Date of Award

2-1993

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical and Civil Engineering

First Advisor

Wassim M. Haddad

Second Advisor

Paavo Sepri

Third Advisor

Emmanuel G. Collins, Jr.

Fourth Advisor

Fredric M. Ham

Abstract

For linear time-invariant systems it has been shown that the solutions to the optimal reduced-order modeling, estimation, and control problems can be characterized using optimal projection equations, sets of Riccati and Lyapunov equations coupled by terms containing a projection matrix. These equations provide a strong theoretical connection between standard full-order results such as linear-quadratic Gaussian theory and have also proved useful in the comparison of suboptimal reduction methods with optimal reduced-order methods. In addition, the optimal projection equations have been used as the basis for novel homotopy algorithms for reduced-order design. This thesis considers linear periodic plants and develops necessary conditions for the reduced-order modeling, estimation, and control problems. It is shown that the optimal reduced-order model, estimator, and compensator is characterized by means of periodically time-varying systems of equations consisting of coupled Lyapunov and Riccati equations. The results presented herein can be readily applied for designing fixed-order (i.e., full- and reduced-order) controllers for spinning satellites, rotor-craft vibrations, and multirate sampled data estimation and control. Extensions to reduced-order multirate sampled data estimation, static output-feedback multirate control, and fixed-order multirate dynamic compensation are also developed. Finally, a novel homotopy (continuation) algorithm, which allows numerical solutions to the associated periodic multirate estimation and control problems, is also presented.

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