P

Abstract -- This paper presents a rotor position estimation technique for a five-phase permanent magnet synchronous motor with independent phases, based on a back-EMF observer. The method involves the use of a proper linear transformation which allows representing the five-phase motor by an equivalent two-phase model. Due to its characteristics, the sensorless strategy can be used in multi-phase motors having non-sinusoidal back-EMF shape, such is the case of brushless DC motors used in fault-tolerant applications. After an overview of the back-EMF model for the five-phase motor, the linear transformation and the observer-based estimation technique are presented. Experimental results show the overall performance during transient and steady-state operation.

Index Terms Brushless DC, estimation techniques, five-phase motor, linear transformation, permanent magnet synchronous motor, sensorless drives, back-EMF observer.

I. NOMENCLATURE

x phase subscript; Vx , Ix phase voltage and current; R , L phase resistance and inductance; Ex magnet-induced back-EMF; fx back-EMF shape function;

Mx magnet flux linkage; m rotor mechanical position; r rotor electrical position; r rotor electrical speed; eK back-EMF constant;

p rotor pole-pairs; eC electromagnetic torque;

X estimated value of variable X; )(1X 1st harmonic of variable X.

II. INTRODUCTION

ermanent Magnet Synchronous Motors (PMSM) are widely employed for their high efficiency, silent

operation, compact form, reliability, and low maintenance. Depending on the application, different typologies of motors are used, with different rotor structure (surface or buried magnets), winding type (distributed or concentrated), and back-EMF shape (sinusoidal or trapezoidal).

Recently, multi-phase PMSM with independent phases have been proposed for safety critical applications such as aircraft brakes, spoiler or flap actuators, [1], [2], [3]. In these cases, the multi-phase machine is fed by a multi-phase power converter, and the whole drive system must satisfy severe fault-tolerant requirements, which involve the control hardware and the drive sensors too.

Giuseppe Fabri, Carlo Olivieri and Marco Tursini are with the Department of Electrical and Information Engineering, University of LAquila, I-67100, LAquila, Italy (e-mail: giuseppe.fabri@univaq.it, carlo.olivieri@univaq.it, marco.tursini@univaq.it).

Brushless DC (BLDC) motors are preferred, with magnets mounted on the rotor surface and trapezoidal shaped back-EMF. Hall-effect bipolar sensors can be used as primary position transducers, in a quite simple and reliable assessment: each stator-fixed Hall sensor, one for each phase, directly detects the polarity of the undergoing rotor magnets with a proper angular displacement. The digital signals are processed by the controller and the rotor position information is computed with the resolution necessary for the electronic commutation of the motor.

In some cases magnetic encoders are adopted, with the role of secondary sensor, and sensor redundancy is provided to match the fault-tolerant requirements. To this matter, in order to extend the fault-tolerant drive capabilities, sensorless strategies can be provided, capable to assure safe operation also in case of fault of one or more sensor [4], [5].

In this paper, an approach to rotor position detection for a multi-phase PMSM is presented, suitable for application with surface mounted PM motors having unknown and whatever shaped back-EMF waveforms, such as BLDC motors. The estimation technique is based on the principle of the back-EMF observer [6], [7], extended in this case to a multi-phase machine, in particular to a five-phase motor.

The core of this approach is the use of a properly designed transformation to bring the multi-phase description of the motor into a two-phase description and then applying to the transformed system the state observer. This last one is used to reconstruct the instantaneous value of the motor back-EMF so we can subsequently calculate the desired angular information through a proper phase detection algorithm. Experimental results are presented to confirm the validity of the proposed approach for the use in multi-phase machines.

III. FIVE-PHASE PM BLDC MOTOR Fig. 1 shows a cross section of the five-phase PM BLDC

motor considered in this paper, [8].

Phas

e B

Fig. 1. Five-phase PM BLDC motor.

Observer-based Sensorless Control of a Five-phase Brushless DC Motor

G. Fabri, C. Olivieri, M. Tursini

XIX International Conference on Electrical Machines - ICEM 2010, Rome

978-1-4244-4175-4/10/$25.00 2010 IEEE

Fig. 2. Power converter for independent phase feeding.

It has 18 rotor poles and 20 stator slots (4 slots per phase). Each phase consists of two series coils mounted on diametrically displaced stator teeth. Due to this structure, independent feeding of each phase is provided by independent H-bridges modules [9] as can be seen in Fig. 2. Hence it results that motor phases are independent from each other, in the sense of electrical, thermal and magnetic interactions, a suitable feature to avoid a single phase faults to affect the remaining safe phases.

A. Five-phase model Dealing with the description of such kind of independent-

phase machine, we can write down the following generalized voltage equation:

)( rxxxx EtILIRV ++=d

d (1)

where the subscript x ( EDCBAx ,,,,= ) indicates a generic phase of the motor, and mr p = the rotor (electric) angle.

The instantaneous value of the back-EMF is given by the time derivative of the magnet flux linkage in the phase, which in turn depends from the position of the rotor:

rr

rr

r

rrr

MxMxMxx tt

E

)(

)()()( ===d

dd

dd

dd

d(2)

with r is the rotor speed. In order to generalize the voltage balance in case of non-

sinusoidal machines, the normalized back-EMF shape functon is defined as follows:

re

rr K

Ef xx )()(

= (3)

where eK the back-EMF constant. From that, we can modify the machine equations into the

following form:

)( rre xxxx fKtILIRV ++=d

d (4)

The shape functions of the motor considered in this paper are reported in Fig. 3, while the electrical parameters are reported in Table I. Depending on the motor design, the back-EMF waveforms are quasi-trapezoidal and they are symmetrically displaced over just one-half of the electrical period, which gives the machine an intrinsic asymmetry.

Regarding to the electromagnetic torque, it can be expressed in the particular case of a multi-phase machine in the following way:

==

E

Axxrx

r

E

Axx

r

rMxe I)(E

pIpC

)( ==d

d (5)

and using the shape functions one obtains:

0 120 240 360 480 600 720

-1

-0.75

-0.5

-0.25

0

0.25

0.5

0.75

1

angle (degrees)

shap

e fu

nctio

ns (p

er u

nits)

Fig. 3. Back-EMF shape functions of the five-phase motor (design data).

=

E

Axxrxee IfKpC )(= . (6)

B. Space-vector representation In order to set-up the sensorless strategy with a minimum

number of equations, an equivalent space-vector representation of the five-phase motor has been developed. The objective is to achieve sine/cosine shapes for the components of the equivalent shape function (i.e. back-EMF) space-vector, in order to set-up a two-phase observer similar to that employed in more standard three-phase motors.

To this purpose, the linear transformation given by matrix (7) can be considered, which allows to represents the five-phase motor by a couple of space-vectors with components denoted as and and an homopolar component.

[ ]

=

)()()()()(

)()()()()(

)()()()(

)()()()()(

58

56

54

520

58

56

54

520

111115

45

35

25

(0)5

45

35

25

0

52

sinsinsinsinsin

coscoscoscoscos

sinsinsinsinsin

coscoscoscoscos

ABCDET (7)

In (7) the first two rows are achieved by the projection of the magnetic axes of the five phase motor on the orthogonal system displaced as shown in Fig. 4, they define a direct sequence space-vector. The third, forth and fifth rows are defined considering the virtual inversion of the magnetic axis direction of phases B and D, i.e. the equivalent motor of phases A,C,E,-B,-D, symmetrically displaced of 2/5 electrical degrees. The third row defines the homopolar (zero sequence) component, while the forth and fifth rows define an inverse sequence space-vector whose values would be null in case of purely sinusoidal motor and safe operation.

Fig. 4. Actual (ABCDE) and equivalent-symmetrical (ACE-B-D) axes of the five-phase

The multiplicative factor is chosen in order to have the same amplitude of the phase and transformed variables (for a purely sinusoidal motor).

The application of the transformation (7) to the back-EMF shape functions of the five-phase motor gives the results reported in Fig. 5.

0 120 240 360 480 600 720-10

1

Alpha - Beta components

0 120 240 360 480 600 720-0.05

0

0.05Zero sequence component

0 120 240 360 480 600 720-0.2

00.2

Alpha' - Beta' components

angle (degrees) Fig. 5. Shape functions of the transformed equivalent model.

Due to the quasi-trapezoidal back-EMF nature of the BLDC motor, both the zero sequence and the inverse sequence components are not equal to zero, nevertheless this aspect will not affect the proposed sensorless strategy.

In fact, in the following we will consider only the direct sequence components for the set-up of the observer-based sensorless strategy. In fact, the information on the rotor position can be extracted by the first harmonic of the direct sequence component independently on the values of the zero and inverse sequence ones.

C. Equivalent back-EMF model Considering the equivalent two-phase stator-fixed alpha-

beta model associated to the direct sequence space-vector of the five-phase motor, the following state form (matrix) equation is obtained:

[ ] [ ] [ ] VBEAIAtI

11211d

d++= (8)

where: [ ] [ ] ABCDE

ABCDE

T VTVVV ==

, ,

[ ] [ ] ABCDEABCDE

T ITIII ==

, ,

( ) [ ] [ ] ( )rABCDEABCDE

Tr ETEEE

==

, ,

and

[ ]

=

10

0111 L

RA , [ ]

=

10

0111 L

B , [ ] [ ]112 BA = are matrices of constant system parameters.

The back-EMF dependence on rotor magnet position can be arranged in the following general form:

( ) ( )

=

=1hr

hrer hfKE )( (9)

where the periodic shape functions are expressed through the Fourier series expansion, and for the conventions assumed in the linear transformation one has:

( ) rr sinf )( =1 ; ( ) rr cosf )( =1 (10)According to (6), the rotor (magnet) position information

is contained in the sine/cosine shapes of the 1st harmonic back-EMFs. If the speed is assumed as a constant (that is the case of speed steady-state operation), the following relations are achieved by time derivatives of these fundamentals:

[ ] )()(

122

1

d

dEA

tE

= (11)

being:

[ ] [ ])( rr AA 222201

10=

= (12)

a speed dependent matrix.

By associating (8) and (11) the following extended model is obtained, which represents the motor dynamics in terms of 1st harmonics back-EMFs at speed steady-state:

][][ VBXAtX

+=d

d (13)

with TEEIIX ],,,[ = state variables, and:

[ ]

=

)]([

][][

rA

BAA

22

111

0, [ ]

=

0

1][BB

system matrices.

In the extended model (13) the currents acts as the system outputs (measurable state-variables), the applied voltages are the system inputs, while the back-EMF components take the role of internal (non measurable) state-variables.

IV. OBSERVER-BASED SENSORLESS STRATEGY

A. Back-EMF observer From the previous extended model a linear state observer

can be built as follows (Luenberger-like observer):

)( ][][][ IIKVBXAtX

++=d

d (14)

with TEEIIX ],,,[ = estimated state variables, and:

[ ] [ ][ ][ ]

=

1

1

KG

KK , [ ]

=

10

0111 kK , [ ]

=

10

01gG

gain matrices (with k1 and g constant gains), where the parameter g stands for a generic proportionality factor that can be used to weight more heavily the back-emfs estimates with respect to the currents estimates.

The observer is used to estimate the run-time waveforms of the 1st harmonic motor back-EMFs. From these we can retrieve the angular position and the speed of the rotor magnet axis by a proper phase detection algorithm as described in the next subsection.

B. Rotor speed and position detection The block scheme of the algorithm employed for rotor

speed and position detection is shown in Fig. 6. The basic principle refers to a quadrature Phase Locked Loop (PLL). It involves the generation of an error signal from the phase

difference between harmonic input signals (in our case the estimated back-EMF components) and corresponding quadrature feedback functions of the estimated angle.

Assuming for the estimated 1st harmonics of the back-EMF the phase relation given by (9) and (10), and using the Werners formula we can write the following expression of the error signal:

)~()~~( rrrrrr sinsincoscossin(t) (15)

where r~ represents the argument of the input waveforms

(assumed as known references) and r is the argument of the feedback signals, i.e. the estimated angle. For small deviations between them one obtains:

)~( rr(t) (16)

Hence, a Proportional Integral (PI) regulator can be used to generate the closed loop feedbacks, in order to correct the angle deviation and bringing the estimated angle to converge to the reference one. The estimated speed signal can be obtained by introducing a further integration block between the output of the PI regulator and the generation of the feedback signals.

Fig. 6. Phase detector scheme.

Hence, the observer-based sensorless strategy for the

five-phase BLDC motor can be resumed by the functional blocks shown in Fig. 8: first, the five-phase motor currents and voltages are measured and transformed into the equivalent components using the first two rows of the linear transformation (7); second, using these measurements, the time-varying alpha-beta components of the 1st harmonic back-EMF are estimated in the back-EMF observer; third, from these estimates, the rotor speed and magnet axis position are computed by the phase detection algorithm.

Due to the dependence of the observer sub-matrix [ ]22A from the rotor speed, the estimate of this signal must be used as an additional run-time input of the observer.

*n

nPI

Fig. 7. BLDC sensorless control scheme.

Fig. 8. Observer-based sensorless strategy.

C. Sensorless drive scheme The drive scheme incorporating the observer-based

sensorless strategy is shown in Fig. 7. Modular architecture is used in current control. Five

independent current control loops regulate the phase currents. In each current loop a comparison between reference and measured current is performed, error is PI regulated and correction is applied through five independent H-bridges in the voltage-source inverter. An external loop regulates the speed by comparison with the respective feedback, the speed error is regulated through a PI regulator and torque requirement in term of current reference is generated.

Fig. 9. BLDC control strategy.

The commutation logic used to compute the current references is shown in Fig. 9. According to the BLDC control strategy, constant torque is generated by feeding the motor phases with constant current in constant back-EMF wave region. To achieve this behavior the rotor electric turn is divided into ten sectors, in each sector only four back-EMFs are constant so that the motor is fed by four quasi-square back-EMF synchronous currents, while the remaining current is controlled at zero.

V. EXPERIMENTAL SET-UP AND RESULTS The experimental set-up arranged to verify the

performance of the sensorless strategy for the five-phase BLDC motor is shown in Fig. 10. The control unit is based on a TMS320F2806 digital signal controller (DSC), whose enhanced peripheral capabilities are used for interfacing the power hardware both for control and diagnostic purposes.

Position sensors are provided, in order to set-up and evaluate the performance of sensorless control: five Hall sensors are used to generate the magnet field sector information needed for the BLDC commutation logic; a square-wave quadrature encoder with 536 (134 x 4) pulses-per-revolution is also present, employed for speed computation.

The experimental set-up includes a host PC, a Digital-to-Analog Converter (DAC) and a scope. The host PC runs the DSC development and debugger tools and the user interface, this last allows data exchange with the control firmware. The scope is used for displaying the variables computed by the control algorithm in real-time, through a 4 channel DAC.

Fig. 10. Drive board description and experimental system set-up.

Figures 11 to 14 report some test results of the five-phase sensorless drive prototype. In a first development step, tests have been carried out with the observer in open-loop, i.e. the estimated speed and position are not used for motor control.

Fig. 11 shows the estimated alpha and beta back-EMF components versus the commutation sector evolution (measured from the Hall sensors) during a no-load test at about rated speed (570 rpm, equal to 85.5 Hz).

According to what expected from theory the shapes of the estimated back-EMFs are close to pure sinusoids, the alpha-beta components are in quadrature with the first one leading on the second one. Being the zero of the actual position located on the center of the first sector (see Fig. 9), this test would prove an estimation error of about one-half sector, i.e. 18 electrical degrees. Investigation about this error is out of the scope of the present paper. Nevertheless, due to intrinsic implementation delays in the acquisition of the Hall sensor signals, the position estimation error computed from the scope outputs represents just an indication.

Fig. 12 shows the response of the back-EMF observer when it operates at low speed condition (60 rpm, equal to 9 Hz). The shapes of the back-EMFs are estimated correctly even in this situation. Also the electrical position is shown: in this case the position reference is aligned with the alpha axis localized in the center of the first sector, leading to position estimation error apparently equal to zero.

Fig. 13 shows the estimated back-EMF during a ramp speed transient from a low value to a medium one: the amplitudes and frequencies increase correctly and smoothly with the speed, the dynamic response of the observer appears to be fast and well damped.

Fig. 11. Alpha (black trace) and Beta (blue trace) components of the back-EMFs, commutation sector (magenta) and speed (green) @ 570 rpm (voltage is scaled to 50V/div).

Fig. 12. Commutation sector (magenta), estimated position (black) and estimated Alpha and Beta back-EMFs (green and blue respectively) @ 60 rpm (voltage is scaled to 20V/div).

Fig. 13. Alpha and Beta back-EMFs (black and blue respectively), commutation sector (magenta) and speed (green) in speed transition from 60 to 390 rpm (voltage is scaled to 20V/div).

Finally, in Fig. 14 are shown the estimated electric position and speed and the corresponding measured signals in a more large speed transition from low to about rated value. It can be noticed that the estimated speed is consistent with the measured speed in a quite satisfactory way.

Fig. 14. Commutation sector (magenta) and actual speed (blue) are reported in the upper axis, estimated position (black) and estimated speed (green) are reported in the lower axis, during a speed transition from 60 to 570 rpm (speed is scaled to 300rpm/div).

VI. CONCLUSIONS An approach to the rotor speed and position estimation in

a five-phase BLDC motor is proposed, based on a back-EMF observer. A linear transformation is developed to represent the five-phase motor by an equivalent two-phase model and a 4th order state observer is implemented including the back-EMFs dynamics. The position is extracted from the estimated back-EMFs using a PLL algorithm.

The presence of saturation is not taken into account because the two-phase linear model developed in this study is able to correctly describe the behavior of the system with good approximation.

The proposed strategy has been validated by experimental results with the observer operating in open-loop, the analysis has pointed out that the rotor position and speed are estimated with good reliability both at high and low speed.

Estimation errors reported at high frequency operation such as the influence of the observer gains set-up require a deeper analysis and will be investigated in the next step of this research.

TABLE I MOTOR PARAMETERS

base speed 600 rpm base voltage 240 Vpk base current 5 Apk rated torque 16 Nm pole pairs 9 phase resistance 3.88 phase inductance 24.1 mH back-EMF constant 0.0972 Vpk / rpm

VII. ACKNOWLEDGMENT The authors want to thanks UmbraGroup (Foligno, Italy)

for making available the five-phase motor prototype considered as test case in this paper.

VIII. REFERENCES [1] B. Mecrow, A. Jack, and J. Haylock, FaultTolerant permanentmagnet machine drives, IEE Proc., Electr. Power Applications, Vol. 143, no. 6, pp. 437442, Dec. 1996. [2] T.H. Liu, J.R. Fu, and T.A. Lipo, A Strategy for Improving Reliability of Field-Oriented Controlled Induction Motor Drives, IEEE Trans. on Ind. Appl., Vol. 29, no. 5, Sept./Oct. 1993, pp. 910-917. [3] L. Parsa, H.A. Toliyat, Fault-Tolerant Five-Phase permanent magnet motor drives, Industry Applications Conference, 2004. 39th IAS Annual Meeting. Conference Record of the 2004 IEEE, Vol. 2, 3-7 Oct. 2004 pp. 1048 - 1054 Vol.2 [4] L. Parsa, H.A. Toliyat, "Sensorless Direct Torque Control of Five-Phase Interior Permanent-Magnet Motor Drives", IEEE Transactions on Industry Applications, Vol. 43 , Issue: 4, 2007 , pp. 952 959. [5] L. Zheng, J . Fletcher, B. Williams, X. HE, A Novel Direct Torque Control Scheme for a Sensorless Five-Phase Induction Motor Drive, IEEE Transactions on Industrial Electronics, Vol. PP, Issue: 99 Publication Year: 2010, pp. 1-1. [6] Joohn-Sheok Kim, Seung-Ki Sul, High performance PMSM drives without rotational position sensors using reduced order observer, Industry Applications Conference, 1995. Thirtieth IAS Annual Meeting, IAS '95, Conference Record of the 1995 IEEE , Vol. 1, pp. 75-82. [7] M. Tursini, R. Petrella, A. Scafati, Speed and position estimation for PM synchronous motor with back-EMF observer, Industry Applications Conference, 2005. Fourtieth IAS Annual Meeting. Conference Record of the 2005, 2005, pp. 2083 - 2090 Vol. 3. [8] M. Villani, M. Tursini, G. Fabri, L. Castellini, Fault-Tolerant PM Brushless DC Drive for Aerospace Application, Proposed for International Conference on Electrical Machines, September 2010. [9] Thomas M. Jahns, Improved Reliability in Solid-State AC Drives by Means of Multiple Independent Phase Drive Units, IEEE Transactions on Industry Applications , Vol. IA-16, 1980, pp. 321 331 [10] A. Eilenberger, M. Schroedl, Extended back EMF model for PM synchronous machines with different inductances in d- and q-axis, 13th Power Electronics and Motion Control Conference EPE-PEMC 2008, pp. 945 - 948, 2008. [11] M. Schrodl, M. Hofer, W. Staffler, Extended EMF- and parameter observer for sensorless controlled PMSM-machines at low speed, European Conference on Power Electronics and Applications, pp.1-8, 2007

IX. BIOGRAPHIES Giuseppe Fabri was born in Rieti, Italy, on January 24, 1982. He graduated from the University of LAquila in 2009 in Electronic Engineering. He is currently a Ph.D. student in the Department of Electrical and Information Engineering, University of LAquila, where is involved in development of electrical motor drives for automotive and aerospace application.

Carlo Olivieri was born in Teramo, Italy, on August 5, 1983. He received his M.S. degree in Computer Science and Automation Engineering in 2008 from the University of LAquila. At present he is a Ph.D. student in the department of Electrical and Information Engineering, at the University of LAquila, working in the field of automotive devoted to the study of the sensorless techniques and in the field of robust control.

Marco Tursini received the M.S. degree in electrical engineering from the University of LAquila, Italy, in 1987. He became an Assistant Professor of power converters, electrical machines, and drives in 1991, and an Associate Professor of electrical machines in 2002. In 1990, he was Research Fellow at the Industrial Electronics Laboratory, Swiss Federal Institute of Technology of Lausanne, where he conducted research on sliding mode control of permanent magnet synchronous motor drives, and in 1994 at the WEMPEC, Nagasaki University. His research interests are focused on advanced control of ac drives, including vector, sensorless, and fuzzy logic control, digital motion control, DSP-based systems for real-time implementation, and modeling and simulation of electrical drives. He has authored more than 90 technical papers on these subjects.

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