New feedback design methodologies for large space structures : a multi-criterion optimization approach
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A few problems of designing structural control systems are addressed, considering optimization of three design objectives: state error energy, control energy and stability robustness. Tradeoff relationships among these selected design objectives are investigated by solving multiple objective optimization problems. Various measures of robustness (tolerance of model errors and disturbances) are also reviewed carefully in the present study and throughout the dissertation, robust control design methodologies are emphasized. Presented in the first part of the dissertation are three new feedback design algorithms: 1) a generalized linear-quadratic regulator (LQR) formulation, 11) a generalized LQR formulation based on Lyapunov stability theorem, and 111) an eigenstructure assignment method using Sylvester's equation. The performance of these algorithms for multi-criterion optimizations are compared by generating three dimensional surfaces of wh1ch d1splay the tradeoff among the three design objectives. In the second part, a noniterative robust e1genstructure assignment algorithm via a projection method is introduced. This algorithm produces a fairly well-conditioned eigenvector matrix and provides an excellent starting solution for optimizations of various design criteria. We also present a specialized version of the projection method for second order differential equatlons, wh1ch offers useful insights to design strategies in regards to conditioning (robustness) of the eigenvectors. Finally, to illustrate the ideas presented in this study, we adopt numerical examples in two sets: 1) 6th order mass-spring systems and 11) various reduced order models of a flexible system. The numerical results confirm that multi-criterion optimizations by using a minimum correction homotopy technique is a useful tool with significant potential for enhanced computer—aided design of control systems. The proposed robust eigenstructure assignment algorithm is successfully implemented and tested for a 24th reduced order model, which establishes the approach to be applicable to systems of at least moderate dimensionality. We show analytically and computationally that constraining closed—loop eigenvectors to equal open-loop eigenvectors generally does not lead to either optimal conditioning (robustness) of the closed-loop eigenvectors or minimum gain norm.
- Doctoral Dissertations