Application of the mixed sensitivity problem H∞ and H<inf>2</inf> to the parallel Delta

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> 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 pre-computed 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 H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> controller. Robustness analysis through methodical simulation results are presented and commented.