A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators

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  • Bruno Siciliano
    Dipartimento di Informatica e Sistemistica Università di Napoli Via Claudio 21, 80125 Napoli, Italy
  • Wayne J. Book
    G. W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, Georgia 30332

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<jats:p> 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. </jats:p><jats:p> 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. </jats:p><jats:p> 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. </jats:p>

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