A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators

Abstract

The control of lightweight flexible manipulators is the focus of this work. Theflexible manipulator dynamics is derived on the basis of a Lagrangian-assumed modes method. The full-order flexible dynamic system does not allow the deter mination of a nonlinear feedback control as for rigid manipu lators, since there are not as many control inputs as output variables. This drawback is overcome by a model order reduction, based on a singular perturbation strategy, where the fast state variables are the elastic forces and their time derivatives. A composite control is adopted. First, a slow control is designed for the slow subsystem, which is shown to be the model of the equivalent rigid-link manipulator. Then a fast control is designed to stabilize the fast subsystem around the equilibrium trajectory set up by the slow subsystem under the effect of the slow control. The one-link flexible-arm prototype in the Flexible Auto mation Laboratory at Georgia Institute of Technology is chosen for developing a case study. Simulation results are illustrated, and a comparison is made between the perform ance achieved with a two-time-scale controller and with a state feedback regulator.