On the Robustness with Respect to Disturbances in Continuous-Time Model Reference Adaptive Control System Based on Weighting Functions

Abstract

This paper presents a model reference adaptive control system (MRACS) for a plant with deterministic disturbances, which are assumed to be outputs of autonomous systems. An MRACS can be designed for an augmented system which is composed of the plant and the autonomous systems. However, an MRACS with a state variable filter needs the degree of the augmented system, which is difficult to be known beforehand.
To dispense with the knowledge of the degree, we use a continuous-time dead-beat observer in stead of the finite dimensional state variable filter. The observer reconstructs the state of the augmented system by a sum of convolution integrals in a finite span of the time. Since the adaptive controller estimates these weighting functions, it does not require the degree of the autonomous system as well as that of the plant.
A new error system is proposed to prove the stability of the MRACS. Simulation results are also presented to show an effectiveness of the proposed method.