Model-free adaptive command-filtered-backstepping sliding mode control for discrete-time high-order nonlinear systems

Abstract

A new model-free adaptive sliding mode control method is proposed to solve some control issues in a class of discrete-time high-order nonlinear systems whose dynamics are unknown in this paper. In order to simplify the nonlinear system, a new concept called pseudo-partial derivative matrix (PPDM) is introduced to facilitate the nonlinear system by using a compact form dynamic linearization approach. Therefore, to estimate the PPDM, the identified adaptive observer is constructed using the input/output data from each subsystem of the higher order discrete time system. Taking into account the amplitude and rate constraints of real-world input signals, an anti-windup dynamic compensator is developed. Furthermore, the problems of complexity explosion and non-causality are solved by using discrete-time command filters while designing the controller. It has been shown that all the control variables in closed-loop systems are uniformly-ultimately bounded. An example of a linear induction motor taking into account the end effects is used to verify the effectiveness of the presented control strategy through simulations and experiments.