Analysis of Robustness of the Inexact Model Matching Structure to Reduced Order Modelling

Abstract

The problem of unmodelled dynamics is very critical in the study of adaptive control systems because a model is merely a finite dimensional approximation of the infinite-dimensional plant. In the context of model reference adaptive control systems, wherein only the output is avalible for measurement, this problem becomes a reduced order adaptive control problem, which is tackled in this paper using the concept of inexact model matching.The inexact model matching structure, which calls for only an approximate matching between the plant and the model, has been shown to be globally stable (Shah and Monopoli, 1982b). This structure does not require a prior knowledge of relative degree or sign of the high frequency gain of the plant and thus has tremendous potential for it’s application to practical systems.It is proven in this paper that the system error, defined as the difference between the plant and the model output, remains bounded under all operating conditions. This robustness property is crucial in all practical systems, which due to the reason mentioned above, are subject to reduce order modelling.