Convergence and frequency-domain analysis of a discrete first-order model reference adaptive controller

Abstract

We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steady-state. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright © 2006 John Wiley & Sons, Ltd.