Controller size reduction in advanced control system design.

The work described in this thesis was undertaken to obtain a unified treatment to the controller size reduction problem in advanced robust control system design. A common feature in state-space solutions to advanced control system design, such as parametrizations of all stabilizing controllers and Hinfinity suboptimal controllers, is that a free parameter matrix is contained in the parametrization to give the designer freedom in designing the required controllers. However, this free parameter can provide unnecessarily high order controllers. This thesis presents a new methodology for controller size reduction. The methodology utilizes the parametrization of all stabilizing controllers and Hinfinity suboptimal controllers, and then generates a set of low-order stabilizing controllers and a set of low-order Hinfinity suboptimal controllers, respectively. The central idea is to achieve a low-order realization of a full-order controller, by deriving and solving two simultaneous matrix equations in order to eliminate unobservable states. Orthogonal canonical forms are employed to solve these simultaneous equations. A consequence of the algorithms employed is that the order of the controller is reduced from n + nq (or n + no) to nq (or no), where n is the order of the weighted plant and nq (or no) is the order of the free parameter. In design applications, a possible solution to the problem of combining the objectives of robust stability and performance requirements is to use a loop shaping design procedure based on normalized coprime factor plant descriptions. The methodology obtained for low-order Hinfinity suboptimal controllers is extended, with slight modifications, to one and two degree-of-freedom loop shaping design procedures. The results are illustrated by numerical examples. Finally, a practical industrial problem of designing a low-order controller for a tetrahedral robot is considered by applying the methodology developed in the thesis.