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.
Highlights
Piezoelectric actuators (PEA), which possess superior advantages of high frequency response, nanometer displacement resolution, high stiffness and miniature size, have been extensively employed in micro/nano electromechanical systems, especially in fast tool servo (FTS) systems for micro/nano fabrications of freeform surfaces and functional structured surfaces [1,2,3,4]
It consists of four main parts, namely: the base, the PEA, the tool holder and the flexure hinges
The tool holder is actuated by the PEA and guided by a group of parallel and symmetric flexure hinges, which are designed as circular notch-type hinges
Summary
Piezoelectric actuators (PEA), which possess superior advantages of high frequency response, nanometer displacement resolution, high stiffness and miniature size, have been extensively employed in micro/nano electromechanical systems, especially in fast tool servo (FTS) systems for micro/nano fabrications of freeform surfaces and functional structured surfaces [1,2,3,4]. To enhance positioning accuracy and compensate hysteresis nonlinearities of this sort of FTS, closed-loop control approaches with various control strategies have been extensively proposed [2,4,7,8]. In these controller design procedures, the behaviors of FTS were described by simplified linear second order dynamics models, ignoring hysteresis nonlinearities. These control strategies should not achieve excellent positioning performances attributing to unmodeled nonlinearities. As for the hysteresis effects of piezoelectrically actuated FTS, for sake of completeness, Wang et al (2008) applied the Preisach model to FTS [11]; Ting et al (2011)
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