Authors : G. H. Jang, J. H. Park and J. H. Chang

IEE Proceedings – Electric Power Applications, Vol. 149, No. 2, March 2002

Department of Electrical Engineering

Southern Taiwan University

Position Detection and Start-Up Algorithm of Position Detection and Start-Up Algorithm of a Rotor in a Sensorless BLDC Motor a Rotor in a Sensorless BLDC Motor

Utilizing Inductance Variation Utilizing Inductance Variation

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 :

LiPMphase PMLi

L

- Flux linkage from the PM

- Flux linkage from current

- Inductance of energized phaseNon-linear characteristic due to magnetic saturation

Denote : ii

- For generating same direction flux with PM

- For generating opposite direction flux with PM

Inductances and are expressed as :L L

iiL

iiL

PMphase

PMphase

- Change of flux linkage due to i

- Change of flux linkage due to i

Inductance variation

Fig.1 Flux change due to direction of the current

The flux change due to , is smaller than

Therefore, the inductance is smaller than

iL L

Inductance variation

The response of a phase current to the inductance variation can be explained through a voltage equation :

sve

dt

diLRivs R

e

- Phase voltage

- Phase resistance

- Back-emf

When the motor is at standstill, there is no back-emf :

tL

Rs eR

vi 1

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

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

i i LL

Fig.2 Response of the current due to direction of the current

i i

Theoretical developments

CSdLAdSB

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 :

BA

- Flux density

- Magnetic vector potential

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

Tab.1 Major design parameters of the finite element model 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

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

In the calculation of the current, the time delay is 20μs and the inductance is calculated every electrical angle of 4°

Fig.4 Calculated current responses(i) AB (ii) BA (iii) CA (iv) AC (v) BC (vi) CB

Theoretical developments

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

Fig.5 First difference between each pair of current responses(i) Δi1 = i1+ - i1- (ii) Δi2 = i2+ - i2- (iii) Δi3 = i3+ - i3-

Theoretical developments

The polarity of ΔΔi can provide information on the rotor position near the magnetic equilibrium points

Fig.6 Second difference between each pair of current responses

(i) ΔΔi1 = Δi1 – Δi2 (ii) ΔΔi2 = Δi2 – Δi3 (iii) ΔΔi3 = Δi3 – Δi1

Theoretical developments

The stationary rotor position can be detected by monitoring the polarity of both Δi and ΔΔi to energize the correct phases of the motor

Tab.3 Polarity of ΔΔi on the rotor position

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

Theoretical developments

In every commutation phase, there are two phases besides the energized phase that can produce positive torque

Fig.7 Torque curves(i) AC (ii) BC (iii) BA (iv) CA (v) CB (vi) AB

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

Theoretical developments

Fig.8 Pulse train and its response(a) Pulse train (b) Current response at the commutation point

When the current response of Ppulse is smaller than that of Pphase with the same time delay, the commutation position is identified

Theoretical developments

Tab.4 Composition of the pulse train on the rotor position

System implementation

TMS320F240 DSP is used for the sensorless BLDC controller

PC is used with a graphical user-interface to monitor variables in real-time

Fig.9 System configuration

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

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-

System implementation

Fig.12 Second difference between each pair of current responses

(i) ΔΔi1 = Δi1 – Δi2 (ii) ΔΔi2 = Δi2 – Δi3 (iii) ΔΔi3 = Δi3 – Δi1

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

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

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

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

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