Low Torque Ripple Pmsm

A Low Torque Ripple PMSM Drive for EPS Applications Guang Liu, Alex Kurnia, Ronan De Larminat, Phil Desmond and Tony O’Gorman Automotive Communications & Electronics Systems Group Motorola Inc. 21440 West Lake Cook Road, Deer Park, IL 60010, USA

Abstract - This paper describes the practical design considerations of a low torque ripple Permanent Magnet Synchronous Motor (PMSM) drive for Electric Power Steering (EPS) application. The impact of various controller elements on torque ripple performance is discussed in detail. The experimental results show that the low cost dc-link current sensing scheme used in the design can achieve excellent and consistent torque ripple performance ( less than 2% peak-to-peak at 1 N.m. ), and is well suited for EPS application.

driver of the vehicle moves the steering wheel, a torque sensor in the steering mechanism sends a torque signal to the EPS controller. The DSP inside the EPS controller receives the torque input and sends it to a torque command algorithm. The torque command algorithm processes the torque input, along with other inputs, such as vehicle speed, motor speed, and generates a torque command to the PMSM drive subsystem. The PMSM drive controls the PMSM motor to generate an output torque that tracks the desired torque demand.

1. Introduction

This paper presents some practical design considerations and trade-offs for the PMSM drive system for EPS application. Section 2 describes design considerations. Section 3 presents some experimental results. Section 4 is the conclusion.

Electric Power Steering (EPS) is a relatively new technology in the Automotive Industry. Compared to traditional Hydraulic Power Steering, EPS reduces fuel consumption, simplifies assembly process and provides some intelligent steering features.

2. PMSM Drive Design Considerations The following aspects of the system design are described in this section: PMSM drive architecture, current measurement scheme, rotor position sensing scheme, Space Vector Modulation scheme and software functional blocks and timing.

A Permanent Magnet Synchronous Motor (PMSM) drive system is the core of an EPS system. Consumer requirements that the steering system have a smooth feel means that the motor and controller must yield a low torque ripple. High torque ripple causes rough steering feel and also may excite mechanical resonance resulting in acoustic noise. Depending on specific system, a peakto-peak torque ripple of less than 2% to 5% is typically required. This paper describes the factors that affect torque ripple and some practical design considerations to achieve low torque ripple cost effectively. Some design considerations for other EPS requirements, such as fast and robust dynamic response and wide operating speed range, are also discussed in this paper.

Rsense MC56F 8345

Based on the EPS requirements and available technology, a Motorola DSP controller (MC56F8345) was selected as the processing engine of the PMSM motor drive. The DSP controller is designed for motor control applications and is equipped with all the peripherals that are necessary for different types of motor drives. These peripherals aid in the design of low cost systems by facilitating motor current measurement through dc-link current sampling.

A1

Figure 1: System Block Diagram of the PMSM Drive A) PMSM Drive Architecture Figure 1 is the system block diagram of the PMSM drive. The inverter power stage consists of 6 low Rds(on)

The PMSM drive in an EPS system can be considered as a torque amplifying and tracking system. When the

0-7803-8269-2/04/$17.00 (C) 2004 IEEE

1130

power MOSFETs. The power stage is driven by a gate drive which level-shifts the 6 PWM signals from the DSP. A low inductance sense resistor with Kelvin connections is used to measure dc link current. An op-amp A1 is connected as a differential amplifier across the resistor Kelvin connections. The bandwidth of the amplifier at the necessary gain should be about 1MHz to avoid distortion of the dc link current signal. The reference voltage for the ADC is 3.3V and the input of the op-amp is biased to 1.65V. Consequently, at zero dc link current, the output of the differential amplifier should be near 1.65V.

I_b I_a

B) Current Measurement Scheme Current measurement accuracy has a major impact on torque ripple performance. Closed loop Hall-effect current sensors can provide accurate motor phase current measurements [1] but the sensor cost is too high for EPS application. A lower cost method is to measure the motor phase current through 3 resistors at the bottom of each leg of the 3-phase inverter, requiring 3 sets of sense resistor, amplifier and filter. More importantly, it is difficult to maintain the same current measurement gain for the three phases as a result of variations among sense resistors and op-amp parameter variations. This accuracy variation can result in torque ripple.

I_dc_link, represents –I_a at this point

I_c

Figure 2 (a) Simulated dc link and phase currents: I_a, I_b and I_c are the simulatied phase currents, I_dc_link is the simulated dc link current.

Represents i_c at this point.

In the PMSM drive described in this paper, the motor current is measured through sampling of the dc link current with a single sense resistor and op-amp. Consequently, the problem of uneven measurement gain for different phases is eliminated. Furthermore, this method is the lowest cost of all the methods reported in the literature. The dc link current sensing method was first reported by T.C. Green [2] in 1989. Since then, numerous publications have documented progress on the dc link current sense method [3, 4]. Although the theory of dc link current sensing is well understood, the implementation plays a major role in the accuracy and robustness of the present solution. With the advent of modern DSP controllers, this need for robustness and accuracy can be achieved cost effectively in an electrically noisy automotive environment.

v_a

i_a

V_i_dc_link, Represents – i_a at this point.

Figure 2 (b): Measured dc link current signal (ch1, 13.3A/div), Phase A current (ch4, 20A/div.) and Phase A voltage (ch3, 2.5V/div.) During the product development process, Matlab/Simulink has been used to study the impact of dc link current sampling error on the torque ripple signature. The simulation helps to identify the effect of specific current measurement errors on torque ripple harmonic components, including specific errors of the dc-link current sense mechanism. Figure 3 shows the Simulink model of the dc-link current sensing subsystem.

Figure 2(a) shows the PSPICE simulation of the dc link current waveform and motor phase current waveforms. From the waveforms in Figure 2(a), it can be seen that if the dc link current waveform is sampled at the right instant, phase A and C current can be obtained from dc link current. Figure 2(b) shows the oscilloscope plot of the dc link current signal at differential op-amp output (V_i_dc_link), motor phase A current (i_a) and phase A voltage (v_a). It is seen that there are spikes on the dc link current signal but with the precise timing function of the DSP, we can sample the dc link current signal when the undesired transient has decayed to zero.

In Figure 3, the current sense outputs are selected by the sector number generated by Space Vector Modulation (SVM) software function. In each of the 6 sectors, two of the three phase currents are simulated accurately in addition to a sector dependent error. The third phase current is derived by using the relation that the sum of the three phase currents equals zero. A quantization

1131

block is used to simulate the limited resolution of the A/D converter.

Vb (1)

Figure 4(b): Measured torque ripple before sampling error is corrected. Channel M2 is torque ripple (0.02 N.m./div), average torque is about 0.45 N.m. Ch4 is ia at 5A/div.

(3)

(5) (4)

Va

(2) (6)

Vc

Figure 3: Motor current measurement model Figure 4(a) shows the simulation result of a 0.15A measurement error on all sectors. The motor peak current is about 10A. As can be seen, the torque has a distinctive character of 3 pulses per electrical period, or 3-per-period torque ripple. Figure 4(b) is the measured torque ripple before the measurement error was corrected. The measured torque ripple signature matches that of the simulation. Modification to the current sensing channel was made to reduce the measurement error. Figure4(c) is the measured torque ripple after the measurement error is corrected. One can see the 3-perperiod torque ripple is completely eliminated.

Figure 4(c): Measured torque ripple after the sampling error is corrected. Channel M2 is torque ripple (0.02 N.m./div), average torque is about 0.45 N.m. Ch4 is ia at 5A/div.

Current sense error = 0.15 (A) 0.465

T orque (N.m .)

0.46 0.455

C) Position Sensing Scheme There are many motor position sensors available in the market. Some of them are very accurate but expensive while others are lower cost but less accurate. For a cost effective PSMS drive, the position sensor should have sufficient accuracy to satisfy torque ripple requirements and must not be overly expensive. Matlab/Simulink can be used to simulate the impact of position measurement error on torque ripple performance. The position sensor error can be approximated as a periodical function of the motor mechanical angle as shown in the following equation:

0.45 0.445 0.44 0.435 0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

0.5

1

1.5

2 Time (Sec.)

2.5

3

3.5

4

15

M otor c urrent (A )

10 5 0 -5 -10 -15

0

θ es = K A ⋅ cos(θ m )

Figure 4(a): Simulation result with 0.15A dc link sampling error. Top trace: torque (N.m.); Bottom trace: ia (A)

… Eq. (1)

Where, θes is the motor electrical angle with the measurement error, KA is the amplitude of the measurement error, and θm is the true mechanical angle.

1132

system moment of inertia, this torque ripple may or may not be acceptable. In our PMSM drive design, we included interfaces for both high accuracy sensors, such as resolvers [7] and low accuracy sensors [8] so that different system requirement can be covered. It should be noted that the position errors given in the horizontal axes of Figure 5 (a) and (b) can be due to many different factors, such as resolution of the sensor, tolerance of the sensor and effective error due to transport delay.

The actual measurement error depends on the specific sensor type used in the system. The reason to choose periodical error in the simulation is that it represents the worst case error pattern in terms of torque ripple. The quantization error due to limited resolution is simulated with a quantization block in Simulink. During simulation, the amplitude of the error KA is varied in 0.5 degree steps in the simulation model. The torque ripple for each error amplitude is recorded. The simulations are conducted for low motor speed and high motor speed (in deep flux weakening region). The results are shown in Figure 5(a) and 5(b).

D) Space Vector Modulation (SVM) Scheme Many SVM schemes have been reported in the literature [9]. Although Minimum Loss SVM and Bus Clamping SVM are good for reducing loss, it is difficult to use these methods for measuring motor current through dc link current when the output voltage vector is very small. In an EPS motor controller, it is very important to maintain current control near zero torque command. As a result, a center aligned (or double edge) SVM scheme is used. With this method, the inverter outputs a maximum line to line voltage equal to the dc bus voltage. Figure 6 is the display of the DSP internal variables for PWM command and motor position angle. The display is obtained with PC Master, a software development tool provided by Motorola.

Torque rippe (N.m.)

Torque ripple at 4.1 N.m. average (low speed) 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0

Torque ripple (N.m.)

0

1

2

3

4

5

Position error (elec. degrees)

Figure 5 (a): Simulated torque ripple at 1 Hz, 4.1 N.m. average. Torque ripple at 1.0 N.m. average (high speed)

Torque rippe (N.m.)

1.2 1 0.8 0.6 0.4

Torque ripple (N.m.)

0.2 0 0

1

2

3

4

5

Figure 6: DSP variables plot by PC Master - Top trace phase A PWM command; Bottom trace – motor position angle. Motor rotates in forward direction.

Position error (elec. degrees)

Figure 5 (b): Simulated torque ripple at 160Hz, 1.0 N.m. average.

E) Software Functional Blocks and Timing Figure 7 is the Simulink block diagram for the PMSM control system. The DSP software is implemented with the same functional blocks as shown in Figure 7. The motor control system has two loops: one is the D and Q axes current control loop updated every 300us, and the other is the flux control loop updated every 1.2ms. Because of the current loops, non-linearity of the inverter stage is compensated and has little effect on torque ripple. The current loops also compensate the parameter drift of the motor and inverter. The complete motor control algorithm takes about 15 MIPS with majority of the code written in “C” language, which is

Figure 5 (a) shows the position measurement error contribution to motor torque ripple at low speed. The torque ripple with a position error of 4 degrees is only 0.015 N.m., with an average output torque of 4 N.m., or 0.38% of the average motor torque. It is clear that at low speed, the position measurement error has very little impact on torque ripple. However, if we look at Figure 5 (b), the position error contribution to torque ripple at high speed, the torque ripple is 1.1 N.m. when the position error is 4 degrees. The average motor torque in this case is 1.0 N.m. The peak to peak torque ripple is therefore 110% of the average torque. Depending on the

1133

torque ripple at above 1 N.m. average is about 1.5% peak-to-peak, which is well within the EPS application requirement (usually 2% to 5%). This torque ripple performance is insensitive to the mismatch of the inverter MOSFET switching characteristics, therefore can be maintained at high volume production.

one quarter of the total DSP processing power available. The remainder of the DSP MIPS is reserved for other EPS controller functions, such as torque command algorithm, CAN communication, system diagnosis and computational integrity checks. The program memory used is about 45 kilobytes, including motor control, diagnosis, computational integrity check functions, fault management and system operating state machine.

Figure 9: Torque ripple at 1.05 N.m. average is 0.015 N.m., or 1.5% (channel M2 at 0.02 N.m./div.), channel 4 is motor current at 10A/div.

Figure 7: Simulink Diagram Represents Software Functional Blocks The flux control loop generates the D and Q axes current reference based on torque command and motor speed. When the motor speed is below the base speed, D axis current reference is set to zero. When the speed is above base speed, a current advance angle is obtained from a look up table. Based on the advance angle, a negative D axis current reference will be generated for flux weakening operation. 3. Experimental Results The DSP based PMSM drive system has been built and experimental results are presented in this section.

Figure 10: Torque ripple at 0.12 N.m. average is 0.012 N.m. (channel M2 at 0.02 N.m./div.), channel 4 is motor current at 2A/div.

Figure 8: Torque ripple at 2.39 N.m. average is 0.034 N.m., or 1.4% (channel M2 at 0.02 N.m./div.), channel 4 is motor current at 20A/div. Figure 8 through 10 show the torque ripple measurement at various average torque levels. The

Figure 11: Motor current when steering wheel is suddenly stopped. Current is limited to 100A (ch3, 50A/div.)

1134

Figure 13 (a) shows the motor torque and speed measurement. The motor base speed is about 90 Hz. It can be seen that the motor speed operates above 90Hz with reduced torque. From Figure 13 (b) it can be seen that at flux weakening region, the motor output power is close to constant. 4. Conclusion A low torque ripple PMSM drive system for EPS application has been presented in this paper. With the modern DSP controller and careful design of motor current and position sensing schemes, excellent torque ripple performance can be achieved without using expensive current sensors. Current measurement accuracy has the highest impact on torque ripple performance. The single sense resistor sampling method used in this design is accurate enough to obtain low torque ripple for volume production. Some other design considerations, such as SVM scheme selection, control software functional blocks, loop timing and MIPS requirement, etc are also presented. Fast and robust dynamic response and flux weakening operation are demonstrated. The experimental results prove that the PMSM drive presented in this paper is very suitable for EPS controllers.

Figure 12: D axis current step response (1.8ms rise time), no overshoot (50A/div.) Figure 11 shows the motor current and torque sensor signals. With the 300us current loop, the motor current is controlled with a pre-set limit. In transient condition, such as sudden stop of the motor (end of rack travel), the motor current is still under control. Fast current control is important in preventing unwanted shutdown due to transient over current. Figure 12 shows the Q-axis current step response. The rise time is about 1.8ms and there is no overshoot.

References Torque vs. Frequency

[1] LEM Group, “Current Transducer LT 100-S/SP30”, website www.LEM.com. [2] T.C. Green and B.W. Williams, “Derivation of motor line-current waveforms from the dc-link current of an inverter”, IEE Proceedings, volume 136, Pt. B, No. 4, pp. 196-204, July 1989. [3] Frede Blaabjerg, John K. Pederson, Ulrik Jaeger, Paul Thoegersen, “Single Current Sensor Technique in the DC-Link of Three-Phase PWM-VS Inverters: A Review and Ultimate Solution”, Industry Applications Conference, 1996. Thirty-First IAS Annual Meeting, IAS '96., Conference Record of the 1996 IEEE , Volume: 2 , pp. 1192 -1202, 6-10 Oct. 1996. [4] Woo-Cheol Lee, Dong-Seok Hyun and Taeck-Kie Lee, “A Novel Control Method for Three-Phase PWM Rectifiers Using a Single Current Sensor”, IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 5, pp. 861- 870, SEPTEMBER 2000. [5] Ion Boldea and S. A. Nasar, “Electric Drives”, CRC Press LLC, ISBN 0-8493-2521-8, 1999. [6] Mathworks, Inc. “Simulink – Dynamic System Simulation for MATLAB”, Release 12, November 2000. [7] NMB Minebea GmbH, “Variable Reluctance Resolver”, http://www.nmbeurope.com/minebea/Data/Pages/rotarycomponents/reso lver.html

6

Torque (N.m.)

5 4 3 2

Torque vs. Frequency

1 0 0

50

100

150

200

250

Frequency (Hz)

Figure 13 (a): Measured motor torque-speed curve above base speed.

Motor output power (W)

Power vs. Frquency 600 500 400 300

Motor output power (W)

200 100 0 0

50

100

150

200

250

Motor eElectrical frequency (Hz)

Figure 13 (b): Measured motor power vs. frequency.

1135

[8] Allegro MicroSystems, Inc. , “Ring Magnet Speed Sensing for Electronic Power Steering”, http://www.allegromicro.com/techpub2/ring_magnet/ [9] Andrzej M. Trzynadlowski and Stanislow Legowski, “Minimum-Loss Vector PWM Strategy for Three-phase Inverters”. Transaction on Power Electronics, VOL. 9, NO. 1, pp. 26-34, January 1994.

1136