MIMO Uncertain Nonlinear System Control via Adaptive High-Order Super Twisting Sliding Mode and its Application to Robotic Manipulator

Abstract

This paper presents a robust, continuous, finite-time convergent, adaptive, high-order super twisting sliding mode controller for a class of multi input–multi output uncertain nonlinear system and its application to robotic manipulator. The limitation on conventional super twisting control (STC) algorithm application only to relative degree one system is eliminated by using a novel homogeneous nonlinear sliding manifold. Moreover, the proposed controller gains are selected by using an adaptive estimation mechanism to tackle the gain overestimation problem. It is ensured that the tracking errors will converge to zero in finite time and the actual control signal is smooth and free from chattering phenomenon, a major known limitation of the conventional sliding mode control and STC. The rejection of the parametric uncertainties and external disturbances is improved due to an extra integration of discontinuous control. The finite-time convergence and stability of the proposed controller is analyzed with the help of homogeneous Lyapunov stability theory. The effectiveness and application feasibility of the proposed controller is revealed by the simulation results obtained from the MATLAB software. Finally, a real-time implementation strategy for the realization of the proposed controller, using MATLAB–Simulink platform and Speedgoat hardware, is also given for robotic manipulator control.