1. Department of Electrical Engineering Southern Taiwan University
Position Detection and Start-Up Algorithm of a Rotor in a Sensorless BLDC Motor Utilizing Inductance Variation
Authors : G. H. Jang, J. H. Park and J. H. Chang
IEE Proceedings – Electric Power Applications, Vol. 149, No. 2, March 2002
Student : Sergiu Berinde
M972B206

2. Outline Abstract Introduction Inductance variation
Theoretical developments
System implementation and experimental verification
Conclusions

3. Abstract
The paper proposes a method of identifying the rotor position of a brushless DC (BLDC) motor and driving a motor smoothly form standstill without position sensors.
Six current pulses are injected into every two phases of the motor and their first and second differences are compared in order to obtain the standstill position of the rotor.
After start-up, a pulse train of alternating long and short pulses, is injected into the commutation phases and the current responses are monitored to get the next commutation timing. **** (poate modific)
A DSP-based BLDC drive is developed in order to verify the algorithm experimentally. It shows the method can drive the motor smoothly up to medium speed without delay

4. Introduction
Brushless DC motors are widely used in various applications because of their high efficiency and good controllability over a wide speed range
Position information, required for energizing the correct armature windings, can be obtained by using hall sensors or encoders
Sensors can be affected by operating conditions and increase the size and cost of the motor
Sensorless methods have been developed for providing the position information without the above restrictions

5. Introduction
The popular back-emf (back electromotive force) method can only be used in high speeds and needs another initial rotor position detection method and a start-up algorithm
The ‘align and go’ start-up algorithm can be used, but it usually incurs a time delay due to aligning the rotor and reaching a sufficient speed for back-emf measuring
Other methods based on inductance variation have been researched, but they all present some drawbacks in actual implementation
This paper uses finite-element analysis to calculate the inductance of a BLDC motor and develops an initial rotor position detection and start-up algorithm, utilising the inductance variation without having the above drawbacks

6. Inductance variation
The total flux linkage of a phase of a BLDC motor :
- Flux linkage from the PM
- Flux linkage from current
Non-linear characteristic due to magnetic saturation
- Inductance of energized phase
Denote :
- For generating same direction flux with PM
- For generating opposite direction flux with PM
Nonlinear char due to magnetic saturation, depending on the rotor position and current
Trecere: if we look at the changes in flux linkage, next slide,…..
Inductances and are expressed as :
- Change of flux linkage due to
- Change of flux linkage due to

7. Inductance variation The flux change due to , is smaller than
Therefore, the inductance is smaller than
Fig.1 Flux change due to direction of the current
Nonlinear char due to magnetic saturation, depending on the rotor position and current

8. Inductance variation
The response of a phase current to the inductance variation can be explained through a voltage equation :
- Phase voltage
- Phase resistance
- Back-emf
When the motor is at standstill, there is no back-emf :
Nonlinear char due to magnetic saturation, depending on the rotor position and current
The phase current shows a different response depending on the inductance variation, which is determined by the relative position of the rotor and the direction of the current

9. Fig.2 Response of the current due to direction of the current
Inductance variation
The current shows a faster response than , because is smaller than
Therefore, the position information of a rotor can be obtained by monitoring the phase currents and in the appropriate time delay
Fig.2 Response of the current due to direction of the current
Nonlinear char due to magnetic saturation, depending on the rotor position and current

10. Theoretical developments
Finite-element analysis of a BLDC motor
The finite-element method (FEM) is used to calculate the magnetic vector potential of the BLDC motor
The total flux linkage of the phase can be expressed as :
- Flux density
- Magnetic vector potential
To first calculate the magnetic potential -> flux linkage -> inductance
The inductance is then determined by calculating the flux linkage from the energized phase and PM, and the flux linkage from the PM only
A 2D finite element program is developed to calculate the magnetic field of a motor with 8 poles and 12 slots

11. Theoretical developments
Fig.3 Inductance variation due to the change of
current and rotor position
(i) 0.5A (ii) 1.0A (iii) 1.5A (iv) 2.0A
Tab.1 Major design parameters of the finite element model

12. Tab.2 Six segments of an electrical cycle
Theoretical developments
Position detection of a stationary rotor
A three-phase motor has six segments of an electrical cycle, in which any two phases out of three are carrying current
Tab.2 Six segments of an electrical cycle

13. Theoretical developments
Fig.4 Calculated current responses
(i) AB (ii) BA (iii) CA (iv) AC (v) BC (vi) CB
We use equation aia cu curentul pt stationar
In the calculation of the current, the time delay is 20μs and the inductance is calculated every electrical angle of 4°

14. Theoretical developments
Fig.5 First difference between each pair of current responses
(i) Δi1 = i1+ - i1- (ii) Δi2 = i2+ - i2- (iii) Δi3 = i3+ - i3-
The polarity of Δi can provide information on the rotor position, because the polarity of one of three Δis changes every electrical angle of 60°, but at magnetic equilibrium positions, one of three Δis is 0

15. Theoretical developments
Fig.6 Second difference between each pair of current responses
(i) ΔΔi1 = Δi1 – Δi2 (ii) ΔΔi2 = Δi2 – Δi3 (iii) ΔΔi3 = Δi3 – Δi1
It’s shifted by 30 degrees compared with Delta_i. We can then say that the stationary rotor position can be detected by monitoring the polarity of both Delta_i and Delta_delta_i to energise the correct phases of the motor.
The polarity of ΔΔi can provide information on the rotor position near the magnetic equilibrium points

16. Tab.3 Polarity of ΔΔi on the rotor position
Theoretical developments
Tab.3 Polarity of ΔΔi on the rotor position
It’s shifted by 30 degrees compared with Delta_i. We can then say that the stationary rotor position can be detected by monitoring the polarity of both Delta_i and Delta_delta_i to energise the correct phases of the motor.
The stationary rotor position can be detected by monitoring the polarity of both Δi and ΔΔi to energize the correct phases of the motor

17. Theoretical developments
Start-up algorithm
Once the standstill position is detected, the correct phases of the BLDC are energized to produce maximum torque
Consequently, the nest commutation position should be detected to energize the next phases whenever the rotor rotates the electrical angle of 60°
As the rotor is moving quickly, six pulses cannot be injected into one commutation period, so the position detection algorithm cannot be applied
Three pulses out of six generate negative torque
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.

18. (i) AC (ii) BC (iii) BA (iv) CA (v) CB (vi) AB
Theoretical developments
Fig.7 Torque curves
(i) AC (ii) BC (iii) BA (iv) CA (v) CB (vi) AB
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.
In every commutation phase, there are two phases besides the energized phase that can produce positive torque

19. Theoretical developments
Position detection by comparing the current response of these positive torque-generating phases with that of the current energized phases
Energizing the current commutation phases and the next commutation phases in an alternate manner overall produces positive torque
A pulse train of long and short pulses Pphase and Ppulse is injected to accelerate the rotor and detect rotor position
The period of Ppulse is selected to be as short as possible so that it only provides comparison data for Pphase
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.

20. Theoretical developments
Fig.8 Pulse train and its response
(a) Pulse train (b) Current response at the commutation point
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.
When the current response of Ppulse is smaller than that of Pphase with the same time delay, the commutation position is identified

21. Tab.4 Composition of the pulse train on the rotor position
Theoretical developments
Tab.4 Composition of the pulse train on the rotor position
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.

22. Fig.9 System configuration
System implementation
Fig.9 System configuration
The position detection algorithm in the previous section cannot be effectively applied during start-up because six pulses cannot be injected during a commutation period as the rotor is moving quickly. Another problem is that 3 pulses out of 6 generate negative torque.
TMS320F240 DSP is used for the sensorless BLDC controller
PC is used with a graphical user-interface to monitor variables in real-time

23. System implementation
BLDC motor with 8 poles and 12 slots used in hard disk drive
Pulse of 12V is injected into all six segments of an electrical cycle whenever a rotor moves at an electrical angle of 8°
Fig.10 Measured current responses
(i) AB (ii) BA (iii) CA (iv) AC (v) BC (vi) CB
The same pattern with the calculated ones

24. (i) Δi1 = i1+ - i1- (ii) Δi2 = i2+ - i2- (iii) Δi3 = i3+ - i3-
System implementation
Fig.11 First difference between each pair of measured current responses
(i) Δi1 = i1+ - i1- (ii) Δi2 = i2+ - i2- (iii) Δi3 = i3+ - i3-
The same pattern with the calculated ones

25. System implementation
Fig.12 Second difference between each pair of current responses
(i) ΔΔi1 = Δi1 – Δi2 (ii) ΔΔi2 = Δi2 – Δi3 (iii) ΔΔi3 = Δi3 – Δi1
The same pattern with the calculated ones

26. Fig.13 Measured six current responses for a stationary rotor
System implementation
A pulse of 12V is applied for all six segments, respectively, of an electrical cycle during 20 μs, to detect the standstill position of the rotor
Based on the polarity of ΔΔi the relative position is between 150° and 210°
Fig.13 Measured six current responses for a stationary rotor
The same pattern with the calculated ones

27. Fig.14 Response of the pulse train during the start-up
System implementation
Two pulses of 12V, Ppulse and Pphase are applied to the current and next commutation phases for the period of 50 and 20μs, respectively
The current response of Ppulse decreases as the rotor rotates
The same pattern with the calculated ones
Fig.14 Response of the pulse train during the start-up
(i) Pphase (ii) Ppulse

28. System implementation
When the current response of Ppulse is smaller than that of Pphase , the next commutation phases are energised
Fig.15 Transition of the response of the pulse train at the
commutation position
(a) Before commutation (b) After commutation
The same pattern with the calculated ones

29. System implementation
Fig.16 Transient response of the speed of the motor to the
switch of the sensorless algorithm
(i) 1000rpm (ii) 2000rpm (iii) 3000rpm
The same pattern with the calculated ones

30. Conclusions
A method of identifying the rotor position of a BLDC motor and of driving a motor from standstill smoothly, without any position sensors, is presented
It also introduces a sensorless BLDC motor controller
The controller shows that the proposed algorithm can drive the BLDC motor to medium speed without any vibration or time delay
The same pattern with the calculated ones