Robust H∞ optimal control of a single flexible link

Abstract

In this paper, we present the results of the controller design of a single flexible link using the H∞ optimization approach. A single flexible link experiment at the University of Waterloo is used to obtain realistic uncertainty models. In this paper, a reduced order model is used by considering the rigid body mode and the first vibratory mode. The neglected higher order modes are modeled as an output multiplicative uncertainty. As well, it is shown that uncertainty in the internal damping of the beam can easily be designed for. The torque disturbances caused by the cable drag of the experimental set up is modeled as an input disturbance. The weighting functions are selected based on these uncertainty models and to satisfy the design specifications. Using the H∞ method, the one parameter and two parameter controllers are designed satisfying robust stability and disturbance rejection. Simulation and experimental results show that the controllers designed for the reduced order model guarantee effective vibration control of the single flexible link against possible uncertainties.