12 - Adaptive robust control scheme with an application to PM synchronous motors

Abstract

This chapter presents a new, adaptive, and robust control scheme for a class of nonlinear uncertain dynamical systems. To reduce the robust control gain and widen the application scope of adaptive techniques, the system uncertainties are classified into two different categories: the structured and nonstructured uncertainties with partially known bounding functions. The structured uncertainty is estimated with adaptation and is compensated. Meanwhile, the adaptive robust method is applied to deal with the nonstructured uncertainty by estimating unknown parameters in the upper bounding function. The backstepping method is also adopted to deal with a system not in the parametric-pure feedback form, which is usually necessary for the application of a backstepping control scheme. It is shown that the new control scheme guarantees the uniform boundedness of the system and assures the tracking error entering an arbitrarily designated zone in a finite time. The effectiveness of the proposed method is demonstrated by the application to permanent magnet (PM) synchronous motors.