piezoelectric bimorph actuator with integrated strain sensing … · 2018-06-07 · gauges can be...

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JSEN.2018.2842138, IEEE SensorsJournal

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Piezoelectric Bimorph Actuator withIntegrated Strain Sensing ElectrodesSepehr Zarif Mansour, Rudolf J. Seethaler The University of British Columbia

Kelowna, [email protected]

Yik R. Teo, Yuen K. Yong, Andrew J. Fleming Precision Mechatronics LabThe University of Newcastle

Callaghan, Australia

Abstract—This article describes a new method for estimatingthe tip displacement of piezoelectric benders. Two resistive straingauges are fabricated within the top and bottom electrodes usingan acid etching process. These strain gauges are employed in ahalf bridge electrical configuration to measure the surface resis-tance change, and estimate the tip displacement. Experimentalvalidation shows a 1.1 % maximum difference between the strainsensor and a laser triangulation sensor. Using the presentedmethod, a damping-integral control structure is designed tocontrol the tip displacement of the integrated bender.

I. INTRODUCTION

Piezoelectric actuators are used in a wide range of posi-tioning applications such as micro-manipulating [1], vibrationcontrol [2], and Atomic Force Microscopy [3]. Piezoelectricbenders are a sub-type that are widely used in industrial andcommercial applications. [4]. Bender actuators can primarilybe classified as either pinned benders or bonded benders. Diskbenders are an example of a pinned type bender [5], [6]. Theyconsist of one or two circular piezoelectric elements glued toa non-piezoelectric layer. The outer edge of the disk is pinnedto a stationary base while an electric field is applied to thebender developing a net displacement and force at the centerof the disk.

Unimorph and bimoph benders are examples of bonded typebenders [4], [7]. Unimorph benders have one piezoelectricplate bonded to a non-piezoelectric layer. Bimorph benders,which are employed in this study, consist of two piezoelectricplates that are bonded together. In order to provide rein-forcement, a third elastic plate is sandwiched between thepiezoelectric plates. In the cantilever configuration, an electricfield is applied so that one plate expands while the other onecontracts, which develops a net force and displacement at thetip.

Control of the tip displacement is a challenging task dueto the lightly damped resonance and hysteresis [7], [8].Feedback control techniques such as, positive position feed-back [9], damping-integral control [10], and integral resonantcontrol [11], measure the tip displacement using an externaldisplacement sensor. The displacement can also be estimatedby bonding a strain gauge to the actuator surface, which isattractive due to the small form factor and low cost. Straingauges can be used as displacement sensors for controllingpiezoelectric stack actuators [12].

This article1 describes a new method for measuring thetip displacement of piezoelectric benders by integrating strainsensors into the top and bottom electrodes. The surface strainis shown to be directly proportional to the tip displacement.The strain gauges are configured in a half bridge circuitwhich requires a bipolar excitation and avoids the need for aninstrumentation amplifier. The performance of the proposedmethod is validated by employing the integrated bender in adamping-integral tracking control structure.

In the remainder of the article, the experimental setupis described in Section II, an electromechanical model isderived in Section III, open-loop performance is demonstratedin Section IV, the controller is designed in Section V, andconclusions are provided in Section VI.

II. EXPERIMENTAL SETUP

The piezoelectric bimorph actuator is a Y-poled T220-A4-503Y from Piezo Systems [13]. The dimensions are63.5 × 31.8 × 0.51 mm. It has a free displacement of ±1 mmand a blocked force of ±0.35 N. The internal constructionis illustrated in Fig. 1. The layers include a 0.1 mm thickbrass reinforcement layer shown in orange, two 0.2 mm thickpiezoelectric plates shown in yellow, and two 5 µm thickNickel electrodes shown in blue. Fig. 1(a) illustrates theprocess used to create the integrated strain gauges. First, a0.1 mm thick resin mask is printed on the electrode using aForm 2 Desktop 3D printer with 5 µm resolution. Then 30%nitric acid is applied to etch the electrode area not coveredby the mask. After removing the resin mask, the desired U-shaped feature, with an effective length of 40 mm and a widthof 1 mm, is isolated from the rest of the electrode. This processis carried out on both the top and bottom electrodes. The U-shaped Nickel features are then employed as resistive metalfoil strain gauges, while the rest of the electrode is used todrive the bender.

Fig. 1(b) describes the experimental setup. The bender iscantilevered with a free length of 57 mm. It is driven in aparallel electrical configuration where the middle brass layeris grounded and a ±90 V signal Vu is applied to the external

1An earlier version of this paper was presented at the 2017 IEEE Sen-sors Conference and was published in its Proceedings. DOI: 10.1109/IC-SENS.2017.8233951



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Resin MaskHNO3 (30%)

1

(a) Construction of strain gauges (b) Experimentation procedure

BottomElectrode

TopElectrode

BrassLayer

PiezoPlate

PiezoPlate

Laser Sensor

Linear Amplifier

Matlab/Simulink

Fig. 1: Experimental setup.

electrodes using a PiezoDrive PD200 amplifier. It is notedthat the strain gauges are isolated from Vu. An alternativeconfiguration is to ground the external electrodes and drivethe middle brass layer. However, as described in Appendix A,this approach creates direct feed-through between the drivingvoltage and strain measurement, which is undesirable.

The strain gauges are excited in a half bridge configurationby applying a DC voltage to the top and bottom strain gauge Vtand Vb respectively. By tuning either Vt or Vb, the voltageat the center of the half bridge Vc can be set to zero. Vc isthen amplified by a gain K, which provides a voltage Vg thatis proportional to the tip displacement. The sensitivity Ks isfound experimentally using the reference sensor. The estimatedtip displacement is y in Fig. 1(b).

A block diagram of the setup is depicted in Fig. 2 where, Wrepresents the linear amplifier dynamics, P represents thebender dynamics, Hl represents the laser dynamics, and Hsgrepresents the strain gauge dynamics. Therefore, the open-looptransfer function of the integrated bender is

G(s) =y

u= W (s)P (s)Hsg(s)Ks. (1)

III. ELECTROMECHANICAL MODEL OF THEPIEZOELECTRIC BENDER

The proposed method uses the same principle as a resistivemetal foil strain gauge. That is, the electrical resistance change

Fig. 2: Block diagram of the piezoelectric bender system withintegrated strain sensors. The tip displacement of the benderis also measured using the laser (ylaser) for sensor calibrationand comparison purposes.

is proportional to the surface strain. In benders, surface strainis also related to the tip displacement. Hence, the tip displace-ment of a bender can be estimated by measuring its surfaceresistance change. Subsection III-A derives a proportionalitybetween surface strain and tip displacement. Subsection III-Brelates the resistance change to tip displacement.

A. Tip Displacement and Surface Strain Relationship in Ben-ders

In this study, Euler-Bernoulli beam theory is used. Tipdisplacement is considered to be relatively small, no externalforces are exerted on the bender, and the driving voltage Vuis assumed to be effective across the thickness h of eachpiezoelectric plate. In Fig. 3, ls is the nominal length of thestrain gauges and t is a 0.5 mm gap which provides isolationfrom the high-voltage electrode. Using the constitutive equa-tion for the inverse piezoelectric effect [14], the stress σ ineach piezoelectric plate is,

σ = d31EVuh

+ Eε(x), (2)

where, d31 is the piezoelectric constant, E is the Young'smodulus, and ε(x) is the strain along the neutral axis. Forrelatively small tip displacements, ε(x) in (2) is replaced withε(x) = −y d2y

dx2 , where y is the vertical distance from theneutral axis. The moment due to the external forces M(x)can then be calculated by taking the integral of σy, over thecross-sectional area of the bender [4], that is

M(x) = d31EVuwh

2− EI d

2y

dx2. (3)

In (3), I is the moment of inertia and w is the width of thebender. Given that external forces are assumed to be absent,M(x) = 0, which simplifies (3) to,

d2y

dx2= d31Vuw

h

2I, (4)

which indicates that the bender is experiencing a pure bendingdue to the applied driving voltage. Solving for y, at x = L,the tip displacement is,

ytip =d31VuwhL

2

2I. (5)

Fig. 3: Electromechanical model of the bender.



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Using (4), the average surface strain εave,t along the top sensorlength ls is

εave,t =1

ls

∫ ls+t

t

ε(x) =−d31Vuwh

2

2I(6)

Comparing (5) with (6), the tip displacement ytip and theaverage strain εave,t are proportional. The proportionality is

ytip

εave,t= −L

2

2h. (7)

B. Surface Resistance change Measurement

Fig. 4(a) illustrates the electrical connection of the inte-grated strain gauges. A conditioning circuit provides the topand bottom strain gauges with constant DC voltages of Vt andVb. The equivalent circuit is shown in Fig. 4(b) where thenominal resistance of the top and bottom gauges is Rt andRb respectively. When the bender moves, the top and bottomgauges experience a change in resistance ∆Rt and ∆Rb.

Assuming that the top and bottom sensors experience iden-tical strain, εave = εave,t = −εave,b,

εave ∝∆Rt

Rt∝ ∆Rb

Rb. (8)

Using (7) and (8), the tip displacement can be estimated bymeasuring the resistance change, which is proportional to Vc.The excitation voltages Vt and Vb are tuned so that the nominalvalue of Vc is zero. When this is achieved,

(Vt

Vb= −Rt

Rb

).

In the presence of strain, assuming that the strain gaugesare identical (Rt = Rb), the voltage Vc is

Vc ∝∆Rt

Rt∝ ∆Rb

Rb. (9)

Using a gain of K, this voltage is amplified to Vg = KVc.From equations (7-9),

Vg ∝ ytip. (10)

The proportionality (10), is experimentally derived in the nextsection. The estimated displacement y is then

y = KsVg. (11)

(b) Strain gauge circuit(a) Electrical connections of starin gauges

Fig. 4: The electrical connection of the strain gauges (a) andthe equivalent circuit (b).

Fig. 5: The tip displacement versus driving voltage, whenthe actuator is driven by a triangular voltage with increasingamplitude.

0 5 10Time [s]

(a) Time Signals

180 V,

2 mm,

2 mm,

-1 0 1

-1

0

1

(b) Nonlinearity

Err

or (

%)

-1

0

1

Fig. 6: The recorded time signals (a) and difference betweenthe reference ylaser and proposed sensor y (b). In (a), thepeak-to-peak values are provided for the actuator voltage Vu,the reference sensor ylaser, and strain sensor y.

IV. VALIDATION OF THE PROPOSED METHOD

A calibration experiment is first carried out where themaximum available driving voltage range Vu= +/-90 V isapplied to the bender and the tip displacement is measuredusing the laser sensor. The sensitivity gain is then calculatedas Ks = ylaser/Vg = 0.9 mm/V.

The performance of the proposed strain sensor is furtherevaluated by applying a triangular driving voltage Vu to theactuator at 33%, 67%, and 100% of the full-scale voltage(±90 V). The resulting tip displacements measured by boththe reference and strain sensor are plotted in Fig. 5. Thevoltage-displacement hysteresis can be clearly observed inboth signals.

Time signals are plotted in Fig. 6(a). A peak-to-peak drivingvoltage of 180 V results in a full-range of 2 mm of thedisplacement. A close agreement between the reference andstrain sensor can be observed. In Fig. 6(b), the output ofthe reference and strain sensor are plotted against each other.The difference between the two sensors is calculated as apercentage of full-range, based on a least-squares fit for the



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-100

-50

0

50

-720

-360

0

360

Mag

nitu

de (

dB)

Pha

se (

deg)

100 101 102103

Frequency (Hz)

Fig. 7: The normalized open-loop frequency response in blue,measured from u to y, in mm/V. The closed-loop frequencyresponse with damping-integral control, measured from r toy, in mm/V. Normalizing the open-loop frequency response isachieved by multiplying the measured data by a gain of 7.9.

sensitivity and offset. The maximum difference is 1.1 % ofthe full-range displacement. A polynomial calibration functioncould be used to significantly reduce the residual error.

V. CONTROLLER DESIGN

In this section the performance of the proposed strainsensor is evaluated in a closed-loop. A damping-integralcontroller [10] is designed and implemented in the feedbackloop where the strain sensor measurement is used.

A. Damping-Integral Controller

The normalized open-loop frequency response from u toy, measured using a Quattro Data Physics signal analyzer,is plotted in Fig 7. Investigating the frequency response, thefirst resonance occurs at 57 Hz. A damping-integral controlleris designed to damp this resonance. Fig. 8 shows the blockdiagram of the closed-loop system with the damping-integralcontrol strategy that includes an integral action

Ci =kis, (12)

a reconstruction filter Fr, and an anti-aliasing filter Fa. Bothfilters are second-order low pass Butterworth filters [10].

Fr = Fa =ωc

s2 +√

2ωcs+ ω2c

. (13)

Fig. 8: Block diagram of the closed-loop system with thedamping-integral controller. The strain sensor output is themeasurement in the feedback loop.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time [s]

-0.2

0

0.2

0.4

0.6

0.8

Reference1

Fig. 9: Reference and measured closed-loop step response ofthe integrated bender using a damping-integral controller.

The controller design criteria is to maximize the closed-loopbandwidth without destabilizing the closed-loop system [10].The closed-loop transfer function is

T =CiFrFaG

1 + CiFrFaG. (14)

Employing the Nelder-Mead optimization algorithm [15], thecut-off frequency of the filters ωc as well as the integral controlgain ki are optimized to fulfill the design criteria. The optimalparameters are summarized in Table I. The resultant loop gainand phase margin is 6 dB and 61◦ respectively.

TABLE I: Parameters of the damping-integral controller.Parameter Value

ωc 123 Hzki 406

B. Performance of the closed-loop system

The measured closed-loop frequency response of the benderwith a damping-integral control is plotted on top of the open-loop frequency response in Fig. 7. It is observed that the firstresonant peak is substantially suppressed by 33 dB and theresultant 3-dB closed-loop bandwidth of the system is 60 Hz.

The step response of the closed-loop system is plottedin Figure 9. A settling time of 0.06 s is recorded with nonoticeable overshoot.

VI. CONCLUSION

The article presents a new method for measuring the tipdisplacement of piezoelectric benders by integrating resistivestrain gauges into the top and bottom electrodes. The changein surface resistance is shown to be proportional to the tipdisplacement in the absence of external forces. The straingauges are employed in a half bridge configuration to measurethe resistance change and tip displacement.

The presented method is experimentally compared to areference sensor. The maximum difference between the two



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sensor outputs was 1.1% of full range. The performance ofthe presented method for control applications is experimentallydemonstrated by employing the method in a damping-integralcontrol structure. The proposed sensing method has limita-tions for high frequency applications due to the capacitivecoupling between the driven surface electrodes and the straingauges, which is in the tens of kilohertz. Future work includesvalidating the high frequency performance of the proposedsensing method. The sensor geometry will also be optimizedfor external force measurement.

ACKNOWLEDGMENT

The authors would like to thank Mr. Ben Routley for hisassistance developing the etching process.

REFERENCES

[1] A. M. El-Sayed, A. Abo-Ismail, M. T. El-Melegy, N. A. Hamzaid, andN. A. A. Osman, “Development of a micro-gripper using piezoelectricbimorphs,” Sensors, vol. 13, no. 5, pp. 5826–5840, 2013.

[2] A. J. Fleming, “Nanopositioning system with force feedback for high-performance tracking and vibration control,” IEEE/Asme Transactionson Mechatronics, vol. 15, no. 3, pp. 433–447, 2010.

[3] Y. K. Yong and A. J. Fleming, “High-speed vertical positioning stagewith integrated dual-sensor arrangement,” Sensors and Actuators A:Physical, vol. 248, pp. 184–192, 2016.

[4] S. A. Rios and A. J. Fleming, “A new electrical configuration forimproving the range of piezoelectric bimorph benders,” Sensors andActuators A: Physical, vol. 224, pp. 106–110, 2015.

[5] P. Woias, “Micropumpspast, progress and future prospects,” Sensors andActuators B: Chemical, vol. 105, no. 1, pp. 28–38, 2005.

[6] C. Jenke, J. Palleja Rubio, S. Kibler, J. Hafner, M. Richter, and C. Kutter,“The combination of micro diaphragm pumps and flow sensors for singlestroke based liquid flow control,” Sensors, vol. 17, no. 4, p. 755, 2017.

[7] S. A. Rios and A. J. Fleming, “Design of a charge drive for reducing hys-teresis in a piezoelectric bimorph actuator,” IEEE/ASME Transactionson Mechatronics, vol. 21, no. 1, pp. 51–54, 2016.

[8] M. N. Islam and R. J. Seethaler, “Sensorless position control forpiezoelectric actuators using a hybrid position observer,” IEEE/ASMETransactions On Mechatronics, vol. 19, no. 2, pp. 667–675, 2014.

[9] J. Fanson and T. K. Caughey, “Positive position feedback control forlarge space structures,” AIAA journal, vol. 28, no. 4, pp. 717–724, 1990.

[10] A. A. Eielsen, M. Vagia, J. T. Gravdahl, and K. Y. Pettersen, “Damp-ing and tracking control schemes for nanopositioning,” IEEE/ASMETransactions on Mechatronics, vol. 19, no. 2, pp. 432–444, 2014.

[11] S. S. Aphale, A. J. Fleming, and S. R. Moheimani, “Integral resonantcontrol of collocated smart structures,” Smart Materials and Structures,vol. 16, no. 2, p. 439, 2007.

[12] A. J. Fleming and K. K. Leang, “Integrated strain and force feedbackfor high-performance control of piezoelectric actuators,” Sensors andActuators A: Physical, vol. 161, no. 1, pp. 256–265, 2010.

[13] S. Z. Mansour, R. J. Seethaler, Y. R. Teo, Y. K. Yong, and A. J.Fleming, “Piezoelectric bimorph actuator with integrated strain sensingelectrodes,” in SENSORS, 2017 IEEE. IEEE, 2017, pp. 1–3.

[14] D. Hall, “Review nonlinearity in piezoelectric ceramics,” Journal ofmaterials science, vol. 36, no. 19, pp. 4575–4601, 2001.

[15] J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Conver-gence properties of the nelder–mead simplex method in low dimensions,”SIAM Journal on optimization, vol. 9, no. 1, pp. 112–147, 1998.

APPENDIX AELECTRICAL CONFIGURATION

Parallel poled benders, such as the Y-poled T220-A4-503Ybender, can be driven in two configurations:

• Configuration 1: The driving voltage Vu is applied to themiddle brass layer and the external electrodes are ground.

• Configuration 2: The middle brass layer is groundedand Vu is applied to the external electrodes.

(a) Configuration 1 (b) Equivalent circuit (c) Simplified circuit

(d) Configuration 2 (e) Equivalent circuit (f) Simplified circuit

Fig. 10: Two electrical configurations for driving the bender.

Configuration 1 is recommended by the manufacturer since itis convenient to have grounded external electrodes. However,this increases dynamic measurement errors. Figure 10 showsboth configurations and their equivalent electrical circuits.

The electrical connections in Configuration 1 are describedin Section II and depicted in Figure 10(a). The electrodesare grounded and Vu is applied to the middle layer. The topand bottom electrodes are electrically modeled as distributedresistances in series, while piezoelectric layers are modeledas distributed capacitors. piezoelectric layers are modeled ascapacitances. The electrical equivalent circuit is describedin Figure 10(b). Assuming that the resistances are equal, thesimplified circuit in Figure 10(c) is a high-pass filter whichallows direct feed-through from Vu to Vc at high frequencies,which is highly undesirable.

In Configuration 2, the equivalent circuit and simplifiedcircuit is depicted in Figures 10(d) and (e) respectively. In thisconfiguration the direct feed-through is eliminated. In practice,there still exists a small capacitive coupling between the drivensurface electrode and strain sensor; however, this is deemedto be negligible in the frequency range of interest.

Sepehr Zarif Manosur received the Bachelor ofapplied science degree in mechanical Engineeringfrom the University of Tehran in 2013 and theMaster of applied science degree in mechanicalEngineering from the University of British Columbiain 2015. He is currently a PhD student in mechanicalengineering at the University of British Columbia.His research interests include the design and controlof high-speed motion control systems.



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Rudolf J. Seethaler (M07) received the Ph.D. de-gree in mechanical engineering from the Universityof British Columbia (UBC), Vancouver, BC, Canada,in 1997. From 1997 to 2005, he was a SeniorControls Engineer for BMW AG, Munich, Germany.He is currently an Associate Professor at UBC. Hisresearch interests include the design and control ofhigh-speed motion control systems.

Yik R. Teo graduated from The University OfNewcastle, Australia (Callaghan campus) with aBachelors of Electrical Engineering in 2008, Mastersof Philosophy in Mechanical Engineering in 2013and a Ph.D in 2018. He is presently a researchassociate at Precision Mechatronics Lab at TheUniversity of Newcastle, Australia. His researchincludes high-precision positioning, scanning probemicroscopy, and nanofabrication. Academic awardsinclude the Glenn and Ken Moss Research HigherDegree Award, Australian Postgraduate Award and

the Vice-Chancellor Award in Outstanding Research Candidate.

Yuen Kuan Yong received the Bachelor of Engi-neering degree in Mechatronics Engineering and thePhD degree in mechanical engineering from TheUniversity of Adelaide, Australia, in 2001 and 2007,respectively. She is presently an associate profes-sor at The University of Newcastle, Australia. Herresearch interests include nanopositioning systems,design and control of micro-cantilevers, atomic forcemicroscopy, and miniature robotics. A/Prof Yong isthe recipient of the University of Newcastle Vice-Chancellors Award for Research Excellence in 2014,

and the Vice-Chancellors Award for Research Supervision Excellence in 2017.She is an associate editor for the IEEE/ASME Transactions of Mechatronics,and Frontiers in Mechanical Engineering.

Andrew J. Fleming graduated from The Universityof Newcastle, Australia (Callaghan campus) with aBachelor of Electrical Engineering in 2000 and Ph.Din 2004. Prof Fleming is the Director of the PrecisionMechatronics Lab at The University of Newcastle,Australia. His research interests include lithography,nano-positioning, scanning probe microscopy, andbiomedical devices. Prof Fleming’s research awardsinclude the ATSE Baterham Medal in 2016, theIEEE Control Systems Society Outstanding PaperAward in 2007, and The University of Newcastle

Researcher of the Year Award in 2007. He is the co-author of three books andmore than 180 Journal and Conference articles. Prof Fleming is the inventor ofseveral patent applications, and in 2012 he received the Newcastle InnovationRising Star Award for Excellence in Industrial Engagement.

piezoelectric bimorph actuator with integrated strain sensing … · 2018-06-07 · gauges can be...

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