Abstract

Vertically rotating flexible beam under the effect of gravity adds some challenges to the existing input- and command shaping techniques. Classical shapers usually have zero initial conditions while vertically rotating beam may have initial or final deflections. These conditions may introduce large residual vibrations at the end of rest-to-rest maneuvers. Furthermore, the system contains some nonlinearities that may reduce the effectiveness of classical input- and command-shapers. In this work, a waveform command shaping profile is used initially and then optimized to reduce rest-to-rest residual vibrations of a vertically rotating flexible beam. The system equation of motion is determined, discretized, and then linearized to find an initial command shaper. The parameters of the proposed command shaper is then optimized to find a better performance. Only the first mode is considered in this work since higher modes usually have negligible amplitudes. To show the importance of the proposed work, comparisons between the uncontrolled shaper, double step shaper, smooth wave form command shaping, and the optimized command shaping are performed. The proposed technique is tested numerically using two cases, with different maximum velocities, flexible beam length, and acceleration times. Results show that the effectiveness of the proposed technique in reducing residual vibrations in rest-to-rest maneuvers.

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