LMI-Based Design of an Affine PD Controller for the Position Control of Robotic Systems with Application to Human Upper-Limb Rehabilitation via an Exoskeleton Robot

Controlling the motion dynamics of robotic systems, notably exoskeleton robots for the rehabilitation of human’s upper/lower limbs, has piqued the interest of researchers as a potential healthcare strategy for treating impairment problems in disabled persons. The controller design methodology can appropriately rely on linearizing the nonlinear dynamics around some desired point. In this chapter, we use the difference between the robotic system’s nonlinear dynamic model and the approximate linear model to generate a nonlinear dynamical system that meets a specific Lipschitz constraint. Using this scaled nonlinear dynamics, we propose an affine PD controller to construct certain LMI conditions ensuring the closed-loop stability of the controlled robotic system using three approaches. Minimization problems based on LMI constraints are then created to determine the maximal Lipschitz constant. Some new LMI conditions are recommended to limit the extent of the controller’s feedback gains. We suggest a two-degree-of-freedom (2-DoF) upper-limb exoskeleton robot as an application. The three methods are used to provide a portfolio of numerical findings for evaluating the feasibility of the designed LMI challenges. Furthermore, some simulation results demonstrating the efficacy of the adopted affine PD control law in the stabilization of the robotic system, and therefore of the 2-DoF upper-limb exoskeleton robot, are accomplished.