松淵 博基, 吉谷 尚樹, 黒田 雅治
機械力学・計測制御講演論文集 2015年8月25日
The history of fractional calculus, in which the order of differentiation and integration are expanded to non-integer values, is actually almost as long as that of classical integer-order calculus. In describing an equation of motion, fractional calculus can express larger region of dynamics than integer-order calculus. For this reason, fractional calculus has been applied in various scientific and engineering fields, for example, rheology, electrochemistry, and general transport problems. However, fractional calculus has been used only in a theory, it has been rarely applied to a real engineering target. In this study, as an application of fractional calculus in the control engineering field, a vibration suppression problem is considered based on feedback control using the fractional derivative response of the mechanical structure. Specifically, a vibration control problem of a thin-cantilevered beam is examined to explain the method of constructing a control system. Compared with conventional PD feedback control, which is widely used in industry, fractional PD feedback control is investigated experimentally. A vibration control problem of a flexible cantilevered beam using the fractional PD (Pf-D) feedback is presented as an example.