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Fujitsu Semiconductor Design (Chengdu) Co. Ltd.
Application Note
MCU-AN-510108-E-11
32-BIT MICROCONTROLLER
MB9A310SERIES
TORQUE COMPENSATION
APPLICATION IN PMSM DRIVE
APPLICATION NOTE
ARM and Cortex-M3 are the trademarks of ARM Limited in the EU and other countries.
Torque Compensation V1.1.0
Revision History
Revision History
Version
Date
Updated by
Approved by
Modifications
1.0.0
2011-08-23
Arthur Zhong
First Draft
1.1.0
2012-06-14
Mona Chen
Modified the format
This manual contains 17 pages.
Specifications are subject to change without notice. For further information please contact each office.
All Rights Reserved.
The contents of this document are subject to change without notice.
Customers are advised to consult with sales representatives before ordering.
The information, such as descriptions of function and application circuit examples, in this document are presented solely
for the purpose of reference to show examples of operations and uses of FUJITSU SEMICONDUCTOR device; FUJITSU
SEMICONDUCTOR does not warrant proper operation of the device with respect to use based on such information. When
you develop equipment incorporating the device based on such information, you must assume any responsibility arising
out of such use of the information.
FUJITSU SEMICONDUCTOR assumes no liability for any damages whatsoever arising out of the use of the information.
Any information in this document, including descriptions of function and schematic diagrams, shall not be construed as
license of the use or exercise of any intellectual property right, such as patent right or copyright, or any other right of
FUJITSU SEMICONDUCTOR or any third party or does FUJITSU SEMICONDUCTOR warrant non-infringement of
any third-party's intellectual property right or other right by using such information. FUJITSU SEMICONDUCTOR
assumes no liability for any infringement of the intellectual property rights or other rights of third parties which would
result from the use of information contained herein.
The products described in this document are designed, developed and manufactured as contemplated for general use,
including without limitation, ordinary industrial use, general office use, personal use, and household use, but are not
designed, developed and manufactured as contemplated (1) for use accompanying fatal risks or dangers that, unless
extremely high safety is secured, could have a serious effect to the public, and could lead directly to death, personal injury,
severe physical damage or other loss (i.e., nuclear reaction control in nuclear facility, aircraft flight control, air traffic
control, mass transport control, medical life support system, missile launch control in weapon system), or (2) for use
requiring extremely high reliability (i.e., submersible repeater and artificial satellite).
Please note that FUJITSU SEMICONDUCTOR will not be liable against you and/or any third party for any claims or
damages arising in connection with above-mentioned uses of the products.
Any semiconductor devices have an inherent chance of failure. You must protect against injury, damage or loss from such
failures by incorporating safety design measures into your facility and equipment such as redundancy, fire protection, and
prevention of over-current levels and other abnormal operating conditions.
Exportation/release of any products described in this document may require necessary procedures in accordance with the
regulations of the Foreign Exchange and Foreign Trade Control Law of Japan and/or US export control laws.
The company names and brand names herein are the trademarks or registered trademarks of their respective owners.
Copyright © 2011Fujitsu Semiconductor Design (Chengdu) Co. Ltd. All rights reserved.
MCU-AN-510108-E-11 – Page 2
Torque Compensation V1.1.0
Contents
Contents
REVISION HISTORY ............................................................................................................ 2
CONTENTS .......................................................................................................................... 3
1 INTRODUCTION .............................................................................................................. 4
1.1
Purpose ................................................................................................................... 4
1.2
Definitions, Acronyms and Abbreviations ................................................................ 4
1.3
Document Overview ................................................................................................ 4
2 PRINCIPLES OF TORQUE COMPENSATION ................................................................ 5
2.1
Torque Equation ...................................................................................................... 5
2.2
Vibration Reason ..................................................................................................... 7
2.3
Measurement .......................................................................................................... 9
2.3.1
VoltageCompensation ............................................................................... 9
2.3.2
Current Compensation ............................................................................. 11
3 THEIMPLEMENTATION OF TC..................................................................................... 13
3.1
Feature.................................................................................................................. 13
3.2
The flowchartof voltage compensation .................................................................. 14
3.3
Waveform of TC .................................................................................................... 15
4 APPENDIX ..................................................................................................................... 17
4.1
List of Figures and Tables ..................................................................................... 17
MCU-AN-510108-E-11 – Page 3
Torque Compensation V1.1.0
Chapter 1 Introduction
1 Introduction
1.1
Purpose
This application note describes the background, principle, implementation and test result of
torque compensation.
As you know, in order to decrease the cost of air conditioner system, more and more
producers use low cost motor, such as single rotor motor. The load torque of this type motor
in one mechanical circle is out of balance, which result in the speed of motor is fluctuated.
Then the air conditioner system will be violent vibration. This phenomenon is very obvious
especially when the frequency of the motor is very low.If we ignore this phenomenon, it will
result in two kinds of bad result. One is noise, once we use air conditioner, it will influence
our life. The other is life of air conditioner system, maybe we use two or three years, the air
conditioner system will break down.
So, we must research a technology to eliminate this phenomenon, torque compensation is
just the technology that we need.
1.2
TC
Definitions, Acronyms and Abbreviations
-
PMSM -
Torque Compensation
Permanent Magnet Synchronous Motor
-
Load torque
-
Electrical torque
-
Rotor inertia
-
Rotor pole pairs
-
Amplitude of natural magnetic flux of permanent magnets
-
Mechanical speed
-
Electrical speed
-
Electrical angle
-
phase current in d axis
-
phase current in q axis
BEMF -
BACKelectromotive force
FOC
-
Field orient control
-
Viscosity coefficient
1.3
Document Overview
The rest of document is organized as the following:
Chapter 2 explains the principles of torque compensation.
Chapter 3 explains the implementation of torque compensation.
MCU-AN-510108-E-11 – Page 4
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
2 Principles of Torque compensation
2.1
Torque Equation
For PMSM, one phase electrical voltage equation could be written like this:
V = z*i = Ri +
= Ri +
(1)
Where the term
this:
corresponds to BEMF, it also could be written like
=
(2)
Where
corresponds to rotor electrical speed.
It is supposed that the flux is sinusoidal,the BEMF has the following equation:
̅=[
]=-
[
]=
(3)
In PMSM system, the torque is expressed like this:
=p*[ ]*
(4)
Where p is the pole pairs of rotor
It could be proven that the best solution to produce a constant torque is to drive sinusoidal
motor by sinusoidal current:
=p*
*(
)
(5)
Knowing that:
(6)
We could obtain:
=p*
*(
(
)
(
=
))
(7)
Because according to the theory of FOC, the d axis current is equal to 0, the q axis current is
equal to , we could obtain:
(8)
MCU-AN-510108-E-11 – Page 5
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
The electrical power delivered to the motor, a part is transformed in joule losses, another
part is going to the energy storing in magnetic field and the last part is transformed in
mechanical energy. The last part could be understood as torque production. The torque
created by energy conversion process is then used to drive mechanical load. Below is the
torque balance equation:
+
+J
(9)
MCU-AN-510108-E-11 – Page 6
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
2.2
Vibration Reason
For single rotor motor, the load torque curve like this:
Torque

Area II
Area I

ѳ
One Mechanical
Circle
Figure 2-1: Torque Curve
In the above illustration, (red line) is the load torque and (black line) is electrical torque.
You could find that the load torque curve is variable in one mechanical circle, this
phenomenon will become graver and graver in low frequency area, especially when the
frequency is less than 30HZ.
MCU-AN-510108-E-11 – Page 7
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
In Area I, because is less than , the speed of rotor will increase. On the other hand, in
area II, the speed of rotor will decrease, the speed curve like this:
Torque

Area II
Area I

ѳ

Average
Speed
Real
time
Speed
ѳ
Figure 2-2: Rotor Speed Curve
Where the green line represents average speed of rotor and the blue line represents the real
time speed of rotor.
MCU-AN-510108-E-11 – Page 8
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
2.3
Measurement
Now, we have known the actual reason of speed ripple, but how to eliminate this
phenomenon? Usually, there are two methods: voltage compensation and current
compensation.
2.3.1 Voltage Compensation

Decrease
voltage
Increase
voltage
ѳ
Figure 2-3: Principle of Voltage Compensation
Above illustration is to explain the principle of voltage compensation. When the speed is
lower than average speed, it needs to increase output voltage so that the real time speed
could increase; but when the speed is higher than average speed, it needs to decrease the
output voltage so that the real time speed could decrease. After compensation, the ripple of
speed curve decreases obviously (blue line is the speed curve before compensation, green
line is the speed curve after compensation).
Where the red line represents the average speed before voltage compensation, the blue line
represents real time speed before voltage compensation; the green line represents real time
speed after voltage compensation.
MCU-AN-510108-E-11 – Page 9
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
After add voltage compensation module, PMSM controlling system will be changed as below:
Voltage
Compensation
ωre +
f
-
PI
Park-1
Vq
Iqref +
-
Idref +
d,q
PI
Vα
SV
PI
Vd
α,β
Vβ
3-Phase
Bridge
PWM
-
A
C
Iq
Id
R
α,β
Park
k
θestim
ωm
Isα
d,q
Position and
speed
Estimator
α,β
Isβ
Isβ
Isα
Vβ
Vα
a,b,c
B
Ib
Ic
Clark
e
M
Software
Figure 2-4: PMSM Control Block with Voltage compensation
MCU-AN-510108-E-11 – Page 10
Hardware
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
2.3.2 Current Compensation
Torque



ѳ
Figure 2-5: Principle of Current Compensation
Above illustration is to explain the principle of current compensation. Core ideology of this
method is to generate one electrical torque curve, whose shape is the same as load torque
curve, but amplitude is bigger load torque curve. The amplitude difference between electrical
torque curve and load torque curve is to keep the rotor running at a certain speed.
Where the blue line represents load torque, red line represents electrical torque before
current compensation; green line represents electrical torque after current compensation.
MCU-AN-510108-E-11 – Page 11
Torque Compensation V1.1.0
Chapter 2 Principles of Torque compensation
After add current compensation module, PMSM controlling system will be changed as below:
Current
Compensation
Iqref
ωre +
f
-
PI
+
-
Idref +
Park-1
Vq
d,q
PI
Vα
SV
Vd
PI
α,β
Vβ
3-Phase
Bridge
PWM
-
A
C
Iq
Id
R
α,β
Park
k
θestim
ωm
Isα
d,q
Position and
speed
Estimator
α,β
Isβ
Isβ
Isα
Vβ
Vα
a,b,c
B
Ib
Ic
Clark
e
M
Software
Figure 2-6: PMSM Control Block with Current Compensation
MCU-AN-510108-E-11 – Page 12
Hardware
Torque Compensation V1.1.0
Chapter 3 Implementation of TC
3 Implementation of TC
Now, we will use voltage compensation as example to explain the implementation of torque
compensation.
3.1
Feature

Set up torque compensation frequency range automatically, 5HZ~37HZ is
recommended frequency range.

Modify the compensation amplitude according to amplitude of load automatically, so
that it could get good performance regardless of heavy load or light load.

Parameters correlative with torque compensation module are less, only need to
change compensate angle and compensate voltage amplitude (different frequency
has different compensate voltage amplitude).
MCU-AN-510108-E-11 – Page 13
Torque Compensation V1.1.0
Chapter 3 Implementation of TC
3.2
Flowchart of Voltage Compensation
Start
Check actual speed
N
TC enable?
Y
Y
Compress and release
circle check complete?
N
Check compress and
release circle
Check load torque
amplitude
Calculate amplitude of
compensate voltage
Compensate q axis voltage
End
Figure 3-1: Flowchart of Voltage Compensation
MCU-AN-510108-E-11 – Page 14
Torque Compensation V1.1.0
Chapter 3 Implementation of TC
3.3
Waveform of TC
Figure 3-2: Current Waveform before Torque Compensation
Compress
circle
Release
circle
Figure 3-3: Current Waveform after Torque Compensation
MCU-AN-510108-E-11 – Page 15
Torque Compensation V1.1.0
Chapter 3 Implementation of TC
The above two illustrations show the phase current waveform before and after torque
compensation. After add torque compensation function, the current waveform has been
changed obviously. In compress circle, because the load becomes bigger and bigger, the
speed of rotor will decrease, the BEMF will decrease at the same time, according to voltage
balance formula:
V= Ri + L
+E
(10)
The phase current will increase. The target of torque compensation is to increase the speed,
so we must increase the output voltage, then phase current will become bigger. On the other
hand, in release circle, because the load becomes smaller and smaller, the speed of rotor
will increase, the BEMF will increase at the same time, according to voltage balance
equation also, the phase current will decrease. The target of torque compensation is to
decrease the speed, so it must decrease the output voltage, then phase current will become
smaller. When you see the phase current is strange after add torque compensation function,
don’t be nervous, because it is just what we want to get.
MCU-AN-510108-E-11 – Page 16
Torque Compensation V1.1.0
Chapter 4 Appendix
4 Appendix
4.1
List of Figures and Tables
Figure 2-1: Torque Curve ....................................................................................................... 7
Figure 2-2: Rotor Speed Curve .............................................................................................. 8
Figure 2-3: Principle of Voltage Compensation ...................................................................... 9
Figure 2-4: PMSM Control Block with Voltage compensation ............................................... 10
Figure 2-5: Principle of Current Compensation..................................................................... 11
Figure 2-6: PMSM Control Block with Current Compensation .............................................. 12
Figure 3-1: Flowchart of Voltage Compensation................................................................... 14
Figure 3-2: Current Waveform before Torque Compensation ............................................... 15
Figure 3-3: Current Waveform after Torque Compensation .................................................. 15
MCU-AN-510108-E-11 – Page 17