MODEL AND CONTROLLER REDUCTION OF UNCERTAIN SYSTEMS USING COVARIANCE EQUIVALENT REALIZATIONS (LARGE SCALE, PARAMETER SENSITIVITY)

DAVID ARNOLD WAGIE, Purdue University

Abstract

In designing controllers for many systems, especially Large Space Structures, there are two general problems. First, due to large system dimension or limited computation capability, the controller must be of smaller dimension than the original system. Secondly, some parameters of the system are only generally known, and hence must be considered uncertain. This research presents a theory to design a controller that accommodates these two concerns. The general approach is to use a projection technique for system reduction which provides a reduced system that matches output covariances and Markov parameters of the original system. In addition, this technique preserves the mean-squared values of the system outputs, an important property since most performance specifications are given in terms of maximum mean-squared output values. The specific steps in using this technique to design a reduced sensitivity controller (a reduced-order controller with decreased sensitivity to parameter variations) are as follows: (1) Given the original system, a subsystem is constructed that reflects the sensitivity of the original system to the uncertain parameters. This subsystem is combined with the original system to form a trajectory sensitivity system. (2) The proposed system reduction technique is then applied to the augmented system in such a way that only the sensitivity subsystem is reduced, leaving the original system unchanged. In addition, an approximation is made to the control sensitivity term such that the final reduced system is in standard linear state-space form. (3) A standard optimal controller is then obtained for this reduced sensitivity system. If desired, the input sensitivity approximation in (2) can be improved by iteratively applying steps (2) and (3). (4) Finally, the system reduction technique is used on the sensitivity controller of step (3) to obtain the reduced sensitivity controller. The dissertation provides a concise theoretical development of the proposed projection approach to system reduction, and discusses its application for model and controller reduction of both continuous and discrete systems. This technique is then used to design a reduced sensitivity controller for a continuous time system with uncertain parameters.

Degree

Ph.D.

Subject Area

Aerospace materials

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