LMI-Based Design of an Affine PD Controller for the Robust Stabilization of the Knee Joint of a Lower-Limb Rehabilitation Exoskeleton

Lower limb exoskeletons have recently received a lot of attention in the world of robotics and have a wide range of uses. This work is concerned with the robust control of an actuated knee exoskeleton robotic system by means of an affine PD controller. Thus, a second-order nonlinear model with solid frictions, viscous frictions and parameters uncertainties is considered. Then, our central idea to design the controller lies in linearizing the nonlinear model around a desired state. Therefore, using the nonlinear model describing the difference between the nonlinear dynamics and its approximate linearized system, we adopt an affine PD control law to robustly stabilize the knee exoskeleton. Furthermore, using the S-procedure lemma, the Young inequality, and the Schur complement, we design LMI stability conditions for the feedback matrix gain of the controller. Finally, we present some results to demonstrate the validity of the developed condition and the robustness of the adopted controller.