H_∞ robust control design for an arm manipulator

This paper deals with the application of the optimal H_∞ control design technique to derive a controller for a 3 DOF arm manipulator affected by nonmodeled dynamics, nonlinearities, actuator dynamics and sensor noise. The control objectives were to obtain a robust stable with robust performance controlled system. A family of nonparametric models for a finite number of the arm configurations was obtained. Then, a multivariable nominal model was proposed and derived together with additive nonparametric uncertainty bounds. Weighting functions were used to normalize the H_∞ norm of the uncertainty and to act on the command, sensor, and error signals. Finally, a controller was computed by solving the corresponding H_∞ optimization problem. The controller was tried on the nominal and worst case configuration models. The results showed robust stability and robust performance of the controlled system.