Fractional derivative system has gained its popularity in modeling and control because of its long memory property. Only recently, residual vibration suppression for the fractional derivative oscillatory system using input shaping has been studied. Input shaping suppresses residual vibration by using destructive interference of impulse responses. So far, only a few types of input shapers have been proposed for the fractional derivative oscillatory system, using only analytical, closed-form solutions. In this paper, input shaper syntheses for explicit fractional derivative systems using nonlinear optimization have been proposed. This work designs input shapers that have never been used with the fractional derivative system before, which include fixed-interval input shaper and specified-insensitivity input shaper, and extends the type that has already been used to a more general, improved input shaper.

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