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This paper presents an approach to design optimal vibration reduction input shapers for systems with non-zero initial conditions. The problem is first formulated as an optimal control problem and the optimal solution is shown to be bang-bang. Once the structure of the optimal shaper is known, a parametric problem formulation is presented for the computation of the switching times. For digital implementation,...
The rapid movement of machines is a challenging control problem because it often results in high levels of vibration. As a result, flexible machines are typically moved relatively slowly to avoid such vibration. Input shaping is a control method that allows much higher speeds of motion by limiting unwanted vibration. To design an input-shaping controller, estimates of the system natural frequency...
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