Design of an H∞ controller for the Delta robot: experimental results

Abstract

This paper deals with an efficient implementation of an H∞ multi-variable controller on the three degrees of freedom (DOF) parallel robot namely the ‘Delta robot’. The H∞ controller is designed by the mixed sensitivity approach in which the sensitivity function matrix S and the complementary sensitivity function matrix T are taken into account. For this purpose, a nonlinear analytical dynamic state model is developed and a tangent linearization procedure is used to obtain a multi-variable linear model around a functional point. Real-time experiments were performed to compare the centralized H∞ controller with a classical decentralized Proportional Integral Derivative (PID) controller. Experimental tracking results show that the performances of the PID compared to those of the H∞ decrease when the movement dynamic is increased. At high dynamic (12 Ge), it is shown that the maximum tracking error and the error around the stop positions of the H∞ are, respectively, 80 and 60% of the PID. The experiments of the load variation have proven that the H∞ is more robust than the PID. The steady-state root mean square error of the H∞ is less than 60% of the one obtained using the PID controller.