1. Position Sensorless Control Based on Coordinate Transformation for Brushless DC Motor Drives
Yuanyuan Wu, Zhiquan Deng, Xiaolin Wang, Xing Ling, and Xin Cao;
IEEE TRANSACTIONS ON POWER ELECTRONICS,
VOL. 25, NO. 9, SEPTEMBER ( )
指導教授：王明賢
學生班級：四電資四甲
學生編號：
學生姓名：林炳宏

2. Outline I.INTRODUCTION II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD
III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES
IV.EXPERIMENTAL RESULTS
V.CONCLUSION
VI.REFERENCES

3. I.INTRODUCTION(1/3)
Permanent magnet (PM) brushless dc (BLDC) motor is increasingly being used in various areas such as automotive, computer, industrial, and household products, etc., and its market is rapidly growing. This is mainly due to its high efficiency,high torque, ease of control, and lower maintenance [1].

4. I.INTRODUCTION(2/3)
The three-phase wye-connected BLDC motors are usually supplied with a six-step 2π/3 inverter, and for assuring the normal system operation, the rotor position signals are necessary.
Traditionally, a rotor position sensor such as hall element is used for detecting the rotor position inBLDCmotor due to its simplicity and low cost.However, the rotor position sensors show some disadvantages from the standpoint of total system cost, size, and reliability[2].
Consequently, for eliminating these sensors from the motor, many research workers have attempted to control the speed of BLDC motors without rotor position sensors or speed sensors [3]–[15].

5. I.INTRODUCTION(3/3)
In the past, the detection of the freewheeling diodes conduction [3], the back electromotive force (EMF) voltage sensing [4], [5], the third harmonic detection [6], the flux estimation [7], and the intelligent control [8]–[10] had been applied to the BLDC drives.

6. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(1/7)
Fig. 1.(a) Phase-voltage method drive system.
(b) Terminal-voltage method drive system.

7. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(2/7)
A.Traditional Sensorless-Control Methods
The back EMF zero-crossing detection circuit is composed of four parts, including the resistance network, the dividing voltage circuit, the first-order low-pass filters, and the comparators in the PVM. R2 , R3 , and R4 constitute the resistance network which is used for simulating the motor neutral point voltage if the neutral wire of the BLDC motor is not available. R0 and R1 constitute the dividing voltage circuit, which is used to reduce the terminal voltage so that the signal sampled is between +15 and –15 V if the comparators are supplied by the +15 V power source.

8. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(4/7)
B. Analysis of the Rotor-Position-Detection Error
In a PM BLDC motor, the transient value of flux linkage in each phase winding is directly related to the rotor position. However, the back EMF is due to the rate of change of flux linkages, which is mainly excited by the PM on the surface of the rotor; hence, the back EMF can be indirectly related to the rotor position, and used for position sensorless control.
Nevertheless, in practical implementation, the two main sources of error, e.g., the armature reaction field and the low-pass filter,should be taken into account. For implementing the proposed method,

9. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(5/7)
Error Caused by the Armature Reaction Field: The back EMF consists of two components, one is the back EMF caused by the PM excitation field, which can reflect the rotor position accurately, and the other is the reaction EMF due to the armature reaction field, which is usually only around 10%–20% of the magnitude of the open-circuit field [21] and may distort the motor air-gap magnetic field excited by PM.
Error Caused by the Low-Pass Filters: Usually, the terminal or phase voltages are used instead for sensorless control, as the back EMF is difficult to be detected directly. The terminal voltage is the combination of dc and harmonic components generated by PWM operation. The magnitude of the dc component varies directly with the duty of PWM, and the frequencies of harmonic components are multiples of the carrier frequency.
其中 R0，R1 分壓電阻器；C 濾波電容；ω=2πf為角頻率和F是根本頻率。

10. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(6/7)
Fig. 2. (a) Commutation instant for the normal rotation.
(b) Commutation instant for the reversing rotation.

11. II.REVIEW OF THE TRADITIONAL SENSORLESS METHOD(7/7)
C. Review of the Error Compensation Methods
Sensorless commutation IC for BLDC motors [2] based on the frequency-independent phase shifter [19], in which the position error could be compensated by decreasing the slew rate γd . In [18], the period Td was calculated which depended strongly on the parameters of the BLDCmotor, such as the back EMF coefficient and the winding inductance. Another low-cost position sensorless-control scheme [20] included a look-up-table-based correction for the phase delay introduced by the filter.

12. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(1/9)
A. Constructed Position Signals Based on Coordinate Transformation
Fig. 3. Coordinate transformation.

13. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(2/9)
To begin with, the phase relationship between Ea and Ea and the characteristics of Ea will be analyzed. Then, Fourier expansions for Ea , Eb , and Ec are given as (3) where Ud is the dc bus voltage.

14. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(3/9)

15. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(4/9)
The back EMF, which is trapezoidal, contains only odd harmonics.Therefore, the phase of E_a is the same as the fundamental phase of Ea . The advantages of the proposed arithmetic can be summarized as follows: 1) using the angle β, the rotorposition-detection error could be compensated; 2) the neutral point voltage in PVM and the Ud/2 in TVM are not needed.Because the dc component is eliminated by the coordinate transform,the zero-crossing points of E_a , E_b , and E_c can be used for commutation; and 3) it can be seen that the amplitude of E_a is 1.5 times the amplitude of the fundamental ofEa ,which enables better estimation of the zero-crossing points than conventional methods [11], E_a could be regarded as fundamental wave if the higher harmonics are neglected.

16. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(5/9)
Fig. 4. Proposed sensorless BLDC motor-drive system

17. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(6/9)
1) Hardware Implementation: The proposed sensorless BLDC motor drive system could be designed as shown in Fig. 4. In comparison with Fig. 1, the back EMF zero-crossing detection circuit is substituted by the back EMF sampling circuit,which includes the low-pass filters, the sampling circuit, and the regulation circuit. The filters are used for eliminating the chopped pulse caused by the PWM operation. The sampling circuit, which is galvanically isolated from the digital signal processor (DSP), would sample the filtered terminal voltage to the regulation circuit, and the regulation circuit would scale down the filtered terminal voltage between 0 and +3 V, which could be read by the DSP.

18. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(7/9)
2) Program Implementation: The program flow of the proposed arithmetic is presented in Fig. 5(a). Since the back EMF is not generated at standstill, a proper starting procedure is necessary. In this paper, an open loop ramping control scheme is adopted to accelerate the motor to a certain speed level. Once the motor reaches the speed at which the back EMF can be reliably detected, the control mode will be changed from the open loop ramping control to the proposed sensorless control. After the starting process, the filtered terminal voltages, e.g., Ea and Eb , are sampled in real time, and the other one Ec is constructed by Ea and Eb . Then, the rotation speed ω can be computed out by using traditional estimation method [2].

19. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(8/9)
Fig. 5. (a) Program flow diagram.
(b) Commutation logic decision diagram.

20. III.PROPOSED ARITHMETIC FOR SENSORLESS BLDC DRIVES(9/9)
The commutation logic decision is shown in Fig. 5(b). After the commutation logic decision, the six PWM signals are transmitted out for sensorless BLDC control by the control unit. The polarity of the signals derived from the back EMF would reverse when the motor rotates in the opposite direction; hence it only needs to switch the β calculation mode as expressed in (2).

21. IV.EXPERIMENTAL RESULTS(1/2)
The proposed arithmetic for sensorless BLDC motor drive has been successfully implemented on the experimental BLDC motor, and its specification is shown in Table I. The overall system configuration of the proposed sensorless drive is shownin Fig. 4.
TABLE I - MOTOR PARAMETERS

22. IV.EXPERIMENTAL RESULTS(2/2)

23. V.CONCLUSION(1/1)
A novel arithmetic for sensorless BLDC motor drives has been presented in this paper. The rotor-position signals, e.g.,E_a , E_b , and E_c , are constructed by the two-phase terminal voltages, which can be used for commutation. The proposed sensorless-control method has the following advantages: 1) it only needs two-phase terminal voltage signals, without using the neutral voltage signal of the motor and 2) in order to obtain the commutation instants, the rotor-position-detection error could be calculated in real time, and compensated by computing the angle β, over the speed range. Experimental results verify the analysis in Section III and demonstrate advantages (1) and (2).

24. VI.REFERENCES(1/5)
[1] T. H. Kim, H. W. Lee, and M. Ehsani, “State of the art and future trends in position sensorless brushless DC motor/generator drives,” in Proc. 31st Annu. Conf. IEEE Ind. Electron. Soc., 2005, p. 8.
[2] K. Y. Cheng and Y. Y. Tzou, “Design of a sensorless commutation IC for BLDC motors,” IEEE Trans. Power Electron., vol. 18, no. 6, pp. 1365– 1375, Nov
[3] S. Ogasawara and H. Akagi, “An approach to position sensorless drive for brushlessDCmotors,” IEEE Trans. Ind. Appl., vol. 27, no. 5, pp. 928–933, Sep
[4] J. X. Shen and Y. B. Liu, “Microcomputer based position-sensorless drive for brushless dc motor,” in Proc. Int. Power Electron. Motion Control Conf., 1994, pp. 402–407.
[5] S. J. Lee, Y. H. Yoon, and C. Y. Won, “Precise speed control of the PM brushless DC motor for sensorless drives,” in Proc. 8th Int. Conf. Electr. Mach. Syst., 2005, vol. 1, pp. 290–295.

25. VI.REFERENCES(2/5)
[6] J. X. Shen and S. Iwasaki, “Sensorless control of ultrahigh-speed PM brushless motor using PLL and third harmonic back EMF,” IEEE Trans. Ind. Electron., vol. 53, no. 2, pp. 421–428, Apr
[7] Y. H. Yoon, T. W. Lee, S. H. Park, B. K. Lee, and C. Y. Won, “New approach to rotor position detection and precision speed control of the BLDC motor,” in Proc. 32nd Annu. Conf. IEEE Ind. Electron., 2006, pp. 1305–1310.
[8] C. Wei and X. Changliang, “Sensorless control of brushless DC motor based on fuzzy logic,” in Proc. 6th World Congr. Intell. Control Autom., 2006, pp. 6298–6302.
[9] B. G. Park, T. S. Kim, J. S. Ryu, and D. S. Hyun, “Fuzzy back EMF observer for improving performance of sensorless brushless DC motor drive,” in Proc. 21st Annu. IEEE Appl. Power Electron. Conf. Expo., 2006, p. 5.
[10] T. S. Kim, J. S. Ryu, and D. S. Hyun, “Unknown input observer for a novel sensorless drive of brushless DC motors,” in Proc. 21st Annu. IEEE Appl. Power Electron. Conf. Expo., 2006, p. 6.

26. VI.REFERENCES(3/5)
[11] J. Shao, D. Nolan,M. Teissier, and D. Swanson, “A novelmicrocontrollerbased sensorless brushless DC (BLDC) motor drive for automotive fuel pumps,” IEEE Trans. Ind. Appl., vol. 39, no. 6, pp. 1734–1740, Nov./Dec
[12] J. Shao, “An improved microcontroller-based sensorless brushless DC (BLDC) motor drive for automotive applications,” IEEE Trans. Ind. Appl., vol. 42, no. 5, pp. 1216–1221, Sep./Oct
[13] G. H. Jang and M. G. Kim, “Optimal commutation of a BLDC motor by utilizing the symmetric terminal voltage,” IEEE Trans. Magn., vol. 42, no. 10, pp. 3473–3475, Oct
[14] T. H. Kim and M. Ehsani, “Sensorless control of the BLDC motors from near-zero to high speeds,” IEEE Trans. Power Electron., vol. 19, no. 6, pp. 1635–1645, Nov
[15] L. Zicheng, C. Shanmei, Q. Yi, and C. Kai, “A novel line-to-line back EMF calculation for sensorless brushless DC motor drives,” in Proc. Int. Conf. Electr. Mach. Syst., 2008, pp. 1406–1411.

27. VI.REFERENCES(4/5)
[16] T. H. Kim and M. Ehsani, “An error analysis of the sensorless position estimation for BLDC motors,” in Proc. 38th IAS Annu. Meeting Conf. Record Ind. Appl. Conf., 2003, vol. 1, pp. 611–617.
[17] D. M. Lee and W. C. Lee, “Analysis of relationship between abnormal current and position detection error in sensorless controller for interior permanent-magnet brushless DC motors,” IEEE Trans. Magn., vol. 44, no. 8, pp. 2074–2081, Aug
[18] J. X. Shen and K. J. Tseng, “Analyses and compensation of rotor position detection error in sensorless PMbrushless DCmotor drives,” IEEE Trans. Energy Convers., vol. 18, no. 1, pp. 87–93, Mar
[19] D. H. Jung and I. J. Ha, “Low-cost sensorless control of brushless DC motors using a frequency-independent phase shifter,” IEEE Trans. Power Electron., vol. 15, no. 4, pp. 744–752, Jul
[20] G. J. Su and J. W. Mckeever, “Low-cost sensorless control of brushless DC motors with improved speed range,” IEEE Trans. Power Electron., vol. 19, no. 2, pp. 296–302, Mar

28. VI.REFERENCES(5/5)
[21] Z. Q. Zhu and D. Howe, “Instantaneous magnetic field distribution in brushless permanent magnet DC motors. II. Armature-reaction field,” IEEE Trans. Magn., vol. 29, no. 1, pp. 136–142, Jan