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A review, supported by experimental results, of voltage, charge and capacitor insertion method for driving piezoelectric actuators

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A piezoelectric actuator consists of ceramic material that expands or contracts when a positive or a negative potential voltage signal is applied. The displacement of a piezoelectric actuator is commonly controlled using a voltage input due to its
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  Pleasecitethisarticleinpressas:MinaseJ,etal.Areview,supportedbyexperimentalresults,ofvoltage,chargeandcapacitorinsertionmethodfor driving piezoelectric actuators. Precis Eng (2010), doi:10.1016/j.precisioneng.2010.03.006 ARTICLE IN PRESS GModelPRE-5743; No.of Pages9Precision Engineering xxx (2010) xxx–xxx Contents lists available at ScienceDirect PrecisionEngineering  journal homepage: www.elsevier.com/locate/precision A review, supported by experimental results, of voltage, charge and capacitorinsertion method for driving piezoelectric actuators  J. Minase ∗ , T.-F. Lu, B. Cazzolato, S. Grainger School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia a r t i c l e i n f o  Article history: Received 1 April 2009Accepted 11 March 2010 Available online xxx Keywords: Piezoelectric actuatorHysteresisCreepVoltageChargeCapacitor insertion a b s t r a c t A piezoelectric actuator consists of ceramic material that expands or contracts when a positive or anegative potential voltage signal is applied. The displacement of a piezoelectric actuator is commonlycontrolledusingavoltageinputduetoitseaseofimplementation.However,drivingapiezoelectricactua-torusingavoltageinputleadstothenon-linearhysteresisandcreep.Hysteresisandcreepareundesirablecharacteristicswhichleadtolargeerrorswhenapiezoelectricactuatorisusedinpositioningapplications.Theamountofhysteresisandcreepcouldbeminimizedtoalargeextentwhenapiezoelectricactuatorisdriven using a charge input. Another method which substantially reduces hysteresis and creep involvestheinsertionofacapacitorinserieswithapiezoelectricactuatorwhichisdrivenusingavoltageinput.Areviewofvoltage,chargeandcapacitorinsertionmethodsfordrivingpiezoelectricactuatorsispresentedin this paper. Experimental results, for a piezoelectric actuator driven using the above three methods,are presented to validate the facts presented in this review. © 2010 Elsevier Inc. All rights reserved. 1. Introduction A piezoelectric actuator is formed of ceramic material [1,2]which is ferroelectric in nature, a property which causes expan-sion or contraction of the actuator when a voltage is applied [3,4].The resolution of a piezoelectric actuator is dependent only on theamountofthedisturbancenoiseintheappliedvoltageandtheres-olution of a sensor used to measure the resulting displacement.Due to the advantage of nanometer resolution in displacement,high stiffness, and fast response time, there are many positioningapplications[5–9]thatutilizeapiezoelectricactuatorforactuation purposes. Being easy to implement, the displacement of a piezo-electricactuatoriscommonlycontrolledusingavoltageinput[10].However, considerable hysteresis and creep is seen in a voltagedriven actuator [2,10].The remainder of this paper is organized as follows: the mate-rials aspect behind the displacement of a piezoelectric actuatoris presented in the background study, in Section 2. In Section 3, voltage, charge and capacitor insertion methods for driving apiezoelectric actuator are reviewed. An experimental setup for apiezoelectricactuatordrivenusingtheabovethreemethodsispre-sentedinSection4andtheresultsobtainedfromtheseexperiments  Abbreviations:  PZT,leadzirconatetitanate;LVPZ,lowvoltagepiezo;DOF,degreeof freedom; ADC, analog to digital converter; DAC, digital to analog converter. ∗ Corresponding author. Tel.: +61 08 8303 6385; fax: +61 08 8303 4713. E-mail address:  jayesh.minase@mecheng.adelaide.edu.au (J. Minase). are presented in Section 5. Finally, the concluding remarks follow in Section 6. 2. Background study  The piezoelectric effect is a fundamental process involvingelectro-mechanical interactions and represents the conversion of energy. It relates the electric field to the mechanical compres-sion/elongation in a piezoelectric material [11]. This fundamental property of piezoelectricity has therefore led to the utilization of such materials in the fabrication of various piezoelectric devicessuch as actuators, sensors, and transducers [11,12].As mentioned before, piezoelectric actuators are built usingpiezoelectric ceramic materials. The type of ceramic material gen-erally used is the lead zirconate titanate (pb(Zr,Ti)O 3 ) crystal [13];commonly called the PZT. Being a polar material the ceramic pos-sesses net external electric dipole moment which is caused bythe alignment of numerous electric dipoles inside the crystal [3].In the absence of an applied electric field or when operated attemperature conditions that exceed the Curie temperature, theindividual electric dipoles in the ceramic material are randomlyoriented (Fig. 1 (a)). In this state the ceramic material becomesunpolarized and paraelectric in nature i.e. it looses the property of piezoelectricity. At this point it is worth mentioning that a piezo-electric actuator after being manufactured is supplied with a highvoltage and thus partially polarized. The individual crystals in theunpolarized ceramic material become symmetric in structure. Asymmetric crystal structure means that the net external electric 0141-6359/$ – see front matter © 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.precisioneng.2010.03.006  Pleasecitethisarticleinpressas:MinaseJ,etal.Areview,supportedbyexperimentalresults,ofvoltage,chargeandcapacitorinsertionmethodfor driving piezoelectric actuators. Precis Eng (2010), doi:10.1016/j.precisioneng.2010.03.006 ARTICLE IN PRESS GModelPRE-5743; No.of Pages9 2  J. Minase et al. / Precision Engineering   xxx (2010) xxx–xxx Fig. 1.  Polarization process for a piezoelectric acutator [4]. dipole moment is equal to zero. Therefore, the ceramic does notexpand/contract [3].Below the Curie temperature the ceramic material undergoesa phase change and becomes ferroelectric in nature i.e. the prop-ertyofpiezoelectricityisregained[3].Thisphasechangemakesthe individualcrystalsintheceramicmaterial,asymmetricinstructure.When the ceramic material is subjected to large electric fields, theelectric dipoles align themselves in a direction close to the appliedelectricfield.Thiscausestheasymmetricaxisofanindividualcrys-tal and all neighbouring crystals to expand in a direction close tothat of the applied electric field. This process is called polariza-tion (Fig. 1 (b)). When the electric field is removed, the electricdipoles do not entirely return to their srcinal position. This phaseofpolarizationiscalledremanentpolarizationinwhichtheceramicremains partially polarized. In this phase the net external electricdipolemomentisnotequaltozero.AsshowninFig.1(b),theactu- ator will have some remanent displacement. When electric field isre-applied, the ceramic material elongates thereby elongating theactuator (Fig. 1(c)). 3. Driving methods for a piezoelectric actuator Apiezoelectricactuatorisgenerallydrivenusingavoltage[10].However,avoltagedrivenpiezoelectricactuatorexhibitshysteresisand creep [2,10]. The amount of hysteresis and creep exhibited by a piezoelectric actuator can be minimized by driving the actuatorusingachargeinputorbyinsertingacapacitorinserieswithavolt-age driven actuator. In this section, voltage, charge, and capacitorinsertion methods are discussed in detail.  3.1. Voltage driven An easy way to drive a piezoelectric actuator is to use a volt-age input [10,14]. Adriaens et al. [14] state that: “From the very beginning of applying piezoelectric materials as actuators, theyare voltage steered, and this is still the standard way of electricalsteering”. Using voltage as an input does not reduce the operatingrange and bandwidth of a piezoelectric actuator [2]. However, it comes with the disadvantage of having to cope up with hystere-sis and creep [2,10]. This affects precise positioning when using a piezoelectric actuator.Hysteresis, caused by the polarization of microscopic ferro-electric particles [3,15], is presumed to be a rate-independent non-linearity [16] which depends on a combination of the cur-rentlyappliedvoltageaswellasonsomepastvaluesoftheappliedvoltage (memory). A traditional hysteresis curve exhibited by apiezoelectric actuator is presented in Fig. 2. The hysteresis curve was obtained by driving a Tokin model AE0505D16 piezoelectricstack actuator using a − 20 to 100V sine wave output from a volt-ageamplifier.Theamountofhysteresiswasapproximately2.4  mat50%voltageswing(40Vinthiscase).Creep,asloweccentricdriftin the displacement of a piezoelectric actuator [2], is the effect of  the remanent polarization which continues to change over time;eventhoughtheappliedvoltagehasreachedaconstantvalue[17].Creep is more prominent in low bandwidth application. A tradi-tional creep curve exhibited by a piezoelectric actuator is shownin Fig. 3. The creep curve was obtained by driving a Tokin model AE0505D16 piezoelectric stack actuator using a 100V step input.The step input was applied at 10s.Hysteresis can lead to large positioning errors in piezo posi-tionerswhichareoperatedoverrelativelylongdisplacementrange[18–20]. In some cases the maximum positioning error can be asmuch as 10–15% of the operating range of a piezoelectric actuator[21]. Hysteresis which is more pronounced over longer operatingrange can be minimized by operating a piezoelectric actuator in alinearrange[22]bykeepingtheamplitudeandthefrequencyofthe applied voltage signal constant and as small as possible. However,insuchacasetheactuator’sabilitytobedisplacedoveralongrangewith high precision needs to be sacrificed. Creep affects absolutepositioning of a piezoelectric actuator in slow or static applica-tions [23]. Operating a piezoelectric actuator fast enough and over shorterdurationoftimecanhelpreducethedriftingcausedbythecreep effect. Hysteresis and creep, together, can lead to inaccuracyin the open loop control and instability in the closed loop control[17].Toinherittheadvantagesofferedbythevoltagedrivingmethodit is important that hysteresis and creep are minimized using acertainmodellingandcontrolapproach.Phenomenologicalmodels Fig. 2.  Hysteresis in a voltage driven actuator.  Pleasecitethisarticleinpressas:MinaseJ,etal.Areview,supportedbyexperimentalresults,ofvoltage,chargeandcapacitorinsertionmethodfor driving piezoelectric actuators. Precis Eng (2010), doi:10.1016/j.precisioneng.2010.03.006 ARTICLE IN PRESS GModelPRE-5743; No.of Pages9  J. Minase et al. / Precision Engineering   xxx (2010) xxx–xxx 3 Fig. 3.  Creep in a voltage driven actuator. such as the Preisach model [24] and the Prandtl–Ishlinskii model [25]havebeenusedtomodelhysteresisinapiezoelectricactuator.Also, analytical models such as the Maxwell slip model [10] andthe first order hysteresis model coupled with a second order massspring damper model [26] have been used to predict the hystere- sis behaviour. Similarly, a logarithmic model [17] has been usedto predict the creep behaviour. However, the phenomenological,the analytical models and the logarithmic models do not provideerror free prediction of hysteresis or creep. To reduce the posi-tioning errors caused by inaccurate prediction of hysteresis andcreep, a robust controller is required. Also, the controller couldbe effective in reducing the positioning error due to the effectof vibrations generated when a piezoelectric actuator is operatedat a frequency close to its resonance. Numerous feedback controlschemes have been proposed to accurately position a piezoelec-tricactuatordrivenpositioningsystem[27–30].Precisepositioning of a piezoelectric actuator using open loop control has also beenimplemented [17,31]. Thus the advantages offered by the voltage driving method are bought at the expense of increased computa-tionalandhardwarecostswhichareassociatedwiththemodellingand control.  3.2. Charge driven One way to reduce hysteresis and creep is to drive a piezoelec-tric actuator using a charge input, instead of voltage input [32,33].Whenconnectedelectrically,theactuatorwhichisadielectricactslikeanon-linearcapacitor[10]whichchangesitscapacitanceevenwhen the input voltage is kept constant. The change in the capac-itance leads to a change in the amount of the charge acting onthe actuator. This causes hysteresis and creep. Regulating the cur-rent and hence the charge prevents the actuator from changing itscapacitance [10] thereby leading to a significant reduction in hys- teresisandcreep.Therefore,achargeinputleadstoapproximatelylinear operation of a piezoelectric actuator [34–36]. As shown in Fig.4,thedisplacementofapiezoelectricactuatorisapproximatelylinear in proportion to the supplied input. The hysteresis curve inFig.4wasobtainedbydrivingaTokinmodelAE0505D16piezoelec-tric stack actuator using a 0–100V sine wave output from a chargeamplifier.The use of charge to drive a piezoelectric actuator was firstpatented by Comstock in 1981 [34]. The actuator considered was a piezoelectric stack actuator exhibiting large amount of hysteresis.On application of an input control signal, the non-inverting differ- Fig. 4.  Hysteresis in a charge driven actuator. ential amplifier (Fig. 5) induces an opposite charge on the surfaces of the actuator. The sensing capacitor,  C  , connected in series withthe actuator acts as a sensor which measures a signal proportionalto the charge on the actuator. The measured signal is then fed intothe buffer amplifier which feeds a voltage signal into the invertingterminal of the differential amplifier thereby changing the outputof the amplifier and, as a consequence, the charge on the actuator.Thisfeedbackapproachforcesthechargeontheactuatortoavaluewhich is approximately proportional to the input control signal.In 1982, Newcomb and Flinn [33] proposed the use of constant current,highimpedance,chargedrivetolinearisethebehaviourof apiezoelectricceramicactuator.Thestudyclaims:“Wehavefoundthat if the extension of such an actuator is plotted as a function of applied charge rather than applied voltage, hysteresis and creepvirtually disappear”. Under quasi-static (steady state) conditionsthe displacement response was found to be approximately lin-ear.Althoughproposed,reductionincreepwasnotexperimentallyvalidated by Newcomb and Flinn. Based on the concept proposedby Comstock [34], a similar charge feedback amplifier was imple- mented by Main et al. [35] but with a couple of changes. A current Fig. 5.  Charge control of piezoelectric stack actuator [34].  Pleasecitethisarticleinpressas:MinaseJ,etal.Areview,supportedbyexperimentalresults,ofvoltage,chargeandcapacitorinsertionmethodfor driving piezoelectric actuators. Precis Eng (2010), doi:10.1016/j.precisioneng.2010.03.006 ARTICLE IN PRESS GModelPRE-5743; No.of Pages9 4  J. Minase et al. / Precision Engineering   xxx (2010) xxx–xxx buffer was added at the output end of the non-inverting differen-tial amplifier to improve the amplifier bandwidth. Also, the circuitdeveloped by Comstock [34] was found to be very sensitive toamplifier bias current caused by the charge bias between the actu-ator and the sensing capacitor,  C   [35]. An initialization circuit wasadded at the input end of the non-inverting differential amplifiertoeliminatethechargebias.Understeadystateconditionsthedis-placement of a piezoelectric stack actuator was seen to increaselinearly with the voltage input. Design and implementation of acharge feedback controller were presented by Yi and Viellette [1].Asopposedtothenon-invertingdifferentialamplifierproposedbyComstock[34],thiscontrollerusesaninvertingoperationalampli- fier and also includes a high voltage amplifier in the feedback looptodriveapiezoelectricstackactuator.Thecontrollerissuccessfulinlinearising the response of the actuator. The inverting operationalamplifierincorporatesresistorstoprovideDCfeedbackpathwhicheliminatestherequirementofaninitializationcircuitsuggestedbyMain et al. [35]. However, saturation of the inverting operational amplifier limits the linear operating range of this charge feedbackcontroller. Also, the DC feedback causes the charge feedback con-troller to act like a voltage source under steady state operatingcondition. Thus, hysteresis is not eliminated under steady stateoperating condition.Designofagroundedloadchargedriveanditscomparisonwitha voltage amplifier to drive a scanning probe microscope positionstage has been presented by Fleming and Leang [36]. It has been shownthattheuseofachargedrivecanreducetheerrorduetohys-teresistolessthan1%ofthescanrangeofthepositionstage.Whenthe position stage was driven using a voltage amplifier, the errordue to hysteresis was found to be 7.2% of the scan range. The basiccircuit diagram of the grounded load charge drive [37] is shown in Fig. 6. A piezoelectric actuator driven by the grounded load chargedriveismodelledusingaloadcapacitor C  L   andavoltagesource V  p .A high gain feedback loop is used to compare the reference volt-age, V  ref  ,tothevoltage V  Z  acrossasensingcapacitor, C  S .Thechargeacting on the actuator is given by (1). q L   = V  ref  C  S  (1)In (1) the value of resistances,  R S  and  R L  , are assumed to be neg-ligible at higher operating frequencies. The grounded load charge Fig. 6.  Basic circuit diagram for grounded load chage drive [37]. amplifier will have no high frequency dynamics. This means thatthe gain of the grounded load charge drive is C  S  (C)/ V   at higher fre-quencies.However,theresistance R S  and R L   areboundtointroduceerror in the charge drive, at low frequencies or in static case. Thiserrorcanbeovercomebylettingtheratiooftheresistancebeequalto the ratio of the capacitance [36]. R s R L  = C  s C  L  (2)Bypreciselytuningtheratioin(2),thegroundedloadchargeampli- fier will have no low/high frequency dynamics and thus have aconstant sensing gain,  C  S , in static as well as dynamic operations.As mentioned previously, the use of a charge input to drive apiezoelectric actuator can provide a linear actuator response withsubstantial reduction in the amount of hysteresis [34,35] as well as creep [32,33]. The reduction in hysteresis and creep is achieved in an open loop fashion without using any sensor to measure thedisplacement of a piezoelectric actuator [38] and hence open loop controltechniquescanthenbeimplemented[39].Itisworthmen- tioning that the sensing capacitor in the charge amplifier circuitis similar to a sensor which measures the charge on the actuatorthereby making the charge drive, a feedback approach. However,the charge drive has some disadvantages. A voltage drop across acharge circuit reduces the voltage applied to a piezoelectric actua-tor which in turn reduces the elongation [36,40]. A higher supply voltageisthereforerequiredtoelongatetheactuatortoitsoriginalvalue. The complexity of a charge control circuit leads to diffi-cultyintheimplementationofthechargedrivenapproach[41–44].Dependingonthecapacitancevalueofapiezoelectricactuator,thegain of a charge amplifier needs to be calibrated [36]. The use of a charge amplifier could also lead to increase in the drift, saturation,and further reduction in the bandwidth of a piezoelectric actuator[45].Theuseofacharge/currentamplifiercanthusbeexpensiveascompared to the more commonly used voltage amplifiers [46]. To summarize, “though charge control of a PZT actuator circumventsthe non-linear behaviour of piezoelectric ceramic and enables theuse of linear control techniques, the simplicity of such linear con-trolisboughtattheexpenseoftheincreasedelectroniccomplexityrequired for effective charge control” [10].  3.3. Capacitor insertion method A voltage driven piezoelectric actuator exhibits considerablehysteresis and creep [2,10]. When driven using a charge input, the amount of hysteresis and creep exhibited by the actuator isreduced [32,33]. However, a charge amplifier needs to be specially designed and then calibrated depending on the capacitance valueof the actuator. This drawback, including others (refer to Section3.2), makes the charge driving method rather complicated toimplement. In 1988, Kaizuka and Siu [41] proposed a simple way of reducing the amount of hysteresis and creep exhibited by avoltage driven piezoelectric actuator. This method, called thecapacitor insertion method, involves insertion of a capacitor inseries with a piezoelectric actuator [41,48]. The voltage across the insertedcapacitorisnowadirectmeasureoftheamountofchargedriving the actuator. At this point it is worth to reiterate that apiezoelectric actuator, similar to a non-linear capacitor, changesits capacitance even at constant voltage input. The change in thecapacitance leads to a change in the amount of charge on theactuator which in turn leads to hysteresis and creep. The insertedcapacitor acts as a charge regulator which reduces the sensitivityof the ratio of charge on the actuator,  Q  actuator  to the change inthe capacitance of the actuator,  C  actuator  [41]. The reduction insensitivity reduces hysteresis and creep.Consider the circuit diagram in Fig. 7. A piezoelectric actuator is connected to a voltage input,  V  total . The voltage across the actu-  Pleasecitethisarticleinpressas:MinaseJ,etal.Areview,supportedbyexperimentalresults,ofvoltage,chargeandcapacitorinsertionmethodfor driving piezoelectric actuators. Precis Eng (2010), doi:10.1016/j.precisioneng.2010.03.006 ARTICLE IN PRESS GModelPRE-5743; No.of Pages9  J. Minase et al. / Precision Engineering   xxx (2010) xxx–xxx 5 Fig. 7.  Actuator driven using voltage input [41]. Fig. 8.  Circuit diagram for capacitor insertion method [41]. ator is given by  V  actuator . A load resistor is connected in series withthe actuator. From Fig. 7, the charge on the actuator and the sen- sitivity of the ratio of charge on the actuator to the change in thecapacitance of the actuator can be given by (3). Q  actuator  = C  actuator V  actuator dQ  actuator dC  actuator = V  actuator (3)InFig.8,acapacitor, C  capacitor  isinsertedinserieswiththeactuator.Let  C  total  be the capacitance of the complete circuit. Assuming thetotalchargeinthecircuittobeequaltothechargeontheactuator,(3) can be re-written as (4): Q  actuator  = C  total V  total dQ  actuator dC  actuator =   C  2capacitor  C  actuator + C  capacitor  2  V  total (4)NormalisationbetweentheexperimentsinFigs.7and8requirethe appliedvoltage onthe actuator to be the same.Therefore, the totalvoltage,  V  total  acting on the circuit is calculated using (5). V  total  =   ( C  actutaor + C  capacitor ) C  capacitor  V  actuator  (5)Substituting (5) in (4) gives the relationship between sensitivity and voltage for a piezoelectric actuator with a capacitor in series.From (6) it can be seen that the sensitivity of the ratio of charge to dQ  actuator dC  actuator =   C  capacitor ( C  actuator + C  capacitor )  V  actuator  (6)the change in the capacitance of a piezoelectric actuator has beenreduced by the insertion of capacitor in series with the actuator.Theamountofreductioninthesensitivity,givenby    in(7),shows that lower the value of   C  capacitor , lower is the value of      i.e. more isthe reduction in the sensitivity and hence more is the reduction inhysteresis and creep. In other words the hysteresis and creep, in apiezoelectricactuatorwhichisdrivenusingthecapacitorinsertion Fig. 9.  Piezoelectric stack actuator. Fig. 10.  Experimental setup to measure hysteresis and creep in piezoelectric stackactuator. method, will be reduced by a factor of     .    = C  capacitor C  actuator + C  capacitor (7)Experiments were conducted, with and without insertion of acapacitor, by Kaizuka and Siu [41] to measure the amount of hys- teresis present in a piezoelectric stack actuator. The actuator wasdriven using a sine wave. The measurements were taken at volt-ages 25%, 50% and 75% into the swing, the results of which aresummarised in Table 1. It can be seen that the amount of hystere- sis reduces with the reduction in the value for    . Thus, the highestreductioninhysteresisisachievedwhenthevaluefor    isthelow-est. For the same stack actuator, experiments were conducted byKaizuka and Siu [41] using a step input. The capacitance values( C  capacitor ) for the inserted capacitor were similar to the ones inTable 1. The creep effect was seen to diminish with a reduction inthe value of     .The capacitor insertion method has been implemented intracking control of a nano-measuring machine [47,48]. The results from this implementation show that a piezoelectric actuator’scharacteristics become more linear with the use of an insertedcapacitor with smaller capacitance value. Other than the abovetwo papers there seems to little published experimentation usingthe capacitor insertion method. The reason behind this not being apopular method is the requirement of higher voltage input. Whena capacitor is inserted in series with a piezoelectric actuator, the  Table 1 Measured hysteresis using capacitor insertion method [41]. C  capacitor     C  actuator  Measured at 25% voltage swing Measured at 50% voltage swing Measure at 75% voltage swingCapacitor not inserted – – 217nm 282nm 218nm464nF 0.886 59.70nF 191nm 251nm 195nm49.21nF 0.458 58.24nF 103nm 133nm 108nm15.19nF 0.207 58.19nF 49nm 56nm 53nm10.03nF 0.148 57.74nF 34nm 40nm 38nm
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