ARTICLE IN PRESS Precision Engineering xxx (2010) xxx xxx

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1 Precision Engineering xxx (2010) xxx xxx Contents lists available at ScienceDirect Precision Engineering journal homepage: A review, supported by experimental results, of voltage, charge and capacitor insertion 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 article info abstract Article history: Received 1 April 2009 Accepted 11 March 2010 Available online xxx Keywords: Piezoelectric actuator Hysteresis Creep Voltage Charge Capacitor insertion 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 ease of implementation. However, driving a piezoelectric actuator using a voltage input leads to the non-linear hysteresis and creep. Hysteresis and creep are undesirable characteristics which lead to large errors when a piezoelectric actuator is used in positioning applications. The amount of hysteresis and creep could be minimized to a large extent when a piezoelectric actuator is driven using a charge input. Another method which substantially reduces hysteresis and creep involves the insertion of a capacitor in series with a piezoelectric actuator which is driven using a voltage input. A review of voltage, charge and capacitor insertion methods for driving piezoelectric actuators is presented in this paper. Experimental results, for a piezoelectric actuator driven using the above three methods, are presented to validate the facts presented in this review 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 expansion or contraction of the actuator when a voltage is applied [3,4]. The resolution of a piezoelectric actuator is dependent only on the amount of the disturbance noise in the applied voltage and the resolution 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 positioning applications [5 9] that utilize a piezoelectric actuator for actuation purposes. Being easy to implement, the displacement of a piezoelectric actuator is commonly controlled using a voltage input [10]. However, considerable hysteresis and creep is seen in a voltage driven actuator [2,10]. The remainder of this paper is organized as follows: the materials aspect behind the displacement of a piezoelectric actuator is presented in the background study, in Section 2. In Section 3, voltage, charge and capacitor insertion methods for driving a piezoelectric actuator are reviewed. An experimental setup for a piezoelectric actuator driven using the above three methods is presented in Section 4 and the results obtained from these experiments Abbreviations: PZT, lead zirconate titanate; LVPZ, low voltage piezo; DOF, degree of freedom; ADC, analog to digital converter; DAC, digital to analog converter. Corresponding author. Tel.: ; fax: address: jayesh.minase@mecheng.adelaide.edu.au (J. Minase). are presented in Section 5. Finally, the concluding remarks follow in Section Background study The piezoelectric effect is a fundamental process involving electro-mechanical interactions and represents the conversion of energy. It relates the electric field to the mechanical compression/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 devices such as actuators, sensors, and transducers [11,12]. As mentioned before, piezoelectric actuators are built using piezoelectric ceramic materials. The type of ceramic material generally used is the lead zirconate titanate (pb(zr,ti)o 3 ) crystal [13]; commonly called the PZT. Being a polar material the ceramic possesses net external electric dipole moment which is caused by the alignment of numerous electric dipoles inside the crystal [3]. In the absence of an applied electric field or when operated at temperature conditions that exceed the Curie temperature, the individual electric dipoles in the ceramic material are randomly oriented (Fig. 1 (a)). In this state the ceramic material becomes unpolarized and paraelectric in nature i.e. it looses the property of piezoelectricity. At this point it is worth mentioning that a piezoelectric actuator after being manufactured is supplied with a high voltage and thus partially polarized. The individual crystals in the unpolarized ceramic material become symmetric in structure. A symmetric crystal structure means that the net external electric /$ see front matter 2010 Elsevier Inc. All rights reserved. doi: /j.precisioneng

2 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 not expand/contract [3]. Below the Curie temperature the ceramic material undergoes a phase change and becomes ferroelectric in nature i.e. the property of piezoelectricity is regained [3]. This phase change makes the individual crystals in the ceramic material, asymmetric in structure. When the ceramic material is subjected to large electric fields, the electric dipoles align themselves in a direction close to the applied electric field. This causes the asymmetric axis of an individual crystal and all neighbouring crystals to expand in a direction close to that of the applied electric field. This process is called polarization (Fig. 1 (b)). When the electric field is removed, the electric dipoles do not entirely return to their original position. This phase of polarization is called remanent polarization in which the ceramic remains partially polarized. In this phase the net external electric dipole moment is not equal to zero. As shown in Fig. 1(b), the actuator will have some remanent displacement. When electric field is re-applied, the ceramic material elongates thereby elongating the actuator (Fig. 1(c)). 3. Driving methods for a piezoelectric actuator A piezoelectric actuator is generally driven using a voltage [10]. However, a voltage driven piezoelectric actuator exhibits hysteresis and creep [2,10]. The amount of hysteresis and creep exhibited by a piezoelectric actuator can be minimized by driving the actuator using a charge input or by inserting a capacitor in series with a voltage driven actuator. In this section, voltage, charge, and capacitor insertion methods are discussed in detail. at 50% voltage swing (40 V in this case). Creep, a slow eccentric drift in the displacement of a piezoelectric actuator [2], is the effect of the remanent polarization which continues to change over time; even though the applied voltage has reached a constant value [17]. Creep is more prominent in low bandwidth application. A traditional creep curve exhibited by a piezoelectric actuator is shown in Fig. 3. The creep curve was obtained by driving a Tokin model AE0505D16 piezoelectric stack actuator using a 100 V step input. The step input was applied at 10 s. Hysteresis can lead to large positioning errors in piezo positioners which are operated over relatively long displacement range [18 20]. In some cases the maximum positioning error can be as much as 10 15% of the operating range of a piezoelectric actuator [21]. Hysteresis which is more pronounced over longer operating range can be minimized by operating a piezoelectric actuator in a linear range [22] by keeping the amplitude and the frequency of the applied voltage signal constant and as small as possible. However, in such a case the actuator s ability to be displaced over a long range with high precision needs to be sacrificed. Creep affects absolute positioning of a piezoelectric actuator in slow or static applications [23]. Operating a piezoelectric actuator fast enough and over shorter duration of time can help reduce the drifting caused by the creep effect. Hysteresis and creep, together, can lead to inaccuracy in the open loop control and instability in the closed loop control [17]. To inherit the advantages offered by the voltage driving method it is important that hysteresis and creep are minimized using a certain modelling and control approach. Phenomenological models 3.1. Voltage driven An easy way to drive a piezoelectric actuator is to use a voltage input [10,14]. Adriaens et al. [14] state that: From the very beginning of applying piezoelectric materials as actuators, they are voltage steered, and this is still the standard way of electrical steering. Using voltage as an input does not reduce the operating range and bandwidth of a piezoelectric actuator [2]. However, it comes with the disadvantage of having to cope up with hysteresis and creep [2,10]. This affects precise positioning when using a piezoelectric actuator. Hysteresis, caused by the polarization of microscopic ferroelectric particles [3,15], is presumed to be a rate-independent non-linearity [16] which depends on a combination of the currently applied voltage as well as on some past values of the applied voltage (memory). A traditional hysteresis curve exhibited by a piezoelectric actuator is presented in Fig. 2. The hysteresis curve was obtained by driving a Tokin model AE0505D16 piezoelectric stack actuator using a 20 to 100 V sine wave output from a voltage amplifier. The amount of hysteresis was approximately 2.4 m Fig. 2. Hysteresis in a voltage driven actuator.

3 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] have been used to model hysteresis in a piezoelectric actuator. Also, analytical models such as the Maxwell slip model [10] and the first order hysteresis model coupled with a second order mass spring damper model [26] have been used to predict the hysteresis behaviour. Similarly, a logarithmic model [17] has been used to predict the creep behaviour. However, the phenomenological, the analytical models and the logarithmic models do not provide error free prediction of hysteresis or creep. To reduce the positioning errors caused by inaccurate prediction of hysteresis and creep, a robust controller is required. Also, the controller could be effective in reducing the positioning error due to the effect of vibrations generated when a piezoelectric actuator is operated at a frequency close to its resonance. Numerous feedback control schemes have been proposed to accurately position a piezoelectric actuator driven positioning system [27 30]. Precise positioning of a piezoelectric actuator using open loop control has also been implemented [17,31]. Thus the advantages offered by the voltage driving method are bought at the expense of increased computational and hardware costs which are associated with the modelling and control Charge driven One way to reduce hysteresis and creep is to drive a piezoelectric actuator using a charge input, instead of voltage input [32,33]. When connected electrically, the actuator which is a dielectric acts like a non-linear capacitor [10] which changes its capacitance even when the input voltage is kept constant. The change in the capacitance leads to a change in the amount of the charge acting on the actuator. This causes hysteresis and creep. Regulating the current and hence the charge prevents the actuator from changing its capacitance [10] thereby leading to a significant reduction in hysteresis and creep. Therefore, a charge input leads to approximately linear operation of a piezoelectric actuator [34 36]. As shown in Fig. 4, the displacement of a piezoelectric actuator is approximately linear in proportion to the supplied input. The hysteresis curve in Fig. 4 was obtained by driving a Tokin model AE0505D16 piezoelectric stack actuator using a V sine wave output from a charge amplifier. The use of charge to drive a piezoelectric actuator was first patented 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 with the actuator acts as a sensor which measures a signal proportional to the charge on the actuator. The measured signal is then fed into the buffer amplifier which feeds a voltage signal into the inverting terminal of the differential amplifier thereby changing the output of the amplifier and, as a consequence, the charge on the actuator. This feedback approach forces the charge on the actuator to a value which is approximately proportional to the input control signal. In 1982, Newcomb and Flinn [33] proposed the use of constant current, high impedance, charge drive to linearise the behaviour of a piezoelectric ceramic actuator. The study claims: We have found that if the extension of such an actuator is plotted as a function of applied charge rather than applied voltage, hysteresis and creep virtually disappear. Under quasi-static (steady state) conditions the displacement response was found to be approximately linear. Although proposed, reduction in creep was not experimentally validated by Newcomb and Flinn. Based on the concept proposed by Comstock [34], a similar charge feedback amplifier was implemented by Main et al. [35] but with a couple of changes. A current Fig. 5. Charge control of piezoelectric stack actuator [34].

4 4 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx buffer was added at the output end of the non-inverting differential amplifier to improve the amplifier bandwidth. Also, the circuit developed by Comstock [34] was found to be very sensitive to amplifier bias current caused by the charge bias between the actuator and the sensing capacitor, C [35]. An initialization circuit was added at the input end of the non-inverting differential amplifier to eliminate the charge bias. Under steady state conditions the displacement of a piezoelectric stack actuator was seen to increase linearly with the voltage input. Design and implementation of a charge feedback controller were presented by Yi and Viellette [1]. As opposed to the non-inverting differential amplifier proposed by Comstock [34], this controller uses an inverting operational amplifier and also includes a high voltage amplifier in the feedback loop to drive a piezoelectric stack actuator. The controller is successful in linearising the response of the actuator. The inverting operational amplifier incorporates resistors to provide DC feedback path which eliminates the requirement of an initialization circuit suggested by Main et al. [35]. However, saturation of the inverting operational amplifier limits the linear operating range of this charge feedback controller. Also, the DC feedback causes the charge feedback controller to act like a voltage source under steady state operating condition. Thus, hysteresis is not eliminated under steady state operating condition. Design of a grounded load charge drive and its comparison with a voltage amplifier to drive a scanning probe microscope position stage has been presented by Fleming and Leang [36]. It has been shown that the use of a charge drive can reduce the error due to hysteresis to less than 1% of the scan range of the position stage. When the position stage was driven using a voltage amplifier, the error due to hysteresis was found to be 7.2% of the scan range. The basic circuit diagram of the grounded load charge drive [37] is shown in Fig. 6. A piezoelectric actuator driven by the grounded load charge drive is modelled using a load capacitor C L and a voltage source V p. A high gain feedback loop is used to compare the reference voltage, V ref, to the voltage V Z across a sensing capacitor, C S. The charge acting 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 negligible 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 that the gain of the grounded load charge drive is C S (C)/V at higher frequencies. However, the resistance R S and R L are bound to introduce error in the charge drive, at low frequencies or in static case. This error can be overcome by letting the ratio of the resistance be equal to the ratio of the capacitance [36]. R s = C s (2) R L C L By precisely tuning the ratio in (2), the grounded load charge amplifier will have no low/high frequency dynamics and thus have a constant sensing gain, C S, in static as well as dynamic operations. As mentioned previously, the use of a charge input to drive a piezoelectric actuator can provide a linear actuator response with substantial 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 the displacement of a piezoelectric actuator [38] and hence open loop control techniques can then be implemented [39]. It is worth mentioning that the sensing capacitor in the charge amplifier circuit is similar to a sensor which measures the charge on the actuator thereby making the charge drive, a feedback approach. However, the charge drive has some disadvantages. A voltage drop across a charge circuit reduces the voltage applied to a piezoelectric actuator which in turn reduces the elongation [36,40]. A higher supply voltage is therefore required to elongate the actuator to its original value. The complexity of a charge control circuit leads to difficulty in the implementation of the charge driven approach [41 44]. Depending on the capacitance value of a piezoelectric actuator, the gain 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]. The use of a charge/current amplifier can thus be expensive as compared to the more commonly used voltage amplifiers [46]. To summarize, though charge control of a PZT actuator circumvents the non-linear behaviour of piezoelectric ceramic and enables the use of linear control techniques, the simplicity of such linear control is bought at the expense of the increased electronic complexity required for effective charge control [10] Capacitor insertion method A voltage driven piezoelectric actuator exhibits considerable hysteresis and creep [2,10]. When driven using a charge input, the amount of hysteresis and creep exhibited by the actuator is reduced [32,33]. However, a charge amplifier needs to be specially designed and then calibrated depending on the capacitance value of the actuator. This drawback, including others (refer to Section 3.2), makes the charge driving method rather complicated to implement. In 1988, Kaizuka and Siu [41] proposed a simple way of reducing the amount of hysteresis and creep exhibited by a voltage driven piezoelectric actuator. This method, called the capacitor insertion method, involves insertion of a capacitor in series with a piezoelectric actuator [41,48]. The voltage across the inserted capacitor is now a direct measure of the amount of charge driving the actuator. At this point it is worth to reiterate that a piezoelectric actuator, similar to a non-linear capacitor, changes its capacitance even at constant voltage input. The change in the capacitance leads to a change in the amount of charge on the actuator which in turn leads to hysteresis and creep. The inserted capacitor acts as a charge regulator which reduces the sensitivity of the ratio of charge on the actuator, Q actuator to the change in the capacitance of the actuator, C actuator [41]. The reduction in sensitivity 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-

5 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx 5 Fig. 7. Actuator driven using voltage input [41]. Fig. 9. Piezoelectric stack actuator. Fig. 8. Circuit diagram for capacitor insertion method [41]. ator is given by V actuator. A load resistor is connected in series with the actuator. From Fig. 7, the charge on the actuator and the sensitivity of the ratio of charge on the actuator to the change in the capacitance of the actuator can be given by (3). Q actuator = C actuator V actuator dq actuator (3) = V actuator dc actuator In Fig. 8, a capacitor, C capacitor is inserted in series with the actuator. Let C total be the capacitance of the complete circuit. Assuming the total charge in the circuit to be equal to the charge on the actuator, (3) can be re-written as (4): Q actuator = C total V total ( ) dq actuator C 2 capacitor (4) = dc actuator ( ) 2 V total Cactuator + C capacitor Normalisation between the experiments in Figs. 7 and 8 require the applied voltage on the actuator to be the same. Therefore, the total voltage, V total acting on the circuit is calculated using (5). ( ) (Cactutaor + C capacitor ) V total = V actuator (5) C capacitor 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 been reduced by the insertion of capacitor in series with the actuator. The amount of reduction in the sensitivity, given by in (7), shows that lower the value of C capacitor, lower is the value of i.e. more is the reduction in the sensitivity and hence more is the reduction in hysteresis and creep. In other words the hysteresis and creep, in a piezoelectric actuator which is driven using the capacitor insertion Fig. 10. Experimental setup to measure hysteresis and creep in piezoelectric stack actuator. method, will be reduced by a factor of. C capacitor = (7) C actuator + C capacitor Experiments were conducted, with and without insertion of a capacitor, by Kaizuka and Siu [41] to measure the amount of hysteresis present in a piezoelectric stack actuator. The actuator was driven using a sine wave. The measurements were taken at voltages 25%, 50% and 75% into the swing, the results of which are summarised in Table 1. It can be seen that the amount of hysteresis reduces with the reduction in the value for. Thus, the highest reduction in hysteresis is achieved when the value for is the lowest. For the same stack actuator, experiments were conducted by Kaizuka and Siu [41] using a step input. The capacitance values (C capacitor ) for the inserted capacitor were similar to the ones in Table 1. The creep effect was seen to diminish with a reduction in the value of. The capacitor insertion method has been implemented in tracking control of a nano-measuring machine [47,48]. The results from this implementation show that a piezoelectric actuator s characteristics become more linear with the use of an inserted capacitor with smaller capacitance value. Other than the above two papers there seems to little published experimentation using the capacitor insertion method. The reason behind this not being a popular method is the requirement of higher voltage input. When a 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 swing Capacitor not inserted 217 nm 282 nm 218 nm 464 nf nf 191 nm 251 nm 195 nm nf nf 103 nm 133 nm 108 nm nf nf 49 nm 56 nm 53 nm nf nf 34 nm 40 nm 38 nm

6 6 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx Fig. 11. Experimental setup for voltage charge driven actuator. input voltage gets divided between the inserted capacitor and the actuator [41,48] consequently reducing the voltage across the actuator as given by (8). V actuator = V total (8) This reduces the elongation of the actuator. For the actuator to achieve the same elongation it is therefore necessary to supply a higher voltage to the circuit. Although more reduction in hysteresis is possible with a smaller value of it also means that more voltage (V total ) would need to be supplied to the capacitor insertion circuit to make sure that the actuator elongates to its original value. 4. Experimental setup Experiments were conducted to measure the amount of hysteresis and creep in a piezoelectric stack actuator which, as shown in Fig. 9, is built using multiple wafers wired in parallel and placed mechanically in series [1]. Each wafer is made up of the PZT ceramic material which is sandwiched between two electrodes [2]. The type of piezoelectric stack actuator used in the experiments was a Tokin model AE0505D16 piezoelectric stack actuator which has a maximum displacement of 17 m, resonance frequency of 69 khz, capacitance of 1.4 F ± 20%, desirable operating voltage of 100 V and operating temperature range of 25 to 85 C. The experimental setup to measure the amount of hysteresis and creep exhibited by the piezoelectric stack actuator is shown in Fig. 10. A block diagram representation of the experimental setup is presented in Fig. 11. A dspace ds1104 controller board, compatible with MATLAB and Simulink, was used to interface the experimental setup to a desktop computer. A Simulink model, driven from the dspace control desk, was built to generate an input signal and to store the measured output. The input signal, through the onboard digital to analog converter (DAC) channel of the dspace platform, was used to drive a low voltage piezo (LVPZ) power amplifier module. The LVPZ power amplifier module (Model P ) which is manufactured by Physik Instruments (PI) has an output voltage range of 20 to V. Since the gain of the LVPZ power amplifier stays constant, it does not require any off-line calibration. As shown in Fig. 10, the output of the LVPZ power amplifier was connected to the actuator through a capacitor insertion box. The capacitor insertion box holds a set of 10 capacitors with different capacitance values. The actuator was mounted inside a one degree of freedom (DOF) translation stage. This assures that the actuator stays preloaded. Measurement Group EA TG-350 strain gauges were used to measure the displacement of the actuator. The strain gauges were assembled in full-bridge fashion to compensate for the drift caused by change in temperature while experiments were conducted. The measured displacement of the actuator was amplified by a strain gauge amplifier (built at electronics and instrumentation lab in the School of Mechanical Engineering at the University of Adelaide) and then fed back to the desktop computer through the onboard analog to digital converter (ADC) channel of the dspace platform. When using the capacitor insertion method to drive the actuator, a specific capacitor was put in series with the actuator by rotating the circular dial located on the front end of the capacitor insertion box. When using the voltage method to drive the actuator, the circular dial was positioned to direct. This way no capacitor was connected in series with the actuator. The actuator was simply driven using a voltage supplied by the LVPZ amplifier. A similar setup (Fig. 10) was used to drive the actuator using the charge input method. The only difference being that the LVPZ amplifier was replaced with the grounded load charge amplifier (Section 3.2). Also, the capacitor insertion box was disconnected from the circuit. The actuator was driven directly using a charge input. Depending on the capacitance value of the actuator, the DC gain of the charge amplifier had to be tuned. Therefore, the charge amplifier required off-line calibration before it was used. Fig. 12. IIysteresis in a voltage driven actuator for a 10 Hz sine wave input.

7 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx 7 Table 2 Results for the capacitor insertion method for the first experiment. Value of capacitor in F Measured (predicted) maximum voltage across actuator in V Measured (predicted) hysteresis in m Displacement of actuator in m (50) (0.3818) (43.75) (2705) (35.71) (0.1558) 2.4 Fig. 13. Hysgteresis in charge driven actuator for a 10 Hz sine wave input. Fig. 14. Hysteresis in voltage driven actuator with 0.7 F capacitor in series for a 10 Hz sine wave input. 5. Results Experiments were conducted by driving the Tokin model AE0505D16 piezoelectric stack actuator using voltage, charge and capacitor insertion methods. Results from the experiments are presented in this section. In the first experiment the actuator was driven using a 10 Hz, V, sine wave input which was selected to measure the amount of hysteresis exhibited by the actuator under dynamic operating conditions. When driven using the LVPZ amplifier, a large amount (2 m) of hysteresis was seen to exist (Fig. 12). Although a linear response (Fig. 13) was observed when the actuator was driven using the grounded load charge amplifier, a reduction in the operating range of the actuator was observed as well. The reduction in operating range of the actuator was due to an approximately 25 V voltage drop across the sensing capacitor, C S, of the grounded load charge amplifier which reduced the actual voltage driving the actuator. When driven with V sine wave output from the grounded load charge amplifier the maximum elongation of the actuator was measured and found to be similar to the value depicted in Fig. 12. Reduction in the amount of hysteresis (Fig. 14), but also in the operating range, was observed when the actuator with a 0.7 F capacitor in series with it was driven using the LVPZ amplifier. When a 0.7 F capacitor was inserted in series with the actuator, the measured voltage across the actuator was found to be approximately 33 V. Table 2 summarises the results for the capacitor insertion method for the first experiment. The predicted hysteresis in Table 2 was determined by multiplying the measured hysteresis from Fig. 12 with the value for. Itcan be inferred that the voltage across the actuator approximately follows the relationship presented in (8) and a reduction in the amount of hysteresis occurs with a reduction in the value for. Fig. 15. Hysteresis and creep in a voltage driven actuator for a V stair case input.

8 8 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx Fig. 16. Hysteresis and creep in charge driven actuator for a V stair case input. Table 3 Experimentally measured hysteresis and creep using capacitor insertion method. Value of capacitor in F Displacement of actuator in m Measured (predicted) hysteresis in m Measured (predicted) creep in m (0.2025) 0.02(0.0184) (0.1444) (0.0131) (0.0803) 0.01 (0.0073) Also, the measured hysteresis does seem to approximately follow its predicted value. In the second experiment the actuator was driven using a V stair case input. A stair case was selected as an input to determine the behaviour of the actuator under quasi-static operating conditions. The displacement response for the LVPZ amplifier driven actuator, to the stair case input, is presented in Fig. 15. Substantial amount of hysteresis and creep can be seen in the voltage driven actuator. In Fig. 16, the displacement of the actuator driven using the grounded load charge amplifier is plotted. Although reduced when compared with Fig. 15, hysteresis does seem to exist in the charge driven actuator in this static case. The existence of hysteresis could be due to the ineffective working of the charge amplifier in static case. It might also be due to the error in the calibration of the DC gain of the charge amplifier. A considerable amount of creep does seem to exist in the charge driven actuator and its elimination is not possible due to fast discharging of the Fig. 17. Hysteresis and creep in a voltage driven actuator with 0.7 F capacitor in series for a V stair case input. sensing capacitor, C S, of the charge amplifier. The sensing capacitor would need to discharge very slowly in order to minimize creep. However, this might not be possible physically. No hysteresis and a very minimal amount of creep were observed (Fig. 17) when the actuator, with a 0.7 F capacitor in series, was driven using the LVPZ amplifier. However, the maximum displacement of the actuator was only 2.25 m. Table 3 summarises the results for the capacitor insertion method for the second experiment. The predicted hysteresis in Table 2 was determined by multiplying the measured hysteresis from Fig. 15 with the value for. From Tables 2 and 3 it can be reiterated that Although more reduction in hysteresis and creep is possible with a smaller value of it also means that more voltage (V total ) would need to be supplied to the capacitor insertion circuit to make sure that the actuator elongates to its original value. 6. Conclusion A review of the voltage, charge and capacitor insertion methods for driving piezoelectric actuators has been presented in this paper. Advantages and disadvantages of each method have been highlighted. Based on the review and the results obtained from the experiments performed, it can be concluded that: Although the implementation of a voltage amplifier to drive a piezoelectric actuator is the easiest of the methods, it leads to large amount of hysteresis and creep. Accurate modelling of hysteresis and creep followed by the design of a robust controller would be required if a piezoelectric actuator, driven using a voltage amplifier, was to be implemented in precise positioning applications. Using a charge amplifier leads to approximate linearisation of a piezoelectric actuator s response. Since the sensing capacitor of the charge amplifier discharges quickly, a reduction in creep might not be possible while using a charge amplifier to drive a piezoelectric actuator. A charge amplifier is not readily available and would thus need to be designed. Moreover, to assure a reduction in hysteresis in static operations, precise calibration of the charge amplifier is required. As compared to a voltage amplifier, a charge amplifier is therefore complicated to implement.

9 J. Minase et al. / Precision Engineering xxx (2010) xxx xxx 9 The easiest and the most economic way to reduce hysteresis and creep in a voltage driven actuator is to use the capacitor insertion method. Depending on the size of the inserted capacitor, this method leads to elimination of hysteresis in static and dynamic operations. The amount of creep in a piezoelectric actuator can be nearly eliminated as well. However, a large reduction in the operating range of a piezoelectric actuator occurs. This drawback can be overcome by either using higher voltage supplies or bigger size stack actuators that would elongate more for similar voltages. Acknowledgements The authors would like to thank Dr. Andrew Fleming from the University of Newcastle for providing the charge amplifier hardware to conduct experiments at the University of Adelaide. 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