Resolver Emulation for PMSMs Using Low Cost Hall-Effect Sensors

Control of permanent magnet synchronous machines (PMSMs) requires absolute rotor position measurement/estimation, as well as the magnet polarity detection for the machine start-up, encoders/resolvers being normally used for this purpose. However, these sensors can account for a large portion of the overall drive cost, and require additional room and cabling, therefore penalizing the size and reliability of the drive. This article proposes a method to emulate a resolver in machines using low cost Hall-effect sensors. The proposed Hall-effect resolver system is a new type of angular position sensor for PMSMs. This allows to control machines which do not include a resolver from inverters which require a resolver signal to operate.


I. INTRODUCTION
P ERMANENT magnet synchronous machines (PMSMs) have become very popular during the last decades due to their high efficiency, high power density, and superior dynamic response compared with other types of machines, e.g., induction, wound field, or synchronous reluctance machines. Control of PMSMs requires the absolute position of the rotor, i.e., including magnet polarity prior to startup of the machine [1], [2]. Both absolute encoders [3]- [6] and resolvers [16]- [22] comply with this requirement. On the contrary, incremental encoders will require some additional mechanism to obtain the rotor initial position. Combined use of incremental encoder and Hall-effect sensors [3]- [10] provides the absolute position. Table I  The the preferred option in general purpose applications; however, they are less robust than magnetic encoders and resolvers, the last being the preferred option for, e.g., hybrid-electric vehicles and electric vehicles motors [13]- [15], aircrafts, satellite antennas, or robots [11]- [13]. Although resolvers provide absolute position, its use always implies additional hardware (a resolver to digital converter is needed [12], [17], [18]), room and cabling, therefore penalizing cost, size, and reliability of the drive.
In addition of conventional position sensors, a number of alternative solutions have been reported in the literature. A planar angular position sensor is proposed in [23], with a similar working principle as a variable reluctance (VR) resolver. However, this sensor is highly sensitive to electromagnetic interference due to its construction and requires and additional electronic circuit to operate. The sensor proposed in [24] provides angular position output that is not compatible with standard encoder or resolver signals. In [25], a contactless capacitive angular position sensor is proposed, but it is characterized for presenting a nonlinear behavior. Other noncontact angular positions sensors based on Hall-effect devices for automotive applications (e.g., throttle position detection, shaft position, etc.) are also commercially available [26], [27]. The main drawbacks of these methods are the robustness decrease, inertia increase, and extra room.
This article proposes a method to emulate resolvers using the signals provided by low-cost Hall-effect sensors, Hall-effect 0093-9994 © 2020 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
resolver (HER), which is an extension of [28]. Stability of the HER system is evaluated and compared with standard sensors. Uses of the HER system could be twofold: first, it would enable the use of machines that do not include a resolver, with electric drives that require a resolver signal to operate and second, a new type of position sensor for PMSM. Appealing properties of the HER system are reduced cost as well as simple, light, and robust construction, as there are no moving parts or couplings. This article is organized as follows: design and operation principles of resolvers are presented in Section II, emulation of a resolver using Hall-effect sensors is presented in Section III, machine and Hall-effect sensors placement is presented in Section IV, experimental results are presented in Section V, and conclusions are presented in Section VI.

II. RESOLVER DESIGN AND PRINCIPLES OF OPERATION
This section briefly reviews the design and operating principles of resolvers. Commercial resolvers can be classified into wound field (WF) [16]- [19] and VR [20], [21]. WF resolvers include an excitation winding in the rotor, which is magnetically coupled with two identical stator windings having 90°mutual electrical phase shift [16]- [19]. A sinusoidal voltage, typically called carrier, is applied to the rotor windings, via brushes and rings or alternatively by means of a magnetic coupling (i.e., rotating transformer) [16]- [19]. The resulting voltages in the two-stator windings are a sine and cosine signal whose angle is modulated by the rotor angle. WF resolvers have a wide temperature range of operation, are small and light, and with a simple and robust construction; in addition they are highly insensitive to noise and tolerate long transmission cables length [16]- [19]. On the other hand, VR resolvers have both the output and the excitation windings in the stator; no brushes or rotating transformer being therefore required. In general, VR resolvers are even less expensive and more robust than WF resolvers [13], [14], [20], [21].
Resolvers can be seen as a special type of rotary transformer that couples a primary winding [Input, see Fig. 1(a)] with two secondary windings [Output 1 and 2, see Fig. 1(a)] that are 90 electrical degrees phase shifted; note that Fig. 1(a) shows a schematic representation of a VR resolver. Excitation signal, i.e., V source in Fig. 1(a), is typically a sinusoidal signal (1), see Fig. 1(b), where V 0 and ω source are the magnitude and frequency of the excitation signal, respectively. The excitation frequency depends on the resolver type. Brushless resolvers typically operate in the range of 1 to 10 kHz, while VR resolvers operate around 10 kHz. For the sake of compatibility with conventional resolvers, frequencies of 2 and 10 kHz will be used in this article.

III. EMULATION OF A RESOLVER USING HALL-EFFECT SENSORS
This section presents the proposed system to emulate a resolver using Hall-effect sensors.
Hall-effect sensors are typically used to convert a magnetic flux density signal into a voltage signal (i.e., Hall voltage). It consists on a semiconductor element (i.e., Hall element), see Fig. 2, which fed with a current I z . In the presence of a magnetic field (B y in Fig. 2), the induced Hall voltage (V H ) is proportional to both the current applied, I z , and the magnetic flux density, B y , (6), where hw is the cross-sectional area of the element, e is the charge of the electron, and n stands for the charge carrier density. Since e, hw, and n are constants, V H, will be proportional to B y and I z . Fig. 3 shows and schematic representation of the test machine that will be used for the experimental verification of the proposed HER system. The HER system consists of two Hall-effect sensors, 90 electrical degrees phase shifted, HALL-1 and HALL-2 in Fig. 3(a). The sensors will be mounted on the end frame of the machine, measuring field in the radial direction; i.e., the sensors will measure the leakage flux in y-axis direction (B y ), see Fig. 3(b) and (c), which will vary as the rotor rotates [29]. The output of HALL-1 and HALL-2 will consist of a sine and cosine waveforms containing the position information [28]- [30].
Hall sensors are normally fed using a dc current. The resulting output signals of the two Hall-effect sensors are shifted by 90°a s shown in Fig. 4(a). However, it is possible to feed the sensors using a sinusoidal signal (either voltage or current), i.e., same as WF and VR resolvers [16]- [21]. The output signals from the two Hall-effect sensors are shown in Fig. 4(b). The peak value of the resulting signals will be proportional to the magnet leakage flux density seen by the sensor and to the current feeding the sensor (7). Similarities between the signals in Fig. 4(b) are those produced by traditional resolvers in Fig. 1(c) and (d) evident, what strongly support the idea that the same signal processing used with the resolver signals could be applied to the signals produced by the Hall sensors. It is noted that in this case, there is no element attached to the rotor, the solution being therefore simple, compact, and robust.
It must be noted that the proposed method assumes a linear response of the sensor with the excitation signal. To validate this assumption, a sensor was placed on top of a PM [see Fig. 5(a)], being subjected therefore to a constant field. The sensor was fed with a sinusoidal voltage V in shown in Fig. 5

IV. EXPERIMENTAL TEST BENCH
The HER system has been implemented in an IPMSM, its design being shown in Fig. 3. Table II shows the ratings and dimensions of the machine. Hall-effect sensors [31] have been attached to the end shield to the machine, see Fig. 3(c); i.e., the sensors are placed between the rotor and end shield.
Assembly of the sensors does not differ from standard Halleffect sensors already available in some machines [34], [35], while cabling between sensors and drive is the same as for standard resolvers [16]- [21]. The phase shift among sensors is 90 electrical degrees, which corresponds to 30 mechanical degrees in a 6-pole machine, see Fig. 6(a); the output of the two Hall-effect sensors will be therefore two sinusoidal signals, 90°phase shifted (i.e., sine and cosine waveforms). Hall-effect  sensors that have been used, [31], are standard sensors typically used for motion control in PMSMs [28]- [30]. Standard Halleffect sensors used in PMSM drives measure the magnetic flux density along one direction, i.e., they are 1-D sensors; Hall-effect sensors used in this work are oriented in the radial direction, i.e., y-axis direction [see Fig. 6(a)], which is expected to provide high sensitivity to PM leakage flux and low sensitivity to stator current [28]- [30].
Stator of the machine is shown in Fig. 6(b). Fig. 6(c) shows the test bench consisting of the test machine and a load machine [36]. Fig. 6(d) shows a schematic representation of the test bench, including load machine, test machine, and connection between the test machine and drive. It can be observed from Fig. 6(d) that the Hall-effect sensors are mounted on the end shield of the nondrive end of the machine; Hall-effect sensors being connected to the "Resolver to digital" control board of the drive [37].

V. EXPERIMENTAL RESULTS
Experimental results of the HER system are presented in this section for different working conditions of the machine. A 2 kHz, 5 V peak signal was used to feed the sensor in Figs. 7 and 8, 10 kHz 10 V was used in Figs. 10 to 13. These signals are similar to those used by conventional resolvers, meaning that they can feed directly any existing circuitry designed for the signal processing of conventional resolvers.
It is finally noted that the input impedance of the Hall sensor is ∼725 Ω [31], the total power consumption of the HER sensor (RMS) being ∼34.5 mW (∼17.2 mW per sensor). Input impedance of conventional resolvers (VR and Brushless) varies from ∼50 Ω to ∼150 Ω, leading to power consumptions in the range of 250 to 500 mW. Fig. 7(b) and (c) shows the output signals of the two Halleffect sensors, V out_1 (sine) and V out_2 (cosine) when the machine is rotating at 40 Hz and with no fundamental current. Fig. 8(a) and (b) shows the speed and position measured using the HER sensor, an encoder with 4096 pulses per revolution is also shown for comparison purposes. Fig. 8(c) shows position error. It is observed that under no load condition the peak error in the estimated position is <0.07 rad. Fig. 9 shows the signal processing used for speed and position estimation. Measured flux densities H 1 and H 2 are multiplied by the carrier signal at the demodulation. A second-order low pass filter with a cutoff frequency of 1 kHz is used to remove high frequency noise. The angle of the resulting V α and V β signals (8) is obtained using a synchronous reference frame phase-locked loop, which provides the estimated rotor speed and position [38] The bandwidth of the proposed HER will depend primarily on the bandwidth of the PLL, which has been set to 230 Hz.  The bandwidth of the Hall sensor 250 kHz, and can be therefore safely neglected [31].

A. Influence of dq Axes Currents
Both d-and q-axis stator currents [29] are expected to interfere with the leakage flux due to the magnets measured by the Fig. 9. Schematic representation of the signal processing used for speed and position estimation.   Hall-effect sensors. d-axis current will affect only to the amplitude of the measured signals, but with no effect on the angles, as it is aligned with the magnet. q-axis current affects the phase of the leakage flux waveform, resulting therefore in a position error. Fig. 10(a) shows the estimated position error when d-axis current is varied from 0 to -1 pu (i.e., flux weakening) in steps of 0.25 pu. As expected, d-axis currents do not affect to the accuracy. Similarly Fig. 9(b) shows the results when q-axis current is varied from 0 to 1 pu in steps of 0.25 pu. As expected, the error increases almost linearly with the q-axis current. However, this error can be compensated, two different options have been evaluated.
1) Linear compensation using (10): the compensation angle, Δθ being proportional to the q-axis current 2) Trigonometric compensation using (11); the compensation angle that relies on two constants, a and b Compensation constants are experimentally approximated. Fig. 10(b) shows the position error using these two compensation methods, both leading to similar results (i.e., error <0.1 rad).
Performance of the proposed HER during transient operation has been also analyzed. Fig. 11 shows the experimental results when a d-axis current step of -0.5 pu is applied at t = 0.35 s with the machine operating at constant speed. Fig. 11(a) shows the measured d-and q-axis currents. Fig. 11(b) shows the rotor position measured with the proposed system without and with compensation of q-axis current effects as well as the rotor position measured with the encoder. It is noted that the error does not increase due to transients in the d-axis current.
Similarly, Fig. 12 shows the case when a q-axis current step of -0.5 pu is applied (at t = 0.35 s for the case of without and with linear compensation, in the second case the error remaining <0.1 rad.

B. Operation at Variable Speed
Performance of the HER is expected to be independent of speed. Fig. 13 shows the sensor signals and the estimated speed and position when the speed varies as shown in Fig. 13(a). Results in Fig. 13(d) show a maximum position error of ±0.05 rad in steady state, which slightly increases during transients. Maximum error of commercially available VR resolvers ranges from ±0.01 rad for four-pole variable resolvers to ±0.018 rad for two-pole variable resolvers. Maximum error of commercially available brushless resolvers is in the range of ±0.006 rad.

VI. CONCLUSION
This article proposes a method to emulate a resolver using low cost Hall-effect sensors. The proposed HER device consists of two Hall-effect sensors, mounted on the end shield of the machine, 90 electrical degrees phase shifted, which measure the magnetic flux leakage of the PMSM.
Compared to commercial resolvers, the proposed HER sensor has higher error, but in turn it provides several advantages. 1) Very low cost.
2) Reduced size, which eases its integration in the drive, its impact on system inertia being negligible. 3) Increased robustness, as there are no moving parts or coupling. 4) Lower power consumption than conventional resolvers and full compatibility with resolver circuitry. 5) Experimental results have been provided to demonstrate the viability of the proposed HER system.