非整数階微分を用いた振動制御

（第6報：非整数階PD制御器の設計法）

抄録

This study aims at developing a design method of a fractional-order PD controller and clarifying merits of the fractional-order PD controller. A fractional-order PD controller contains the non-integer differential order as a design parameter in addition to the proportional gain and the derivative gain. Therefore, the fractional-order PD controller can satisfy one more design specification than a normal integer-order PD controller can. In this report, besides the requirements on the gain crossover frequency and the phase margin, the condition on robustness is added. Based on those relationships, the proportional gain, the derivative gain and the non-integer differential order of the fractional-order PD controller are obtained with a graph-aided design method. Finally, the proposed design procedure of the fractional-order PD controller is applied to a vibration suppression problem of a flexible cantilever beam. Comparing with a usual PD controller, some control effects of the fractional-order PD controller are investigated by numerical simulation. Especially, the characteristics of the proportional gain, the derivative gain and the non-integer differential order of the fractionalorder PD controller are obtained as the gain crossover frequency is varied. It is confirmed that the fractional-order PD controller can be designed in the gain crossover frequency range where the normal PD controller can not satisfy the design specifications.