Input shaping is a simple and effective method for reducing the residual vibration when positioning lightly damped systems, and it remains an active research area. In this paper, a continuous and differentiable function is introduced to define the desired motion, and then the input is shaped by inverse dynamic analysis. In the proposed method the only parameter that needs to be defined is the output speed, which is limited only by the physical constraints of the drive system. The calculation of an optimum speed is demonstrated by simulation examples. It is also shown that, under certain circumstances, the process can be further simplified and the need for inverse dynamics is eliminated.
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