AFMBC for a Class of Nonlinear Discrete-Time Systems with Dead Zone

Abstract

This paper is fretful about an adaptive fuzzy model-based controller (AFMBC), which is studied and implemented for class of nonlinear discrete-time system with dead zone. Due to immeasurable states and the presence of symmetric/non-symmetric dead zones, design of controller becomes more challenging. AFMBC is design for approximation of such nonlinear system to a relative degree of accuracy, which can be used for adaptation of nonlinear discrete-time systems with or without the presence of symmetric/non-symmetric dead zones. AFMBC employs as a reference model which is useful to closed-loop pure feedback form of fuzzy controller. AFMBC provides approximation of immeasurable states and minimizes effects of unknown bounded disturbances in the system. Based on Lyapunov method, it is proved that proposed scheme for discrete-time nonlinear systems is asymptotically stable. Hence, not only stability of proposed system is assured, but it is also shows that tracking error of model lies in closed neighbourhood of zero after sufficient number of iterations, i.e. tracking error $$ (e(t) \to 0\;{\text{as}}\;t \to \infty ) $$ . The feasibility of the AFMBC is demonstrated by well-known direct current (DC) motor example and other nonlinear discrete-time problem through simulation.