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.

A New Adaptive RISE Feedforward Approach based on Associative Memory Neural Networks for the Control of PKMs

“…Robust linear control techniques such as the H ∞ are used for systems affected by the presence of external disturbances and parametric variations [13]. An efficient implementation of a H ∞ multivariable controller PKMs is presented in [14]; in such scheme, a linearized model around an operating equilibrium point is determined to obtain a state-space representation of the DPR, besides that, the sensitivity and complementary sensitivity transfer functions are calculated. This technique utilizes the perturbations in the design of the controller, but the design of this scheme is very sophisticated and complex.…”

Control of rotary double inverted pendulum system using mixed sensitivity H∞ controller

“…18 Thus mixed sensitivity approach can be differed mixed sensitivities, such as S/T in Peng et al 19 and M. Rachedi et al, 20 S/KS in Wei-qian et al, 21 Ozana et al, 22 and Xinping Bao, 23 or S/KS/T in Alfaya et al, 24 Bejarano et al, 25 Delettre et al, 26 Iannino et al, 27 and Fragoso et al 28 Peng et al 19 proposed H1 controller to solve the S/T problem for the pneumatic manipulator with parameter variation, and low or high frequency disturbances acting on the pneumatic manipulator as uncertainties. Rachedi et al 20 used mixed sensitivity controller for position control of a "Delta" parallel robot. The controller showed better performance against disturbance forces applied on the traveling plate compared to Proportional Integral Derivative (PID) controller.…”

Nonlinear PD plus sliding mode control with application to a parallel delta robot

“…Delta robot is a parallel manipulator invented by R. Clavel [12] in order to execute pick and place operations at a high dynamic movement. Many control strategies have been implemented on the Delta robot such as, PD plus feedforward control [13], a linear robust Hinfinity control that was synthesised around an operating point [14] and an adaptive control that was developed for uncertain model in [15]. However, the drawback of the above-mentioned works is that knowing the exact dynamic model is crucial to satisfy the required performances.…”