Materials 2012, 5(12), 2465-2485; doi:10.3390/ma5122465
Article

A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo

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Received: 22 August 2012; in revised form: 5 November 2012 / Accepted: 14 November 2012 / Published: 23 November 2012
(This article belongs to the Special Issue Advances in Microelectromechanical Systems (MEMS) Materials)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: The main contribution of this paper is the development of a linearized model for describing the dynamic hysteresis behaviors of piezoelectrically actuated fast tool servo (FTS). A linearized hysteresis force model is proposed and mathematically described by a fractional order differential equation. Combining the dynamic modeling of the FTS mechanism, a linearized fractional order dynamic hysteresis (LFDH) model for the piezoelectrically actuated FTS is established. The unique features of the LFDH model could be summarized as follows: (a) It could well describe the rate-dependent hysteresis due to its intrinsic characteristics of frequency-dependent nonlinear phase shifts and amplitude modulations; (b) The linearization scheme of the LFDH model would make it easier to implement the inverse dynamic control on piezoelectrically actuated micro-systems. To verify the effectiveness of the proposed model, a series of experiments are conducted. The toolpaths of the FTS for creating two typical micro-functional surfaces involving various harmonic components with different frequencies and amplitudes are scaled and employed as command signals for the piezoelectric actuator. The modeling errors in the steady state are less than ±2.5% within the full span range which is much smaller than certain state-of-the-art modeling methods, demonstrating the efficiency and superiority of the proposed model for modeling dynamic hysteresis effects. Moreover, it indicates that the piezoelectrically actuated micro systems would be more suitably described as a fractional order dynamic system.
Keywords: fast tool servo; piezoelectric actuation; dynamic hysteresis nonlinearity; fractional order calculus; linearized hysteresis model
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MDPI and ACS Style

Zhu, Z.; Zhou, X. A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo. Materials 2012, 5, 2465-2485.

AMA Style

Zhu Z, Zhou X. A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo. Materials. 2012; 5(12):2465-2485.

Chicago/Turabian Style

Zhu, Zhiwei; Zhou, Xiaoqin. 2012. "A Novel Fractional Order Model for the Dynamic Hysteresis of Piezoelectrically Actuated Fast Tool Servo." Materials 5, no. 12: 2465-2485.

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