Vali Uddin

Reduced Order LTR Controller

Friday, February 11, 2000
1:00 PM
410 Dana

Abstract

It is well-known that Linear Quadratic Regulator (LQR) has impressive robustness properties. However, when an observer is used to estimate the state variables for feedback implementation, such robustness properties will no longer be guaranteed. Several methodolgies have been proposed to overcome this problem with limited success and none of them address the recovery methods with low order compensators.

The purpose of this research is to discuss various aspects of the subject pertinent to the design of LTR controllers with minimal order. To facilitate the basic understanding of the fundamental mechanism of LTR, a common framework for the design of various types of observers are presented. Different methods for the design of functional observer based controller having pre-specified or post-specified eigenvalues are given. A simple algorithm for the design of minimal-order observer capable of reconstructing several linear functional of the states of the system is outlined. The main idea behind this new method is the use of consistency condition from matrix generalized inverse along with a geometric constraint. We translate the problem to a constrained algebraic equation and provide an efficient algorithm to construct an observer of least possible order with pre-specified eigenvalues. A complete analysis of loop transfer recovery problem using observer based and compensator based systems is given, and necessary and sufficient conditions for a given plant to have a recoverable target loop are presented. Methods for the design of functional-observer based LTR controllers for SISO and MIMO systems are developed.

Finally, the problem of optimal H_infinity norm approximation of an LTR controller with specified eigenvalues is considered. A structurally pre-defined fixed order LTR controller is introduced which has the same dimension as the number of transmission zeros in the left half s-plane. It is shown that the design problem can be reduced into an equivalent convex optimization problem involving LMI which can be solved efficiently.

Thesis Committee:
Prof. B. Shafai (advisor)
Prof. B. Lehman
Prof. S. Stankovic
Prof. B. Wilson (Mechanical Engineering Department)