Engineering Application of Fractional Calculus

2014 Fiscal Year Final Research Report

• Project/Area Number: 23560076
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Engineering fundamentals
• Research Institution: University of Hyogo (2013-2014); National Institute of Advanced Industrial Science and Technology (2011-2012)
• Principal Investigator: KURODA Masaharu 兵庫県立大学, 大学院工学研究科, 教授 (60344222)
• Research Collaborator: ARAKI Nozomu ; MATSUBUCHI Hiroki ; YOSHITANI Naoki
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 微積分 / 振動 / 制御 / PID制御 / 柔軟構造物 / ロバスト性

Outline of Final Research Achievements

Fractional calculus in which the order of the differentiation/integration is expanded to a non-integer value is applied to vibration control engineering. First, the definition of the fractional differentiation/integration is discretized. Then its algorithm is downloaded to a digital signal processor (DSP). The output signal from one sensor can be differentiated/integrated to a fractional order with the DSP. Furthermore, a technique is developed by which a linear combination of the output signals from multiple displacement and velocity sensors is converted into a fractional differentiation/integration response. Finally, vibration control experiments of a flexible cantilevered beam are conducted using fractional PID feedback control. In contrast to conventional PID feedback control, the fractional PID feedback control can achieve not only the equivalent vibration-suppression effect, but also better robust stability against parameter variation.

Free Research Field

機械力学・計測制御