IM-EncoderFOCSpeedNoLoad

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Application Note
MCU-AN-510124-E-12
32-BIT MICROCONTROLLER
MB9AXXX/MB9BXXX SERIES
SMO BASED FIELD ORIENTED
CONTROL OF INDUCTION
MOTOR WITH SPEED SENSOR
APPLICATION NOTE
ARM and Cortex-M3 are the trademarks of ARM Limited in the EU and other countries.
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Revision History
Revision History
Version
Date
Updated by
1.0.0
2012-08-31
Kartik Liao
1.1.0
2012-09-12
Kartik Liao
1.2.0
2012-10-09
Kartik Liao
Approved by
Modifications
First Draft
Add Field weakening
This application note contains 19 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 © 2012 Fujitsu Semiconductor Design (Chengdu) Co. Ltd. All rights reserved.
MCU-AN-510124-E-12 – Page 2
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
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 ................................................................................................ 5
2 OFF-LINE PARAMETER MEASUREMENT ..................................................................... 6
2.1
Overview ................................................................................................................. 6
2.2
Off-line Parameter Measurement ............................................................................ 6
2.2.1
Equivalent Circuit of Induction Motor.......................................................... 6
2.2.2
DC Test ..................................................................................................... 6
2.2.3
Lock-Rotor Test ......................................................................................... 6
2.2.4
No-Load Test ............................................................................................. 7
3 FOC DRIVE OF INDUCTION MOTOR ............................................................................. 8
3.1
3.2
Rotor Flux Field Oriented Control ............................................................................ 8
3.1.1
Mathematic Model of Induction Motor ........................................................ 8
3.1.2
Rotor Flux FOC Principle ........................................................................... 9
FOC Algorithm Realization .................................................................................... 10
3.2.1
Back Calculation and Tracking PID regulator ........................................... 10
3.2.2
Sliding Mode Rotor Flux Observer ........................................................... 11
3.2.3
Dead Time Compensation ....................................................................... 12
3.2.4
Field Weakening Control.......................................................................... 14
4 EXPERIMENT RESULT ................................................................................................. 16
4.1.1
Parameter Measurement ......................................................................... 16
4.1.2
Sensor-FOC Drive Performance .............................................................. 16
5 APPENDIX ..................................................................................................................... 19
5.1
List of Figures and Tables ..................................................................................... 19
MCU-AN-510124-E-12 – Page 3
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 1 Introduction
1 Introduction
1.1
Purpose
This document describes three-phase squirrel-cage induction motor drive by sensor-FOC
scheme, which applies sliding mode algorithm for rotor flux estimation.
1.2
Definitions, Acronyms and Abbreviations
FOC ...................................................................................... Field Oriented Control
PID ...................................................... Proportion, Integration, Derivation Regulator
SMO ..................................................................................... Sliding Mode Observer
SVPWM ........................................................Space Vector Pulse Width Modulation
DOF .......................................................................................... Degree of Freedom
RLS .................................................................................... Recursive Least Square
........................................................................................Stator voltage in -axis
........................................................................................Stator voltage in -axis
......................................................................................... Stator current in -axis
......................................................................................... Stator current in -axis
................................................................................. Stator flux linkage in -axis
................................................................................. Stator flux linkage in -axis
........................................................................................ Rotor voltage in -axis
........................................................................................ Rotor voltage in -axis
......................................................................................... Rotor current in -axis
.......................................................................................... Rotor current in -axis
.................................................................................. Rotor flux linkage in -axis
.................................................................................. Rotor flux linkage in -axis
........................................................................................ Stator voltage in -axis
........................................................................................ Stator voltage in -axis
......................................................................................... Stator current in -axis
......................................................................................... Stator current in -axis
................................................................................. Stator flux linkage in -axis
..................................................................................Stator flux linkage in -axis
........................................................................................ Rotor voltage in -axis
.........................................................................................Rotor voltage in -axis
......................................................................................... Rotor current in -axis
.......................................................................................... Rotor current in -axis
.................................................................................. Rotor flux linkage in -axis
.................................................................................. Rotor flux linkage in -axis
.................................................................................................. Stator resistance
MCU-AN-510124-E-12 – Page 4
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 1 Introduction
................................................................................................... Rotor resistance
............................................................................................... Mutual inductance
.................................................................................... Stator leakage inductance
.................................................................................... Rotor leakage inductance
..........................................................................Stator self-inductance
.......................................................................... Rotor self-inductance
.................................................................................................... Rotor flux angle
........................................................................................ Rotor speed (electrical)
...............................................................................................Synchronous speed
.......................................................................................Electrical torque of motor
..................................................................... Maximum available voltage of
.................................................................... Maximum available voltage of
1.3
Document Overview
The rest of document is organized as the following:
Chapter 2 describes off-line parameter measurement method.
Chapter 3 explains the realization of FOC scheme.
Chapter 4 shows the experiment result of the design control system.
MCU-AN-510124-E-12 – Page 5
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 2 Off-Line Parameter Measurement
2 Off-Line Parameter Measurement
In this chapter, off-line motor parameter measurement is introduced.
2.1
Overview
In the field oriented control, induction motor parameters are necessary since the flux
observer is founded by motor model. For widely application and adaption of this scheme,
parameter measurement becomes crucial before driving motor.
This chapter introduces an off-line parameter measurement method, which measures motor
parameter through DC test, lock-rotor test and no load test. Although off-line parameter
measurement cannot be precise enough, it is possible to implement FOC algorithm and then
add on-line parameter identification to realize accurate driving for unknown induction motor.
2.2
Off-line Parameter Measurement
2.2.1 Equivalent Circuit of Induction Motor
𝑅𝑠
𝑅𝑟 /𝑠
𝑖𝑠
𝐿𝑙𝑟
𝐿𝑙𝑠
𝐿𝑚
𝑈𝑠
𝑖𝑟
𝑖𝑚
Figure 2-1 Equivalent circuit of an induction motor
Figure 2-1 shows the equivalent circuit of an induction motor in steady state with balanced
three-phase input. To measure motor parameters, three steady states are established, which
are DC test, lock-rotor test, and no-load test.
2.2.2 DC Test
In the DC test, a DC voltage is imposed on stator, thus the inductances ( ,
, and
) are
regarded to be shorted. In another hand, rotor current becomes zero and the equivalent
circuit is simplified as Figure 2-2, therefore, stator resistance
is measured. In this
application, a recursive least square (RLS) filter is applied to extract resistance information
from imposed voltage and measured current.
𝑅𝑠
𝑈𝑠
𝑖𝑠
Figure 2-2 Equivalent circuit under DC test
2.2.3 Lock-Rotor Test
In motor manufacturing, the lock-rotor test is usually done by block rotor with special tools,
and then a balanced three-phase AC voltage is injected.
Figure 2-3 shows the equivalent circuit of an induction motor under lock-rotor test. The
equivalent impendence at rotor side becomes
because the slip rate ( ) equals to 1. In this
case, the paralleled two impendences is assumed that
.
MCU-AN-510124-E-12 – Page 6
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 2 Off-Line Parameter Measurement
𝑅𝑠
𝑈𝑠
𝑅𝑟
𝑖𝑠
𝐿𝑙𝑟
𝐿𝑙𝑠
𝑖𝑟
Figure 2-3 Equivalent circuit under Lock-rotor test
In practice, the rotor is difficult to lock without special tool, thus another conduction mode is
introduced as Figure 2-4 shows. It is easy to prove that in this conduction mode, the phase
equivalent circuit is same as Figure 2-3.
𝐿𝑠
𝑅𝑠
𝑈𝑠 ~
Figure 2-4 Conduction pattern for lock-rotor test
Now assuming
, when
is known, the equivalent impendence can be measured
through input power, voltage, and current, and
and
can be calculated sequentially.
2.2.4 No-Load Test
In no-load case, the rotor speed is assumed be equal to synchronous speed, and slip rate
is obviously obtained. Thus right hand part of the equivalent circuit in Figure 2-2 is an
open circuit and was simplified as Figure 2-5. Therefore, the stator self-inductance
can be measured.
𝑅𝑠
𝑖𝑠
𝑈𝑠
𝐿𝑙𝑟
𝐿𝑙𝑠
𝐿𝑚
𝑖𝑚
Figure 2-5 Equivalent circuit under no-load test
MCU-AN-510124-E-12 – Page 7
𝑖𝑟
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
3 FOC Drive of Induction Motor
This chapter introduces induction motor model, principle of FOC drive, and the realization
algorithm of FOC drive.
3.1
Rotor Flux Field Oriented Control
3.1.1 Mathematic Model of Induction Motor
𝑏𝑠
𝛽
𝑑
𝑞
𝜃Ψ
𝑎𝑠(𝛼)
𝑐𝑠
Figure 3-1 Reference frame for motor modelling
Same as most of electric rotating machine, a three-phase induction motor can be modelled
in stationary
reference frame and synchronous rotating
reference frame.
Applying Clark transformation to three-phase squirrel cage induction motor model, motor
dynamics in
reference frame is described as below
(3.1)
(3.2)
(3.3)
(3.4)
where the flux linkages has the following relationship with current
(
)
(3.5)
(
)
(3.6)
(
)
(3.7)
(
)
(3.8)
Taking Park transformation to above equations, induction motor model in
is
reference frame
(3.9)
(3.10)
(
)
MCU-AN-510124-E-12 – Page 8
(3.11)
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
(
)
(3.12)
(
)
(3.13)
(
)
(3.14)
(
)
(3.15)
(
)
(3.16)
The electric torque of induction motor can be expressed by the cross product of flux vector
and current vector that
(
)
(
)
(3.17)
3.1.2 Rotor Flux FOC Principle
There are kinds of FOC schemes for induction motor drive, such as rotor flux FOC, stator
flux FOC, and air gap flux FOC. In this document, rotor flux FOC is introduced.
From equation (3.17), it can be found that the electric torque is maximized for a given
magnitude of rotor flux if set the current vector perpendicular to the flux vector, and this is
how rotor flux FOC works.
Let’s set the flux vector and current vector as below
[
(3.18)
[
(3.19)
It is apparent that equations (3.18) and (3.19) define two perpendicular vectors such as rotor
flux FOC requires. Substitute above two equations into motor model, the magnitudes of rotor
flux vector and current vector are
(3.20)
(3.21)
(3.22)
Above equations show that if (3.18) and (3.19) satisfy, rotor flux level is set solely by , and
electric torque is controlled by . Thus, rotor flux vector and electric torque are controlled
by
and
independently.
Based on aforementioned knowledge, the rotor flux field oriented control is established.
Figure 3-2 depicts the control structure of a sensor based rotor FOC driving, in which sliding
mode observer is applied to estimate rotor flux vector.
MCU-AN-510124-E-12 – Page 9
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
𝐴𝐶~
Inverter
IM
𝜔𝑟
𝜔𝑟
𝑉𝑞
SVPWM
𝜔𝑟
PID
Flux
controller
𝑖𝑞
PID
𝑉𝑞
𝛼𝛽
𝑑𝑞
𝑖𝑞
𝑖𝑑
PID
𝑖𝑑
𝑉𝑑
𝑉𝛼
𝑉𝛼
𝑉𝛽
𝑎𝑏𝑐
𝛼𝛽
𝑖𝛼 𝑖𝛽
Dead time
compensation
𝑉𝛽
SMO flux
observer
𝜃Ψ
𝛼𝛽
𝑑𝑞
Figure 3-2 Induction motor sensor-FOC control scheme
In the demo system, the sensor-FOC scheme mainly contains three modules. The control
module is designed in
reference frame that drives
to a constant to assure constant
is generated by speed regulator thus
rotor flux linkage, and the reference torque current
speed is tracked.
Another important module is SMO flux observer, which is designed in
estimate rotor flux vector, including its magnitude and position angle.
reference frame to
The dead time compensation algorithm and SVPWM is implemented to realize command
voltage. And finally sensor based feedback FOC control system is constructed.
3.2
FOC Algorithm Realization
3.2.1 Back Calculation and Tracking PID regulator
The PID regulator is widely applied in most of control occasions, and its transfer function is
( )
(
) ( )
(3.23)
Equation (3.23) shows a 1-DOF PID regulator, and it suffers reference kick and response
kick due to direct proportion term and derivative term. In another hand, once the PID
parameters are tuned, its performance on handling noise is also inherent. To overcome
above shortages, a 2-DOF PID regulator is designed by modifying (3.23) in form of equation
(3.24), and Figure 3-3 shows the block diagram of this algorithm.
( )
(
)
⁄
)
Furthermore, an anti-windup scheme is implemented into I-regulator that its input
shaped by back calculation and tracking algorithm
{
(3.24)
is re-
(3.25)
MCU-AN-510124-E-12 – Page 10
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
𝑏
𝑦
𝑟
𝑠
𝑒
𝐾𝑑
𝑢𝑑
𝑠/𝑁
𝐾𝑖
𝑠
𝑒𝑖
𝑢𝑝
𝑢
𝑢
𝑢𝑖
𝑒𝑢
𝐾𝑡
Figure 3-3 2-DOF PID regulator with back calculation and tracking algorithm
In this PID regulator, the tuning parameters goes up to 5 with the limitation that
,
√
, and
is recommended for stability reason,
is a large number of the order of 100 for filtering the input of D-regulator.
3.2.2 Sliding Mode Rotor Flux Observer
Considering induction motor model in
reference frame, equations (3.1)~(3.8) is simplified
by eliminating
, ,
, and , therefore motor model is reassembled as
(
)
(3.26)
(
)
(3.27)
(3.28)
(3.29)
Let
space form is
be the states of system, induction motor model expressed in state(3.30)
where
[
] is the input stator voltage vector.
,
[
Now, let ̂
designed as
̂
]
̂
̂
̂
̂
[
]
be the estimated states, and a sliding mode observer is
̂
(3.31)
MCU-AN-510124-E-12 – Page 11
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
where
[
], and
[
(
(
̂ )
̂ )
]
It is not difficult to demonstrate that the output of observer ( ̂) converges to when is a
relative large positive constant. Figure 3-4 shows the block diagram of the designed sliding
mode observer, and the rotor flux angle is calculated by estimated flux vector
̂
(̂ )
𝑉𝑠
(3.32)
IM
𝜔𝑟
𝑖𝑠
𝜃Ψ
𝑎𝑟𝑐𝑡𝑎𝑛
𝑘
Current
Model
𝑖̂𝑠
Flux 𝜆̂ 𝑟
Model
Figure 3-4 Block diagram of sliding mode rotor flux observer
3.2.3 Dead Time Compensation
To avoid the shoot-through of DC link, a short period named dead time is enforced in the
SVPWM scheme, and thus a load dependent voltage distortion causes the mismatch
between command voltage and actual voltage. Besides this dead time, the voltage loss on
thyristors and diodes also result in voltage error, and the output voltage mismatch due to the
adversity of these three factors is called “dead time effect”.
Figure 3-5 shows a typical connection of three-phase inverter. Taking the bridge of a-phase
as an example, the magnitude of in a switch period is analysed in Figure 3-6, in which
is dead time,
is the delay time when switch on thyristor,
is the delay time when
switch off thyristor, is voltage loss on thyristor,
is voltage loss on diode,
is DC
voltage, is ideal conduction time, and is SVPWM period. Hence, the actual voltage can
be calculated by average theory as
{
(3.33)
MCU-AN-510124-E-12 – Page 12
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
𝑆𝑎
𝑉𝑑𝑐
𝑆𝑏
𝑆𝑐
𝑖𝑎𝑠
𝑉𝑎
𝑖𝑏𝑠
𝑉𝑏
𝑖𝑐𝑠
𝑉𝑐
𝑆𝑎
𝑆𝑏
Moto
r
𝑆𝑐
Figure 3-5 Typical three-phase inverter schematic
𝑇
𝑂𝐶𝐶𝑃
𝑖𝑑𝑒𝑎𝑙
𝑆𝑎
𝑡
𝑖𝑑𝑒𝑎𝑙
𝑆𝑎
𝑎𝑐𝑡𝑢𝑎𝑙
𝑆𝑎
𝑡𝑑
𝑡𝑜𝑓𝑓
𝑡𝑜𝑛
𝑡𝑑
𝑎𝑐𝑡𝑢𝑎𝑙
𝑆𝑎
𝑉𝑑
𝑖𝑑𝑒𝑎𝑙 𝑉𝑎
𝑉𝑑𝑐
𝑖𝑎
𝑉𝑠
𝑉𝑑
𝑖𝑎
𝑉𝑠
𝑉𝑑𝑐
𝑖𝑑𝑒𝑎𝑙 𝑉𝑎
𝑎𝑐𝑡𝑢𝑎𝑙 𝑉𝑎
𝑎𝑐𝑡𝑢𝑎𝑙 𝑉𝑎
Figure 3-6 Dead time effect on output voltage
And the compensation voltage thus is defined as (3.34)
{
(3.34)
Equation (3.34) shows that voltage loss in
reference frame relates to current direction,
which means current direction is a criterion of feeding compensation voltage. Particularly,
MCU-AN-510124-E-12 – Page 13
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
when the current is crossing zero, voltage loss becomes ambiguity. Thus, solutions are
made such that rotating current is usually used to judge compensation scheme. In this
document, current vector in
reference frame is utilized to calculate compensation voltage.
3.2.4 Field Weakening Control
As the motor runs at higher speed, back-EMF will occupy a large proportion of feeding
voltage and thus rotor speed is limited since voltage is not tuneable. Field weakening control
is a suitable solution that operates motor in constant power region and enlarges speed
operation region.
Consider steady state of induction motor model (3.9)~(3.16), and assume rotor field oriented
control is achieved, stator voltage model thus is written as
(3.35)
(3.36)
Ignore voltage drop on resistance, voltage
that
(
)
(
and
are limited due to inverter capability
)
(3.37)
In another hand, the maximum current capability of motor is also a limitation of operation,
and is expressed as
(3.38)
Equation (3.37) and (3.38) indicates the actual available operation region due to voltage and
current limitation, and Figure 3-7 plots the limitation curves as function of current, where the
ellipses (dash lines) are voltage limitation curve, the cycle (red, solid line) is current limitation
curve, and the hyperbola (blue, solid line) are equal-torque curves.
𝑖𝑞𝑠
𝜔
𝜔
𝑖𝑑𝑠
Figure 3-7 Voltage and current limitation curves
In this firmware, a gradient method is applied to generate reference d-axis current
Investigating voltage equation (3.35) and (3.36), and define a cost function as
(
)
(
)
.
(3.39)
Therefore, a control target is set to minimize the cost function. Taking partial difference to
equation (3.39)
(
)
MCU-AN-510124-E-12 – Page 14
(3.40)
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 3 FOC Drive of Induction Motor
(
)
(3.41)
Then the gradient method can be designed in digital form that
( )
where
(
)
(
)
(
is the gradient gain of flux controller.
MCU-AN-510124-E-12 – Page 15
)
(3.42)
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 4 Experiment Result
4
Experiment Result
4.1.1 Parameter Measurement
Table 4-1 Parameter measurement result
Motor Parameter
Stator Resistance
Rotor Resistance
Mutual Inductance
Stator Leakage Inductance
Rotor Leakage Inductance
Spec. Value
1.6173
1.6477
170.7246
6.7255
9.0637
Measured Value
1.6076
2.7116
128.63
13.47
13.47
Unit
Error
0.6%
64.6%
24.7%
100.1%
48.6%
4.1.2 Sensor-FOC Drive Performance
Load
Torque sensor
Induction motor
Figure 4-1 Experiment Platform
Figure 4-1 shows the configuration of experiment platform. The PMSM is controlled by a
converter in tracking reference torque mode. The torque sensor is installed between load
and testing motor thus the output torque of induction motor is measurement.
The experiment motor has parameters as Table 4-1 shows.
𝑖𝛼
𝑖̂𝛼
𝜃Ψ
c). Estimated current (2A/div) and flux angle @30Hz
d). Motor phase current at acceleration and
deceleration (2A/div)
Figure 4-2 FOC drive performance (
MCU-AN-510124-E-12 – Page 16
)
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 4 Experiment Result
𝑖̂𝛼
𝑖𝛼
𝑒𝑖
𝑖𝑢
𝑖𝑣
𝜃Ψ
a). Estimated current (5A/div) current
error (1A/div), and flux angle @30 Hz
b). Stator current at startup, decrease load, and increase load @30 Hz
Figure 4-3 FOC drive performance (
)
Figure 4-4 shows the field weakening performance of the induction motor. In this experiment,
the DC voltage is set to 110 volt, and the reference speed is set 50Hz with/without field
weakening operation. From picture (a), it can be seen that with rated magnetizing current,
the maximum speed is about 20Hz and (b) shows stator current in this case.
Picture (c), (d), (e), and (f) show the field weakening performance, and the maximum speed
goes up to 45Hz. Picture (c) shows the magnetizing current and speed response when
motor switches operation mode from normal region to field weakening region, and picture (d)
shows stator current response in this procedure.
Picture (e) shows the same state when motor switches operation mode from field weakening
region to normal region, and picture (f) shows stator current response in this procedure.
𝑖𝑑
𝑖𝑑
𝜔𝑟
𝑖𝑢
𝜔𝑟
a). Magnetizing current (2A/div) and speed
(15Hz/div)response without field weakening
b). Stator current (2A/div) without field weakening
𝑖𝑑
𝑖𝑑
𝜔𝑟
𝑖𝑢
𝜔𝑟
c). Magnetizing current (2A/div) and speed
(15Hz/div) response with field weakening
d). Stator current (2A/div) with field weakening
MCU-AN-510124-E-12 – Page 17
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 4 Experiment Result
𝑖𝑑
𝑖𝑑
𝜔𝑟
𝑖𝑢
𝜔𝑟
e). Magnetizing current (2A/div) and speed
(15Hz/div) response with field weakening
f). Stator current (2A/div) with field weakening
Figure 4-4 Motor response with/without field weakening control
MCU-AN-510124-E-12 – Page 18
SMO Based Field Oriented Control of Induction Motor with Speed Sensor V1.2.0
Chapter 5 Appendix
5 Appendix
5.1
List of Figures and Tables
Figure 2-1 Equivalent circuit of an induction motor ................................................................. 6
Figure 2-2 Equivalent circuit under DC test ............................................................................ 6
Figure 2-3 Equivalent circuit under Lock-rotor test ................................................................. 7
Figure 2-4 Conduction pattern for lock-rotor test .................................................................... 7
Figure 2-5 Equivalent circuit under no-load test ..................................................................... 7
Figure 3-1 Reference frame for motor modelling .................................................................... 8
Figure 3-2 Induction motor sensor-FOC control scheme ...................................................... 10
Figure 3-3 2-DOF PID regulator with back calculation and tracking algorithm ...................... 11
Figure 3-4 Block diagram of sliding mode rotor flux observer ............................................... 12
Figure 3-5 Typical three-phase inverter schematic ............................................................... 13
Figure 3-6 Dead time effect on output voltage ...................................................................... 13
Figure 3-7 Voltage and current limitation curves .................................................................. 14
Figure 4-1 Experiment Platform ........................................................................................... 16
Figure 4-2 FOC drive performance (
) ......................................................................... 16
Figure 4-3 FOC drive performance (
) ......................................................................... 17
Figure 4-4 Motor response with/without field weakening control ........................................... 18
MCU-AN-510124-E-12 – Page 19