Modeling and control of a flexible-link manipulator

Abstract

The behaviour of a flexible-link robotic manipulator is studied using an experimental apparatus. The system is modeled based on the physical laws governing system dynamics. A non-linear rigid body model is developed which includes backlash and friction. Through comparison of experimental and simulation results, the small backlash in the system is shown to have little effect on the system behaviour. Friction is shown to have a considerable effect on the system dynamics. The finite element method is used to develop a flexible body model for the flexible link. Experimental results show that the lateral vibration of the manipulator exhibits the behaviour of a clamped-free beam or a pinned-free beam during different stages of the motion. A combined dynamic model has been developed. The model is comprised of both a clamped-free beam model and a pinned-free beam model with the choice of model being determined by the boundary conditions at the hub that change due to the non-linear friction term included in the model. Experimental and simulation results demonstrate that, at low speeds of rotation, the hub friction causes the pinned frequencies of vibration to approach the clamped frequencies. Vibration suppression controllers are considered based on the coupling torque from the clamped beam model. Different vibration-suppressing controllers are found to be effective in the pinned, high-speed region, the pinned, low-speed region and the clamped region. The effectiveness o f vibration-suppressing controllers when added to a classical PD controller is studied.