APPLICATION OF SENSORLESS ELECTRIC DRIVE TO UNMANNED UNDERSEA VEHICLE PROPULSION

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1 Copyright IFAC 15th Trinnial World Congrss, Barclona, Spain APPLICATION OF SENSORLESS ELECTRIC DRIVE TO UNMANNED UNDERSEA VEHICLE PROPULSION Todd D. Batzl a, Danil P. Thivirg b, and Kwang Y. L c a Applid Rsarch Laboratory, Stat Collg, PA 1684 b Naval Undrsa Warfar Cntr, Nwport, RI 841 c Th Pnnsylvania Stat Univrsity, Univrsity Park, PA 1684 Abstract: Snsorlss lctric driv is an nabling tchnology in th ralization of submrsibl propulsion systms such as th intgratd motor/propulsor (IMP). Th IMP concpt faturs an lctric motor mbddd within th shroud of an undrsa vhicl's propulsor. This arrangmnt provids many advantags ovr convntional propulsion systms but prvnts th us of convntional rotor position snsors bcaus of rliability issus in th harsh submrgd nvironmnt. In this papr, a position snsorlss driv is applid to th IMP and xprimntal rsults ar prsntd to dmonstrat th ffctivnss of th proposd tchniqu. Copyright IFAC Kywords: Autonomous vhicls, lctric vhicls, propulsion control, brushlss motors, snsorlss drivs, motor control, obsrvrs, stimation, automatic control 1 INTRODUCTION Dvlopmnt of an Intgratd Motor Propulsor (IMP) for application on an Unmannd Undrsa Vhicl (UUV) is undrway as part of a joint ffort btwn th Naval Undrsa Warfar Cntr/Nwport and th Applid Rsarch Laboratory of th Pnnsylvania Stat Univrsity. Th IMP concpt faturs an lctric motor mbddd within th shroud of an undrsa vhicl's propulsor. Th prmannt magnt synchronous motor (PMSM) is th motor of choic for th IMP du to its suprior powr dnsity, fficincy, and xcllnt acoustic charactristics. In ordr to fully xploit th favorabl charactristics of th PMSM, high rsolution rotor angl information is rquird. Typically a rsolvr or ncodr attachd to th shaft of th machin provids this information. Th structur of th IMP, whr th lctromagntics ar submrgd and installd in th propulsor's shroud, crats difficulty in th us of such position fdback dvics. Th shaftlss IMP systm cannot asily accommodat convntional shaft position snsing dvics, and th submrgd nvironmnt poss rliability issus with th us of such snsors. Hall position snsors could b usd in clos proximity to th submrgd magntics but ar undsirabl from a rliability and cabl routing standpoint. Th us of coars rotor position fdback from Hall ffct snsors is also known to gnrat torqu rippl in th PMSM (Jahns, 1984). Th intgration of th PMSM stator into th UUV propulsor shroud mphasizs th nd for torqu rippl minimization, sinc th us of isolation mounts found in convntional shaft drivn propulsion systms is not possibl. To addrss th problms associatd with placing a rotor position snsor in th IMP assmbly, a position snsorlss stratgy is adoptd (Batzl and L, 1998, Batzl and L, ). Th hardwar implmntation for th driv systm is dscribd, and xprimntal rsults ar prsntd to dmonstrat th ffctivnss of th proposd controllr.

2 IMP CONCEPT Th IMP faturs an lctric motor mbddd within th shroud of an undrsa vhicl's propulsor. This arrangmnt liminats th nd for a convntional motor cooling jackt, auxiliary motor cooling systm, driv shaft, and shaft coupling. Th vhicl intrior volum rclaimd by this compact arrangmnt provids many bnfits. Th additional payload volum can b usd for additional snsors or nrgy storag to incras mission capability and nduranc. In this concpt th lctromagntic stator is installd in th shroud and th prmannt magnt rotor is attachd to th tip of th hydrodynamic rotor blads. Th motor phas lads ar routd through th stationary propulsor stator blads to th vhicl hull. Th us of convntional fin actuators mountd to th propulsor s shroud is no longr fasibl so an nginrd lastomr control nozzl has bn adoptd. Th nozzl and associatd articulation mchanism ar shown schmatically in Fig. 1. Hydrodynamic Rotor Nozzl Articulation Mchanism Shroud Elctric Motor Fig. 1. IMP propulsor configuration. Hydrodynamic Stator Stabilizing Vans Enginrd Elastomr Control Nozzl SENSORLESS STRATEGY Th ability to gnrat smooth torqu and prform accurat angular vlocity control is of utmost importanc toward th succss of th proposd IMP concpt. Ths rquirmnts ar important from both th vhicl dynamics and control, and radiatd nois prspctivs. Th satisfaction of ths rquirmnts without th us of a rotor position snsor rquirs th adoption of a robust, high fidlity position snsorlss stratgy. Th dsign and dvlopmnt of such a stratgy is prsntd in th following sctions..1 Snsorlss PMSM Modl Th flux linkag modl of th non-salint PMSM in th two-phas stationary rfrnc fram (Batzl and L, ) is: d dt v v pm pm, (1) whr R L av ; pm pm m cos. () sin Th trms, and v, rprsnt th flux linkags and voltags corrsponding to th two fictitious windings phas and. Th symbols L av, m, R, and rprsnt th slf inductanc, PM flux constant, rsistanc, and rotor angl, rspctivly. To dvlop a modl for a rotor position obsrvr, th vctor T pm pm dfind in () is considrd to b a disturbanc stat that satisfis a known diffrntial quation. Combining th disturbanc stat vctor with th stat variabls dfind in (1) yilds th mtastat vctor, x: x x x x T T x. () 1 4 pm pm Th input vctor is th applid phas voltag in th stationary two-phas rfrnc fram u u T v T v u, (4) 1 and th output vctor, y, is chosn to b th masurabl currnts: y y T i T i y. (5) 1 Thus, th mtasystm stat and output quations ar dscribd by rspctivly, whr A C R dx / dt A x Bu (6) y Cx, (7) 1 1 ; B R R R. (8) Th trm rprsnts th angular vlocity of th rotor shaft in lctrical radians pr scond. Th subscript associatd with th A matrix is usd to indicat variation with th rotor angular vlocity. Undr th assumption that rotor vlocity is approximatly constant ovr th systm sampling priod, th angular vlocity may b considrd to b a slowly varying PMSM paramtr. This assumption is consrvativ givn th larg mchanical tim

3 constant of th IMP structur rlativ to th fast lctrical tim constant of th motor. With this assumption, th rsulting modl is a linar tim varying systm, allowing th us of wll-dvlopd linar control mthods. It is also strssd that th modl givn in (6) and (7) dos not contain any mchanical variabls such as torqu, friction, and inrtia in th stat quations. This is advantagous, sinc torqu and inrtia ar oftn unknown and vary during th opration of th systm.. Rotor Position Obsrvr With angular vlocity considrd to b a slowly varying paramtr, (6) and (7) may b usd to construct a full ordr obsrvr (Lunbrgr, 1971). Th obsrvr is usd to stimat th stat vctor x of () from knowldg of th input vctor u and a dirct masurmnt of th output vctor y. Not that from th stimation of x and x 4, th rotor position stimat ˆ may b dtrmind from ˆ 1 xˆ 4 tan. (9) xˆ Using standard obsrvr dsign tchniqus for a linar systm (Brogan, 1991), th form of th proposd rotor position obsrvr is d A GC dt (1) whr is th stat stimation rror vctor x xˆ, (11) G is th obsrvr gain matrix, and xˆ is th stimatd stat vctor. Th convrgnc of th stimatd stat variabls toward thir actual valus is achivd by convntional pol-placmnt tchniqus. Th ignvalus of th charactristic quation I ( A GC) (1) ar chosn to hav ngativ ral componnts so that asymptotic stat rconstruction is achivd. Clarly, obsrvability of th systm is a rquirmnt for th stimation of PMSM stats. Th condition for obsrvability is dtrmind by th rank of th obsrvability matrix (Philips and Harbor, 1991): T C CA CA CA. (1) From (1), th systm is obsrvabl for non-zro angular vlocity. This rsult supports th wllknown drawback of th snsorlss PMSM its inability to stimat rotor angl at zro and low angular vlocitis (Krishnan and Ghosh, 1986; Wu and Slmon, 199). Thus, spcial provisions must b mad to start th snsorlss PMSM and to oprat th systm at xtrmly low angular vlocity. For th IMP systm, th obsrvr fdback is disabld at spds blow 1 r/s (19 RPM), which rprsnts an xprimntally dtrmind low-spd thrshold.. Angular Vlocity Estimation It is clar from (8) that rotor vlocity is a rquird paramtr for th implmntation of th proposd rotor position obsrvr. In addition, angular vlocity fdback is rquird to accuratly track th vlocity rfrnc in a spd control loop usd in th IMP propulsion systm. Thrfor, in th absnc of an angular vlocity snsor, a suitabl stratgy must b dvlopd to dtrmin this paramtr. Two stratgis ar dscribd in th following sctions, and th strngths of ach tchniqu ar combind to form an adaptiv vlocity stimation schm. Quasi Stady Stat Vlocity Estimation: A quasi stady stat stimat for magnitud of th angular vlocity (Batzl and L, 1998) is ˆ v Ri v Ri. (14) m This rsult suggsts th us of th input and output vctors, u and y, to stimat th magnitud of th angular vlocity. Th dirction of th angular vlocity stimat at sampling intrval k is thn obtaind from whr ˆ ( k 1) ˆ sgn, (15) 1 Ri v tan. (16) v Ri Th strngth of this mthod is its ability to dtrmin vlocity vn at zro and vry low spds. Th waknss is its dpndncy on PMSM paramtrs. Tim Drivativ of Estimatd Rotor Angl: An altrnativ to th mthod givn in (15) is to us th tim drivativ of th stimatd rotor angl ˆ dˆ. (17) dt This mthod obviously rquirs a stabl position obsrvr, and th obsrvr pol locations should b much fastr than th angular vlocity. Both of ths constraints may b nforcd by propr slction of th systm ignvalus at non-zro angular vlocity. Subjct to ths constraints, th stimatd angular vlocity obtaind by (17) approachs th actual valu whn avragd ovr a sufficint priod of tim.

4 Th drawback to this mthod is th nois that rsults from th diffrntiation procss and its inability to obtain an accurat spd stimat at startup, whr th rotor position is not obsrvabl. Th strngth of this mthod is th accuracy of th spd stimats throughout th mdium to high spd rang. Adaptiv Vlocity Estimation: Th two proposd vlocity stimation mthods complmnt ach othr nicly. Th us of (15) yilds good prformanc at vry low spds, but is subjct to paramtr uncrtainty. Th us of (17), howvr, is ssntially indpndnt of th paramtr stimation rrors so long as th systm pols ar chosn to b fastr than th angular vlocity and th vlocity is sampld ovr a sufficint priod of tim. Thus, th strngths of ach mthod may b combind to form th vlocity stimation corrction schm, as shown in Fig.. v i ^ Adaptiv Vlocity Est. d/dt ^ adaptiv ^ d d t + PI control - Fig.. Vlocity stimation corrction block. To us (17) to corrct for vlocity stimation rrors obtaind by (15), (14) is modifid to includ an uncrtainty trm, which rprsnts th uncrtainty in th prmannt magnt flux linkag: ˆ v Ri v Ri m. (18) Initially, th rror trm is st to zro. Howvr, as long as th magnitud of th stimatd vlocity is abov th low spd thrshold whr th position obsrvr is assumd to b stabl, th adaptiv vlocity stimation procss is activatd. Th adaptation procss compars th output of (18) with (17) to gnrat th vlocity stimation rror. A PI controllr oprats on th stimation rror, adjusting th output to corrct for th paramtr uncrtainty. Th tim constant of th PI controllr is chosn to b slow, sinc th tmpratur ffct that causs th paramtr drift is a vry slow ffct as wll. This has th bnfit that th nois gnratd by th diffrntiation of th rotor angl stimat is smoothd ovr tim. Thus, as long as th rotor position stimator rmains stabl, th avrag valu of its drivativ is clos to th actual rotor spd. This vlocity stimation schm has bn shown through xprimntation (Batzl and Thivirg, ) to produc accurat tracking of th vlocity rfrnc, dspit th absnc of th position/vlocity snsor. This is of critical importanc in undrsa vhicls whr th rotor angular vlocity is usd to achiv th dsird forward vhicl spd. An ovrall block diagram of th proposd position obsrvr, including th angular vlocity stimation block, is shown in Fig.. u B PMSM ẋ G A intg. y y yˆ Fig.. Block diagram of rotor position stimator. 4 HARDWARE IMPLEMENTATION Th computing hardwar for th snsorlss lctric driv consists of both a Sharc 161 floating point digital signal procssor (DSP), and a fixd point motor control DSP (ADMC41). Th floating point DSP prforms rotor position and vlocity stimation at 1 s, and.5 ms intrvals, rspctivly. Th fixd point motor control DSP is usd to sampl th stator voltags and currnts, provid th PWM signals to th invrtr, and implmnt th currnt control function. Th two DSPs communicat dirctly using a dual-port RAM structur. Th DSP controllr board is intrfacd to a -phas H-bridg powr stag consisting of two Powrx 6V, 1Arms six-pack IGBT Intllignt Powr Moduls (IPMs), and puls width modulation (PWM) signal isolation and DC/DC convrtr boards. Th IMP motor is a 1 HP prmannt magnt synchronous motor manufacturd by Magmotor. Th motor controllr and powr stag ar shown in Fig. 4, whil th IMP motor is shown coupld to an ddycurrnt dynamomtr in Fig. 5. controllr ˆ C xˆ ŷ powr stag Fig. 4. DSP-basd controllr and powr stag. ˆ

5 Tabl I. IMP motor paramtrs. Rsistanc.1 Inductanc.1 mh PM Flux Linkag.4469 v-s Ratd Powr 1 HP Pols 64 Fig. 5. IMP motor (lft) and dynamomtr (right). 5 EXPERIMENTAL RESULTS To valuat th prformanc of th prototyp snsorlss driv, a st of xprimnts wr prformd on th IMP whr th rotor position obsrvr xcuts th snsorlss algorithm in a ral tim, closd loop systm. Th IMP motor paramtrs ar includd in Tabl I, and Fig. 6 shows input, output, and stat variabl vctors dfind in ()-(5) for opration at 15 RPM and 95 n-m load torqu. Mas. Volts (V) Est. Curr. (A) Est. Flux (v-s) Mas. Currnt (A) 1 a b c alpha bta Stat Vars 1.1 alpha bta cos sin alpha bta tim (s) Fig. 6. IMP stat stimation at 15 RPM, 95 n-m. 5.1 Rotor Position Estimation Accuracy In ordr to valuat th rotor position stimation accuracy, a rsolvr was tmporarily attachd to th hub of th IMP motor. Th rsolvr was usd only as a rfrnc for valuating th accuracy of th stimatd rotor position, whil th stimatd rotor angl was usd to commutat th PMSM. Low spd opration is known to pos difficultis to th snsorlss driv du to obsrvr ill conditioning. Fig. 7 shows rotor position stimation accuracy at RPM, which is just abov th aformntiond low spd vlocity thrshold. At this spd, th maximum diffrnc btwn th rsolvr position and stimatd angl is lss than two lctrical dgrs, an accuracy that is rprsntativ of opration across th IMP spd rang (<6 RPM). Angl Est. Err. (r) Rotor Angl(r) Tim (s) Fig. 7. Low-spd angl stimation accuracy. 5. Rotor Position Estimation Robustnss In practical applications, xtrnal disturbancs such as load torqu variations occur rgularly, and an ffctiv rotor position stimator must b robust to ths vnts. In this sction, robustnss to load torqu variation is xamind. Bcaus th PMSM modl usd to construct th rotor position obsrvr dos not includ mchanical paramtrs such as friction, inrtia, and load torqu, th angl stimation accuracy is not xpctd to b affctd by th load torqu disturbanc. This xpctation is confirmd in th xprimnt shown in Figs. 8 and 9, which dpict th angl stimation at an angular vlocity of 15 RPM at 1 and 95 n-m load torqu, rspctivly. From ths figurs, th stimation accuracy is not significantly affctd by th load torqu, as prdictd in prvious xprimnts (Batzl and Thivirg, ). 5. Snsorlss Startup from Zro Spd Th startup of th snsorlss IMP is shown in Fig. 1, whr an initial angl stimation rror of

6 approximatly 11 lctrical dgrs is prsnt. In this xprimnt, th initial angl stimat was obtaind by forcd alignmnt mthods (Matsui and Shigyo, 199). Th figur shows a smooth, dithr-fr startup dspit th vlocity stimation polarity rvrsals at vry low spd, whr th obsrvr fdback is disabld. 6 CONCLUSIONS Th dsign of an lctric driv systm suitabl for th Intgratd Motor/Propulsor (IMP) has bn prsntd. An nabling tchnology for th implmntation of th IMP is a position snsorlss lctric driv systm for th PMSM. Th algorithm, and hardwar implmntation of such a snsorlss driv systm is st forth in this papr. A sris of ral-tim, closd-loop xprimnts dmonstrat th ffctivnss of th proposd snsorlss control mthod ovr a wid varity of oprating conditions. Furthrmor, th snsorlss systm shows robustnss to mchanical paramtrs such as load torqu, inrtia, and friction. Est Vloc(r/s) Est Err (r) Rotor Ang.(r) Tim (s) Fig. 8. Angl stimation at 15 RPM, 1.6 n-m. Est Vl(r/s) Rotor Ang (r) Ang Est Err (r) Tim (s) Fig. 9. Angl stimation at 15 RPM, 95 n-m. Rotor Ang.(r) Est Vl (r/s) Ang Est Err (r) Tim (s) Fig. 1. Snsorlss startup from zro spd. 7 ACKNOWLEDGEMENTS Th work outlind in this papr was supportd by th Offic of Naval Rsarch undr Grant N as wll as ONR Undrwatr Wapons Propulsion and Powr Sourcs program. 8 REFERENCES Batzl, T.D. and K.Y. L (1998). Commutation torqu rippl minimization for prmannt magnt synchronous motors with Hall ffct position fdback. IEEE Trans. on Enrgy Conv., v. 1, no., pp Batzl, T.D. and K.Y. L (). Slotlss prmannt magnt synchronous motor opration without a high rsolution rotor angl snsor. IEEE Trans. on Enrgy Conv., v. 15, no. 4, pp Batzl, T.D. and D.P. Thivirg (). Elctric driv for 1 UUV. rd Naval Symposium on Elctric Machins, Philadlphia, PA. Brogan, W.L. (1991). Modrn Control Thory, Prntic-Hall, Englwood Cliffs, NJ. Jahns, T.M. (1984). Torqu production in prmannt magnt synchronous motor drivs with rctangular currnt xcitation. IEEE Trans. on Industry Applications, vol., pp Krishnan, R. and R. Ghosh (1986). Starting algorithm and prformanc of a PM DC brushlss motor driv systm with no position snsor. Powr Elctronic Spcialists Confrnc, pp Lunbrgr, D. (1971). An introduction to obsrvrs. IEEE Trans. on Automatic Control, vol. AC-16, no. 6, pp Matsui, N. and M. Shigyo (199). Brushlss DC motor control without position and spd snsors. IEEE Trans. on Ind. Apps., vol. 8, no. 1, pp Phillips, C. and R. Harbor (1991). Fdback Control Systms, Prntic Hall, Englwood Cliffs, NJ. Wu, R. and G. Slmon (1991). A prmannt magnt motor driv without a shaft snsor. IEEE Trans. on Ind. Apps., vol. 7, no. 5, pp