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.

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This paper discusses the design of an H∞ MIMO centralized feedback controller applied to a 3 DOF parallel robot namely the "Delta robot". The designed controller is used in combination with a feed-forward pre-computed torque (a priori torque). The simulation results for a complex trajectory used in pick and place operation with high acceleration (12 G) show the performance improvements obtained by the total controller (a priori torque + H∞ feedback) in comparison to the conventional decentralized PID controller used with the a priori torque.

This paper deals with an efficient application of the mixed sensitivity problem for the position control of the "Delta" parallel robot. The dynamic model of this three degrees of freedom robot is highly nonlinear. An H∞ controller is synthesized in two steps. We first develop the tangential linearized model of the robot around an operating point. The mixed sensitivity problem is then solved. This consists of shaping both the sensitivity and the complementary sensitivity functions of the closed loop system. For the implementation of the control law, a Simmechanics 1 multibody mechanical model has been developed to simulate the kinematics and the dynamics of the robot and to validate the control results. The controller is implemented without using the feed forward precomputed torque and the performances remain satisfactory by decreasing the travel time of the semi-elliptic trajectory for pick and place up to 0.25s. The simulations results of the H∞ controller are compared to those of H2 controller. Robustness analysis through methodical simulation results are presented and commented.