Improved convergence and increased flexibility in the design of model reference adaptive control systems

Abstract

A modified Liapunov design technique for model reference adaptive control system is shown to result in improved system convergence. An adaptive rule, derived on the basis of a new Liapunov function, is compared to the previous rule. A local stability analysis applied to the modified design shows that the error response is more rapidly convergent. Furthermore, system simulations show that the transient response for the adjustable parameters is also improved. A second result presented is a design technique for a class of plants whose parameters cannot be adjusted directly. This design leads to a system with a set of prefilter and feedback adjustable gains as the adaptive parameters and physically realizable linear time-invariant filter networks in both the feedback and prefilter paths. It eliminates the problem of nonunique adaptive laws previously encountered and requires only n - m - 1 derivative networks for its implementation (nth order plant with m zeros); hence, if m = n - 1, no derivative networks are required for implementation. In order to maintain a bounded plant input signal, the zeros of the plant transfer function must be restricted to the open left-half plane.