An LMI-based Composite Nonlinear Controller Design for Robust Stabilization of a Knee Rehabilitation Exoskeleton Robot

Abstract

This paper introduces a novel robust control strategy specifically designed for a one-degree-of-freedom (1-DoF) knee rehabilitation exoskeleton robot, focusing on position control. Our approach addresses several key challenges, including state constraints, parameter uncertainties, solid and viscous frictions, and external disturbances. We suggest a composite controller that combines a nonlinear controller with a linear state feedback controller in order to successfully address these issues. By utilizing a quadratic Lyapunov function, we derive the expression of the nonlinear control law and establish the Linear Matrix Inequality (LMI) conditions for computing the matrix gain of the linear controller, ensuring robust stabilization of the exoskeleton robot to the desired position. These conditions are derived through the application of advanced mathematical techniques such as the matrix inversion lemma, the Young inequality, the Schur complement, and the S-procedure lemma. Numerical results show the effectiveness of our suggested control law, demonstrating the continuous convergence of the intended angular position to the real one, even when external disturbances and uncertainties are present. Overall, our research not only presents a novel methodology for robust control but also delivers promising results that underscore the efficacy of our approach in achieving stable and reliable performance for 1-DoF knee exoskeleton robots.