The application of an input precompensation scheme for vibration suppression in slewing flexible structures, with particular application to flexible-link robotic manipulator systems, is considered. The control from such input shaping schemes corresponds to a feedforward term that convolves in real time the desired reference input with a sequence of impulses and produces a vibration-free output. The robustness of such an algorithm with respect to modal frequency variations is not satisfactory but can be improved by convolving the input with a longer sequence of impulses, the tradeoff being a decrease in the transient response speed. An adaptive precompensation scheme that can be implemented by combining a frequency domain identification scheme, used to estimate the modal frequencies online, with a subsequent scheme for adjusting the spacing between the impulses is proposed. The combined adaptive input shaping scheme provides the most rapid slew that results in a vibration-free output. Experimental results for a single flexible link are presented to verify the technique.
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