Input shaper is a pre-filter, designed to suppress residual vibration of flexible systems. The input shaper can be placed inside the feedback loop, in front of the flexible plant, to avoid exciting the plant vibratory modes. The performance of this so-called closed-loop signal shaping is limited due to the time delay brought about by the input shaper. The input shaper has more time delay when the plant mode parameters are uncertain. In this paper, an inner-loop controller based on the quantitative feedback theory is designed to match the uncertain flexible plant to a reference model. As a result, the input shaper needs not be robust, and the time delay is reduced. Other benefits include shorter input shaper length, increasing controller bandwidth, applicable to time-varying plant, and reducing cost of feedback. Simulation and experiment have confirmed the effectiveness of the newly proposed technique.

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