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1 American Control Conference (ACC) Washington, DC, USA, June -, UHFLVLRQ&KDUJH'ULYHZLWK/RZ)UHTXHQF\ROWDJH)HHGEDFN IRU/LQHDUL]DWLRQRILH]RHOHFWULF+\VWHUHVLV Andrew J. Fleming, Member, IEEE Abstract² A new charge drive circuit is proposed that utilizes a low frequency voltage feedback loop to linearize piezoelectric hysteresis down. Hz. This approach eliminates many of the present difficulties and allows extremely low transition frequencies without a long transient response. Experimental results demonstrate that the proposed charge amplifier can effectively reduce piezoelectric hysteresis and creep to less than.% at scan-rates of Hz, Hz, and. Hz. I. INTRODUCTION Piezoelectric actuators are utilized in a wide range of industrial, scientific and commercial applications including scanning probe microscope positioning systems [, ], fuel injection valves [], and laser beam manipulation []. Although piezoelectric actuators have a number of desirable characteristics, a major disadvantage is the hysteresis exhibited at high electric fields [, ]. To avoid positioning errors, many applications require some form of compensation to account for non-linearity. The most popular technique for compensation of hysteresis is sensor-based feedback control using integral or Proportional-Integral (PI) control [, ]. Such controllers are simple but are disadvantaged by cost, complexity, limited bandwidth, and sensor-induced noise []. In some applications the requirement for a sensor can be relaxed by self-sensing the position from the actuator current [, ]. Alternatively, feedforward approaches use a model to invert nonlinearity [, ]. A survey of feedforward and feedback compensation techniques can be found in references [] and []. An alternative technique for reducing hysteresis is to drive the actuator with charge or current rather than voltage [, ]. Simply by regulating the current or charge, the hysteresis non-linearity can be reduced from approximately % of the range to % [,, ]. This technique was originally reported by Comstock in []. Following this work, a number of variations and improvements *This work was supported in part by the Australian Research Council Discovery Project DP. PATENT PENDING. A. J. Fleming is with the School of Electrical Engineering and Computer Science, University of Newcastle, Callaghan, NSW, Australia. (phone:+---; andrew.fleming@newcastle.edu.au). appeared. For example: resistive feedback to compensate for drift []; grounded loads []; switched capacitor implementation []; and dynamics compensation []. Although the circuit topology of a charge or current amplifier is much the same as a simple voltage amplifier, the uncontrolled nature of the output voltage typically results in the load capacitor being charged. To avoid this problem, a resistive feedback network is commonly employed to stabilize the low frequency behavior []. Unfortunately, this introduces a number for problems. ) The voltage gain is inversely proportional to the load capacitance; ) the DC gain must be tuned to match the AC gain, which can be an extremely slow process; ) the transition frequency is fixed by the component values, and ) transition frequencies below Hz are not practical due to the extremely long transient response. Due to these practical difficulties, the potential benefits of driving a piezoelectric actuator with charge have been largely ignored in commercial applications. To overcome these difficulties, this article proposes a new method for DC stabilization that utilizes a controlled current source. This method dramatically improves the ease-of-use of a charge drive and has the potential to directly replace a voltage amplifier in many applications. In the following section, present charge drive circuits are discussed, followed by a description of the active DC stabilization technique. The performance of the active DC stabilization technique is then examined experimentally by driving a standard piezoelectric stack actuator. The key performance characteristics and advantages of active DC stabilization are summarized in the conclusions. II. EXISTING CHARGE DRIVE CIRCUITS The schematic diagram of a floating-load charge drive circuit is shown in Figure. The piezoelectric load, modeled as a capacitor % Å and voltage source R ã, is shaded in gray. The high-gain feedback loop works to equate the applied reference voltage Üá to the voltage across a sensing capacitor % æ. Neglecting the resistances Å and æ, the charge M is MLR Üá % æ () That is, the gain is % æ Coulombs/V, which implies an inputto-output voltage gain of % æ % Å V/V. ----/$. AACC

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4 top to provide a suitable sensor target. The capacitive sensor is a Microsense active probe with a sensitivity of. um/v, a range of um, and a stand-off distance of um. error was.%. Furthermore, the maximum nonrepeatability of the charge driven actuator was nm (.%) versus nm (.%) for a voltage amplifier. (a) Hz Voltage Driven (b) Hz Charge Driven Figure. A horizontally mounted piezoelectric actuator facing a capacitive displacement sensor Since the load capacitance is. uf, a charge gain of % æ Lstr uc/v was selected. This provides a maximum voltage gain of.. A major benefit of the proposed charge drive is that extremely low transition frequencies are possible. To achieve a transition frequency of mhz, a current gain of. ua/v was required. With present techniques, such a low transition frequency would result in a settling time of more than seconds, which is not practical. The AC gain of the amplifier was calibrated by applying a. V (peak) sine-wave with an offset of. V. The charge gain G ä was adjusted until the peak amplitude of the load voltage was equal to the DC value. To evaluate the linearity of the charge driven piezoelectric actuator, a V triangular scanning pattern was applied at Hz, Hz, and. Hz. The resulting actuator displacement when driven by voltage and charge is plotted in Figure. In this plot, the input signal was normalized to allow a straight-forward linearity comparison between the input and displacement. With a Hz input frequency, the maximum deviation from linear is +/-.% and the RMS error is.%. The maximum non-repeatability in the charge driven case is nm at Hz (.%) versus nm (.%) with a voltage amplifier. Although the actuator is not perfectly linearized, the remaining non-linearity is primarily static. That is, the residual non-linearity could be inverted by a polynomial, spline, or look-up table. When the scan speed is reduced to Hz, there is no significant change in performance. At Hz, the maximum deviation from linear was +/-.% and the RMS error was.%. The maximum non-repeatability in the charge driven case was nm (.%) versus nm (.%) for the voltage driven case. With present charge amplifier designs, the lowest practical frequency of operation is approximately Hz. However, due to the low-frequency stabilization provided by the proposed design, operation at. Hz and below is feasible without loss of performance. At. Hz, the maximum deviation from linear was +/-.% and the RMS..... (c) Hz Voltage Driven.... (e). Hz Voltage Driven..... (d) Hz Charge Driven.... (f). Hz Charge Driven Figure. The displacement resulting from a V triangular scan pattern at Hz, Hz, and. Hz Due to the low frequency of the. Hz scan, a significant amount of creep is also exhibited by the voltage driven actuator. The full-scale displacement at Hz is. um, while at. Hz the displacement increases to. um, which is an increase of.%. When the actuator is driven by charge, the full-scale displacement only increases.% from. um to. um when the frequency is changed from Hz to. Hz. The maximum repeatability error.% exhibited by the charge driven actuator may eliminate the need for closedloop control in applications that require accurate periodic motion, such as scanning probe microscopy [, ].

5 VI. CONCLUSIONS Although charge drives can significantly reduce piezoelectric non-linearity, they are rarely used due to: the limited low-frequency performance, the dependence of voltage gain on the load capacitance, and the requirement for time-consuming tuning procedures. In contrast to present designs that use resistive feedback, the proposed charge amplifier uses a controlled current source with voltage feedback to stabilize the low frequency behavior. This approach eliminates many of the present difficulties and allows extremely low transition frequencies without a long transient response. Experimental results demonstrate that the proposed charge amplifier can effectively reduce piezoelectric hysteresis and creep at Hz, Hz, and. Hz in a V piezoelectric stack actuator. At all speeds, the maximum difference between the forward and backward scan paths is less than.% of the scan range. This is approximately oneninth of the error experienced when using a voltage amplifier. In many applications such as scanning probe microscopy, a scan error of.% may reduce or eliminate the necessity for closed-loop control. Hence, the use of a charge amplifier could significantly reduce the size, complexity, and cost of piezoelectric positioning systems. References [] S. M. Salapaka and M. DODSDND ³FDQQLQJ SUREH PLFURVFRS\ IEEE Control Systems Magazine, vol., no., pp. ±, April. [] J. A. Butterworth, L. Y. Pao, and D. <$EUDPRYLWFK³$ comparison RIFRQWURODUFKLWHFWXUHVIRUDWRPLFIRUFHPLFURVFRSHV Asian Journal of Control, vol., no., pp. ±, March. [] D. Mehlfeldt, H. Weckenmann, and G. W KU³RGHOLQJRI SLH]RHOHFWULFDOO\DFWXDWHGIXHOLQMHFWRUV Mechatronics, vol., no. ±, pp. ±,. [] S. Z. S. Hassen, M. Heurs, E. H. Huntington, I. R. Petersen, and M. -DPHV³)UHTXHQF\ORFNLQJRIDQRSWLFDOFDYLW\XVLQJ linear±txdgudwlfjdxvvldqlqwhjudofrqwuro Journal of Physics B: Atomic, Molecular and Optical Physics, vol., no., p.,. [] S. H. Chang, C. K. Tseng, and H. & &KLHQ ³$Q XOWUD- SUHFLVLRQ [\ SLH]R-PLFURSRVLWLRQHU L GHVLJQ DQG DQDO\VLV Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol., no., pp. ±, July. [] H. Jiang, H. Ji, J. Qiu, and Y. &KHQ³$PRGLILHGSUDQGWOishlinskii model for modeling asymmetric hysteresis of SLH]RHOHFWULFDFWXDWRUV Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol., no., pp. ±,. [] P. Ge and M. -RXDQHK³UDFNLQJFRQWURORIDSLH]RFHUDPLF DFWXDWRU IEEE Transactions on Control Systems Technology, vol., no., pp. ±, May. [] A. J. Fleming, S. S. Aphale, and S. O. RKHLPDQL³$QHZ method for robust damping and tracking control of scanning probe PLFURVFRSH SRVLWLRQLQJ VWDJHV IEEE Transactions on Nanotechnology, vol., no., pp. ±, September. [] A. J. Fleming and K../HDQJ³,QWHJUDWHGVWUDLQDQGIRUFH feedback for high performance control RISLH]RHOHFWULFDFWXDWRUV Sensors and Actuators A, vol., no. -, pp. ±, June. [] A. Badel, J. Qiu, and T. DNDQR³HOI-sensing force control RI D SLH]RHOHFWULF DFWXDWRU Ultrasonics, Ferroelectrics and Frequency Control, IEEE Transactions on, vol., no., pp. ±, December. [] A. J. Fleming and S. O. RKHLPDQL³&RQWURORULHQWHG synthesis of high performance piezoelectric shunt impedances for VWUXFWXUDO YLEUDWLRQ FRQWURO IEEE Transactions on Control Systems Technology, vol., no., pp. ±, January. [] A. A. Eielsen, J. T. Gravdahl, and K. <HWWHUVHQ³$GDSWLYH feed-iruzdug K\VWHUHVLV FRPSHQVDWLRQ IRUSLH]RHOHFWULF DFWXDWRUV Review of Scientific Instruments, vol., no., p.,. [] Y. Wu and Q. =RX³,WHUDWLYHFRQWURODSSURDFKWRFRPSHQVDWH IRUERWKWKHK\VWHUHVLVDQGWKHG\QDPLFVHIIHFWVRISLH]RDFWXDWRUV IEEE Transactions on Control Systems Technology, vol., no., pp. ±, September. [] K. K. Leang, Q. Zou, and S. 'HYDVLD³)HHGIRUZDUGFRQWURO RISLH]RDFWXDWRUVLQDWRPLFIRUFH PLFURVFRSHV\VWHPV IEEE Control Systems, vol., no., pp. ±, February. [] S. Devasia, E. Eleftheriou, and S. O. RKHLPDQL ³$ VXUYH\RIFRQWUROLVVXHVLQQDQRSRVLWLRQLQJ IEEE Transactions on Control Systems Technology, vol., no., pp. ±, September. [] C. V. Newcomb and I. )OLQQ³,PSURYLQJWKHOLQHDULW\RI SLH]RHOHFWULFFHUDPLFDFWXDWRUV IEE Electronics Letters, vol., no., pp. ±, May. [] R. &RPVWRFN³&KDUJHFRQWURORISLH]RHOHFWULFDFWXDWRUVWR UHGXFHK\VWHUHVLVHIIHFWV Japan Journal of Applied Physics, part - Letters,. [] K. A. Yi and R. -HLOOHWWH³$FKDUJHFRQWUROOHUIRUOLQHDU operation of a piezoelectric stack actuawru IEEE Transactions on Control Systems Technology, vol., no., pp. ±, July. [] A. J. Fleming and S. O. RKHLPDQL³HQVRUOHVVYLEUDWLRQ suppression and scan compensation for piezoelectric tube QDQRSRVLWLRQHUV IEEE Transactions on Control Systems Technology, vol., no., pp. ±, January. [] A. J. Fleming and K../HDQJ³&KDUJHGULYHVIRUVFDQQLQJ SUREHPLFURVFRSHSRVLWLRQLQJVWDJHV Ultramicroscopy, vol., no., pp. ±, November. [] L. Huang, Y. T. Ma, Z. H. Feng, and F..RQJ³ZLWFKHG capacitor charge pump reduces hysteresis of piezoelectric actuators RYHUDODUJHIUHTXHQF\UDQJH Review of Scientific Instruments, vol., no., p.,. [] G. M. Clayton, S. Tien, S. Devasia, A. J. Fleming, and S. O. RKHLPDQL³,QYHUVH-feedforward of charge controlled SLH]RSRVLWLRQHUV Mechatronics, vol., pp. ±, June. [] A. -)OHPLQJ³XDQWLWDWLYHWRSRJUDSKLHVE\FKDUJH OLQHDUL]DWLRQ RI WKH YHUWLFDO DFWXDWRU Review of Scientific Instruments, vol., no., pp. (±), October.