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TECHNICAL PAPERS

# 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 $ℓ$, 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 $(=T∕km)$ and the electrical capacitance $(=T2∕ke)$ 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

## Abstract

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.

###### FIGURES IN THIS ARTICLE
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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

The mechanical schematic of the PEA model

Figure 2

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

Figure 3

A typical hysteresis curve for a PEA

Figure 4

Anti-symmetry in the hysteresis loop

Figure 5

Definitions of variables used in the identification procedure

Figure 6

Hysteresis curves corresponding to different initial states

Figure 7

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

Figure 8

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

Figure 9

A magnification of the minor hsyteresis loop near the right extreme

Figure 10

The control voltage responses

Figure 11

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

Figure 12

The error responses

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