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Sensors and Actuators A 172 (2011) 245– 252

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

jo u rn al hom epage: www.elsev ier .com/ locate /sna

odeling and measurement of creep- and rate-dependent hysteresis inerroelectric actuators

elix Wolf ∗, Alexander Sutor, Stefan J. Rupitsch, Reinhard Lerchhair of Sensor Technology, University of Erlangen-Nuremberg, Paul-Gordan-Str. 3/5, 91052 Erlangen, Germany

r t i c l e i n f o

rticle history:vailable online 26 February 2011

eywords:reisach modelnalytic weight function

a b s t r a c t

We present a new model for the simulation of the hysteretic large-signal behavior in ferroelectric materi-als. The model is based on the Preisach operator and takes advantage of an analytic weight function for theunderlying fundamental switching operators. The five independent parameters describing this weightfunction have been determined for a discoidal piezoceramic actuator by adapting the model output tomeasurements of the polarization. Since the classical Preisach model is only valid for creep- and rate-

reepate-dependenceiezoceramic transducerolarization measurementiezoelectric hysteresiserroelectric large-signal behavior

independent hysteresis loops, it is inappropriate to describe the entire ferroelectric material behavior.Therefore, we extended our model by an additional drift operator to consider creep phenomena. Fur-thermore, the rate-dependence of the hysteresis loops is described by a frequency-dependent parameterof the analytic weight function. For the identification and verification of the model, measurements havebeen performed using two different measurement principles: A modified Sawyer–Tower circuit as wellas a method based on the integration of the electrical current. The agreement between measurements

ts the

and simulations highligh

. Introduction

Piezoelectric sensors and actuators have widely been used inesearch and industrial applications due to their ability to convertechanical into electrical energy and vice versa. In particular, the

eason for their popularity lies in their outstanding properties, suchs extremely large forces, high displacement accuracy and excellentesponse times. Current research topics include the generation ofltrasound [1,2], nano positioning and motion tasks [3–5], energyarvesting [6–8], as well as the integration of piezoelectric trans-ucers into smart structural elements [9,10] for tasks such as healthonitoring and vibration suppression.The functional parts of such applications are usually based on

iezoceramic materials like lead zirconate titanate (PZT). Theseiezoelectric materials consist of crystalline grains which are sub-ivided into domains, i.e. regions with the same electric dipolerientation of the underlying crystal unit cells. If an electrical fields applied to such a material, the dipoles attempt to orientate alonghe electric flux lines. For low excitation fields, this behavior is

eversible. It then can be described by linear constitutive equa-ions, leading to a set of ten independent material parameters forhe 6 mm crystal class. Since these parameters suffer from strongariations, techniques for parameter identification [11,12] are nec-

∗ Corresponding author. Tel.: +49 91318523148; fax: +49 91318523133.E-mail address: felix.wolf@lse.eei.uni-erlangen.de (F. Wolf).

924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2011.02.026

benefits of the enhanced hysteresis model.© 2011 Elsevier B.V. All rights reserved.

essary, for example to perform a precise finite element analysis[13,14].

However, at sufficiently large electrical fields, the elementarydipoles do not only orientate along the electric flux lines. Theyalso switch by 90◦, as well as 180◦ onto the crystallographic axis,aligned closest to the direction of the applied electrical field. Theresulting irreversible hysteretic large-signal behavior prevents theactuators from providing an easily predictable displacement. Inaddition, it also leads to a lower piezoelectric coupling coefficienton a small signal view. The ferroelectric hysteresis is furthermoreinfluenced by environmental conditions such as temperature [15]and mechanical pre-stress. Here, we focus on the investigation ofthe dynamic behavior, in particular creep and rate-dependence ofthe ferroelectric polarization hysteresis. These effects are typical forcommon piezoceramic materials and modify the hysteresis curvesalready at very low frequencies. To be able to understand and pre-dict this sophisticated nonlinear large-signal behavior, there is aneed for precise measurements as well as efficient hysteresis mod-eling. In this paper, we present a Preisach-based hysteresis modelwith an analytic weight function for the fundamental switchingoperators and validate it by measurements on piezoceramic trans-ducers. In order to describe the dynamic behavior, we proceed in

two distinct steps. First, we extend our model by an additionaldrift operator to consider creep phenomena. In a second step,the rate-dependence of the hysteresis loops is taken into accountby introducing a frequency-dependent parameter of the analyticweight function. The comparison of measurements and simula-

246 F. Wolf et al. / Sensors and Actuat

Table 1Typical material properties as well as selected small signal parameters of Pz27. Fur-ther material properties can be found in the material datasheet, available on themanufacturer website [16].

Density � 7.70 · 103 kg/m3

Curie temperature TC 350 ◦CPiezoelectric chargecoefficient

d33 4.25 · 10−10 C/N

Elasticity modulus (const.electrical field)

sE33 2.32 · 10−11 m2/N

Relative permittivity(const. mechanical stress)

εT33 1.80 · 103

Coupling coefficient k33 0.70

tt

smaemt

2

tsesohc

sibo

pch

pfi

Dielectric dissipation factorat 1 kHz

tan ı 17 · 10−3

ions highlights the benefits of these enhancements with respecto dynamic hysteresis modeling.

The paper is organized as follows: Section 2 illustrates the mea-urement principles we utilize. A brief overview about hysteresisodeling in general is given in Section 3, as well as some details

bout our Preisach-based hysteresis model. Section 4 explains thextension of this Preisach model regarding dynamic hysteresisodeling and provides measurement and simulation results. Sec-

ion 5 gives conclusions.

. Measurement

For the identification of the model parameters and the verifica-ion of our model, measurements have been performed on a Pz27ample, a soft piezoceramic PZT material, manufactured by Ferrop-rm Piezoceramics A/S. Some typical material properties as well aselected small signal parameters of the initial, fully polarized statef the actuator are provided in Table 1. The discoidal transduceras a diameter of 25 mm and a thickness of 2 mm. Silver electrodesover its plane-parallel front faces.

Since clamping of the actuator strongly influences the hystere-is curve, the sample was fixed between two tips, one of whichs a spring tip to allow free oscillation (Fig. 1). To avoid dielectricreakdown, the aluminum test fixture is filled with an insulatingil bath.

The measurement setup is automated by means of a LabVIEWrogram. After numerically generating the excitation signal, it isonverted to an analog signal and amplified using a Trek 10/10B

igh-voltage amplifier.

We consider two different methods for measuring the electricalolarization: For the first method, the lower electrode of the testxture is directly connected to ground (Fig. 1). The time-dependent

Fig. 1. Schematic view of the high-voltage test fixture.

ors A 172 (2011) 245– 252

polarization can then be written as

Pmeas(t) = Dmeas(t) − ε0 · Emeas(t). (1)

Here, ε0 denotes the vacuum permittivity. The electrical fieldstrength

Emeas(t) = Umeas(t)h

(2)

is given by the applied voltage Umeas(t) divided by the thicknessh of the transducer. Due to the reorientation of the ferroelec-tric domains, electrostatic charges are induced on the electrodes,leading to a measurable electrical current Imeas(t). The dielectricdisplacement Dmeas(t) results from integrating this current withrespect to time and dividing it by the electrode surface A

Dmeas(t) =∫ t

0Imeas(�) d�

A. (3)

The quantities to be measured are thus the excitation voltage, theinduced current and the geometrical dimensions of the sample.Because of the capacitive behavior of the piezoceramic transducers,the measured current for a sinusoidal excitation is given as

Imeas(t) = Cpiezo(t) · Umeas 2�f cos(2�ft). (4)

The so-called integration method, as described above, works verywell if the product of the applied maximum excitation voltage Ûmeas

and the frequency f is high enough. Otherwise, the noise of the mea-sured current leads to significant errors in the polarization signal.

For low frequencies, we therefore use a modified Sawyer–Towercircuit [17]. For this measurement setup, a precision capacitor isconnected in series between the lower electrode of the test fix-ture (Fig. 1) and ground. This measuring capacitance Ccap is chosenmuch higher than the capacitance of the sample, i.e. Ccap � Cpiezo(t).Therefore, the electrical field strength can be approximated to

Emeas(t) = Upiezo(t)h

≈ Upiezo(t) + Ucap(t)h

= Umeas(t)h

, (5)

with Umeas(t) representing the excitation voltage to be measured.The voltage across the measuring capacitance Ucap(t) is acquiredusing a Keithley 2700 multimeter, offering a very high input resis-tance of 10 G�. The charge Qcap(t) on the precision capacitor cantherefore be considered as equal to the charge on the electrodes ofthe sample. Thus, the polarization is calculated as

Pmeas(t) = Qpiezo(t)A

− ε0 · Emeas(t) ≈ Ucap(t) · Ccap

A− ε0 · Emeas(t).(6)

The measurements in Sections 3.1 and 4.1 have been performedwith the integration method, whereas the measurements in Section4.2 were conducted using the modified Sawyer–Tower circuit.

3. Hysteresis modeling

Modeling of the piezoelectric large-signal behavior has been achallenge for many researchers for quite a long time. The resultingapproaches can be divided into the following three categories:

(i) Thermodynamically consistent models aim to describe themicroscopical behavior in a macroscopic view, satisfying thesecond law of thermodynamics [18].

(ii) Micromechanical models are sometimes also based on ther-

modynamic considerations, but discretize the material ontothe level of single grains or domains [19].

(iii) Phenomenological models establish the third category. Theydescribe, generalize and predict experimental results on amacroscopic scale [20].

F. Wolf et al. / Sensors and Actuators A 172 (2011) 245– 252 247

Ft

btuntsh

3

mclahotltma

pfmw(

P

TaF

fsBo

tbatwFPwmonif

Table 2Parameters of the weight function �DAT(˛, ˇ) obtained for the transducer under test.

1 1.18 · 102

2.13 · 101

4. Modeling of dynamic behavior

The classical Preisach model only covers the static hysteresisbehavior. The model output is just depending on past input extremabut not on the time-dependence of these values. This type of hys-

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Pol

ariz

atio

n in

C/m

2

Measurement

Model

ig. 2. Fundamental switching operator �˛ˇ and Preisach plane, graphically illus-rating the weighting �(˛, ˇ).

Hysteresis models of the first two categories reflect the physicalehavior very well but are usually accompanied by a high computa-ional effort. That is why these models are mainly useful for a deepernderstanding of the investigated materials. Contrary to that, phe-omenological models are more suitable for device design, wherehe emphasis is usually not on displaying the accurate microscopictructure but on efficient modeling. A more detailed discussion ofysteresis models can be found in [21].

.1. Preisach hysteresis model

A frequently used approach to phenomenological hysteresisodeling is the Preisach-type models, which are based on the so-

alled Preisach hysteresis operator [20]. Several enhancements,ike generalized Preisach models or vector Preisach models [22],s well as the integration into a finite element formulation [23]ave been developed. A challenging task is also to find an inversef the Preisach model in order to compensate the influence of theransducer’s hysteresis. This is related to many open- and closed-oop control applications, such as vibration suppression, wherehe actuator’s hysteresis strongly influences the controller perfor-

ance [24]. A method for the determination of such an inverse of Preisach model is illustrated in [25].

In our previous work, we proposed a new Preisach-basedhenomenological model [26]. This model was first applied toerromagnetic hysteresis. Now we also investigate ferroelectric

aterials [27]. The Preisach hysteresis operator H is based on theeighted superposition of fundamental switching operators �˛ˇ

see Fig. 2)

model,n(t) = H[En] (t) =∫ ∫

˛≥ˇ

�(˛, ˇ)�˛ˇ[En] (t) d dˇ. (7)

hese switching operators can only feature two distinct values (−1nd 1) and the corresponding thresholds are restricted to ≥ (seeig. 2).

The input and output of the Preisach operator are for theerroelectric case the normalized time-depending electrical fieldtrength En(t) and the normalized electrical polarization Pmodel,n(t).oth are orientated perpendicular to the plane-parallel electrodesf the sample.

A decisive point is to find an appropriate weighting �(˛, ˇ) ofhe fundamental switching operators, often also denoted as distri-ution function or Preisach function. Since the weighting mainlyffects the shape of the hysteresis loops, formulating such a func-ion is an issue which is related to quite a lot of publications. Theeighting can be displayed graphically on the Preisach plane (see

ig. 2). A common approach to the identification is to discretize thereisach plane into a multitude of elements and to determine theeight of every single element by adapting the model output to

easurements [21,23]. However, the accurate simulation results

ften achieved with such methods are accompanied by the highumber of coefficients which have to be determined. Thus, there

s a need for analytic functions, describing the weighting of theundamental switching operators. We use such an analytic weight

2

B 2.57 · 102

1.33h 5.77 · 10−1

function �DAT(˛, ˇ), motivated by the arcus-tangent-like shape ofthe outer hysteresis loops [26]

�DAT (˛, ˇ) = B

1 + {[( + ˇ)1]2 + [( − − h)2]2} . (8)

Since this function is based on only five independent parameters,the computing time is reduced by far. The parameters are deter-mined by means of an Inverse Method [11,28]. We use a standardNewton algorithm with the time-discrete objective function

1N

·N∑

k=1

(Pmeas,n[k] − Pmodel,n[k])2, (9)

where Pmeas,n denotes the normalized polarization measurementfor the same excitation as the normalized model output Pmodel,n.Both vectors have the length N. Further information on the param-eter identification process as well as a robustness validation andsome remarks on the choice of a reasonable set of initial values aregiven in our previous work [26].

The model parameters for the transducer under test (Section 2)were identified for a set of measured hysteresis loops (Table 2). Acomparison between measurement and simulation is displayed inFig. 3. The agreement for the outer hysteresis loops is satisfying.But there is a significant mismatch for minor loops with a maxi-mum field strength close to the coercive field strength. The smoothedges of the measured hysteresis in Fig. 3 indicate that the dynamicbehavior of the piezoceramic transducer cannot be neglected closeto field strengths with a high polarization gradient.

−2 −1 0 1 2−0.4

Electrical Field in kV/mm

Fig. 3. Hysteresis measurement compared to simulation with classical Preisachmodel.

248 F. Wolf et al. / Sensors and Actuators A 172 (2011) 245– 252

0 5 10 15 20−3

−2

−1

0

1

2

3

Ele

ctric

al F

ield

in k

V/m

m

tmdtdcttea

hrprf

iewfsn

tsir

4

tF

iriccg(

−3 −2 −1 0 1 2 3−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Pol

ariz

atio

n in

C/m

2

Measurement

Model

Model with drift

described in Section 3.1. In addition to the measured hysteresiscurve, Fig. 5 displays simulations with and without drift operatorfor the same excitation.

The simulation using the enhanced model follows the creep-induced steps of the measured hysteresis curve very well (Fig. 7).

0 1 2 3 4 5 6 7

−0.32

−0.3

Pm

eas

in C

/m2

Time t in sec

10 11 12 13 14 15 160.28

0.3

0.32

Pm

eas

in C

/m2

Time t in se c

Fig. 4. Excitation signal for the creep experiment.

eretic nonlinearities are known as rate-independent non-localemories [22]. For ferromagnetic materials this time-invariant

escription might be sufficient. But for ferroelectric materials,he dynamic properties cannot be neglected. The reason for theynamic effects is not exclusively due to the domain switching pro-esses, being rather instantaneous in nature. Instead, vacancies inhe crystal lattice of the doped PZT materials lead to dipoles andhus contribute to the polarization signal [29]. To change the ori-ntation of such dipoles, time-dependent ion diffusion processesre required, which lead to creep and rate-dependence.

Especially for open- and closed-loop applications, the dynamicysteresis behavior always presents a major challenge toesearchers. Creep induced deviations are reported, e.g. for nano-ositioning and manipulation tasks [30,31]. The effect of theate-dependence of the actuator’s hysteresis on the controller per-ormance of a vibration suppression task is investigated in [32].

A common approach to model the dynamic behavior is to super-mpose a set of fundamental creep operators with different creepigenvalues [33]. Other approaches take into account a Preisacheight function depending on the slope of the input. The weight

unction is identified, e.g. using neuronal networks [34]. Recently,ome other rate-dependent models based on training of a neuronaletwork have been published, e.g. [35].

To our opinion, the effects of creep and rate-dependence haveo be treated separately, since they affect the shape of the hystere-is loops in different ways. Therefore, we first consider creep byntroducing a drift operator into our model (Section 4.1) [27]. Theate-dependence is treated afterwards in Section 4.2.

.1. Modeling of creep

For the investigation of the ferroelectric creep behavior, theransducer was excited with an electrical field as displayed inig. 4.

The resulting polarization hysteresis measurement is displayedn Fig. 5. As the time signals of the polarization during holding timeeveal (Fig. 6), the creep phenomena lead to a change of the polar-zation amplitude, even if the applied electrical field remains at a

onstant level. The same effect gives rise to the smooth edges, whichan be observed in Fig. 3 for field strengths with a high polarizationradient. Motivated by the low-pass behavior of the step-responseFig. 6), our drift operator D is expressed as the solution of the

Electrical Field in kV/mm

Fig. 5. The resulting hysteresis curve for the excitation signal as displayed in Fig. 4.Measurement compared to simulations with and without drift operator.

first-order differential equation

ddt

Pdrift,n(t) − ˛D · (Pn(t) − Pdrift,n(t)) = 0. (10)

In mechanics, this behavior is described by the lumped-elementmodel of a spring and a damper in parallel.

Applied to the output of the Preisach model Pmodel,n, the polar-ization Pdrift,n is thus calculated as follows

Pdrift,n(t) = D[Pmodel,n](t) = D[H[En]](t) = P0 e−˛D(t−t0)

+t∫

t0

˛D e−˛D(t−�)Pmodel,n(�) d�, (11)

with the initial value P0 = D[Pmodel,n](t0). The additional driftparameter ˛D is determined within the identification process

Time t in sec

Fig. 6. Polarization signals during holding times, excited with signal as displayed inFig. 4.

F. Wolf et al. / Sensors and Actuators A 172 (2011) 245– 252 249

−1.5 −1 −0.5 00

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4P

olar

izat

ion

in C

/m2

Measurement

Model

Model with drift

FF

spud

4

npie

qsici

F

1 1.2 1.4 1.6 1.8 20

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Pol

ariz

atio

n in

C/m

2

0.01 Hz0.03 Hz0.05 Hz0.07 Hz0.1 Hz

Electrical Field in kV/mm

ig. 7. Detail of hysteresis curve (Fig. 5) resulting from excitation as displayed inig. 4. Measurement compared to simulations with and without drift operator.

Fig. 8 depicts a minor loop measurement, excited with a sinu-oidal signal of 1.5 Hz. It reveals, that the smooth edges for turningoints close to the coercive field strength can now also be sim-lated. Thus, the influence of creep on the hysteresis curve isescribed with only one additional parameter.

.2. Modeling of rate-dependence

The additional drift operator now allows for the simulation ofonlinear creep phenomena. But the rate-dependent behavior ofiezoceramic materials is still not covered by this enhancement. To

llustrate this, measurements have been performed for sinusoidalxcitation signals with different frequencies (Figs. 9 and 10).

For hysteresis loops excited up to saturation (Fig. 9), the fre-uency of the excitation signal mainly affects the coercive field

trength. Contrary to that, the amplitude of the polarization signals also changed significantly for minor loops at different frequen-ies, whereas the impact on the coercive field strength is smallern nature (Fig. 10). However, this behavior cannot be characterized

−1.5 −1 −0.5 0 0.5 1 1.5−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Electrical Field in kV/mm

Pol

ariz

atio

n in

C/m

2

MeasurementModelModel with drift

ig. 8. Measured minor loop compared to model with and without drift operator.

Electrical Field in kV/mm

Fig. 9. Detail of measured major loops for excitation with sinusoidal signals ofdifferent frequencies.

by a single drift operator as described in Section 4.1. Therefore, arate-dependent weight function seems to be reasonable.

A sensitivity analysis was performed for each single parameterof the weight function �DAT(˛, ˇ). The parameter h is especiallysuitable to cover the rate-dependent behavior, since it shows simi-lar properties in terms of maximum polarization Pmax and coercivefield strength Ec, if it is altered (Fig. 11): For major loops, a higherparameter h gives rise to a higher coercive field strength, but themaximum polarization is practically not affected. On the otherhand, the coercive field strength of a minor loop is only alteredmarginally, whereas the maximum polarization is decreasing forhigher frequencies.

Thus, the parameter h of our weight function �DAT(˛, ˇ) seemsto be the right choice to formulate a frequency-dependence.

The measured coercive field strength for major loops at different

frequencies (Fig. 12) can be approximated very well as

Ec(f )∼�1 − �2

f �3. (12)

0.2 0.3 0.4 0.5 0.6 0.7 0.80.015

0.02

0.025

0.03

Electrical Field in kV/mm

Pol

ariz

atio

n in

C/m

2

0.01 Hz

0.03 Hz

0.05 Hz0.07 Hz

0.1 Hz

Fig. 10. Detail of measured minor loops for excitation with sinusoidal signals ofdifferent frequencies.

250 F. Wolf et al. / Sensors and Actuators A 172 (2011) 245– 252

−10 −5 0 5 100.25

0.3

0.35

deviation of h in percent

Ec

Major loop

Minor loop

−10 −5 0 5 100

0.5

1

deviation of h in percent

Pm

ax

Major loop

Minor loop

Ff

0.02 0.04 0.06 0.08

1.16

1.18

1.2

1.22

1.24

1.26

1.28

Coe

rciti

ve F

ield

Str

engt

h in

kV

/mm

2 kV/mm

1.7 kV/mm

Approximation

ig. 11. Model output for coercive field strength Ec and maximum polarization Pmax

or variation of parameter h.

Frequency in Hz

Fig. 12. Measured coercive field strength for sinusoidal excitation with two differentamplitudes as well as approximation with analytic function Ec(f).

1 1.5 2−0.2

−0.1

0

0.1

0.2

0.3

0.4

Emeas

in kV/mm

Pm

eas

in C

/m2

Measurement

1 1.5 2−0.2

−0.1

0

0.1

0.2

0.3

0.4

Emeas

in kV/mm

Pm

odel

in C

/m2

Simulation

Fig. 13. Major loop – comparison of measurement and simulation using rate-dependent weight function �DAT(˛, ˇ, f).

0 0.2 0.4 0.6 0.80.01

0.015

0.02

0.025

0.03

Emeas

in kV/mm

Pm

eas

in C

/m2

Measurement

0 0.2 0.4 0.6 0.80.01

0.015

0.02

0.025

0.03

Emeas

in kV/mm

Pm

odel

in C

/m2

Simulation

Fig. 14. Minor loop – comparison of measurement and simulation using rate-dependent weight function �DAT(˛, ˇ, f).

Actuat

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5

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[

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[

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F. Wolf et al. / Sensors and

Due to the linear influence of the parameter h on the varia-ion of the coercive field strength (Fig. 11), its frequency-dependentormulation can also be expressed as

(f ) = �1 − �2

f �3, (13)

ith different parameters �i. For the identification of the frequency-ependent weight function �DAT(˛, ˇ, f), the same procedure asescribed in Section 3.1 is applied, except for using hysteresis

oops at four different frequencies instead of loops at one singlerequency.

Figs. 13 and 14 show the resulting simulations, performedith the enhanced, rate-dependent model in comparison to rate-ependent measurements. In principle, the same behavior can bebserved for both, measurements and simulations. As can be clearlyeen, the variation of the polarization amplitude of minor loops islso covered by using a frequency-dependent parameter h(f). How-ver, the smooth edges of the measurement cannot be simulatedy a rate-dependent weight function, which justifies the need ofhe additional drift operator.

. Conclusions

Our Preisach model takes advantage of an analytic weightunction for the fundamental switching operators. The dynamicehavior of the ferroelectric hysteresis is considered by two dis-inct methods. Creep-induced modifications of the hysteresis curvere covered by a drift operator, whereas the rate-dependent vari-tions are described by a frequency-dependent weight function.imulations performed with both procedures reflect the measuredehavior very well. Further research is concentrated on analyz-

ng a wider frequency range and including both methods into oneodel, describing the entire dynamic behavior. Moreover, we want

o investigate multi-frequent signals by considering the dominantrequencies for the rate-dependent formulation of our model.

cknowledgement

The underlying research is gratefully supported by the Germanesearch Foundation (DFG) as part of the special research fieldFB/TR39.

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Biographies

Felix Wolf was born in Geislingen an der Steige, Germany, in 1981. He receivedhis M.S. degree (Dipl.-Ing.) in electrical engineering from the Friedrich-Alexander-University of Erlangen-Nuremberg, Germany in 2007. Currently, he is a Ph.D.Student and assistant lecturer at the Chair of Sensor Technology of the Univer-sity of Erlangen-Nuremberg. His research is focussed on the characterization offerroelectric materials by means of simulation and measurements.

Alexander Sutor was born in 1970 in Aschaffenburg, Germany. He received his M.S.degree (Dipl.-Ing.) in electrical engineering in 1997 and his Ph.D. degree (Dr.-Ing.)in 2004 from the Friedrich-Alexander-University of Erlangen-Nuremberg. He has

been working as assistant lecturer at the Chair of Technical Electronics until 1999and now as a researcher and lecturer at the Chair of Sensor Technology, Universityof Erlangen-Nuremberg. His major research interests are in the fields of materialproperty determination of magnetic, magnetostrictive and piezoelectric materialsfor sensor and actuator applications. He deals with measurement setups for bulk andthin film materials, as well as model and simulation based measurement methods.

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52 F. Wolf et al. / Sensors and

tefan Rupitsch was born in Kitzbuehel, Austria, in 1978. He received his Diplomand Ph.D. degrees in mechatronics from the Johannes Kepler University, Linz,ustria, in 2004 and 2008, respectively. In 2004, Dr. Rupitsch was a Junior Researchert the Linz Center of Mechatronics. From 2005 to 2008, he was with the Institute foreasurement Technology, Johannes Kepler University, Linz. In 2009, he received

he Award of the Austrian Society of Measurement and Automation Technologyor his Ph.D. thesis. Currently, he is a Postdoctoral Researcher at the Friedrich-lexander-University Erlangen-Nuremberg (Chair of Sensor Technology), Germany.is research interests include electromechanical transducers, simulation-basedaterial characterization, digital signal and image processing as well as noncon-

acting measurements.

einhard Lerch was born in Lauterbach, Germany in 1953. He received theaster’s degree in 1977 and the Ph.D. degree in 1980 in electrical engineering

rom the Technical University of Darmstadt, Germany. From 1977 to 1981, heas engaged in the development of a new type of audio transducer based oniezoelectric polymer foils at the Institute of Electroacoustics at the University

ors A 172 (2011) 245– 252

of Darmstadt. From 1981 to 1991, he was employed at the Research Center ofSiemens AG in Erlangen, Germany, where he was responsible for the implementa-tion of new computer tools supporting the design and development of piezoelectrictransducers. Dr. Lerch is author of more than 100 papers in the field of electrome-chanical sensors and actuators, transducers, acoustics, and signal processing. In1982, he received the Award of the German Nachrichtentechnische Gesellschaftfor his work on piezopolymer microphones. In 1990, he was honored with theOutstanding Paper Award of the IEEE-UFFC Society and in 1991, he was therecipient of the German Philipp-Reis-Award. From 1991 to 1999, he had a fullprofessorship for mechatronics at the University of Linz, Austria. Since 1999 heis head of the Chair of Sensor Technology at the Friedrich-Alexander-University of

Erlangen-Nuremberg, Germany. His current research is directed toward establishinga computer-aided design environment for electromechanical sensors and actuators,especially piezoelectric ultrasound transducers and microacoustic components.Future areas of research are piezoelectric and magnetic sensors in thin film technol-ogy. In 2009, he was honored with the Distinguished Service Award of the IEEE-UFFCSociety.