Chin S. Hsu

Realization algorithms and approximation methods of bilinear systems

High-dimensional mathematical models of bilinear control systems are often not amenable due to the difficulty in implementation. In this paper, we address the problem of order-reduction for both discrete and continuous time bilinear systems. Two model-reduction algorithms are presented; one is based on the singular value decomposition of the generalized Hankel matrix (the Hankel Approach) and the other is based on the eigenvalue / eigenvector decomposition of the product of reachability and observability Gramians (the Gramian Approach). Equivalence between these two algorithms is established. The main result of this paper is a systematic approach for obtaining reduced-order bilinear models. Furthermore, the bilinear reachabiiity and observability Gramians are shown to be obtainable from the solutions of generalized Lyapunov equations. Computer simulations of a neutron-kinetic system are presented to illustrate the effectiveness of the proposed model-reduction algorithms.

Reduced-Order H^ Compensator Design for an Aircraft Control Problem

A recently introduced method for designing //<» compensators based on minimal-order observers is considered for an aircraft control problem. The purpose of this paper is to bridge the gap between theory and application by presenting a practical utilization of a new design approach. Manual flight control systems for the lateral axis of a fighter aircraft are developed using both full-order and reduced-order compensators, and the results are compared. It is demonstrated that this method can be used to directly design reduced-order compensators that result in a system satisfying a closed-loop //« bound.

Reduction of large-scale systems via generalized Gramians

System analysis and control design of large-scale dynamic systems are important in many applications. However, due to high dimensionality of the system, practical implementation of the theoretic results in large-scale systems is a difficult and expensive task, even with the aid of modern computers. In this paper, a different approach is undertaken to overcome the computational difficulty which is often associated with the nearly singular large-scale mathematical models. Instead of using the standard dynamic equations to represent a large-scale system, mathematical models in the descriptor form (generalized dynamic equations) are used. It is shown that via numerically reliable algorithms, the generalized dynamic model can be balanced in the sense that the balanced model is equally controllable and observable. Moreover, the balancing transformation can be obtained by solving generalized Lyapunov equations for observability and controllability Gramians, Based upon the balanced model, reduced-order models which closely match the input-output behavior of the system can be derived. Computer simulations of a power machine system will be presented to illustrate the effectiveness of the model reduction algorithm.

Reduced order H/sub /spl infin// filter design for time varying systems

This paper is concerned with the reduced-order H/sub /spl infin// filter design for linear time varying continuous systems in which all measurements are contaminated with noise (nonsingular case). The proposed filters have the Luenberger observer structure in a more general form and their order can be as low as n-p, where n and p are the order of signal systems and the number of measurements, respectively. Several bounded real lemmas are developed for the infinite-horizon and finite-horizon cases. They are the only tools used to establish the reduced-order filter design in this paper. It is shown that the full order filters in Nagpal and Khargonekar (1991) are special cases of the results presented in this paper.<<ETX>>

Minimal-order observer based H/sub /spl infin// control for a flight control problem

A recently introduced method for designing H/sub /spl infin// compensators based on minimal-order observers is considered for an aircraft control problem. The purpose of this paper is to bridge the gap between theory and application by presenting a practical utilization of a new design approach. Manual flight control systems for the lateral axis of a fighter aircraft are developed using both full-order and reduced-order compensators and the results are compared. It is demonstrated that this method can be used to directly design reduced-order compensators which result in a system satisfying a closed-loop H/sub /spl infin// bound.<<ETX>>

Fixed Order H∞ Compensator Design

Abstract A method is presented for the construction of fixed-order compensators to provide H ∞ norm constraint for linear control systems with exogenous disturbances. The method is based on the celebrated bounded-real lemma that predicates the H ∞ norm constraint via a Riccati inequality. The synthesis of fixed-order controllers whose dimensions are less than the order of a given plant, is demonstrated by a set of sufficient onditions along with a numerical algorithm.

H ∞ /LTR: a loop shaping method for h ∞ , output fibdback compensator design

This paper addresses the issue of H_∞, loop transfer recovery and loop shaping when an H_∞ output feedback controller is used. A method of selecting the H_∞ design parameters to achieve asymptotic loop transfer recovery is presented. It is shown that the problem of approximate loop transfer recovery is dual to H_∞ state feedback design. A special class of H_∞/LTR design problems is also presented.

A stability bound for systems with periodic output feedback

The authors present a stability bound on additive perturbations in the plant state matrix for systems with piecewise-constant, periodic output feedback. The bound does not require the calculation of the matrix exponential, but instead uses the matrix measure as an upper limit on its norm. This limit and a special norm based on the closed-loop eigenvectors are used to show that if the stability bound is satisfied, all the eigenvalues of the closed-loop discrete-time state matrix have magnitude less than one. It is also shown that if the stability bound is satisfied for two extreme perturbations, then the system is stable for all of the intermediate perturbations. Use of the stability bound is demonstrated by a numerical example.<<ETX>>