SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED … · SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED ... Este artigo apresenta um m¶etodo de controle sensorless de velocidade ...

SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED ON FOUR-SWITCHINVERTER

Eisenhawer de M. Fernandes∗, Euzeli C. dos Santos Jr.†, Welflen R. N. Santos‡

∗Department of Mechanical EngineeringFederal University of Campina Grande (UFCG)

Aprıgio Veloso Ave., 882, ZIP 58429-970Campina Grande-PB, Brazil

†Department of Electrical and Computer EngineeringIndiana University - Purdue University Indianapolis (IUPUI)

Indianapolis-IN, U.S.A.‡Department of Electrical EngineeringFederal University of Piauı (UFPI)

Petronio Portela Ave., ZIP 58109-970Teresina-PI, Brazil

Emails: [email protected], [email protected], [email protected]

Abstract— This paper proposes a speed sensorless control for PMSM motor drive system. The sensorlessstrategy is based on back-emf estimation of the motor, suited for applications at high speed. The drive systemuses a four-switches three-phase inverter. This topology is attractive specially in fault conditions in one leg of theconventional three-phase converter. The speed sensorless vector control based on the proposed converter providesa motor drive system with reduction of cost and volume. Relevant characteristics of the converter is presented,such as: voltage capability, capacitor currents, PWM modulation. Details of the vector control implemented isaddressed. Simulation results are shown and validates the proposed system. The proposed method has beenimplemented in an industrial converter and preliminary experimental results are presented.

Keywords— Sensorless control, vector control, permanent-magnet synchronous motor (PMSM), four-switchthree-phase inverter.

Resumo— Este artigo apresenta um metodo de controle sensorless de velocidade para motor sıncrono a ımapermanente (PMSM). A estrategia de controle sensorless implementada esta baseada na estimacao da fcem domotor, destinada a aplicacoes em alta velocidade. O acionamento do motor utiliza um conversor a quatro chaves.Esta topologia e interessante para condicoes de falha em um dos bracos do conversor trifasico convencional. Aestrategia de controle vetorial implementada sem sensor mecanico de posicao utilizando o conversor a quatrochaves proporciona um sistema de acionamento com reducao de custo e volume. Sao apresentadas as principaiscaracterısticas do conversor, tais como: tensao maxima do barramento CC, correntes dos capacitores e modulacaoPWM. Resultados de simulacao sao apresentados para validacao da proposta. O sistema sensorless proposto foiimplementado em laboratorio em um conversor industrial e resultados experimentais preliminares da propostasao apresentados.

Keywords— Controle sensorless, controle vetorial, motor sıncrono a ıma permanente (PMSM), inversortrifasico com quatro chaves.

1 Introduction

Permanent-Magnet Synchronous Motors (PMSM)are widely used in industrial applications such asservo positioning systems, robots and printing ma-chines and transportation such as electrical vehi-cles and hybrid vehicles. This type of machineprovides a unique set of advantages and oppor-tunities compared to induction machines. Theseadvantages are compactness, higher efficiency, ro-bustness, reliability (Pillay and Krishnan, 1991),(Consoli et al., 2001), (Bolognani et al., 2000a).

PMSM motor drives require rotor position in-formation which is provided by a rotor positionsensor mounted in motor shaft (encoders or re-solvers). The use of rotor position sensors repre-sent drawbacks such as increasing cost, volume,necessity of mechanical adaptation and reduc-tion of feasibility of drive system (Consoli et al.,

2001),(Jang et al., 2003),(Andreescu et al., 2008).In this manner, scientific investigation has aimedat eliminating the position sensor and estimaterotor position from electrical quantities of themotor, using the motor itself as position sensor.These solutions are known in literature as sensor-less or self-sensing control.

Sensorless control methods can be classified intwo categories: signal injection methods (Corleyand Lorenz, 1998),(Jang et al., 2003),(Caruanaet al., 2006),(Holtz, 2008),(Fernandes et al., 2013),and back-emf estimation methods. Signal injec-tion methods are based on tracking of rotor mag-netic saliency or anisotropy of the motor in the lowspeed region, exploiting the high-frequency modelof the motor when an extra signal is applied. Sec-ond category estimates rotor position from theback-emf estimation based on the fundamentalmodel of the motor. The performance of the es-

Anais do XX Congresso Brasileiro de Automática Belo Horizonte, MG, 20 a 24 de Setembro de 2014

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timators is dependent on the back-emf amplitude(Jang et al., 2003),(Ribeiro et al., 2006) thereforethey are suited for applications at medium andhigh speed range.

On the other hand, in most of applications,the PMSM motor is conventionally driven by thethree-phase voltage source inverter. In literature,motor control research focused on cost-effectivedesign has presented the four-switch inverter todrive AC motors (Jacobina et al., 2005),(Linet al., 2008). In (Lin et al., 2008), it has beenproposed the use of the four-switch three-phaseinverter to drive BLDC motor with trapezoidalback-emf. Besides, this configuration has beenadopted in fault-tolerant solutions when in open-switch fault occurs in the inverter (Bolognaniet al., 2000b),(Wallmark et al., 2007).

The objective of this paper is to propose theuse a four-switch three-phase inverter in a speedsensorless system for PMSM motors. The configu-ration have been designed for applications where itis necessary to control two motors independentlyby using a standard three-leg inverter. Besides,it is possible to implement a sensorless strategyto drive the PMSM in order to increase the me-chanical robustness of the overall system (Corleyand Lorenz, 1998). In this work, it was applieda sensorless strategy based on the fundamentalcomponent voltage model of the machine (Chenet al., 2000),(Kim et al., 2002).

The paper presents relevant characteristics ofthe converter, such as i) voltage capability, shared-leg and capacitor currents, ii) pulse-width modu-lation techniques based on scalar approaches; iii)control strategies for providing current control;and iv) simulation and experimental results.

Figura 1: Four-switch three-phase inverter sup-plying a PMSM motor.

2 Proposed Configuration

The proposed configuration is illustrated in Fig.1.This section addresses the model of the PMSMmotor and the characteristics of the converter.

2.1 Permanent-Magnet Synchronous Motor -PMSM

A three-phase permanent-magnet motor is com-posed by three windings in the stator and by arotor where the magnet is placed. The model writ-ten in terms of dq variables in synchronous rotorreference frame describes the dynamic behavior ofthe machine given by (Pillay and Krishnan, 1991),(Corley and Lorenz, 1998):

vrsd = rsi

rsd +

d

dtφr

sd − ωrφrsq (1)

vrsq = rsi

rsq +

d

dtφr

sq + ωrφrsd (2)

φrsd = lsdi

rsd + φpm (3)

φrsq = lsqi

rsq (4)

Te = P (irsqφpm + (lsd − lsq)irsdirsq) (5)

where vrsd and vr

sq are d,q-axis stator voltages, irsd

and irsq, are the d, q-axis stator currents, φsd andφsqare the stator flux linkages. rs is the phaseresistance, lsd and lsq are d, q-axis inductances.Te is the electromagnetic torque; ωr is the angularfrequency of the rotor; φpm is the flux linkage dueto the rotor magnets; and P is the number of pairof poles.

2.2 Four-switch three-phase inverter

The configuration comprises four switches, a dc-bus constituted by a capacitor bank with mid-point connection. The converter is composed byswitches q1, q1, q2, q2. The switch-pairs q1− q1,q2− q2 and q3− q3 are commanded complemen-tary.

2.3 PWM Control

The configuration proposed in this work is shownin Fig 1. In this topology both machines are con-nected to the dc-bus mid-point. The PMSM ma-chine voltages (vs1, vs2, vs3) are given by:

vs1 =23v10 − 1

3v20 (6)

vs2 = −13v10 +

23v20 (7)

vs3 = −13(v10 + v20) (8)

Besides, the PWM relations obtained aregiven by:

v∗10 = v∗s1 − v∗s2 (9)

v∗20 = v∗s2 − v∗s3 (10)


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Once the pole voltage v∗10 and v∗20 have beendetermined (9)-(10), the pulse-widths τ1 to τ3 arecalculated by using:

τ j =Ts

2+

Ts

Ev∗j0 for j = 1 to 2. (11)

These pulse-widths values are used to gener-ate the gating signals for the switches by a pro-grammable registers by comparing the modulationreference signal v∗10 and v∗20 with a high-frequencytriangular carrier signal.

3 Voltage Analysis

The voltage limit can be determined by consider-ing that all voltages are purely sinusoidal. In (12),it is written have the limit conditions associatedwith the proposed configuration. In (12), Vs is thevoltage amplitude of the three-phase machine andE is the DC-link voltage, respectively.

E =√

3Vs (12)

This topic will be better addressed in the finalversion of the paper.

4 Capacitor Currents

The capacitors average currents ic1 and ic2, overthe sampling time Ts for the proposed configura-tion are given by:

ic1 =is32

(13)

ic2 = − is32

(14)

The capacitor average currents (13), (14) in-dicate the discharging of capacitor bank, i.e., thelevel of DC-bus voltage ripple.

5 Back-emf tracking method

For PMSM sensorless operation at medium andhigh speeds it is required the use of estimationmethods based on back-emf tracking. The in-formation of the rotor position is extracted fromback-emf estimation, thus, it is not necessary theapplication of extra signal. In this work, it hasbeen implemented the method proposed by (Kimet al., 2002). The method employs two cascadedestimators, one for back-emf estimation and otherfor rotor position estimation.

The back-emf estimator is a current state-filter implemented in the stationary referenceframe (Fig. 2). The structure is based onthe extended back-emf model proposed by (Chenet al., 2000). From the machine model (1)-(5), it

can be written in manner that can be obtainedthe extended back-emf (Eex):

vssd = (rs +

d

dt)issd − ωr(lsd − lsq)issq − Eex sin θr (15)

vssq = (rs +

d

dt)issq + ωr(lsd − lsq)issd + Eex cos θr (16)

Where:

Eex = ωr[(lsd − lsq)issd + φpm]− (lsd − lsq)d

dtissq (17)

From (17) it can be seen that it includes theeffects caused by rotor saliency (lsd− lsq) and thecontribution of flux linkage of the rotor’s mag-nets (ωrφpm). The extended back-emf presentsthe rotor position information, thus, the rotor po-sition can be estimated from the estimation ofthe back-emf. The back-emf can be estimatedfrom the currents and voltages terminals measure-ments according to different methods in literaturesuch as flux observers (Corley and Lorenz, 1998),state filters (Kim et al., 2002) and Kalman filters(Bolognani et al., 1999).

In this work, it has been applied the struc-ture presented in combined with a extended Lu-enberger observer (Corley and Lorenz, 1998),(Kimet al., 2002), illustrated in Fig.2. The transferfunction obtained for estimated extended back-emf and the extended back-emf from model (1)-(5):

Eex =Ros + Rio

lsds2 + (rs + Ro)s + RioEex (18)

Figura 2: State-filter for stationary current andback-emf estimation.

The estimated back-emf presents the positioninformation (θr), the estimation error is applied tothe input of the rotor position observer. The rotorposition observer is composed by a heterodyningprocess, a controller(kio, kpo, kdo) and the physicalmodel of the motor. The rotor position observeris a Luenberger observer providing the estimatedmechanical rotor speed (ωrm) and rotor position(θrm). The observer is illustrated in Fig. 3.


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Figura 3: Rotor position observer based on back-emf tracking.

The transfer function of the rotor position es-timation can be written as:

θr(s)θr(s)

=J

(lsd−lsq

lsd−lsq

)s3 + kdos

2 + kpos + kio

Js3 + kdos2 + kpos + kio

(19)

The rotor position estimator has the property ofzero lag estimation due to the reference torquefeedforward input (T ∗e ).

6 Sensorless control system

The control block diagram of the proposed systemis shown in Fig. 4. The control strategy of thesystem is composed by the speed control in cas-cade with torque and current control loops. Thespeed controller is a PI regulator type. The ’vectorcontrol’ block defines the reference currents of dq-axis. The reference current (irsq) is obtained fromthe reference torque (T ∗e ) of the speed controlleroutput. The d-axis reference current (irsd) is setto be zero, thus, irsq defines the required torque.

The stator currents are controlled by two PI-controllers in the synchronous reference frame.The reference voltages vr∗

sd , vr∗sq are transformed to

the reference phase voltages, v∗s1, v∗s2, v

∗s3. Based

on the phase reference voltages, the reference polevoltages are calculated according to (9)-(??).

The phase currents are measured and trans-formed back to the synchronous reference frame.The current controller gains has been designedaccording the pole placement criteria. The con-troller gains cancels the machine poles. As aresult, the controller gains are determined fromthe desired bandwidth of the closed-loop transferfunction. The same procedure is applied to definethe gains of the speed controller.

The measured currents and the reference volt-ages are used as input of the back-emf estimator.The rotor position observer provides the rotor po-sition used in the transformations between refer-ence frames. Besides, the estimated rotor speed isused in the speed control loop replacing the me-chanical transducer.

Figura 4: Control block diagram of the proposeddrive system.

7 Simulation results

The speed sensorless control system has been sim-ulated in Matlab. The system has been evalu-ated for in sensorless manner using the four-switchthree-phase inverter.

The speed controller bandwidth has been setto 10 Hz. The current controller’s bandwidths hasbeen set to 250 Hz. The switching frequency is 10kHz. The sampling time of the variables is 100µs.The reference speed is set to 900rpm (60Hz).TheDC-link voltage is 300V. The PMSM motor hasthe following rated parameters: rs = 0.67Ω,lsd =22mH,lsq = 33mH,J = 0.084.10−3kg.m2,Iphase =2.0A,Vphase−phase = 200V,P = 400W, N = 3.000rpm.

The back-emf estimator gains (Rio,Ro) weredetermined from the characteristic polynomial ofthe back-emf estimator transfer function, in thiscase a 2nd order polynomial. Thus, the estima-tor gains has been chosen according the band-width necessary to estimate the back-emf. Onthe other hand, it has been adopted a 3rd or-der characteristic polynomial to the rotor positionobserver transfer function to define the observergains (ki,kp,kd).

The speed reference is 900 rpm (60Hz). InFig. 5 is shown the results for sensorless opera-tion using rotor position observer based on back-emf tracking. In Fig. 5 is shown rotor speed (ωr),measured position (θr), estimated position (θr)and phase currents. In Fig. 6 is shown rotor speed(ωr), measured position (θr), dq-axis stator cur-rents (irsd, i

rsq). During this test is applied a load

torque equal to 30% of the rated torque. Basedon the results, one can observe a small estimationerror demonstrating a satisfactory performance ofthe rotor position estimator.

7.1 Experimental results

In order to verify the performance of the proposedsystem, it was mounted a test setup in laboratory(Fig. 7). The experimental setup is composed bya microcomputer equipped by a DSP program-


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0.36 0.365 0.37 0.375 0.38 0.385 0.390

5

0.36 0.365 0.37 0.375 0.38 0.385 0.39360

370

380

0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39−1

0

1

Figura 5: Simulation results for sensorless con-trol using four-switch three-phase inverter(top tobottom): measured position (θr) and estimatedposition (θr), measured speed (ωr) and estimatedspeed (ωr), phase currents is1, is2, is3.

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8360

365

370

375

380

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8

0

0.5

1

Figura 6: Simulation results for sensorless controlusing four-switch three-phase inverter:(top to bot-tom): measured speed (ωr) and estimated speed(ωr), dq-axis currents irsd, i

rsq.

ming board and two commercial PMSM servo-drives. The servodrives consist of PWM VSI with8kHz switching frequency and power modules witha dead-time of 1µs. The three-phase PMSM mo-tor is driven by Converter 1 which is programmedwith the desired control algorithm. On the otherhand, Converter 2 and PMSM2 are used to emu-late different load conditions to PMSM1. The con-trol algorithm is programmed to the internal DSPof Converter 1 (Renesas SH7047). It performsclosed loop speed and current control and gener-ates the PWM relations (9)-(10). Bandwidths ofthe speed controller and current controllers are setto be 15 Hz and 120 Hz, respectively. The com-mand signals are generated with a sampling timeof 140µs.

In Figs. 8-9 presents the experimental re-sults for the speed control system based on sen-sorless control using conventional three-phase in-verter. In Fig. 8 is shown the measured rotor po-sition (θr) and estimated rotor position (θr) andphase current (is1). In Fig. 9 is shown the mea-sured and estimated speed for the same condition.The experimental results for the sensorless strat-

egy based on the four-switch three-phase inverterare still ongoing. A complete set of experimental

Figura 7: Experimental setup: two three-phaseservodrives, two three-phase PMSM motors and aSPIM machine.

Figura 8: Experimental results for sensorless con-trol using standard three-phase inverter(top tobottom): measured position (θr) and estimatedposition (θr), estimation error (θr − θr), is1.

results will be addressed in the final version of thepaper.

8 Conclusions

The paper presents a speed sensorless control sys-tem based on four-switch three-phase inverter.This topology is interesting specially in fault con-ditions in one-leg of the conventional three-phaseconverter. The speed sensorless vector controlbased on the proposed converter provides a motordrive system with reduction of cost, volume andincrease the reliability of the overall drive system.

The speed sensorless control is based on theback-emf tracking of the PMSM motor. The back-emf is estimated from a current state-filter andapplied to a Luenberger-style rotor position ob-server. The estimated rotor position and speedare used replacing the information provided bymotion transducers. Then, the rotor position isextracted by using the motor itself. Details ofstructure and characteristics have been shown.

The performance of sensorless control hasbeen validated by simulations. Preliminary resultsof the control system in a test setup are shown.Experimental results for the proposed system are


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Figura 9: Experimental results for sensorless con-trol using standard three-phase inverter(top tobottom): measured speed (ωr) and estimatedspeed (ωr), is1.

still ongoing.

Referencias

Andreescu, G., Pitic, C. I., Blaabjerg, F. andBoldea, I. (2008). Combined flux observerwith signal injection enhancement for widespeed range sensorless direct torque controlof ipmsm drives, IEEE Transactions on En-ergy Conversion 23: 393–401.

Bolognani, S., Oboe, R. and Zigliotto, M. (1999).Sensorless full-digital pmsm drive with ekf es-timation of speed and rotor position, IEEETrans. on Industrial Electronics .

Bolognani, S., Zordan, M. and Zigliotto, M.(2000a). Experimental faul-tolerant controlof pmsm drive, IEEE Trans. Ind. Electron.47(5): 1134–1141.

Bolognani, S., Zordan, M. and Zigliotto, M.(2000b). Experimental fault-tolerant controlof a pmsm drive, IEEE Trans. on IndustrialElectronics 47.

Caruana, C., Asher, G. M. and Summer, M.(2006). Performance of hf signal injectiontechniques for zero-low-frequency vector con-trol of induction machines under sensorlessconditions, IEEE Trans. on Industrial Elec-tronics 53(1): 225–238.

Chen, Z., Tomita, M., Ichikawa, S., Doki, S. andOkuma, S. (2000). Sensorless control of in-terior permanent magnet synchronous motorby estimation of an extended electromotiveforce, Proc. IEEE IAS Annual Meeting .

Consoli, A., Scarcella, G. and Testa, A. (2001).Industry application of zero-speed sensorlesscontrol techniques for pm synchronous mo-tors, IEEE Transactions on Industry Appli-cations 37: 513–521.

Corley, M. J. and Lorenz, R. (1998). Rotor posi-tion and velocity estimation for a salient-polepermanent magnet synchronous machine atstandstill and high speeds, IEEE Trans. onIndustry Applications 34: 784–789.

Fernandes, E. M., Oliveira, A. C., Lima, A. M. N.,Jacobina, C. B. and Santos, W. R. N. (2013).A comparative evaluation of signal injectionmethods for pmsm self-sensing control, Proc.of COBEP 2013 pp. 821–827.

Holtz, J. (2008). Acquisition of position error andmagnet polarity for sensorless control of pmsynchronous motors, IEEE Trans. on Indus-try Applications 44(4): 1172–1180.

Jacobina, C. B., dos Santos Jr., E. C., Correa, M.B. R. and da Silva, E. R. C. (2005). Ac motordrives with a standard number of switchesand boost inductors, Proc. of IEEE AppliedPower Electronics, APEC 2005 pp. 733–739.

Jang, J.-H., Ha, J.-I., Ohto, M., Ide, K. and Sul,S.-K. (2003). Analysis of permanent-magnetmachine for sensorless control based on high-frequency signal injection, IEEE Trans. In-dustry Applications 39: 1595–2004.

Kim, H., Harke, M. C. and Lorenz, R. D. (2002).Sensorless control of interior permanent mag-net machine drives with zero-phase lag esti-mation, IEEE IAS Annual Meeting 2: 86–91.

Lin, C.-T., Hung, C.-W. and Liu, C.-W. (2008).Position sensorless control for four-switchthree-phase brushless dc motor drives, IEEETrans. on Power Electronics 23.

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Ribeiro, L. A., Harke, M. C. and Lorenz, R. D.(2006). Dynamic properties of back-emfbased sensorless drives, Conf. Rec. IAS An-nual Meeting, 2006 4: 2026–2033.

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SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED … · SPEED SENSORLESS PMSM MOTOR DRIVE SYSTEM BASED ... Este artigo apresenta um m¶etodo de controle sensorless de velocidade ...

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