generalized) plant. This has an advantage of alleviating the computation burden associated with the ?-iteration required for determining the attainable minimum of ||E(s)||[infinity]. The Hinfinity approach to feedback design with multiple objective functions is studied in this thesis. For a system with two objective functions T[i](s), (i = 1, 2) a design criterion of minimizing the function max (||T[1](s)||[infinity], ||T[2](s)||[infinity]) subject to internal stability of the closed-loop system is proposed. The problem is formulated as an Hinfinity control problem and an iterative algorithm for obtaining a solution is given. A numerical example is given to illustrate the effectiveness of the proposed design technique for tightly bounding and shaping the frequency responses of two objective functions. The application of Hinfinity feedback design techniques to the control of flexible structures is investigated. Experiments are conducted in order to evaluate the use of the Hinfinity approach to the control of flexible structures. An Hinfinity optimal controller is designed and implemented in a laboratory system to manoeuvre a cantilever flexible beam and simultaneously control its vibrations. The controller performance is then assessed. The results obtained are shown to be satisfactory and encouraging.