This paper presents a novel Modified Rayleigh model for compensating hysteresis problem of an XY scanner actuated by 4 piezoelectric stack actuators for a high speed Atomic Force Microscope (AFM). At high driving fields, because most piezoelectric actuators have both ferroelectric and ceramic properties, they have severe hysteresis and intricate nonlinear characteristics such as creep, fatigue, and thermal drift, which often have common microscopic origin [1]. Hysteresis can cause serious displacement errors (ca. 15%), which disallow precise position control.
The classical Rayleigh model is the most typical phenomenological approach for hysteresis under sub-coercive fields. The classical Rayleigh model is expressed with the quadratic equation composed of a Rayleigh coefficient and material coefficients. While it can predict the hysteresis curve of the whole field by using one equation, the shape of the modeled curve is symmetric. The polarization and displacement curves measured in piezoelectric stack ceramics under subswitching field intensities are not always symmetrical, in contrast to the predictions of the Rayleigh model. Therefore, a modified Rayleigh model is proposed. In the model, each coefficient should be defined differently according to field direction (i.e., increasing or decreasing) in order to predict the hysteresis curve more accurately, due to the increase of the asymmetry at the high fields. In addition, according to the various electromechanical experiments by our experimental setup, increasing and decreasing rate is the same regardless of the magnitude of the electrical fields. By this idea, we derived a Modified Rayleigh model. By using an inverse form of this Modified Rayleigh model, we show that hysteresis can be compensated to yield a position error <5% This model has the merits of reducing complicated fitting procedures, and of saving computation time compared to the Preisach model.
1. Damjanovic, D. and M. Demartin, The Rayleigh law in piezoelectric ceramics. Journal of Physics D-Applied Physics, 1996. 29(7): p. 2057-2060.
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