Reducing vibrations on flexible rotating arms through the movement of sliding masses: Modeling, optimal control and simulation

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Terceiro E.
Fleury A.T.
International Conference on Integrated Modeling and Analysis in Applied Control and Automation
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This paper brings contributions on the proposal of use of translational motions of sliding masses to minimize vibrations induced by the rotational motion of a light flexible manipulator (rotating arm). This system is inspired by rotating cranes used to transport loads. Optimal control methods have been used to generate the slider trajectories while the flexible manipulator performs a rotational maneuver from a fixed to other fixed configuration. This approach has led to good solutions even in case of quite quick maneuvers, as, for example, a 90° beam rotation in just 1 second, using 1 or 2 sliders (Terceiro, 2002). In the present paper, the complete motion equations for any number of masses are firstly presented, in order to emphasize the complexity of the coupled elastic-rotational-translational motions. Simplifying assumptions are pointed out and the corresponding optimal control problems (OCP) are obtained. Optimal trajectories, generated according to different Indexes of Performance and different problem parameters, are analysed and compared in order to get feasible movements for the set.