Surface-Mounted PMBM Sensorless Control Based On EMF Extraction And Simple Digital Filtering

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1 Suface-Mounted PMBM Sensoless Contol Based On EMF Extaction And Simple Digital Filteing Case I: Pemanent Magnet Synchonous Moto Osama M. Aafa a, Osama A. Mahgoub b, Mona N. Eskande a a Electoncis Reseach Institute, Caio, b Caio Univesity, EGYPT Abstact- In this pape, a poweful method fo sensoless contol of pemanent magnet bushless motos (PMBM) is explained. The method doesn t include any modification to the classical constuction of such motos and can be easily integated within the dive electonics. It is applicable to both moto types, i.e. those with sinusoidal o tapezoidal back EMF. The method is independent of excitation cuent pofile. It is also vitually independent of system paametes. The back EMF wavefom is extacted on-line using simple and integation-fee algebaic expession though a newly poposed measuement setup. Appopiate simple digital filtes to make it diectly usable fo calculating oto position and speed ae then used to filte the extacted wavefoms. This pape discusses the method application on the PMBM whose back EMF wavefoms ae sinusoidal; its application on the tapezoidal back EMF machine is left fo a sepaate pape. System pefomance using the poposed method is tested using simulation and expeimentation. Results obtained in both cases ensue the effectiveness of the poposed technique. I- INTRODUCTION Pemanent magnet bushless moto (PMBM) is widely used as a basic element in high pefomance sevo dive systems due to its high efficiency and toque density. Recently, a lot of eseach has been focusing on the sensoless contol of PMB motos, which nomally opeates using position and speed sensos. Two diffeent types of suface-mounted (SM) PMBM ae available, the sinusoidal back EMF type and the tapezoidal back EMF type. The fist type is fequently efeed to as pemanent magnet synchonous moto (PMSM) and the second type is fequently efeed to as bushless DC moto (BDCM). Sensoless contol is an attactive solution to mechanical senso poblems, which include exta cost, wiing complexity, educed eliability and demand fo additional mounting space. The authos of this study believe that space limitations [1], incompatibility with some hash woking envionment (e.g. inside efigeant compessos) [] and weight eduction consideations (e.g. aviation industy) epesent the most appaent motives behind sensoless contol eseach effots. This is paticulaly tue if we conside one of the potential fields of application of such motos, i.e. disk dives whee miniatuization and eliability come as top design pioity [3]. Sensoless contol schemes fo suface-mounted (SM) PMBM ae mostly depending on diect o indiect back EMF detection since the othe schemes employing inductance changes with oto position ae applicable only to inteio magnet (IM) PMBM [3]. Pevious woks developed sensoless contol schemes fo BDCM based on diect EMF detection include [3],[4],[5] and [6] whee EMF zeo cossings povide position and speed infomation six times the numbe of pole-pais evey oto cycle. The majo dawback of such technique is the availability of speed infomation once evey one sixth of the electical cycle. Tying to povide continuous position and speed infomation, Hamid A. Toliyat et al suggested a novel scheme fo indiect back EMF detection [7], [8]. The scheme involves some modification to the classical stuctue of such motos and it is geneally inconvenient fo automatic windes; Seving the same taget, a compaative study [1] have poven that substantial impovement in BDCM pefomance can be ealized by adopting an extended Kalman filte (EKF) algoithm utilizing the open phase voltage measuement in its coection mechanism [9]. Unfotunately the implementation is dedicated to BDCM only and can t be extended to PMSM. Silveio Blognanai, et al [11] intoduced a high-pefomance sensoless PMSM dive based on EKF. Howeve EKF methods ae chaacteized by intensive math manipulations and ae some how difficult to tune. 1

2 In this study we ty to make benefits fom the special constuction of PMBM as is, thus avoiding any stuctual modifications. A unified and geneal appoach fo position and speed estimation capable of handling both PMSM and BDCM is intoduced. The poposed technique is also independent of the excitation cuent pofile (sinusoidal o quasi-squae). The poposed technique is based on a newly poposed method fo indiect back EMF extaction. Pat I though VI of this pape has the theoy and pat VII has the simulation and esults while pat XX intoduces the expeimental esults. II- SM PMBM MODEL The effective ai gap of SM PMBM is vitually lage and unifom due to the consideable magnet depth in the adial diection and due to the fact that magnet mateials has pemeability close to that of fee ai [1]. The lage ai gap helps maintain the magnetic cicuit vitually fee fom satuation and keeping the winding s inductance nealy constant and independent of oto position and excitation cuent. Cuent contol loop can futhe suppot ou assumption egading the lineaity of magnetic cicuit by enfocing cuent limits that maintain magnetic cicuit s lineaity. A quite geneal voltage equation of both suface-mounted PMBM moto types can be witten as: v a s = vb s vc ia L M pia e a + ib + L M pib e.(1) b s ic L M pic ec whee: v a,v b,v c : stato teminal voltage of phases a, b and c espectively in Volt. i a, i b, i c : cuents of phases a, b and c in Amp P : diffeential opeato. L : self-inductance pe phase in Heny. M : mutual inductance in Heny. s : stato esistance pe phase in Ohm. e a, e b, e c : back EMF of phases a, b and c espectively in Volt, they ae given by e a cos θ ' dθ ( ) ( ) e = λ cos θ π..() b m 3 dt e cs cos θ + π 3 Whee: ' λ m : the EMF constant in volt.s/elect. ad. θ : Electical angula displacement in ad. dθ : Deivative of displacement ad/s. dt Electomagnetic toque T e is given in N.m by : ' P 3 3 T ( )( ( ) e = λ ia cosθ + ib ic sinθ ) (3) m whee P : Numbe of poles. The mechanical system dynamics is given by: Te = TL + Bω m + J pω m..(4) T e, T L : electomagnetic developed toque and load toque in N.m espectively. B :damping coefficient in N.m.s/ad. ω m : oto s mechanical speed dθ ω m = P.. dt J : moment of inetia in N.m.s /ad Equation (1), which is valid unde the condition of isolated neutal point, shows that the thee moto phases seem as if they wee thee independent coils of equivalent inductance (L- M). The thee windings subject to the flux of a otating magnet which induces a back EMF of value e ph. III- BACK EMF DETECTION III-1 Theoy i Rx Lx P Rph Lph EMF N Neutal Ext. Inducto A Phase Winding Fig. 1: Extenal small inducto connected to each phase of PMBM In the cicuit shown in Fig.1, let the cicuit pat fom P to N epesent one of these thee independent coils of the PMBM, a small extenal coil is placed between points I (invete s feeding point) and P (moto teminal). Witing the voltage dop equations fo the two pats : V = R. i + L. di / dt e.....(5) PN ph ph + ip Rx. i + Lx. di / dt V =.(6) Whee: V pn : voltage dop fom P to N in Volt V ip : voltage dop fom P to I in Volt. e : back EMF geneated due to pemanent magnet excitation in Volt. L ph : equivalent inductance (L-M) of the phase winding in Heny. R ph : esistance ( s ) of the phase winding in Ohm. L x,r x : inductance and esistance of the extenal inducto espectively. i : phase cuent in Amp. Solving the two pevious equation fo e yields: L ph R x L ph e = Vip + ( R ph ) i + V....(7) PN L L x x

3 The pevious equation can be applied fo each moto phase independently. Fo PMSM we need a total of fou voltage measuements since the EMFs of the thee phases ideally sum to zeo. III- Conditions of validity Equation (7) can be used on line to calculate the instantaneous value of the back EMF wavefom to a easonable degee of accuacy if the following pesumptions could be satisfied. The moto magnetic cicuit is opeated in the linea egion. Inductive voltage dops acoss windings inductance ae too lage compaed with the esistive voltage dops; this is tue due to high fequency switching pocess. Diffeential voltage measuement (and associated pocessing) at the selected points in Fig.1 is simultaneous and fast enough elative to the cuent contol switching fequency. The extenal inductos ae to be made identical to each othe with low-loss coe, with constant inductance, minimum esistance and should have no-mutual coupling. IV. NOISE ANALYSIS AND PROPOSED FILTER In ou system, noise is expected as: white noise due to suounding envionement. impulse noise due to high fequency cuent switching. While simple finite impulse esponse (FIR) digital filtes can be used to effectively filte white noise, impulsive noise can t be filteed by FIR without intoducing lage phase shift and amplitude attenuation. Median filtes ae moe suitable to deal with impulsive noise since they intoduce vey little phase shift and ideally no magnitude attenuation. Also it s paticulaly useful in peseving the flat top of the back EMF wavefom in BDCM types. IV.1 Digital FIR Filte The mathematical fomula descibing this filte (Fig. ) is given by the following equation: N Y = ai X ( n i)....(8) i= Whee Y is the cuent filte output, the X(ni) ae cuent o pevious filte inputs. The a i s ae the filte s feed fowad coefficients coesponding to the filte s zeos. If this filte is excited with an impulse, the output is pesent fo only a finite (N) numbe of computational cycles. Due to its all zeo stuctue (no poles at all), the FIR filte has a linea phase esponse in most standad filte applications. Fig. (): FIR Filte implementation. IV. Median Filte Fo an input signal V, the vecto U is an n- element vecto whose elements ae taken fom the elements of V by a window sliding ove the input signal V whee n is the window size of the median filte. Nomally n is chosen to be an odd numbe, then if Y = median (U) and S is the soting of the elements of U by value. The output Y is the cental element of the soted vecto S as follows Y = S (( n +1) / ) (9) Fo on-line filteing this implies that the last n samples of a noisy signal should be always kept in memoy and efeshed in a fist-in fistout dopping style. V DIRECT EMF-BASED POSITION AND SPEED CALCULATION The tansfomation of the extacted thee phase EMF fom stationay fame to the two phase stationay fame esults nomally in a vecto whose magnitude epesents the oto electical speed and whose angle epesents the electical oto position. V.1 Related Poblems Since both vecto s magnitude and phase would be affected by filteing, we ve got two poblems. A speed calculation eo due to amplitude attenuation caused by filte. A position calculation eo due to phase lag intoduced by filte. Anothe poblem is invited if the dive opeation equiements involve speed-evesing. As the speed gets close to zeo, position estimation eo gets highe and highe due to poo signal to noise atio, and eventually we may 3

4 loose any tustable infomation about the eal oto position. Theefoe a modified estimation technique should be povided fo position and speed in the vicinity of zeo speed unde speed evesal conditions. A simila situation at dive s statup is fixed by open loop moto acceleation. V. Poblems Fixing Speed Eo Compensation The fist poblem can be esolved by consideing a hypothetical value of the pemanent magnet flux coefficient λ '. This m hypothetical coefficient s value is initially assumed equal to the machine EMF constant upon dive statup. Then it can be tuned on line by popely diffeentiating the position signal ove integal electical cycles to get the actual speed unde steady state conditions. The hypothetical magnet flux coefficient is then efeshed using a fesh value of the moto actual speed and a fesh value of the EMF s vecto magnitude in the α-β fame afte filteing. Position Eo Compensation Though off-line simulation, the elation between phase shift intoduced by any given filte combination with known paametes and speed can be pedicted stating fom standstill and up to ated moto speed. It has been shown by simulation that it has a linea change pofile, which makes on-line compensation easie. Assuming that the extacted back EMF vecto mapped in the two-phase stationay fame afte applying digital filteing is E α β. The vecto E α β has a space angle θ with espect to the axis α of the coodinate system α -β. Accoding to the estimated speed and the linea lag coefficient E α β is lagging the actual back EMF vecto of the machine E αβ when the late is mapped in the same efeence fame by an angle δ. We can imagine that thee is some new efeence fame o coodinate system α-β, obtained by otating the oiginal stationay coodinate system α -β against the sense of moto otation with an angle δ (advance) such that the pojections of the vecto E α β on its α-β axis would give a esultant vecto angle θ whee θ = θ ' δ. In this way, the phase shift intoduced by the filteing pocess can be coected. The pojections of the vecto E α β on the axes of the new coodinate system can be deduced fom the geomety of Figue (3) and they ae given by equation (1): β E E α β Ε β δ β' E β' cos δ = sin δ δ θ' θ shifted vecto E α'β' E α' E α Fig. (3): fame otation sin δ E cos δ E α ' β ' α α' sense of moto otation (1) Estimation at speed s zeo-cossing Fotunately, the moto speed changes linealy with time-unde almost all loading conditions-in the vicinity of zeo speed duing speed evesal. The ate of change can be captued on-line; extapolation can be used to pedict the moto speed once the estimated speed dops unde a pedefined theshold. The oto position can be estimated by simple integation pocess (e.g. tapezoidal ule) applied on the pedicted speed. VI SIMULATION RESULTS Simulation esults of PMSM with sinusoidal-type excitations ae shown in Figue (4)-a though Figue (4)-e. At the neighbohood of zeo speed unde speed evesal conditions, the altenative estimation technique is used. It is geneally noticed fom multiple simulation sessions that the highe the noise level, the highe the estimation eo. Howeve, the eo limits eached unde wost conditions ae well toleable. Simulation esults fo the case of light noise level ae pesented as a epesentative case, unde pactical conditions a compaable pefomance have been aleady obtained. 4

5 8 6 T-load N.m speed ad/s T-comm N.m T-Dev. N.m oto e-pos ad Est. ot. epos. ad Eo Elect Deg a) Moto Speed Pofile b) Electical Roto Position (Actual/Estimated/Eo) Ea,volt Eb volt Ec,volt c) EMF Extacted by the Poposed Method (A/ B/ C) Ia Amp Ib Amp Ic Amp d) Roto Cuent Wavefoms (phase A/phase B/phase C) e) Moto Toque Pofile (Load/Command/Developed) Fig. (4): PMSM pefomance cuves with sinusoidal-type excitation VII EXPERIMENTAL RESULTS VII.1 On-line EMF detection On-line extaction of the back EMF is veified though oscilloscope taces in this section. In Figue (5) the uppe yellow coloed tace shows the diffeential voltage measuement acoss the extenal inducto connected to phase A, the high fequency voltage component is due to the inducto eaction to the fast switching pocess of the invete while the lowe fequency voltage changes is due to the inducto eaction with the fundamental component of the winding cuent. The next blue coloed tace shows the teminal voltage measued at the moto teminal of phase A. The tace esembles potions boken out of a sinusoid wave and impaied by some offset and high fequency noise. The thid pink coloed tace shows the extacted EMF esulting fom applying the algebaic filteing fomula given in equation (7), the impovement established in the wavefom is evident since it gets close to a sinusoid without intoducing any phase shift o magnitude attenuation. The fouth geen coloed wavefom shows the EMF esulting afte applying simple Finite Impulse Response (FIR) digital filteing, it is clea that some phase shift is now intoduced due to this additional filteing. The filte s math is executed on line upon acquiing each new fesh sample. Figue (6) futhe illustates phase lag due to additional filteing. Consequently, the shift is epoduced in the estimated position as shown in Figue (7), whee the geen coloed tace epesents the measued position, the blue coloed tace epesents the position estimated fom the filteed EMF and the yellow coloed uppe tace epesents the algebaic diffeence between them. The appaently high eo pulses nea the π tansitions actually have a low value 5

(by dopping π epesenting the complete cycle). VII.

initial oto position, which is andom and unknown.

Reaching a minimum speed to make the EMF detection moe accuate and hence tustable.

within the open loop acceleation outine which is used to povide the excitation voltage to the moto.

6 (by dopping π epesenting the complete cycle). VII. Open Loop Acceleation Although the poposed technique is capable of stating the dive in sensoless mode fom zeo speed, the esulting sense of otation may confom to the commanded one o not based on the initial oto position, which is andom and unknown. Theefoe, the fist step in any unning session is to povide an open loop acceleation peiod to seve two puposes: Guiding the sense of otation to ensue confomance with the commanded one. Reaching a minimum speed to make the EMF detection moe accuate and hence tustable. Figue (8) illustates the time pofile of open loop acceleation though the oto position infomation, the uppe tace shows the actual oto position, while the lowe tace shows the oto position consideed within the open loop acceleation outine which is used to povide the excitation voltage to the moto. When the acceleation ate is well tuned to the moto and load inetia, the eo between the assumed position and the actual position deceases and the expected tansient due to switching fom open loop to closed loop sensoless acceleation becomes a minimum and gets moe toleable. Fig.( 5): Voltage wavefoms / phase A Fig. (8): Open loop acceleation, fist cycles Fig. (6): Phase shift added by subsequent digital Filteing VII.3 Nomal Sensoless Opeation Once the moto acquies a easonable speed value, the estimated speed and position can be tusted and diectly used fo closing the cuent and the speed contol loops. Figue (9) gives a compaative vision of the actual (measued) oto position and the estimated one unde moto loading conditions when the moto is unning in sensoless closed loop contol mode with phase shift compensato enabled. The high fequency ipples supeimposed on the yellow tace (measued oto position) is meely a picked up noise Fig. (7): Phase lag due to filteing 6

Figue (1) illustates the speed step esponse unde loading conditions, the yellow is the speed command, and the blue is the measued speed esponse.

7 Fig. (9): Roto position duing nomal sensoless opeation The thid tace epesents the eo between the actual and the estimated position. The picked up noise is epoduced in the eo signal accodingly, the coincidence between the two signals ae othewise excellent. Figue (1) illustates the speed step esponse unde loading conditions, the yellow is the speed command, and the blue is the measued speed esponse. The open loop acceleation is clea at the ealy beginning whee the moto builds up some speed, duing which the estimated position gets moe tusted and the sense of otation is defined (clockwise otation is selected hee). Fig. (1): Speed step-esponse Contol is then tansfeed to closed loop mode, fist the speed efeence was step changed fom zeo to 59.6% of ated speed. Then a peiodic change of speed efeence fom 59.7% to 4.6 % of ated speed and fom the lowe to the highe again is enfoced. The moto takes longe to deceleate to the lowe speed efeence because it is left fo fee etadation duing this peiod. VIII- CONCLUSION The advantages obtained by using simple digital filteing along with effective extaction of EMF fom excited windings fo PMSM sensoless contol is discussed in this pape. Based on the concept pesented hee, powe cable only is needed to connect the moto to the dive electonics; exta taps o winding modifications ae not needed. Effective fixing pocedues fo canceling position and speed eos due to filteing ae also poposed. These pocedues ty to avoid static dependence on moto paametes by on-line efeshing of those paametes affecting the estimated speed. The only noticeable dawback is the exta voltage amount that should be supplied by the invete to compensate fo voltage dop acoss the extenal inductos; selecting inductos of pope values can minimize this dawback. Vey small inducto value would esult in a low measuement accuacy due to poo signal to noise atio. A compomise between educing additional voltage and measuement accuacy impovement is best deciding the extenal inducto value. In ou simulation a value of 1% of moto equivalent inductance pe phase fo extenal inducto was used. The on-line math powe equiement can be satisfied by a suitable cheap micocontolle solution. IX- APPENDIX The paametes of a 4-watt SM PMSM moto used in simulation ae listed below: R (Resistance pe phase) =.56 Ω L =L s -L M =5.945e-4 H ' λ m (Back EMF const) =.73 V/ad/s J (Inetia) =831e-7 Kgm B (fiction coeff.) =1.139e-4 N.m.s/ad P (Numbe of poles) = pole Rated continuous toque =66e-3 N.m Rated Speed =58 R.P.M. Rated powe =4 W Rated Cuent =4.51 A IX- REFERENCES [1] Ogasawaa S., Akagi H., "An Appoach to Position Sensoless Dive fo Bushless DC Moto", IEEE Tansactions on Industy Applications, Septembe/Octobe, 1991, PP [] Kinichi IIzuka, Hideo Uzuhashi, Minou Kano, Tsunehio Endo, Micocompute Contol fo Sensoless Bushless Moto", IEEE Tansactions on Industy Applications, Vol. IA-1, No. 3, May/June 1985, PP

8 [3] L. Cadoletti, A. Cassat, M. Jufe, "Sensoless Position and Speed Contol of a Bushless DC Moto fom Stat-up to Nominal Speed",EPE Jounal, Vol., No.1 (199), PP [4] D. M. Edman, H. B. Hams, J. L. Oldenkamp, "Electonically Commutated DC motos fo the Appliance Industy", IEEE-IAS Conf. Rec., Oct. 1984, PP [5] N. A. Demedash, T. W. Nehl, E. Maslowski, "Dynamic modeling of bushless dc motos in electic populsion and electomechanical actuation by digital techniques", IEEE IAC Confeence Rec., 198, PP [6] P. Zimmemann, "Electonically commutated D.C. dives fo machine tools", Motocon Poceedings, 198, PP [7] Deepak S. Shet, Hamid A. Toliyat, Thomas A. Nondahl, "Position Sensoless Contol of Suface Mount Pemanent Magnet AC (PMAC) Motos at Low Speeds", Poceeding of the Ameican Contol Conf. San Diego, Califonia, June 1999 PP [8] Khawaja M. Rahman, Hamid A. Toliyat, "Sensoless Opeation of Pemanent Magnet AC (PMAC) motos with Modified Stato Windings, Industy Application. Conf., 31st Annual IAS Meeting, 1996, vol.1 PP [9] Paul Kettle, Aengus Muay, Finba Moynihan, "Sensoless Contol of a Bushless DC Moto using an Extended Kalman Estimato", PCIM'98 Intelligent Motion. Nuenbeg, May 1998, Poceedings, PP [1] Pete Minciunescu, Tom Flint, Finba Moynihan, Paul Kettle, "Sensoless Contol of Bushless DC Motos Using Extended Kalman Filte Estimato and Back EMF Integation Algoithm: A Compaison", Embedded Contol Systems, Analog Devices Inc. [11] Silveio Blognanai, Mauo Zigliotto, Maco Zodan, "Extended-Range PMSM Sensoless Speed Dive Based on Stochastic Filteing", IEEE Tansactions on Powe Electonics, Vol.16, No.1, Jan 1, PP [1] T.W. Nehl, N.A. Demedash, F.A. Fouad, "Impact of Winding Inductance and Othe Paametes on the Design and Pefomance of Bushless DC motos", IEEE Tansactions on Powe Appaatus and Systems, Vol. PAS-14, No. 8, August 1985, PP [13] Pete S. Maybeck, "Stochastic Models, estimation, and Contol Volume 1, Academic Pess Inc (AP) New Yok, [14] Katsuhiko Ogata, "Moden Contol Engineeing", Pentice-Hall Engineeing-4th Edition, 1. 8

where and are polynomials with real coefficients and of degrees m and n, respectively. Assume that and have no zero on axis.

where and are polynomials with real coefficients and of degrees m and n, respectively. Assume that and have no zero on axis. function whee is an unknown constant epesents fo the un-modeled dynamics The pape investigates the position contol of electical moto dives that can be configued as stuctue of Fig 1 This poblem is fomulated