Abstract
Abstract In this paper, we are interested in the position control problem of Lagrangian robotic systems via an affine PID-based control law. To achieve such problem and in order to design the condition on the feedback gains ensuring the stabilization of the closed-loop system, we introduce the approximate linear dynamic model and we consider some Lipschitz condition on the nonlinear term defining the difference between the nonlinear dynamics and its linear model. Thus, we use the Linear Matrix Inequality (LMI) approach to design the stability conditions, which allow at the same time the maximization of the Lipschitz constant and reduction of the size of the feedback gains. This idea contributes therefore in reducing the control effort applied to the robotic system. Finally, a two-degree-of-freedom manipulator robot is considered in order to verify the validity of the adopted affine PID-based control law.
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