ポリダイン曲線の再定義と再評価

抄録

The polydyne cam profile provides ‘perfect tracking’ with no transient vibrations and has been used in important mechanical applications like automotive valve cams. In this paper, the polydyne curve was redefined and re-evaluated as the feedforward control input. Firstly, the polydyne curve was redefined as an acceleration trajectory and it was shown that the feedforward control with polydyne input is equivalent to the vibration suppression perfect tracking controller (PTC) in terms of the nominal output (position of the control object). It was also clarified that the conditions of polydyne mean the pole-zero cancelation and continuity at the beginning and end of the input, and that the principle to suppress vibrations is different from the dead-beat control such as the input shaping. Secondly, the enhancements of polydyne were introduced. The sampled-data polydyne is the formulation in discrete-time domain. The condition of continuity in discrete-time domain can show the order of smoothness of sampled data. And it is available for generating low-vibration bang-bang trajectory, in which the acceleration is smoothly ramped between the acceleration and deceleration sections. Thirdly, the concept of polydyne was adapted to general functions like trigonometric functions. For example, the vibration manipulation function (VMF) satisfies the conditions of polydyne for the undamped system. In conclusions, feedforward control using the polydyne curve is a unique method to suppress the transient vibration completely and effective in high-speed and high-precision digital control like servo control in a hard drive.