Tracking Control for Electromechanical Systems Using Robust Discrete Time H∞

Abstract

In this work we propose a robust controller to do tracking using the sub-optimal H∞technique with the approach of differential game theory. The problem is solved in two steps using the Block Control technique. The controller is designed in discrete time and it is synthesized for electromechanical systems which are modeled by means of the Euler-Lagrange formulation. Making use of the discrete Hamilton-Jacobi-Isaacs equation and the discrete Riccati equation the control law is derived. The control law is then applied to a continuous-time 6-DOF bipedal robot model in order to track the walking pattern references for each link. The system along with the control law is simulated, where the system is subjected to a disturbance that emulates the action of a group of external unknown bounded forces over the links of the bipedal robot. The simulation results are shown displaying robustness against the disturbance, torques required from the motors are plot and since the control input was optimized the values lie within a reasonable bound. Furthermore, this work is compared to a similar approach that uses H∞ technique in continuous time.