LMI-based robust composite position control of a knee rehabilitation exoskeleton robot subject to motion constraints

This paper presents a robust control strategy for the position control of a knee rehabilitation exoskeleton. The proposed approach combines a linear state-feedback controller with a nonlinear control law to address the system's nonlinear dynamics, including challenges like parameter uncertainties, external disturbances, friction, and motion constraints. A quadratic Lyapunov function is used to derive linear matrix inequality (LMI) conditions for calculating the controller's feedback gain. These conditions are established using advanced mathematical tools such as the matrix inversion lemma, Schur complement, and the S-procedure. The LMI-based design assumes that nonlinear functions are bounded by linear constraints. The effectiveness and robustness of the controller are demonstrated through numerical simulations, which show stable knee-joint position control, even under disturbances and uncertainties. A comparative analysis with an existing control method highlights the advantages of the proposed approach in achieving robust stabilization of the knee rehabilitation exoskeleton.