A Singular Perturbation Approach to Control of Lightweight Flexible Manipulators
Book, Wayne John
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The control of lightweight flexible manipulators moving along predefined paths is the focus of this work. The flexible manipulator dynamics is derived on the basis of a Lagrangian-assumed modes method. The full order flexible dynamic system does not allow the determination of a tracking control as for rigid manipulators, since there are not as many control inputs as output variables. This drawback is overcome by accomplishing a model order reduction, based on a singular perturbation strategy, where the perturbation parameter can be identified as the ratio of speeds of the slow versus the fast dynamics. A composite control is adopted. First a slow control is designed with the purpose to track the trajectory in the joint space as accurately as possible. A quasi steady-state trajectory is then determined for the fast variables, and a fast control is in charge of stabilizing them along that trajectory. The one link flexible arm prototype in the Flexible Automation Laboratory at Georgia Tech is chosen for developing a case study. Extensive simulation results are illustrated.