An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems

This paper proposes a new nonlinear sliding surface for a terminal sliding mode (TSM) controller to achieve robustness and high performance tracking for the disturbed MIMO systems. The proposed method improves the transient performance and steady state accuracy in a finite time simultaneously. The control law is designed to guarantee the existence of the sliding mode around the nonlinear surface, and the damping ratio of the closed-loop system is increased as the output approaches the set-point. The conditions on the state error bound in finite time are expressed in the form of linear matrix inequalities (LMIs). A DC motor position tracking problem is considered as a case study. Simulation results are presented to show the effectiveness of the proposed method as a promising approach for controlling similar nonlinear systems.