Filtered Sliding Mode Tracking Controller for Robot Joint Using Linear Matrix Inequalities Design

In this paper, a Linear Matrix Inequalities (LMI) design of a filtered sliding mode controller is proposed, and applied to a robot joint for tracking control. The robot joint dynamics are linearised through the compensation of nonlinear terms (i.e. frictions, gravity, and coriolis torques), and a filtered control action is designed in order to prevent the chattering problem. The optimal control design using LMI technique can then be applied to the combined low pass filter and robot joint system, ensuring the stability of the closed loop. The proposed method is evaluated through numerical simulations of two degrees of freedom (2-DOF) end-effector type therapeutic robot, showing the robustness and performances of the controlled system under tracking task.