A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators

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.

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