Robust control of multilink flexible manipulators

This paper deals with some robustness aspects of a model based controller used for trajectory tracking in multi-link flexible manipulators. It is known in literature that the finite element formulation over-estimates the natural frequencies of the original system. We show that over-estimation of natural frequencies may lead to unstable closed-loop response for flexible manipulators using a model based inversion control algorithm. A robust controller design based on the second method of Lyapunov using simple quantitative bounds on the model uncertainties is illustrated for use during the trajectory tracking phase in multi-link manipulator control. In order to actively suppress the link vibrations excited during the trajectory-tracking phase, a second controller based on end-point sensing and the rigid Jacobian of the manipulator is used. The performance of the two-stage controller is illustrated with the help of numerical simulations of a flexible elbow manipulator.