A new robust MRAC using variable structure design for relative degree two plants

Abstract

Variable structure design concept has been shown not only useful in dealing with uncertain systems but also useful in establishing controllers in the adaptive context. Continuing the work, this research proposed a new robust model reference adaptive control for single-input-single-output linear plants with relative degree two, a class which encompasses a large number of linearized mechanical systems. When compared with the conventional MRAC schemes, the current approach drastically improves the transient behavior and the tracking performance of the closed loop system from several numerical simulations. Furthermore, if the reference input satisfies the persistently exciting condition or if the prior knowledge about the interval in which the true parameter vector lies is available, the magnitude of the input force can be considerably reduced into a more realistic level. In the presence of mild unmodelled dynamics and bounded output disturbances, the proposed scheme possesses similar well behaved properties. It can be shown that the tracking error will, in fact, fall into a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances.