Robust model reference tracking for uncertain second‐order nonlinear systems with application to robot manipulator

Abstract In this article, robust model reference control for uncertain second‐order nonlinear systems is investigated by applying fully actuated system approaches. A robust stabilizing control law is constructed for the uncertain systems based on the Lyapunov stability theory. With the obtained robust control results, a robust model reference tracking (RMRT) control scheme is proposed to ensure the tracking error finally converges globally into a bounded ellipsoid. The established RMRT controller is composed of three parts, the basic part cancels the known nonlinearities in the system and simultaneously assigns the linear dominant term in the closed‐loop system, the robustness part overcomes the effects of the nonlinear uncertainties in the system, the compensator part compensates the effect of the reference model state and reference control input to the tracking error. Furthermore, based on a general parametric solution to the type of Sylvester matrix equations, simple and complete parameterization of the RMRT control designs is provided. An application to robot manipulator indicates satisfactory control system performances with the proposed RMRT control scheme.