LMI-Based Robust Control of a Knee Rehabilitation Exoskeleton Robot Using a Nonlinear Composite Controller

Abstract

The present study proposes a control approach designed to achieve robust stabilization of a 1-DoF knee joint exoskeleton system intended for rehabilitation purposes. The proposed method combines a linear state-feedback control law with a nonlinear control law to address the nonlinear dynamics of the knee-joint exoskeleton, addressing parameter uncertainties and external disturbances. The model simplifies the nonlinear function by assuming it to be bounded by linear constraints. By considering two different expressions of the term existing in the nonlinear controller, two design methods for LMI conditions are developed. These methods use a quadratic Lyapunov function to ensure stability and robustness. The controller’s performance is assessed through simulations under external disturbances, and a comparative analysis confirms its efficacy in maintaining stability despite parametric uncertainties.