A Resonant Driver for a Piezoelectric Motor with Single Transistor Direction Switches

Transcription

1 1 A Resoat Driver for a Piezoelectric Motor with Sigle Trasistor Directio Switches Sa Be-Yaakov 1*, Evgey Rozaov 1, Toer Wassera, Tzachi Rafaeli, Lior Shiv ad Gregory Ivesky 1 1 Power Electroics Laboratory, Departet of Electrical ad oputer Egieerig Be-Gurio Uiversity of the Negev, P. O. Box 53, Beer-Sheva 8105, ISRAEL. Tel: ; Fax: ; Eail: sby@bguee.ee.bgu.ac.il Naootio Ltd., P. O. Box 3, Yokea 09, ISRAEL. Tel: ; Fax: ABSTRAT A resoat driver for a Piezoelectric Motor (PZM) is preseted, aalyzed ad tested experietally. Followig a short descriptio of the liear PZM applied i this study, the paper covers the aalytical relatioships of the buck drive push-pull parallel resoat iverter stage that icludes a ovel sigle trasistor directio switches. It is show that the proposed topology is copatible with the drive requireets of the PZM powered fro a low voltage (). It is also deostrated that, ulike siple resoat coverters, the proposed topology is relatively isesitive to the resoat copoet values ad that it ca tolerate added capacitace as itroduced whe coectig a PZM to the driver via a log cable. 1. INTRODUTION Applicatio of piezoelectric (PZ) otors [1, ] is liited, aog other thigs, by the lack of iexpesive drivers that will atch the perforace ad low cost of the PZ otors (PZM). I this paper we describe a ewly developed PZ otor resoat driver that has ay advatages over the preset solutios. First we describe the liear PZM for which the driver was developed, preset its siplified electrical equivalet circuit ad give the drive requireet. The classical approach of a series resoat iverter is the covered, poitig to its liitatios. We preset the proposed Push-Pull Resoat Iverter (PPRI) ad derive its basic atheatical operatioal relatioships. We the describe a ewly developed PZ otor resoat driver ad directio switches that are sipler ad hece less costly tha previous desigs. Fially, we show siulatio ad experietal results ad discuss the erits ad drawback of the PPRI ad ovel sigle trasistor directio switches as copared to the classical series resoat iverter ad A switch approach.. THE LINEAR PIEZOELETRI MOTOR The basic operatio of the Naootio Ltd. (Israel) PZM higes o the flexure ad liear expasio of a PZ slab (Fig. 1). The PZ eleet has three electrodes, two (A B) are deposited o oe surface (Fig. 1) while the third oe () is deposited o the botto surface of the PZ eleet. Electrodes A ad B are of two parts. Each part is placed diagoally o the upper PZ surface (Fig. 1). Whe a electrical excitatio is iposed betwee A or B electrodes ad electrode, the eleet will flex ad expad ad cosequetly the ste attached to oe ed of the PZ eleet, will ove i the X ad Y diesios (Fig. 1). Hece, whe the PZ eleet of Fig. 1 is placed agaist a flat surface as show i Fig., it will exert echaical force o the surface ad ca ove the platfor if the PZ is echaically achored. Excitatio of the A- electrodes will cause oveet to oe directio while excitatio of the B- electrodes will cause oveet i the other directio. For rotary otio the PZM is placed agaist the circuferece of a wheel. Fro a electrical poit of view, the PZM ca be represeted to a first approxiatio by a resoat etwork (L s, s, R s ) i parallel with the electrical capacitace p of the electrodes (Fig. 3a). At the fixed operatig frequecy, the equivalet circuit ca be siplified to a resistor ( R ) i parallel with a capacitor ( ) (Fig. 3b). This approxiatio is valid aroud the operatig frequecy. The required otor excitatio for full power of the PZ eleet is 50rs at about 0kHz. Beig resoat eleet [1, ] oly the relevat resoat frequecies will develop force. Hece, the ideal drive for the PZM is a siusoidal wavefor sice the o relevat haroics are ieffective ad oly icrease the circulatig reactive curret. Noetheless soe distortio (30-50%) ca be tolerated * orrespodig author

2 3LH]RHOHFWULF HOHPHW (OHFWURGH S 5 (OHFUWRGH % 9 D ; < (OHFWURGH 9 Fig. 1. Electrode cofiguratio i a piezoelectric eleet of a PZM operatig i logitudial plus flexural ode (Naootio Ltd., Israel) P E Fig. 3. Equivalet circuit of a piezoelectic eleet. (a) geeral circuit for oe vibratio ode. (b) siplifies equivalet circuit at PZM operatig frequecy. 5(11 1(:5. %( LHDU OLGH 30 9 FEO 3LH]RHOHFWULF PRWRU (a) 9DF 9 FEO P 5 P Fig.. Method used to geerate a liear otio by the piezoelectric eleet show i Fig. 1. without ill effect. ovetioal drivers for a PZM [3] are orally based o a resoat etwork. I such a cofiguratio the PZM is coected parallel to the capacitor of a series L-circuit which is fed fro the ac etwork (Fig. ) or a square wave drive. To achieve a siusoidal wavefor ad to obtai a voltage gai, the L-circuit is orally operated ear resoace. I ay evet, cosiderig the high of practical PZM, the power of the otor will be aily govered by the first haroic of the drive voltage ( ( 1 ) ). I practical cases the cable coectig the driver to the PZM is of variable legth ad therefore its capacitace cbl (Fig. ) ay have differet values. As a result, the total capacitace + cbl + is ot costat, a fact that ight deteriorate the perforace of the circuit due to the oveet of the resoat frequecy. I a earlier study [] we derived the depedece of s o f f ro for 01. i the covetioal L (b) Fig.. L type PZM driver. (a) syste cofiguratio. (b) equivalet circuit. ()pk 1 ()pk 1 Relative first haroic peak, R L Relative frequecy, fro Fig. 5. Output voltage sesitivity of the L driver to chages i total capacitace as a fuctio of operatig frequecy. Y axis relative chage i voltage aplitude due to a relative chage of 0.1 i total circuit capacitace.

3 3 driver (Fig. 5), where f ro is the ideal resoat frequecy of the L circuit. It is clear that the relative chage ca be uch higher tha, especially at high values of the quality factor. However, high is eeded for good filterig of the square wave orally used as drive ad to achieve the voltage gai eeded i practical circuits. It is thus clear that the high sesitivity of the output voltage to capacitace chages akes the covetioal L driver useful oly whe the total capacitaces is costat. However, i ay practical cases capacitace chages are expected due to ay factors: variable cable legth, teperature rise of the PZ eleet which icreases its capacitace, practical spread of copoets value etc. I these situatios, the covetioal L driver is clearly disadvatageous. 3. THE PUSH PULL PARALLEL RESONANT INERTER (PPRI) The proposed resoat driver is built aroud a curret fed PPRI [5], [] ad a frot ed Buck coverter (Fig. ). The fuctio of the Buck coverter is to cotrol the average voltage fed to the PPRI ad hece the voltage across the otor. The PPRI is ru at a costat frequecy ad the MOSFET switches 1 ad are drive at 50% duty cycle. The resoat circuit coprises a iductor L, a capacitor, capacitace of the cable cbl, capacitace ad resistace R of the otor (Fig. ). I practice, the agetizatio iductace of the trasforer T serves as the resoat iductor L. The operatio of the PPRI ca be described by the siplified circuit diagras of Fig.. The iput iductor L i (Fig. ) is replaced here by a curret source I i uder the assuptio: L Li >> (1) where is the trasforer turs ratio., cbl,, L ad R are capacitaces, iductace ad resistace reflected to the priary of the trasforer: () ; cbl cbl (3) () ; L L (5) ; R R () The drive period T s ust be loger tha the resoat period T r of the real L R circuit: L Ts > Tr () 1 1 where is the quality factor : R L Each half cycle of the PPRI coprises two operatioal odes: a resoat ode whe oe trasistor is coductig ad both atiparallel diodes are ot coductig (Fig. b) ad a boost ode whe the resoat tak is shorted through the coductig trasistor ad the diode coected atiparallel to the other trasistor (Fig. c). The duratio of the boost ode is depedet o the differece betwee the drive period Ts ad the resoat period Tr. As a result of these two odes, the voltage across the otor v will be early a siewave with soe dead tie betwee the two half cycles (Fig. 8). (8) %( 30 L FEO 9 *DWH GULYHU *DWH GULYHU Fig.. Basic cofiguratio of proposed PPRI driver. S 1 S cotrol directio of otio (see Figs. 1 ).

4 9EXFN 9EXFN 9EXFN,L,L,L (a) (b) (c) P FEO P FEO P FEO Fig.. Equivalet circuit of the PPRI driver (Fig. ) with the secodary reflected to priary. (a) geeral circuit. (b) resoat ode. ( c ) boost ode. The dead tie ca be reduced by atchig the resoat frequecy fr 1 Tr to the drive frequecy 1 Ts. We assue that switches, diodes, trasforer, iductor ad capacitors are ideal ad that the wavefor of capacitors voltage (i. e. the voltage across the otor v) durig the resoat ode is a siusoidal: v pkcos( ) λ ϑ (9) where pk is the peak otor voltage, ϑ fr t is oralized tie i radias with zero value whe v pk, t is the tie ad λ is oralized duratio of the resoat ode: Tr λ (10) Ts fr The peak otor voltage pk is foud fro the coditio that the average voltage across the ideal iput iductor L i is zero. Therefore, the average voltage at poit A (Figs.,) Aav is equal to the average voltage across the diode D 3 of the buck coverter buck : Aav buck Dbucks (11) where D buck is the duty cycle of the buck coverter ad s is the supply voltage of the driver (Fig. ). O the other had, Aav ca be obtaied fro (9): λ 1 pk λ pk Aav cos( ϑ)dϑ λ λ (1) Fro (10)-(1) we fid: fr fr pk buck Dbucks (13) Applyig (9) the peak of the first haroic of the otor voltage ca was derived: λ ( pkcos( )cos )d λ ϑ ϑ ϑ λ 1 pk cos( λ ) (1) λ λ Takig ito accout (10) ad (13) we trasfor (1) ito: cos ( λ ) Dbucks 1 ( ) λ cos ( ) fr D bucks (15) 1 ( fr) Eqs.(15) ad () are used to derive the depedece of o (Fig. 5) : [ 1 ( ) ]cos[ 1+ ] fr fr 1 [ 1 ( ) ( 1+ )]cos( ) f f r r (1) This relatioship is show i Fig. 9 as a fuctio of f s fr λ λ 05. f r 05. f s SN Fig. 8. Output voltage wavefor (PZM voltage) of the PPRI driver. ϑ

5 5 ( 1 )pk ( 1 )pk Relative first haroic peak, Relative frequecy, Fig. 9. Output voltage sesitivity of PPRI driver to chages i total capacitace as a fuctio of operatig frequecy. Y axis relative chage i voltage aplitude of the first haroics due to a relative chage of 0.1 i total circuit capacitace. for 01.. It is see that i this case is very sall, uch lower tha. Hece the proposed PPRI topology is clearly advatageous i situatios that the capacitace is ot costat. That is a very iportat feature of the proposed driver. fro. THE DIRETIONAL SWITH The directio cotrol schee of Fig. calls for A bidirectioal switches. A popular realizatio of such switches is the back-to-back coected two MOSFET trasistors cofiguratio (Fig. 10). However, this topology ot oly requires two trasistors but calls for floatig gate drives. The solutio proposed here is the applicatio of oe trasistor per switch (Fig. 11). The operatio of these A switches ca be uderstood by cosiderig the relevat equivalet circuit of Fig. 1 whe oe trasistor is o (a) ad oe trasistor is o-coductig (b). Notice that b itself is ot affectig the operatio of the circuit i the off state, oly its diode Db. I this equivalet circuit t represets the total capacitace at the drai of b, i is the priary excitatio of the driver, while out represets the voltage of the ope PZM terials. The resoat circuit braches (LssRs)i eulate the electroechaical couplig of the PZM eleet. A uber of resoat braches are cosidered sice the PZM is subjected to ulti-ode vibratios. osiderig Fig. 1, it is evidet that the operatio of the sigle MOSFET trasistor i the preset applicatio is cotrolled by two attributes: (a) the bidirectioal coductio capability of the MOSFET whe o ad (b) the presece of the iheret atiparallel diode. The bidirectioal curret carryig capability allows A curret to flow through the excited terials (a-c). The diode does ot iterfere with the 9H[ a c b Fig. 10. Directio cotrol by two trasistors A switched. 9 DF a F D E b Fig. 11. Proposed sigle trasistor directio switches. 9DF 9L L a F R D W E b 9RXW Fig. 1. Equivalet circuit of a PZM cotrolled by the directio switches of Fig. 11 whe a is o ad b is off. blockig requireet for terial (b-c) sice terial (c) is i fact coected to a uloaded peak detector. Aside fro the iitial chargig curret, it will pass o curret except for the curret through t. Note that such a leakage curret copoet will also be preset i the classical two trasistor A switch cofiguratio (Fig. 10). The total A voltage fed to this peak detector is b i +out ad hece the expected voltage across the blockig trasistor will be the peak to peak voltage of this cobied voltage (b)pk-pk.

6 5. RESULTS AND DISUSSION A resoat driver was desiged for SP1 PZM (Naootio Ltd.). The paraeters of the PZM were as follows: drive frequecy 39.kHz, axiu drive voltage: 0rs, equivalet circuit of PZM: 1.3F, R3.5kΩ. Noial supply voltage to driver. The siulatio, aalytical ad experietal results of the PPRI driver were foud to be i excellet agreeet. Typical wavefors of the otor voltage are show i Fig. 13. The robustess of the topology agaist capacitace chages was tested by addig a capacitace across the PZM. The effect of this extra capacitace o the otors voltage, otor velocity (Fig. 1) ad otor force (Fig. 15) were foud to be rather sall eve whe a large capacitace is added (F, correspodig to a cable legth of 10). The experietal results verify the postulated operatio of the sigle trasistor A switch (Fig. 1). The peak voltage of a blockig switch-trasistor was foud to be about the sae as the priary excitatio peak voltage. The results of this study suggest that the proposed PPRI topology is uch less sesitive to capacitace variatios tha 9ROWDJH9 9ROWDJH9 LPH PLFURHF LPH PLFURHF Fig. 13. PZM voltage whe drive by proposed PPRI drive. (A) 3 cable (0. F). (B) 10 cable ( F). 9HORLW\ PPHF YHORFLW\ ILUW KDUPRLF 9UP DEOH FDSDFLWDFH ) Fig. 1. PZM velocity ad rs of first haroics whe drive by proposed PPRI driver, as a fuctio of added capacitace. % )LUW KDUPRLF UP 9 the covetioal L driver. Other advatages are also iportat. 1. I both the covetioal L driver ad the proposed PPRI, the relative capacitace chage ( ) ca be ade sall by purposely icreasig. This however will reduce the characteristic ipedace ad hece icrease the reactive curret. The advatage of the PPRI i this case will be i the fact that the circulatig curret passes through the switches oly durig the boost period [5]. I the L driver all the circulatig curret passes through the switches. osequetly, everythig beig equal, the PPRI is expected to have a higher efficiecy.. The icorporatio of a trasforer i the basic desig of the PPRI eables oe to use ay iput voltage to geerate the rather high (ad floatig) voltage eeded to drive the PZM. 3. Fro the electroics poit of view, the fact that the drive of the push pull trasistors is referred to the groud of the circuit siplifies the desig. The circuitry ivolved is rather siple ad ca be realized by low cost coercial copoets.. Motor voltage regulatio ca be easily achieved by just addig a extra switch to for the Buck frot ed. Motor voltage is liear with the duty cycle, akig the cotrol circuitry siple. 5. The proposed sigle trasistor A switch is uch sipler tha the covetioal two trasistor cofiguratio. Aside fro the fact that the proposed switchig schee eeds half the uber of trasistors, its drive requireets are easier to eet sice the drive sigals are referred to groud (Fig. 11). The ai disadvatage of the proposed A switch is the relatively high peak voltage whe the switch is blockig.. ONLUSIONS The proposed resoat driver is show to be a viable choice for PZM applicatios. The ai advatages of the proposed PPRI topology is relatively isesitivity to added capacitace, siplicity ad ease of cotrol. The atheatical expressio developed i this study ca )RUFH 1 DEOH FDSDFLWDFH ) Fig. 15. PZM force whe drive by proposed PPRI driver, as a fuctio of added capacitace.

7 9 FD 9 ED Fig. 1. Excitatio voltage (upper trace) ad voltage across a blockig directio switch (Fig. 11). Horizotal scale: 10 Secdiv. ertical scale: 80 div, upper trace; 100 div, lower trace. be easily used as desig guides for this topology. The proposed sigle trasistor directioal switch is sipler ad ore ecooical tha covetioal A switches. Its ai disadvatage is the higher blockig voltage. REFERENES [1] W. R. hyoweth, J. F. Elliott, H. W. Katz, E. B. Mulle,. A. Rose, N. Schwartz, B. Silvera,. F. Spitzer, S. W. Teho, H. J. eea, "Solid state agetic ad dielectric devices", New York, Joh Wiley Sos, Ic., [] H.P. Shoer, "Piezoelectric otors ad their applicatio," Europea Tras. o Electrica Power Egieerig, vol.,., NoveberDeceber, 199, pp [3] Faa-Jeg Li, "Fuzzy adaptive odel - followig positio cotrol for ultrasoic otor", IEEE Tras. o Power Electroics, vol. 1,., March 199. [] S. Be-Yaakov, E. Rozaov, T. Wassera, T. Rafaeli, L. Shiv, G. Ivesky, "A resoat driver for a piezoelectric otor", Power oversio ad Iteliget Motor oferece, PIM 99, vol.39, Jue 1999, pp [5] G. Ivesky, A. Abraovitz, M. Gulko, S. Be-Yaakov, "A resoat dc-dc trasforer", IEEE Tras. o Aerospace ad Electroic Systes, vol. 9,. 3, July 1993, pp [] M. Gulko, S. Be-Yaakov, "urret-sourcig push-pull parallel-resoace iverter (S-PPRI): theory ad applicatio as a discharge lap driver", IEEE Tras. o Idustrial Electroics, vol. 1,. 3, Jue 199, pp