Starting Method for Sensorless Operation of Slotless Permanent Magnet Synchronous Machines

Todd D. Batzel and ICY. Lee, Senior Member, IEEE Department of Electrical Engineering

The Pennsylvania State University University Park, PA 16802

Abstract: Slotless permanent magnet synchronous motors (PMSM) are receiving much attention for drive applications because of their high efficiency, high power-to-volume ratio, and their elimination of cogging torque. Furthermore, motor control without a rotational transducer is a subject that is receiving significant attention. In order to eliminate the need for high-resolution rotor position sensors, many sensorless techniques have been developed. It is well known, however, that sensorless operation is problematic at standstill - especially for a round rotor machine such as the slotless PMSM. Unless the initial rotor position is known, it is not possible to start the machine at full torque or to guarantee dither free startup. This paper presents a sensorless drive for a slotless PMSM with emphasis placed on stable startup by estimating the initial rotor position before starting. To estimate initial position, voltage pulses are applied to the stator windings. The resultant current measurements are then used to estimate the initial rotor position before starting. The proposed starting method for standstill rotor position identification is verified by experiment on a slotless PMSM.

Keywords permanent magnet synchronous motor, sensorless operation, slotless motor, zero speed

I. INTRODUCTION

In recent years, there has been significant interest in the slotless permanent magnet synchronous motor (PMSM). The advantages of the slotless PMSM are an excellent torque-to- volume and power-to-volume ratio, decreased core losses and increased efficiency, and quiet, cog-free operation.

Typical PMSM drives rely on a rotor angle sensor such as a resolver or encoder to perform the commutation of the phase currents. The use of such feedback devices presents a disadvantage in many applications, such as increased physical size and cost. Furthermore, these sensors present reliability issues in harsh environments. As a result, there has been a significant interest in the development of sensorless strategies to eliminate the position sensor.

An impedient often associated with sensorless operation is the difficulty in determining the rotor position at zero speed. Thus, the startup of a sensorless drive often results in an undesirable dither in velocity and torque due to position uncertainty. This dithering is unacceptable in applications such as disk drives, electric propulsion, and high performance

The starting of a sensorless PMSM has been accomplished by several methods. Open loop starting strategies with a fixed PWM pattern have been suggested [ 11. This open loop method yield to a sensorless controller when suitable back emf has been developed. With such open loop methods, full torque and correct torque polarity cannot be guaranteed at startup. Another strategy is forced rotor alignment [2] in which a dc current is applied to the stator before startup. The dc current acts to align the permanent magnet field with the magnetic field generated by the stator excitation. In this method, the initial alignment torque is of a polarity determined by the initial position. Thus, a dithering of velocity and torque is associated with this starting method. Starting methods applicable to a salient-rotor PMSM have been suggested where the rotor position dependent stator inductance is utilized to obtain position information [3,4,5]. Another stand-still rotor position detection method that injects high frequency test currents to the machine at standstill has been reported [6]. This method relies on the presence of a pliable coupling between the rotor and load.

This paper investigates an approach to sensing the rotor angle at zero speed for a round-rotor slotless PMSM. The validity of the methods established is verified with a two- dimensional finite-element analysis of the machine.

SeTVOS.

d axis Phase a

Fig. I Cross-seaion of a slotless PMSM.

0-7803-5569-5/99/$10.00 0 1999 IEEE 1243

11. SLOTLESS PMSM CHARACTERISTICS

A. Slotless PMSM Construction Fig. 1 shows a cross-section of a three-phase, 8 pole radial airgap slotless PMSM. The rotor is constructed of parallel magnetized arc permanent magnets mounted on a ferromagnetic shaft. By utilizing windings held together with suitable epoxies, the slots found on the conventimal PMSM stator are eliminated. The elimination of the stator slots has several effects on the machine operation such as the elimination of cogging torque and increased efficiency.

More permanent magnet material volume is required to achieve the flux density required in the relatively large airgap assuciated with slotless PMSM [7]. Thus, the permanent magnets found in a radial airgap slotless PMSM are typically very thick when compared to the magnets in conventional machines

Torque per unit volume in the slotless PMSM has been found to be comparable to the slotted configuration. If a slotless and slotted PMSM are the same size, use the same materials, fill factors, and insulation thickness and have the same resistance, they will produce about the same torque [8].

B. Rotor Position Dependent Inductance

Although the slotless PMSM shown in Fig. 1 is a round- rotor machine, there is a small dependence of the stator inductance on the rotor position. This dependence is due in part to the thickness and relative permeability of the permanent magnets in the airgap. Typical high energy density permanent magnets used in the slotless PMSM (NdFeB) have a relative permeability of approximately 1.1. Thus, the reluctance presented to a stator winding varies as the permanent magnets and airgap sequentially are aligned with the magnetic axis of the winding in question. That is, reluctance decreases as the poles of the permanent magnet align with the magnetic pole of the winding. Since there are two permanent magnet arcs per pole, the resulting position- dependent inductance is a function of twice the rotor angle.

Additional reluctance variation in the slotless PMSM under test has been identified through finite element analysis (FEA). Fig. 2 reveals a relatively large flux density in the small fkagment of the rotor that lies directly between the permanent magnets. The flux density in this region is slightly above the knee of the B-H curve for the rotor core material used in the design. As a result, the relative permeability of this segment of the rotor core is slightly lower than other core segments with lower flux density. The reluctance variation due to this local saturation effect is a characteristic of the slotless machine considered in this paper and not necessarily a characteristic of the slotless PMSM in general. On the other hand, reluctance variation due to the permanent magnet material is a general characteristic of the slotless PMSM.

111. INDUCTANCE MEASUREMENT AT STARTUP

Given the dependence of the phase inductance on the rotor angle, it follows that the measurement of this inductance can be used to detect the rotor angle at zero speed. The phase

Rg. 2. Flux density in slotless PMSM at no load.

v- Ts I Va

v + 7 s 3 \1 V

V- fig. 3. Single phase PMSM model at zero speed.

inductance of the slotless PMSM under test may be determined by the application of a test voltage to the phase under test. The hardware used to apply the test voltage to a single phase is shown in Fig. 3, which is implemented by a standard H-bridge inverter used for motor control.

The test voltage pulse train is applied to the single phase equivalent shown in Fig. 3 by sequentially activating the SI, S4 and S2, S3 switch pairs at a constant frequency. By monitoring the applied voltage and sampling the resulting current waveforms, the phase inductance can be measured.

If the phase inductance is assumed to be constant during a switching period, the phase inductance is represented by

where i, ( t , ) and i,(tz) are the peak currents sampled at times t and t 2 respectively and Ar represents a value equal to half the switching period of the voltage pulse train. Fig. 4 shows the voltage control signal and resulting current response at zero speed. The peak currents i,(t,)and i, ( t z ) are shown in this figure. The switching frequency for this test is 15 kHz.

0-7803-5569-5/99/$10.00 0 1999 IEEE 1244

i Voltageswitchsignal f i 4 .... +.* .......

fig. 4. Current response used to measure inductance.

O-"

1 2 3 4 5 6 7 0247;

mtof angle (elec. rad.)

Fig. 5. Measured phase inductance versus rotor position.

Using the setup shown in Fig. 3 to apply test voltages to each of the three phases of a slotless PMSM under study, the phase inductances were measured using (1). The measured inductances of each phase are shown in Fig. 5 as a function of the rotor angle 6 .

Considering only the fundamental component of the inductance measurements shown in Fig. 3, the per phase self inductances of the slotless PMSM motor may be described by

(2)

(3)

(4)

where 6 is the rotor angle, Lw0 is the self inductance due to the fundamental airgap flux and Le is a component of the self inductance due to rotor position dependent flux.

It should be noted that in a salient pole PMSM such as an inset pennanent magnet motor, the ratio of the direct to quadrature axis inductances is generally greater than 1.2. In contrast, the ratio for the slotless PMSM under study is 1.02. Thus, the problem of accurately determining the inductances is extremely important for the slotless application.

L, = Lano +Le ~ ~ ( 2 8 )

Lbb = Lmo + Le co~(28 + 2 4 3 ) Lcc = Lmo + Le c0~(28 - h / 3 )

IV. INITIAL, ROTOR ANGLE ESTIMATION

Since the inductance was found to be a function of the rotor angle 6 , it follows that the measured inductance of the phase windings can be used to estimate rotor position. Measuring the inductance of two or three phases, however, yields only the direction of the rotor direct axis with an uncertainty of n electrical radians since the inductance terms are a function of 26 . Therefore, an additional test must be performed to resolve the orientation of the direct axis.

In the first stage of zero speed rotor angle detection, the axis of the direct axis is determined by measuring the inductance of two of the three motor phases. By storing the inductance map shown in Fig. 5 in a lookup table, the measured inductances are used to obtain two candidate rotor angles separated by n electrical radians. Note that the two candidate rotor angles both are aligned with the rotor direct axis. The correct candidate rotor angle is determined in the second stage of the zero speed rotor angle estimation process.

In the second stage of z&o speed rotor angle estimation, the current is increased to a value near the peak current rating of the machine. This large test current is injected in the direction of the rotor direct axis in both forward and reverse directions by coordinated switching of the SI, S4 and S2, S3 switch pairs shown in Fig. 3. The phase that is subjected to the large current test is determined from the stage one test, which revealed the orientation of the direct axis.

Although the flux in the main magnetic circuit is predominantly from the pennanent magnet in the slotless PMSM, at large currents the effects of armature reaction can alter the magnetic setpoint. In one direction, the resulting stator magnetic field will add to the peamanat magnet field, while the other polarity of current results in opposing fields. Therefore, in only one direction, the stator back iron will be saturated. The saturation can be detected through the inductance measurements, and the correct orientation of the direct axis is resolved. The application of such large currents results in tittle torque since the currents are applied only to the direct axis.

Figs. 6 and 7 show the voltage control signal and resulting stator current for the second stage test of the zero speed rotor position estimator. For these tests, the switching frequency of the test voltage is decreased so that larger peak currents and saturation in one direction result.

In Fig. 6, the rotor angle is aligned such that positive currents generate a magnetic field in the same direction as the permanent magnet field. Thus saturation occurs for the large positive current and no saturation results due to the negative current. The increased di/dt and peak current associated with saturation in Fig. 6 is easily detected by sampling the current waveform. The increased di/& is due to the decreased permeability of the core as it enters saturation.

Fig. 7 shows the current waveform when the rotor angle is displaced by n electrical degrees from the situation depicted in Fig, 6. As expected, in this figure, negative current induces saturation while positive current does not.

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" '1""1""1""1""- . . . . . : 10Ndiv . * . * - . . . . . ....................... . * . . - .

. . . . . * . . . . . . . . . . t , , , , ~ t , , , , t , , , , , , , , t " " " L 3 ' 1 1 1 1 " "

Fig. 6 Rotor d-axis aligned with magnetic axis of phase under test.

~ * " l " ' ~ l " " l " ' . . . . . . . . * * + . ...................... . . . .

. . . . l I l t l l l , t l , , , t , l , , l , , , I

Fig. 7. Rotor d-axis displaced from magnetic axis of phase by n

Figs. 8 and 9 show the magnetic flux densities obtained through FEA for the large direct currents applied to the slotless PMSM under test as part of the second stage of the zero speed test. Figs. 8 and 9 correspond to current aligned with, and opposing the rotor direct axis, respectively.

For the slotless PMSM under test, the m e material enters saturation at approximately 1.0 Tesla. In Fig. 8, the flux density in the stator core is seen to be above the saturation level. Similarly, the magnetic flux density for phase currents that oppose the direct axis is shown in fig. 9. Note that the flux density is significantly lower in this situation, since the stator and permanent magnet fluxes oppose one another.

The FEA analysis shown in Fig. 8 was used to determine the second stage test current that would result in saturation. For the slotless machine under consideration, this current was found to be slightly above the peak current rating. Since the current is applied to the winding for an extremely short time, this was not considered to be a problem. The E A map of Fig. 9 was used to verify that large currents opposing the rotor direct axis would not permanently demagnetize the magnets.

V. EXPERIMENTAL RESULTS

To evaluate the performance of the proposed zero speed rotor position estimator, a set of experiments was performed on a slotless PMSM whose parameters are given in Table 1. The test setup is shown in Fig. 10, where the rotor position

- \

Fig. 8. Saturation due to large d-axis currents.

Fig. 9. Flux density with current in the negative d-axis.

Table 1. Parameters of slocless motor 1.35 n

Inductance .131 mH Permanent Magnet Flux .12 v-s

Pole Pais

I I encoder U

A 0

Fig. IO. Experimental setup.

observer block consists of the sensorless algorithm described in [9].

The effectiveness of the zero-speed rotor angle estimator is demonstrated by a comparison of Figs. 11 and 12, which show the startup of a sensorless PMSM without and with the

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proposed initial rotor position estimator, respectively. Sensorless startup from zero speed with no knowledge of the initial rotor angle often results in a dithering in torque and velocity, as demonstrated in Fig. 11.

The use of the zero-speed rotor angle estimate allows for a smooth, dither free startup, as shown in fig. 12. In this figure, a rotor speed of 20 RPM is reached at d.46 seconds, and the sensorless algorithm described in [9] begins estimating the rotor angle. The rotor angle estimation error then quickly converges toward zero.

For this test, the initial angle was determined to within approximately 5 electrical degrees. Typical accuracy of the zero-speed estimator was found to be f 15 electrical degrees, which is sufficient to guarantee dither-free startup from standstill. This level of accuracy represents a significant improvement over the use of discrete Hall sensor devices for startup as described in [9].

8

time($)

1501 I

P I /

time(@

Fig. I I Sensorless startup without initial rotor angle estimator.

time (5)

0.1 I

-- d'&.4 0.45 0:5 0.k 0:6 0.86 0:7 0;s

(SI

Fig. I2 Rotor angle estimation from zero speed.

VI. CONCLUSIONS

This paper describes the implementation of a zero speed rotor position sensing algorithm for sensorless operation of a slotless PMSM. Though the slotless PMSM is a round rotor machine, it was determined through experimentation and Finite Element Analysis that there is a detectable rotor position dependent inductance that is a function of twice the

rotor angle. To exploit this positiondependent inductance, test voltages are first applied to the machine in order to determine the orientation of the rotor direct axis to within 180 electrical degrees. The orientation of the direct axis is then resolved by introducing an asymmetry in the current resulting from stator core saturation. Thus, absolute rotor position is obtained. Experimental results show that the zerc~speed rotor position estimator was effective in the elimination of speed and torque dithering often associated with sensorless startup .

VII. ACKNOWLEDGEMENT

The work outlined in this paper was supported by Office of Naval Research under Gant NOOO14-98- 1-0718. Additional support W ~ S provided by NSF under m t INT-9605028 and ECS-9705105.

VIII. REFERENCES

[ I ] R Wu, G. Slemon "A permanent Magnet Motor Drive without a shaft sensor,", IEEE Transactions 05 Indusiry Applicaiims. vol. 27. no. 5. pp.

[2] N. Matsui, M. Shigyo "Brushless dc motor control without position and speed sensors." IEEE Transactions on Industry Applications. vol. 28, no. I. pp. 120-l27.1992.

[3] N. Matsui, T. Takeshita "A novel starling method of sensorless salient- pole brushless mota, '' IEEE Tmnsactions on Industry Applications, pp

[4] M. Schroedl "Operation of the permanent magnet synchronous machine without a mechanical sensor," IEE Conf: Atblic&*on, pp51-56, 1991.

[5] T. Aihara, A. Toba, T. Yanase. "Sensorless torque control of salient-pole synchronous motor at zero speed operation," IEEE Applied Power Electronics Conference and Exposirion. vol. 2, pp. 715-120. 1997.

[6] J.S. Kim S.K. SUI. "New stand-still position detection strategy for PMSM drive without rotational transducers, " IEEE Applied Power Electronics Conference. pp 363-369, 1994

[7] T. Harned S. Huard, "A comparison of slotted and slotless brushless dc motor technology." Proceedings of the Annual Symposicrm on Incremental Motion Conirol Sysiems and Devices, pp. 289-296. 1993.

[8] M. Jufer, C. Fleury, "Design and comparison of slotless brushless DC motors," Symposicrm of incremental motion control sysiems and devices, pp. 97-104.1992.

(91 T. Batzel and ICY. Lee, "Sinusoidal commutation of slotless permanent magnet synchronous machines using disuete hall sensor feedback" , Proc. IEEE Power Engineering Society Winter Meeting. New York NY, pp. 53-58, January, 1999.

1005-101l. 1991.

386-392.1994.

Todd D. Batzel received his B.S,. degree in Electrical Engineering from the Pennsylvania State University. State CoUege. PA, in 1984, and his M.S. degree in Electrical Engineering from the University of Piasburgh, Pittsburgh, PA, in 1989. He is presently a Research Assistant with the Applied Research Labaatory of the Pennsylvania State University and a Ph.D. 'candidate in Electrical Engineering at the Pennsylvania State University. His research interests include mchine controls, electric drives, and power electronics.

Krmng Y. Lee received his B.S. degree in Electrical Engineering from Seoul National University, Korea, in 1964, his M.S. degree in Electrical Engineering from Na-th Dakota State University, Fargo, ND, in 1968, and his Ph.D. degree in Systems Science from Michigan State University, East Lansing. MI, in 1971. He has been on the faculties of Michigan State, Oregon State, University of Houston. and the Pennsylvania State University. where he is currently a Rofessor of Electrical Engineering. He is DieUor of Power Systems Control Laboratory and a Co-Director of Intelligent Distributed Controls Research Labaatory at Penn State. His interests include control systems, artificial intelligence, neural networks, fuzzy logic control, genetic algorithms, and their applications to power plants and power systems control. operation and planning. He is a Senior Member of EEE. active in Power Engineering Society and Control Systems Society.

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