A New Approach to the Design of an Adaptive Control System

Abstract

Monopoli established the design of a model reference adaptive control system which does not need derivatives of plant output for a very general class of plants. Monopoli’s method, moreover, uses a control input synthesis scheme so that the design method is of highly practical use. However, since abundant filters are used in Monopoli’s adaptive control system, the total adaptive control system is extremely complex. A quite different design method from that of Monopoli is presented in this paper. Noticing that the total adaptive control system reduces to a linear time-invariant system at the steady state that follows the completion of the adapting operation, the author examined the realizability condition for adaptive control and determined the form of filters at the steady state. The adaptive control system is obtained by merely replacing the constant coefficients of the filters by the estimates of unknown plant parameters which are available from Anderson’s adaptive identifier arranged into the system. The adaptive control system needs only model input, model output and plant output, but does not need plant output derivatives. The assumption imposed on plant and model are that plant is n-th order system with (n-l)-th polynomial as the numerator of plant transfer function, all poles as well as zeros of plant must lie in the region of Re[s]<0 and model is asymptotically stable n-th order system.