COVARIANCE EQUIVALENT REALIZATIONS: DEVELOPMENT AND APPLICATIONS TO MODEL AND CONTROLLER REDUCTION

AJMAL YOUSUFF, Purdue University

Abstract

The controller design to meet the mission requirements of a large scale system typically involves two steps: (a) model reduction and (b) control design. This dissertation presents a theory to unify steps (a) and (b). Of particular interest will be partial realizations that preserve the steady state covariance of the uncontrolled variables of a higher order realization. The unification is achieved via the following steps. (1) First a reduced order model (of 'Riccati-solvable' dimension) is obtained which preserves the mean-squared values of every controlled variable (a desirable property since mission requirements are often given in terms of the root-mean-squared values of the controlled variables). (2) Based upon this reduced model, an optimal LQG controller is designed to meet the mission requirements. This determines the optimal control inputs. (3) Since the "Riccati-solvable dimension" may be larger than the order of the desired controller, a reduction of the LQG controller is now desired. The controller reduction problem aims at producing reduced order controllers that preserve the steady state covariance (in particular, the mean-squared values) of the optimal control inputs of step (2). Thus, the model reduction and the control design problems are unified by consistently using the mission requirements in all steps (1)-(3). The theory described herein offers a flexibility which is used to advantage to accommodate the different requirements of the model reduction and the controller reduction problems. Furthermore, the algorithm presented herein is easily applicable to both the model- and controller-reduction problems, thus permitting the use of the same software package for both the problems. In addition, this dissertation presents the mathematical properties of the reduced models and the reduced controllers that are produced by the theory. The proposed technique is applied to the design of a controller for a solar optical telescope which is representative of large scale systems.

Degree

Ph.D.

Subject Area

Aerospace materials

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