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

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

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

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

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

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

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

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

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

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

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

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

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°

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

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

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

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.

(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

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.

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

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.

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

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

(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

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

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

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

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

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

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