Linear control system optimization using a model-based index of performance

Abstract

This paper deals with a method of optimizing the free coefficients in the characteristic equation of a linear feedback control system. The optimization is carried out by minimizing an index of performance associated with the system's response to a given test disturbance. The index of performance is the integral of a quadratic function of the system state variables. The structure of the index rests upon a logical interpretation of the regulator nature of the control problem. The index for an tr— order system contains n I'll weighting factors whose values are determined from an n-~- order model system. This determination is such that the optimization of a completely free system will yield the model system. A system with fewer than n degrees of freedom in the state variable feedbacks may be optimized with respect to the free feedback coefficients, yielding a system whose dynamic response to a given disturbance is, for this optimization scheme, a best approximation to that of the model. Examples are presented for illustration of the salient features of the method. It is also shown by example that systems with closed- loop zeros may be optimized by this method. The author wishes to thank Dr. Harold A. Titus for his guidance in this investigation.