Extension of the algorithms with saturation functions for a nonlinear H∞/PID controller

In this paper an extension of the algorithms with saturation functions to the nonlinear H∞ control for robot manipulators introduced in [4] has been carried out. Based on the classical algorithm, this extension copes with a nonlinear equation of the closed-loop error. The resulting Lyapunov´s equation in the linear case is substituted for a Hamilton-Jacobi-Bellman-Isaacs equation. A modified expression for the control signal increment is supplied, and the local closed-loop stability of this approach is discussed. Finally, simulation results for an industrial robot — the RM-10- have been presented. Results obtained with this method have been compared with the ones attained with the original controllers to show the improvements supplied by this method.