Transcript Theoretical developments

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 :
 phase  PM  Li
PM - Flux linkage from the PM
Non-linear characteristic due to
magnetic saturation
Li
L
 Denote :
i
i
 Inductances

L 
L 
- Inductance of energized phase
- For generating same direction flux with PM
- For generating opposite direction flux with PM
L
and
 phase  PM
i
 phase  PM
i
- Flux linkage from current
L
are expressed as :

 
i

 
i

- Change of flux linkage due to
i

- Change of flux linkage due to
i

Inductance variation
 The flux change
 due to i  , is smaller than 
 Therefore, the inductance
L
is smaller than
L
Fig.1 Flux change due to direction of the current
Inductance variation
 The response of a phase current to the inductance variation can be
explained through a voltage equation :
di
vs  Ri  L  e
dt
vs
R
e
- Phase voltage
- Phase resistance
- Back-emf
 When the motor is at standstill, there is no back-emf :
R
 t
vs 
i  1  e L 
R

 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

than L
i
shows a faster response than
i  , because L
is smaller
 Therefore, the position information of a rotor can be obtained by monitoring


the phase currents i and i in the appropriate time delay
Fig.2 Response of the current due to direction of the
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 :
   B  dS   A  dL
S
C
B
A
- 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
Fig.4 Calculated current responses
(i) AB (ii) BA (iii) CA (iv) AC (v) BC (vi) CB
 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
 The polarity of ΔΔi can provide information on the rotor position near the
magnetic equilibrium points
Theoretical developments
Tab.3 Polarity of ΔΔi on the rotor position
 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
Theoretical developments
Fig.7 Torque curves
(i) AC (ii) BC (iii) BA (iv) CA (v) CB (vi) AB
 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
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
Fig.9 System configuration
 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
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