Robust Proportional Control for Trajectory Tracking of a Nonlinear Robotic Manipulator: LMI Optimization Approach

This paper proposes a new control configuration that is simple, model free and robust for trajectory tracking control of a multi-input-multi-output nonlinear robotic manipulator system. The proposed controller consists of two terms. The first term is a linear controller in proportional (P) control structure, and the second term is a nonlinear robustness term in sliding mode structure. This combined nonlinear controller exploits the simplicity and easy implementation properties of proportional-integral-derivative control and robustness properties of the sliding mode control (SMC) against system uncertainties and parameter variations. Important feature of the proposed controller is avoiding the need to determine the accurate dynamic model of the plant, which is a necessity in standard SMC. Stability analysis is performed, and stability in closed loop is proved for the proposed control method. A control problem is restated as a convex optimization problem based on linear matrix inequality technique, and optimal gain of P controller is obtained. A simulation model of the plant is built in MATLAB-Simulink environment for testing the proposed controller. Closed-loop system performances are observed for standard SMC, computed torque control, SMC with proportional-derivative control and proposed control. Simulation results reveal the effectiveness of proposed method in response to system uncertainties, random noise and external disturbance.