Modeling and Identification of Hysteresis in Piezoelectric Actuators

[+] Author and Article Information
T.-J. Yeh

Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu, Taiwan 30043, R. O. C.tyeh@pme.nthu.edu.tw

Shin-Wen Lu, Ting-Ying Wu

Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu, Taiwan 30043, R. O. C.

The model presented in Ref. 4 can also be represented by a block diagram similar to Fig. 2.

Therefore, in the procedure , the total number of break points, is assumed to be N.

For example if ki<0, the associated deformation xi will go unbounded during model simulation.

While the mechanical stiffness km can be directly found in the technical data, T and ke can be computed from the nominal voltage-displacement ratio (=Tkm) and the electrical capacitance (=T2ke) provided by the manufacturer.

In Table 1, k10 is much larger than the other spring constants. During the course of input excitation, the tenth massless cart stays motionless except that it is about to slide at the extremes of input, so it can be considered as a fixed spring. The linear programming automatically generates this large spring constant to compensate for the error in estimating km and ke.

J. Dyn. Sys., Meas., Control 128(2), 189-196 (May 02, 2005) (8 pages) doi:10.1115/1.2192819 History: Received June 18, 2004; Revised May 02, 2005

In this paper, a model and the associated identification procedure are proposed to precisely portray the hysteresis behavior in piezoelectric actuators. The model consists of basic physical elements and utilizes a Maxwell-slip structure to describe hysteresis. By analyzing the model, the influence of initial strain/charges on the hysteresis behavior is revealed. It is also found that if all the spring elements in the model are linear, the resultant hysteresis loop is anti-symmetric and does not match the experimental behavior. To account for this mismatch, a nonlinear spring element is included into the model. The constitutive relation of the nonlinear spring and the parameters of the basic elements in the model are identified from experimental data by linear programming. Simulations of the identified model indicate that the model can reproduce the major as well as the minor hysteresis loops. An inverse control is further implemented to validate the accuracy of the identified model. Experiments show that hysteresis is effectively canceled and accurate tracking of a reference trajectory is achieved.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

The mechanical schematic of the PEA model

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Figure 2

The block diagrams of the physical model and the Preisach model: (a) the physical model, (b) the Preisach model

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Figure 3

A typical hysteresis curve for a PEA

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Figure 4

Anti-symmetry in the hysteresis loop

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Figure 5

Definitions of variables used in the identification procedure

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Figure 6

Hysteresis curves corresponding to different initial states

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Figure 7

The hysteresis loops (v-y curves) from simulation and experiment

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Figure 8

The constitutive relation of the spring keqx+g(x)

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Figure 9

A magnification of the minor hsyteresis loop near the right extreme

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Figure 10

The control voltage responses

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Figure 11

The desired trajectory yd(t) and displacement responses y(t)

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Figure 12

The error responses




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