Adaptive Back-Stepping Data-Driven Terminal Sliding-Mode Controller for Nonlinear MIMO Systems With Disturbance Observer

This paper presents an Adaptive Back-stepping Data-Driven Terminal Sliding Mode Controller (ABDTSMC) for non-affine MIMO systems with general disturbances including internal uncertainties and external disturbances. The proposed controller with new reaching law is used to reduce the controller’s dependence on the mathematical model and eliminate the chattering phenomenon. Furthermore, to solve the problem of the coupling effect and to estimate the uncertainties and disturbances, the Disturbance Observer (DOB) based on neural network with adaptive weights is utilized. Afterwards, it is implied that the DOB variables are Uniformly Ultimately Bounded (UUB). Next, for the integrated controller, the closed-loop stability based on the Lyapunov and back-stepping theory is investigated and the new adaptive law for the Pseudo Jacobian Matrix (PJM) elements is derived. This method contributes to the reduction of complexity and conservatism, which facilitates analysis of the closed-loop stability. To evaluate performance of the controller, the proposed method is applied to a 2-DOF robot manipulator. The simulation results are compared with Model-Free Adaptive Sliding-Mode Controller (MFASMC) and Model-Free Adaptive controller (MFAC), which are reported recently in related literature. The results demonstrate the precision of the tracking capability is significantly enhanced in the presence of time-varying disturbances. Moreover, the chattering phenomenon is successfully removed. In addition, the number of required data is significantly reduced. Finally, to show practicality of the proposed controller, it is applied to the 2-DOF laboratory manipulator.