pmsm equation mod index space vector modulated – direct torque controlled (dtc – svm) ...
TRANSCRIPT
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 1/175
Warsaw University of Technology
Faculty of Electrical Engineering Institute of Control and Industrial Electronics
Ph.D. Thesis
Marcin Żelechowski, M. Sc.
Space Vector Modulated – Direct
Torque Controlled (DTC – SVM)Inverter – Fed Induction Motor Drive
Thesis supervisor
Prof. Dr Sc. Marian P. Kaźmierkowski
Warsaw – Poland, 2005
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 2/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 3/175
Acknowledgements
The work presented in the thesis was carried out during author’s Ph.D. studies at the
Institute of Control and Industrial Electronics in Warsaw University of Technology,
Faculty of Electrical Engineering. Some parts of the work were realized in cooperation
with foreign Universities:
• University of Nevada, Reno, USA (US National Science Foundation grant –
Prof. Andrzej Trzynadlowski),
• University of Aalborg, Denmark (Prof. Frede Blaabjerg),
and company:
• Power Electronics Manufacture – „TWERD”, Toruń, Poland.
First of all, I would like to express gratitude Prof. Marian P. Kaźmierkowski for the
continuous support and help during work of the thesis. His precious advice and
numerous discussions enhanced my knowledge and scientific inspiration.
I am grateful to Prof. Andrzej Sikorski from the Białystok Technical University and
Prof. Włodzimierz Koczara from the Warsaw University of Technology for their
interest in this work and holding the post of referee.
Specially, I am indebted to my friend Dr Paweł Grabowski for support and
assistance.
Furthermore, I thank my colleagues from the Intelligent Control Group in Power
Electronics for their support and friendly atmosphere. Specially, to Dr Dariusz Sobczuk,
Dr Mariusz Malinowski, Dr Mariusz Cichowlas, and Dariusz Świerczyńki M.Sc.
Finally, I would like thank to my whole family, particularly my parents for their love
and patience.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 4/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 5/175
Contents
Pages
1. Introduction 1
2. Voltage Source Inverter Fed Induction Motor Drive 6
2.1. Introduction 6
2.2.
Mathematical Model of Induction Motor 6
2.3.
Voltage Source Inverter (VSI) 12
2.4. Pulse Width Modulation (PWM) 17
2.4.1. Introduction 17
2.4.2. Carrier Based PWM 18
2.4.3. Space Vector Modulation (SVM) 22
2.4.4.
Relation Between Carrier Based and Space Vector Modulation 282.4.5. Overmodulation (OM) 31
2.4.6. Random Modulation Techniques 35
2.5. Summary 39
3. Vector Control Methods of Induction Motor 40
3.1. Introduction 40
3.2. Field Oriented Control (FOC) 40
3.3. Feedback Linearization Control (FLC) 45
3.4. Direct Flux and Torque Control (DTC) 49
3.4.1.
Basics of Direct Flux and Torque Control 49
3.4.2.
Classical Direct Torque Control (DTC) – Circular Flux Path 533.4.3. Direct Self Control (DSC) – Hexagon Flux Path 61
3.5. Summary 64
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM) 66
4.1. Introduction 66
4.2. Structures of DTC-SVM – Review 66
4.2.1. DTC-SVM Scheme with Closed – Loop Flux Control 66
4.2.2. DTC-SVM Scheme with Closed – Loop Torque Control 68
4.2.3. DTC-SVM Scheme with Close – Loop Torque and Flux Control
Operating in Polar Coordinates 69
4.2.4.
DTC-SVM Scheme with Close – Loop Torque and Flux Control
in Stator Flux Coordinates 70
4.2.5. Conclusions from Review of the DTC-SVM Structures 71
4.3. Analysis and Controller Design for DTC-SVM Method with
Close – Loop Torque and Flux Control in Stator Flux Coordinates 71
4.3.1. Torque and Flux Controllers Design – Symmetry Criterion Method 75
4.3.2.
Torque and Flux Controllers Design – Root Locus Method 78
4.3.3. Summary of Flux and Torque Controllers Design 88
4.4. Speed Controller Design 94
4.5. Summary 98
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 6/175
Contents
5. Estimation in Induction Motor Drives 99
5.1. Introduction 99
5.2. Estimation of Inverter Output Voltage 100
5.3.
Stator Flux Vector Estimators 104
5.4. Torque Estimation 110
5.5.
Rotor Speed Estimation 1105.6. Summary 112
6. Configuration of the Developed IM Drive Based on DTC-SVM 113
6.1. Introduction 113
6.2. Block Scheme of Implemented Control System 113
6.3. Laboratory Setup Based on DS1103 115
6.4.
Drive Based on TMS320LF2406 118
7. Experimental Results 122
7.1. Introduction 122
7.2.
Pulse Width Modulation 1227.3.
Flux and Torque Controllers 125
7.4. DTC-SVM Control System 129
8. Summary and Conclusions 138
References 141
List of Symbols 151
Appendices 156
A.1. Derivation of Fourier Series Formula for Phase Voltage
A.2. SABER Simulation Model
A.3. Data and Parameters of Induction Motors
A.4. Equipment
A.5. dSPACE DS1103 PPC Board
A.6. Processor TMS320FL2406
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 7/175
1. Introduction
The Adjustable Speed Drives (ADS) are generally used in industry. In most drives
AC motors are applied. The standard in those drives are Induction Motors (IM) and
recently also Permanent Magnet Synchronous Motors (PMSM) are offered. Variable
speed drives are widely used in application such as pumps, fans, elevators, electrical
vehicles, heating, ventilation and air-conditioning (HVAC), robotics, wind generation
systems, ship propulsion, etc. [16].
Previously, DC machines were preferred for variable speed drives. However, DC
motors have disadvantages of higher cost, higher rotor inertia and maintenance problem
with commutators and brushes. In addition they cannot operate in dirty and explosive
environments. The AC motors do not have the disadvantages of DC machines.
Therefore, in last three decades the DC motors are progressively replaced by AC drives.
The responsible for those result are development of modern semiconductor devices,
especially power Insulated Gate Bipolar Transistor (IGBT) and Digital Signal Processor
(DSP) technologies.
The most economical IM speed control methods are realized by using frequency
converters. Many different topologies of frequency converters are proposed and
investigated in a literature. However, a converter consisting of a diode rectifier, a dc-
link and a Pulse Width Modulated (PWM) voltage inverter is the most applied used in
industry (see section 2.3).
The high-performance frequency controlled PWM inverter – fed IM drive should be
characterized by:
•
fast flux and torque response,
• available maximum output torque in wide range of speed operation region,
• constant switching frequency,
• uni-polar voltage PWM,
•
low flux and torque ripple,
• robustness for parameter variation,
•
four-quadrant operation,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 8/175
1. Introduction
2
These features depend on the applied control strategy. The main goal of the chosen
control method is to provide the best possible parameters of drive. Additionally, a very
important requirement regarding control method is simplicity (simple algorithm, simple
tuning and operation with small controller dimension leads to low price of final
product).
A general classification of the variable frequency IM control methods is presented in
Fig. 1.1 [67]. These methods can be divided into two groups: scalar and vector .
Variable
Frequency Control
Scalar based
controllers
Vector based
controller
U/f=const.
Volt/Hertz
( )r s f i ω=
Field OrientedFeedback
Linearization
Scalar based
controllers
Direct Torque
Control
Rotor Flux
Oriented
Stator Flux
Oriented
Direct Torque
Space - Vector
Modulation
Passivity Based
Control
Circle flux
trajectory
(Takahashi)
Hexagon flux
trajectory
(Takahashi)
Direct(Blaschke)
Indirect(Hasse)
Closed Loop
Flux & Torque
Control
Open Loop NFO (Jonsson)o&&
Stator Current
Fig. 1.1. General classification of induction motor control methods
The scalar control methods are simple to implement. The most popular in industry is
constant Voltage/Frequency (V/Hz=const.) control. This is the simplest, which does not
provide a high-performance. The vector control group allows not only control of the
voltage amplitude and frequency, like in the scalar control methods, but also the
instantaneous position of the voltage, current and flux vectors. This improves
significantly the dynamic behavior of the drive.
However, induction motor has a nonlinear structure and a coupling exists in the
motor, between flux and the produced electromagnetic torque. Therefore, several
methods for decoupling torque and flux have been proposed. These algorithms are
based on different ideas and analysis.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 9/175
1. Introduction
3
The first vector control method of induction motor was Field Oriented Control
(FOC) presented by K. Hasse (Indirect FOC) [45] and F. Blaschke (Direct FOC) [12] in
early of 70s. Those methods were investigated and discussed by many researchers and
have now become an industry standard. In this method the motor equations are
transformed into a coordinate system that rotates in synchronism with the rotor flux
vector. The FOC method guarantees flux and torque decoupling. However, the
induction motor equations are still nonlinear fully decoupled only for constant flux
operation.
An other method known as Feedback Linearization Control (FLC) introduces a new
nonlinear transformation of the IM state variables, so that in the new coordinates, the
speed and rotor flux amplitude are decoupled by feedback [81, 83].
A method based on the variation theory and energy shaping has been investigated
recently, and is called Passivity Based Control (PBC) [88]. In this case the induction
motor is described in terms of the Euler-Lagrange equations expressed in generalized
coordinates.
In the middle of 80s new strategies for the torque control of induction motor was
presented by I. Takahashi and T. Noguchi as Direct Torque Control (DTC) [97] and by
M. Depenbrock as Direct Self Control (DSC) [4, 31, 32]. Those methods thanks to the
other approach to control of IM have become alternatives for the classical vector control
– FOC. The authors of the new control strategies proposed to replace motor decoupling
and linearization via coordinate transformation, like in FOC, by hysteresis controllers,
which corresponds very well to on-off operation of the inverter semiconductor power
devices. These methods are referred to as classical DTC . Since 1985 they have been
continuously developed and improved by many researchers.
Simple structure and very good dynamic behavior are main features of DTC.
However, classical DTC has several disadvantages, from which most important is
variable switching frequency.
Recently, from the classical DTC methods a new control techniques called Direct
Torque Control – Space Vector Modulated (DTC-SVM) has been developed.
In this new method disadvantages of the classical DTC are eliminated. Basically, the
DTC-SVM strategies are the methods, which operates with constant switching
frequency. These methods are the main subject of this thesis. The DTC-SVM structures
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 10/175
1. Introduction
4
are based on the same fundamentals and analysis of the drive as classical DTC.
However, from the formal considerations these methods can also be viewed as stator
field oriented control (SFOC), as shown in Fig. 1.1.
Presented DTC-SVM technique has also simple structure and provide dynamic
behavior comparable with classical DTC. However, DTC-SVM method is characterized
by much better parameters in steady state operation.
Therefore, the following thesis can be formulated: “The most convenient industrial
control scheme for voltage source inverter-fed induction motor drives is direct
torque control with space vector modulation DTC-SVM”
In order to prove the above thesis the author used an analytical and simulation based
approach, as well as experimental verification on the laboratory setup with 5 kVA and
18 kVA IGBT inverters with 3 kW and 15 kW induction motors, respectively.
Moreover, the control algorithm DTC-SVM has been introduced used in a serial
commercial product of Polish manufacture TWERD, Toruń.
In the author’s opinion the following parts of the thesis are his original achievements:
• elaboration and experimental verification of flux and torque controller design for
DTC-SVM induction motor drives,
• development of a SABER - based simulation algorithm for control and
investigation voltage source inverter-fed induction motors,
• construction and practical verification of the experimental setups with 5 kVA and
18 kVA IGBT inverters,
• bringing into production and testing of developed DTC-SVM algorithm in Polish
industry.
The thesis consist of eight chapters. Chapter 1 is an introduction. In Chapter 2
mathematical model of IM, voltage source inverter construction and pulse width
modulation techniques are presented. Chapter 3 describes basic vector control method
of IM and gives analysis of advantages and disadvantages for all methods. In this
chapter basic principles of direct torque control are also presented. Those basis are
common for classical DTC, which is presented in Chapter 3 and for DTC-SVM method.
Chapter 4 is devoted to analysis and synthesis of DTC-SVM control technique. The
flux, torque and speed controllers design are presented. In Chapter 5 the estimations
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 11/175
1. Introduction
5
algorithms are described and discussed. In Chapter 6 implemented DTC-SVM control
algorithm and used hardware setup are presented. In Chapter 7 experimental results are
presented and studied. Chapter 8 includes a conclusion. Description of the simulation
program and parameters of the equipment used are given in Appendixes.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 12/175
2. Voltage Source Inverter Fed Induction Motor Drive
2.1. Introduction
In this chapter the model of induction motor will be presented. This mathematical
description is based on space vector notation. In next part description of the voltage
source inverter is given. The inverter is controlled in Pulse Width Modulation fashion.
In last part of this chapter review of the modulation technique is presented.
2.2. Mathematical Model of Induction Motor
When describing a three-phase IM by a system of equations [66] the following
simplifying assumptions are made:
• the three-phase motor is symmetrical,
• only the fundamental harmonic is considered, while the higher harmonics of the
spatial field distribution and of the magnetomotive force (MMF) in the air gap
are disregarded,
• the spatially distributed stator and rotor windings are replaced by a specially
formed, so-called concentrated coil,
• the effects of anisotropy, magnetic saturation, iron losses and eddy currents are
neglected,
• the coil resistances and reactance are taken to be constant,
• in many cases, especially when considering steady state, the current and voltages
are taken to be sinusoidal.
Taking into consideration the above stated assumptions the following equations of
the instantaneous stator phase voltage values can be written:
dt
d Ψ R I U A
s A A += (2.1a)
dt
d Ψ R I U B
s B B += (2.1b)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 13/175
2.2. Mathematical Model of Induction Motor
7
dt
d Ψ R I U C
sC C += (2.1c)
The space vector method is generally used to describe the model of the induction
motor. The advantages of this method are as follows:
• reduction of the number of dynamic equations,
• possibility of analysis at any supply voltage waveform,
• the equations can be represented in various rectangular coordinate systems.
A three-phase symmetric system represented in a neutral coordinate system by phase
quantities, such as: voltages, currents or flux linkages, can be replaced by one resulting
space vector of, respectively, voltage, current and flux-linkage. A space vector isdefined as:
( ) ( ) ( )[ ]t k t k t k C B A ⋅+⋅+⋅= 2aa1k
3
2 (2.2)
where: ( ) ( ) ( )t k t k t k C B A ,, – arbitrary phase quantities in a system of natural
coordinates, satisfying the condition ( ) ( ) ( ) 0=++ t k t k t k C B A ,
1, a, a
2
– complex unit vectors, with a phase shift
2/3 – normalization factor.
Im
)(2 t k a C
)(t ak B
)(t k A
Re
k
k 2
3
A
C
a
2a
1
Fig. 2.1. Construction of space vector according to the definition (2.2)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 14/175
2. Voltage Source Inverter Fed Induction Motor Drive
8
An example of the space vector construction is shown in Fig. 2.1.
Using the space vector method the IM model equation can be written as:
dt
d R s
sss
ΨIU += (2.3a)
dt
d Rr
rrr
ΨIU += (2.3b)
rss IIΨ m j
s Me L γ += (2.4a)
srr IIΨ m j
r Me L γ −+= (2.4b)
These are the voltage equations (2.3) and flux-current equations (2.4).
To obtain a complete set of electric motor equations it is necessary to, firstly,
transform the equations (2.3, 2.4) into a common rotating coordinate system and
secondly bring the rotor value into the stator side and thirdly. These equations are
written in the coordinate system K rotating with the angular speed K Ω .
K K K
K s K Ωdt
d R s
sss Ψ
ΨIU j (2.5a)
K mb K K
K r K Ω pΩdt
d R rr
rr Ψ jΨ
IU (2.5b)
K M K s K L L rss IIΨ
(2.6a)
K M K r K L L srr IIΨ
(2.6b)
The equation of the dynamic rotor rotation can be expressed as:
[ ]m Le
m
BΩ
M M J dt
d Ω
−−=
1
(2.7)
where: e M – electromagnetic torque,
L M – load torque,
B – viscous constant.
In further consideration the friction factor will be negated ( )0= B .
The electromagnetic torque e M can be expressed by the following formulas:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 15/175
2.2. Mathematical Model of Induction Motor
9
( )rs II*Im
2 M
sbe L
m p M −= (2.8)
( )ss IΨ
*Im2
sbe
m p M = (2.9)
Taking into consideration the fact that in the cage motor the rotor voltage equals zero
and the electromagnetic torque equation (2.9) a complete set of equations for the cage
induction motor can be written as:
K K K
K s K Ωdt
d R s
sss Ψ
ΨIU j (2.10a)
K mb K K
K r Ω pΩ
dt
d R r
rr Ψ
ΨI j0 (2.10b)
K M K s K L L rss IIΨ
(2.11a)
K M K r K L L srr IIΨ
(2.11b)
L s
bm M
m p
J dt
d Ωss IΨ
*Im2
1 (2.12)
Equations (2.10), (2.11) and (2.12) are the basis of further consideration.
The applied space vector method as a mathematical tool for the analysis of the
electric machines a complete set equations can be represented in various systems of
coordinates. One of them is the stationary coordinates system (fixed to the stator) β α −
in this case angular speed of the reference frame is zero 0= K Ω . The complex space
vector can be resolved into components α and β .
β α s s K U U jsU (2.13a)
β α s s K I I j+=sI , β α r r K I I jrI (2.13b)
β α s s K Ψ Ψ j+=sΨ , β β r r K Ψ Ψ jrΨ (2.13c)
In β α − coordinate system the motor model equation can be written as:
dt
d Ψ I RU s
s s sα
α α += (2.14a)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 16/175
2. Voltage Source Inverter Fed Induction Motor Drive
10
dt
d Ψ I RU
s
s s s
β
β β += (2.14b)
β α
α r mbr
r r Ψ Ω pdt
d Ψ I R ++=0 (2.14c)
α
β
β r mb
r
r r Ψ Ω pdt
d Ψ I R −+=0 (2.14d)
α α α r M s s s I L I LΨ += (2.15a)
β β β r M s s s I L I LΨ += (2.15b)
α α α s M r r r I L I LΨ += (2.15c)
β β β s M r r r I L I LΨ += (2.15d)
( )
−−= L s s s s
sb
m M I Ψ I Ψ m
p J dt
d Ωα β β α
2
1 (2.16)
The relations described above by the motor equations can be represented as a block
diagram. There is not just one block diagram of an induction motor. The lay-out
Construction of a block diagram will depend on the chosen coordinate system and input
signals. For instance, if it is assumed in the stationary β α − coordinate system that the
input signal to the motor is the stator voltage, the equations (2.14-2.16) can be
transformed into:
α α α
s s s s I RU
dt
d Ψ −= (2.17a)
β β
β
s s s
s I RU
dt
d Ψ −= (2.17b)
β α α
r mbr r r
Ψ Ω p I Rdt
d Ψ −−= (2.17c)
α β
β
r mbr r
r Ψ Ω p I R
dt
d Ψ +−= (2.17d)
α α α σ σ
r
r s
M s
s
s Ψ L L
LΨ
L I −=
1 (2.18a)
β β β σ σ
r
r s
M s
r
s Ψ L L
LΨ L
I −= 1 (2.18b)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 17/175
2.2. Mathematical Model of Induction Motor
11
α α α σ σ
s
r s
M r
r
r Ψ L L
LΨ
L I −=
1 (2.18c)
β β β σ σ
s
r s
M r
r
r Ψ L L
LΨ
L I −=
1 (2.18d)
( )
−−= L s s s s
sb
m M I Ψ I Ψ m
p J dt
d Ωα β β α
2
1 (2.19)
These equations can be represented in the block diagram as shown in Fig. 2.2.
β sΨ
mΩ
b p
α s I
α r I
α sΨ α sU
s R s R
∫∫
∫
s Lσ 1
r s
M
L L
L
σ r s
M
L L
L
σ
r Lσ
1r R
α r Ψ
∫
r Rr Lσ
1 β r I
∫
s R
s Lσ
1
r s
M
L L
L
σ r s
M
L L
L
σ
β r Ψ
β sU
2
sb
m p
e M
∫
L M
β s I
J
1
Fig. 2.2. Block diagram of an induction motor in the stationary coordinate system β α −
This representation of the induction motor is not good for use to design a control
structure, because the output signals flux, torque and speed depend on both inputs. Fromthe control point of view this system is complicated. That is the reason why there are a
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 18/175
2. Voltage Source Inverter Fed Induction Motor Drive
12
few methods proposed to decouple the flux and torque control. It is achieved, for
example, by the orientation of the coordinate system to the rotor or stator flux vectors.
Both control systems are described further in Chapter 3.
The equations (2.17), (2.18), (2.19) and the block diagram presented in the Fig. 2.2can be used to build a simulation model of the induction motor. It was used in a
simulation model, which is presented in Appendix A.2.
2.3. Voltage Source Inverter (VSI)
The three-phase two level VSI consists of six active switches. The basic topology of
the inverter is shown in Fig. 2.3. The converter consists of the three legs with IGBTtransistors, or (in the case of high power) GTO thyristors and free-wheeling diodes. The
inverter is supplied by a voltage source composed of a diode rectifier with a C filter in
the dc-link. The capacitor C is typically large enough to obtain adequately low voltage
source impedance for the alternating current component in the dc-link.
D1
D2
D3
D4
D5
D6
C2
dcU
2dc
U
C
0
SB+
SB-
SA+
SA-
SC+
SC-
T1
T2
T5
T6
T3
T4
DC side
U ABA B C
N
I A
I B
I C
U A
R A
L A
E A
U B
R B
L B
E B
U C
RC
LC
E C
AC side
IM
PWM Converter
Fig. 2.3. Topology of the voltage source inverter
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 19/175
2.3. Voltage Source Inverter (VSI)
13
The voltage source inverter (Fig. 2.3) makes it possible to connect each of the three
motor phase coils to a positive or negative voltage of the dc link. Fig. 2.4 explains the
fabrication of the output voltage waves in square-wave, or six-step, mode of operation.
The phase voltages are related to the dc-link center point 0 (see Fig. 2.3).
a)
0
U B0
ω t2π
dcU 2
1
dcU 2
1
π
0
U A0
ω t2π
1 2 3 4 5 6
dcU 2
1
dcU 2
1
π
0
U C0
ω t2π
dcU
2
1
dcU 2
1
π
dcU 3
2
dcU 3
2
0
U AB
ω t
2π
dcU 3
1
dcU 31
dcU
dcU
π
dcU 3
2
dcU 3
2
0
U A
ω t2π
dcU
3
1
dcU 3
1
π
b)
c)
d)
e)
Fig. 2.4. The output voltage waveforms in six-step mode
The phase voltage of an inverter fed motor (Fig. 2.4e) can be expressed by Fourier
series as [16, 66]:
( ) ( ) ( )∑∑ ∞
=
∞
=
==11
sinsin12
n
nm
n
dc A t nU t nn
U U ω ω π
(2.20)
where:
dcU - dc supply voltage,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 20/175
2. Voltage Source Inverter Fed Induction Motor Drive
14
dcnm U n
U π
2=
- peak value of the n-th harmonic,
n = 1+6k , k = 0, ±1, ±2,…
Derivation of the formula (2.20) is presented in Appendix A.1.
a) b)
c) d)
e) f)
g) h)
U1(100)
A B C
U dc
U2
(110)
A B C
U dc
U3(010)
A B C
U dc
U4
(011)
A B C
U dc
U5(001)
A B C
U dc
U6
(101)
A B C
U dc
U0(000)
A B C
U dc
U7
(111)
A B C
U dc
Fig. 2.5. Switching states for the voltage source inverter
From the equation (2.20) the fundamental peak value is given as:
dcm U U π
21 = (2.21)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 21/175
2.3. Voltage Source Inverter (VSI)
15
This value will be used to define the modulation index used in pulse width
modulation (PWM) methods (see section 2.4).
For the sake of the inverter structure, each inverter-leg can be represented as an ideal
switch. The equivalent inverter states are shown in Fig. 2.5.
There are eight possible positions of the switches in the inverter. These states
correspond to voltage vectors. Six of them (Fig. 2.5 a-f) are active vectors and the last
two (Fig. 2.5 g-h) are zero vectors. The output voltage represented by space vectors is
defined as:
=
==
−
7,00
6...13
2 3)1(
v
veU v j
dc
v
π
U (2.22)
The output voltage vectors are shown in Fig. 2.6.
U1
(100)
U2(110)U
3 (010)
U4 (011)
U5 (001) U
6 (101)
U7 (111)
U0 (000)
Im
Re
Fig. 2.6. Output voltage represented as space vectors
Any output voltage can in average be generated, of course limited by the value of the
dc voltage. In order to realize many different pulse width modulation methods are
proposed [13, 27, 30, 38, 46, 47, 51, 52, 105] in history. However, the general idea is
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 22/175
2. Voltage Source Inverter Fed Induction Motor Drive
16
based on a sequential switching of active and zero vectors. The modulation methods are
widely described in the next section.
Only one switch in an inverter-leg (Fig. 2.3) can be turned on at a time, to avoid a
short circuit in the dc-link. A delay time in the transistor switching signals must beinserted. During this delay time, the dead-time T D transistors cease to conduct. Two
control signals SA+, SA- for transistors T1, T2 with dead-time T D are presented in Fig.
2.7. The duration of dead-time depends of the used transistor. Most of them it takes 1-
3µ s.
t
t
T s
T D
T D
SA-
SA+
Fig. 2.7. Dead-time effect in a PWM inverter
Although, this delay time guarantees safe operation of the inverter, it causes a serious
distortion in the output voltage. It results in a momentary loss of control, where the
output voltage deviates from the reference voltage. Since this is repeated for every
switching operation, it has significant influence on the control of the inverter. This is
known as the dead-time effect. This is important in applications like a sensorless direct
torque control of induction motor. These applications require feedback signals like:
stator flux, torque and mechanical speed. Typically the inverter output voltage is needed
to calculate it. Unfortunately, the output voltage is very difficult to measure and it
requires additional hardware. Because of that for calculation of feedback signals the
reference voltage is used. However, the relation between the output voltage and the
reference voltage is nonlinear due to the dead-time effect [8]. It is especially important
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 23/175
2.4. Pulse Width Modulation (PWM)
17
for the low speed range when voltage is very low. The dead-time may also cause
instability in the induction motor [52].
Therefore, for correct operation of control algorithm proper compensation of dead-
time is required. Many approaches are proposed to compensate of this effect [2, 3, 8, 29,54, 64, 76].
The dead-time compensation is directly connected with estimation of inverter output
voltage. Therefore, compensation algorithm, which is used in final control structure of
the inverter is presented in Chapter 5.
2.4.
Pulse Width Modulation (PWM)
2.4.1. Introduction
In the voltage source inverter conversion of dc power to three-phase ac power is
performed in the switched mode (Fig. 2.3). This mode consists in power semiconductors
switches are controlled in an on-off fashion. The actual power flow in each motor phase
is controlled by the duty cycle of the respective switches. To obtain a suitable duty
cycle for each switches technique pulse width modulation is used. Many different
modulation methods were proposed and development of it is still in progress [13, 27,
30, 38, 46, 47, 51, 52, 105].
The modulation method is an important part of the control structure. It should
provide features like:
• wide range of linear operation,
• low content of higher harmonics in voltage and current,
• low frequency harmonics,
• operation in overmodulation,
• reduction of common mode voltage,
• minimal number of switching to decrease switching losses in the power
components.
The development of modulation methods may improve converter parameters. In thecarrier based PWM methods the Zero Sequence Signals (ZSS) [46] are added to extend
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 24/175
2. Voltage Source Inverter Fed Induction Motor Drive
18
the linear operation range (see section 2.4.2). The carrier based modulation methods
with ZSS correspond to space vector modulation. It will be widely presented in section
2.4.4.
All PWM methods have specific features. However, there is not just one PWMmethod which satisfies all requirements in the whole operating region. Therefore, in the
literature are proposed modulators, which contain from several modulation methods.
For example, adaptive space vector modulation [79], which provides the following
features:
• full control range including overmodulation and six-step mode, achieved by the
use of three different modulation algorithms,
• reduction of switching losses thanks to an instantaneous tracking peak value of
the phase current.
The content of the higher harmonics voltage (current) and electromagnetic
interference generated in the inverter fed drive depends on the modulation technique.
Therefore, PWM methods are investigated from this point of view. To reduce these
disadvantages several methods have been proposed. One of these methods is random
modulation (RPWM). The classical carrier based method or space vector modulation
method are named deterministic (DEPWM), because these methods work with constant
switching frequency. In opposite to the deterministic methods, the random modulation
methods work with variable frequency, or with randomly changed switching sequence
(see section 2.4.6).
2.4.2. Carrier Based PWM
The most widely used method of pulse width modulation are carrier based. This
method is also known as the sinusoidal (SPWM), triangulation, subharmonic, or
suboscillation method [16, 52]. Sinusoidal modulation is based on triangular carrier
signal as shown in Fig. 2.8. In this method three reference signals U Ac, U Bc, U Cc are
compared with triangular carrier signal U t , which is common to all three phases. In this
way the logical signals SA, SB, SC are generated, which define the switching instants of
the power transistors as is shown in Fig. 2.9.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 25/175
2.4. Pulse Width Modulation (PWM)
19
U dc
A B C
N
Carrier
U Ac
U Bc
U Cc
U t
SA
SB
SC
Fig. 2.8. Block scheme of carrier based sinusoidal PWM
U t
U Ac
U Bc
U Cc
0
1
0
1
0
1
0
SB
SC
0
dcU 32
dcU 31
dcU 32− dcU 31−
0
dcU
dcU
0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
2dcU
SA
AU
ABU
2dcU
Fig. 2.9. Basic waveforms of carrier based sinusoidal PWM
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 26/175
2. Voltage Source Inverter Fed Induction Motor Drive
20
The modulation index m is defined as:
)(t m
m
U
U m = (2.23)
where:
mU - peak value of the modulating wave,
)(t mU - peak value of the carrier wave.
The modulation index m can be varied between 0 and 1 to give a linear relation
between the reference and output wave. At m=1, the maximum value of fundamental
peak voltage is 2
dcU
, which is 78.55% of the peak voltage of the square wave (2.21).
The maximum value in the linear range can be increased to 90.7% of that of the
square wave by inserting the appropriate value of a triple harmonics to the modulating
wave. It is shown in Fig. 2.10, which presents the whole range characteristic of the
modulation methods [67]. This characteristic include also the overmodulation (OM)
region, which is widely described in section 2.4.5.
1
0.785 0.907 1
1.155 3.24 M
m
[ ]%1002
⋅dc
A
U U π
78.5
90.7
100
SPWM
SVPWM
or SPWM with ZSS OM
Six step
operation
Fig. 2.10. Output voltage of VSI versus modulation index for different PWM techniques
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 27/175
2.4. Pulse Width Modulation (PWM)
21
If the neutral point N on the AC side of the inverter is not connected with the DC
side midpoint 0 (Fig. 2.3), phase currents depend only on the voltage difference
between phases. Therefore, it is possible to insert an additional Zero Sequence Signal(ZSS) of the 3-th harmonic frequency, which does not produce phase voltage distortion
and without affecting load currents. A block scheme of the modulator based on the
additional ZSS is shown in Fig. 2.11 [46].
N
U dc
A B C
SA
SB
SC
Carrier
U t Calculation
of ZSS
U Ac
U Bc
U Cc
U Ac
*
U Bc*
U Cc
*
Fig. 2.11. Generalized PWM with additional Zero Sequence Signal (ZSS)
The type of the modulation method depends on the ZSS waveform. The most popular
PWM methods are shown in Fig. 2.12 where unity the triangular carrier waveform gain
is assumed and the signals are normalized to2
dcU . Therefore,
2
dcU ± saturation limits
correspond to ±1. In Fig. 2.12 only phase “A” modulation waveform is shown as the
modulation signals of phase “B” and “C” are identical waveforms with 120º phase shift.
The modulated methods illustrated in Fig. 2.12 can be separated into two groups:
continuous and discontinuous. In the continuous PWM (CPWM) methods, the
modulation waveform are always within the triangular peak boundaries and in every
carrier cycle triangle and modulation waveform intersections. Therefore, on and off
switchings occur. In the discontinuous PWM (DPWM) methods a modulation
waveform of a phase has a segment which is clamped to the positive or negative DC
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 28/175
2. Voltage Source Inverter Fed Induction Motor Drive
22
bus. In this segments some power converter switches do not switch. Discontinuous
modulation methods give lower (average 33%) switching losses. The modulation
method with triangular shape of ZSS with 1/4 peak value corresponds to space vector
modulation (SVPWM) with symmetrical placement of the zero vectors in a sampling
period. It will be widely describe in section 2.4.4. In Fig. 2.12 is also shown sinusoidal
PWM (SPWM) and third harmonic PWM (THIPWM) with sinusoidal ZSS with 1/4
peak value corresponding to a minimum of output current harmonics [63].
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
SPWM THIPWM SVPWM
U A
U N0
U A0
U A
=U A0
U N0
U N0
U A
U A0
a) b) c)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
U N0U N0
U N0
U A0
U A0U
A0
U A
U A
U A
DPWM1 DPWM2 DPWM3d) e) f)
Fig. 2.12. Waveforms for PWM with added Zero Sequence Signal a) SPWM, b)THIPWM, c) SVPWM,
d) DPWM1, e) DPWM2, f) DPWM3
2.4.3. Space Vector Modulation (SVM)
The space vector modulation techniques differ from the carrier based in that way,
there are no separate modulators used for each of the three phases. Instead of them, the
reference voltages are given by space voltage vector and the output voltages of the
inverter are considered as space vectors (2.22). There are eight possible output voltage
vectors, six active vectors U1 - U6, and two zero vectors U0, U7 (Fig. 2.13). The
reference voltage vector is realized by the sequential switching of active and zero
vectors.
In the Fig. 2.13 there are shown reference voltage vector Uc and eight voltage
vectors, which corresponds to the possible states of inverter. The six active vectors
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 29/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 30/175
2. Voltage Source Inverter Fed Induction Motor Drive
24
The times t 1 and t 2 are obtained from simple trigonometrical relationships and can be
expressed in the following equations:
( )α π π
−= 3sin32
1 s MT t (2.24a)
( )α π
sin32
2 s MT t = (2.24b)
Where M is a modulation index, which for the space vector modulation is defined as:
dc
c
step six
c
U
U
U
U M
π
2)(1
==
−
(2.25)
where:
cU - vector magnitude, or phase peak value,
)(1 step sixU − - fundamental peak value π dcU 2 of the square-phase voltage
wave.
The modulation index M varies from 0 to 1 at the square-wave output. The length of
the Uc vector, which is possible to realize in the whole range of α is equal to dcU 3
3.
This is a radius of the circle inscribed of the hexagon in Fig. 2.13. At this condition the
modulation index is equal:
907.0
2
3
3
==
dc
dc
U
U
M
π
(2.26)
This means that 90.7% of the fundamental at the square wave can be obtained. It
extends the linear range of modulation in relation to 78.55% in the sinusoidal
modulation techniques (Fig. 2.10).
After calculation of t 1 and t 2 from equations (2.24) the residual sampling time is
reserved for zero vectors U0 and U7.
70217,0 )( t t t t T t s +=+−= (2.27)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 31/175
2.4. Pulse Width Modulation (PWM)
25
The equations for t 1 and t 2 are identically for all space vector modulation methods.
The only difference between the other type of SVM is the placement of zero vectors at
the sampling time.
The basic SVM method is the modulation method with symmetrical spacing zero
vectors (SVPWM). In this method times t 0 and t 7 are equal:
( ) 22170 t t T t t s −−== (2.28)
For the first sector switching sequence can be written as follows:
U0→ U1 → U2 → U7 → U2 → U1 → U0 (2.29)
This vector switching sequence in the SVPWM method is shown in Fig. 2.15a. In
this case zero vectors are placed in the beginning and in the end of period U0, and in the
center of the period U7. In one sampling period all three phases are switched. To realize
the reference vector can also be used an other switching sequence, for example:
U0→ U1 → U2 → U1 → U0 (2.30)
or
U1 → U2 → U7 → U2 → U1 (2.31)
These sequences are shown in Fig. 2.15b and 2.15c respectively. In these cases only
two phases switch in one sampling time, and only one zero vector is used U0 (Fig.
2.15b) or U7 (Fig. 2.15c). This type of modulation is called discontinuous pulse width
modulation (DPWM).
1
0 1
0 0 1
1
01
001
1 1 1
1 1
1
111
11
1
T s
U7
t 0
t 2/2
SA
SB
SC
U1
U2
U2
U1
t 1/2t
1/2 t
2/2
0
0 0
0
00
0 1 1
0 1
0
01
0
T s
U0
U1
U2
U1
U0
t 2
t 1/2 t
0/2t
0/2 t
1/2
SA
SB
SC
0
0 0
0 0 0
0
00
000
1 1 1
1 1
1
111
11
1
T s
U0
U1
U2
U7
U7
U2
U1
U0
t 0/4 t
1/2 t
2/2 t
0/4t
0/4 t
1/2 t
2/2 t
0/4
SA
SB
SC
a) b) c)
Fig. 2.15. Space vectors in the sampling period a) SVPWM, b), c) DPWM
The idea of discontinuous modulation is based on the assumption that one phase is
clamped by 60° to lower or upper of the dc bus voltage. It gives only one zero state per
sampling period (Fig. 2.15b, c). The discontinuous modulation provides 33% reduction
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 32/175
2. Voltage Source Inverter Fed Induction Motor Drive
26
of the effective switching frequency and switching losses. The discontinuous space
vector modulation techniques, like all the space vector methods, correspond to the
carrier based modulation method. It will be widely described in the next section.
DPWM4
U7 (111)
U0 (000) U
1(100)
U2(110)
U3 (010)
U4 (011)
U5 (001)
U6 (101)
t 7 = 0
t 7 = 0
t 7 = 0
t 0= 0
t 0= 0
t 0= 0
DPWM1
U7 (111)
U0 (000) U
1(100)
U2(110)
U3 (010)
U4 (011)
U5 (001)
U6 (101)
t 7 = 0
t 7 = 0
t 7 = 0
t 0= 0
t 0= 0
t 0= 0
t 0= 0
t 7 = 0
t 0= 0
t 7 = 0
t 7 = 0
t 0= 0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
U N0
U A0
U A
DPWM2
U7 (111)
U0 (000) U
1(100)
U2(110)
U3 (010)
U4 (011)
U5 (001)
U6 (101)
t 7 = 0
t 7 = 0t
7 = 0
t 0= 0 t
0= 0
t 0= 0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
U N0
U A0
U A
DPWM3
U7 (111)
U0 (000) U
1(100)
U2(110)
U3 (010)
U4 (011)
U5 (001)
U6 (101)
t 7 = 0
t 7 = 0
t 7 = 0
t 0= 0
t 0= 0
t 0= 0
t 0= 0
t 7 = 0
t 0= 0
t 7 = 0
t 7 = 0
t 0= 0
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
U N0
U A0
U A
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time
U A
U A0
U N0
a)
b)
c)
d)
Fig. 2.16. The discontinuous space vector modulation
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 33/175
2.4. Pulse Width Modulation (PWM)
27
In the Fig. 2.16 there are shown several different kinds of space vector discontinues
modulation. It can be seen that the type of method depends on the moved do not switch
sectors. These sectors are adequately moved on 0°, 30°, 60°, 90° and denoted as
DPWM1, DPWM2, DPWM3 and DPWM4. Fig. 2.16 also shows voltage waveforms for
each methods. For the carrier based methods with ZSS these waveforms are identical
(Fig. 2.12).
From the type of modulation it depends also harmonic content, what is presented in
Fig. 2.17 for the SVPWM and DPWM1 methods.
Fig. 2.17. The output line to line voltage harmonics content a) SVPWM, b) DPWM 1
In Fig. 2.17 harmonics of output line to line voltage are shown. The voltage
frequency domain representation is composed of the series discrete harmonics
components. These are clustered about multiplies of the switching frequency. In this
case the switching frequency was 5 kHz. Spectrum for every modulation methods is
different. In Fig. 2.17 the differences between SVPWM and DPWM1 modulation
method can be seen. However, characteristic feature for all methods, which work with
constant switching frequency is clustered higher harmonics round multiplies of the
switching frequency. These type of modulation methods are named deterministic PWM
(DEPWM). The modulation method influence also for current distortion, torque ripple
and acoustic noise emitted from the motor. Modulation techniques are still being
improved for reduction of these disadvantages. One of the proposed methods is a
random PWM (RPWM) (see section 2.4.6).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 34/175
2. Voltage Source Inverter Fed Induction Motor Drive
28
2.4.4. Relation Between Carrier Based and Space Vector Modulation
All the carrier based methods have equivalent to the space vector modulation
methods. The type of carrier based method depends on the added ZSS, as shown in
section 2.4.2, and type of the space vector modulation depending on the time of zero
vectors t 0 and t 7 .
A comparison of carrier based method with SVM is shown in Fig 2.18. There is
shown a carrier based modulation with triangular shape of ZSS with 1/4 peak value.
This method corresponds to the space vector modulation (SVPWM) with symmetrical
placement of zero vectors in sampling period. In Fig. 2.18b is presented discontinuous
method DPWM1 for carrier based and for SVM techniques.
In the carrier based methods three reference signals U Ac*, U Bc
*, U Cc* are compared
with triangular carrier signal U t , and in this way logical signals SA, SB, SC are generated.
In the space vector modulation duration time of active (t 1, t 2) and zero (t 0, t 7 ) vectors are
calculated, and from these times switching signals SA, SB, SC are obtained. The gate
pulses generated by both methods are identical.
The carrier based PWM methods are simple to implement in hardware. Through the
compare reference signals with triangular carrier signal it receives gate pulses.
However, a PWM inverter is generally controlled by a microprocessor/controller
nowadays. Thanks to the representation of command voltages as space vector, a
microprocessor using suitable equations can calculate duration time and realize
switching sequence easily.
It is possible to implement all carrier based modulation methods using the space
vector technique. The active vector times t 1 and t 2 equations are identically for all space
vector modulation methods. But every method demand suitable equation for the zero
vectors t 0 and t 7 .
The eight voltage vectors U0 - U7 correspond to the possible states of the inverter
(Fig. 2.13). Each of these states can be composed by a different equivalent electrical
circuit. In Fig 2.19 the circuit for the vector U1 is presented.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 35/175
2.4. Pulse Width Modulation (PWM)
29
0
0 0
0 0 0
0
00
000
0 1 1
0 1
0
011
01
0
T s
U0
U1
U2
U1
U0
t 2
t 1/2 t
0/2t
0/2 t
1/2
SA
SB
SC
U Ac
*
U Bc
*
U Cc
*
SA
SB
SC
b)
C a r r i r b a s e d P W M
S p a c e v e c t o r P W M
U Ac
*
0
0 0
0 0 0
0
00
000
1 1 1
1 1
1
111
11
1
T s
U0
U1
U2
U7
U7
U2
U1
U0
t 0/4 t
1/2 t
2/2 t
0/4t
0/4 t
1/2 t
2/2 t
0/4
U Bc
*
U Cc
*
SA
SB
SC
SA
SB
SC
a)
C a r r i r b a s e d P W M
S p a c e v e c t o r P W M
Fig. 2.18. Comparison of carrier based PWM with space vector PWM a) SVPWM, b) DPWM1
U A
U B
U C
U N0
A
B C
N0
2dcU
2dc
U
U B 0 = U
C 0
U A 0
Fig. 2.19. Equivalent circuit of VSI for the U1 vector
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 36/175
2. Voltage Source Inverter Fed Induction Motor Drive
30
Taking into consideration the electrical circuit in Fig. 2.19 the voltage distribution
can be obtained. The voltages can be written as:
dc A U U
3
2= ; dc B U U
3
1−= ; dcC U U
3
1−= (2.32)
dc A0 U U 2
1= ; dc B0 U U
2
1−= ; dcC0 U U
2
1−= (2.33)
dc AN A0 N0 U U U U 6
1−=−= (2.34)
This analysis may be repeated for all vectors provided to obtain voltages presented in
Table 2.1.
Table 2.1. The voltages for the eight converter output vectors
A0U B0U AU BU C U C0U N0U
0U
1U
2U
3U
4U
5U
6U
7U
dcU 2
1dcU
2
1−
dcU 3
2dcU
3
1−dcU
2
1−
dcU 3
1− dcU
6
1−
dcU 2
1dcU
3
2−dcU
3
1dcU
2
1− dcU
6
1
dcU 21dcU
21− dcU
32dcU
31−dcU
21− dcU
31− dcU
61−
dcU 2
1dcU
3
1
dcU 2
1dcU
2
1− dcU
3
2−
dcU 3
1dcU
2
1dcU
3
1dcU
6
1
dcU 2
1− dcU
2
1− dcU
3
2dcU
3
1−dcU
2
1dcU
3
1− dcU
6
1
dcU 2
1dcU
2
1− dcU
3
1dcU
3
1dcU
2
1dcU
3
2− dcU
6
1
dcU 2
1− dcU
2
1− 0 0 dcU
2
1−0dcU
2
1−
dcU 2
1dcU
2
10 0 dcU
2
10dcU
2
1
The average value for sampling time of U NO voltage can be written as follows:
++−−= 7 210
dc
s
N0 t t t t U
T U
3
1
3
1
2
1 for the sectors I, III, V (2.35)
and
++−−= 7 120
dc
s
N0 t t t t U
T U 3
1
3
1
2
1 for the sectors II, IV, VI (2.36)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 37/175
2.4. Pulse Width Modulation (PWM)
31
From the above equations and taking into consideration equations (2.24) and (2.27)
the zero vectors times for different kinds of modulation can be calculated.
Relations between carrier based and SVM methods are presented in Table 2.2. This
table presents also the zero vector (t 0, t 7 ) times equations for the most significant
modulation methods.
Table 2.2. Relation between carrier based and SVM methods
−= α π
cos4
12
M T
t s0
( )
+−= α α π sin3cos
2
12 M
T
t s
0
Calculation of t 0 and t
7
for sectors I, III, V
for sectors II, IV, VI
210 s7 t t t T t −−−=
Waveform of the
ZSS (Fig. 2.13)
( )0= N0U
Modulation
method
SPWM
Sinusoidal with
1/4 amplitude
no signal
THIPWM
−−= α α
π 3cos
4
1cos
41
2 M
T t s0
−+−= α α α
π 3cos
2
1sin3cos
21
2 M
T t s0
for sectors II, IV, VI
210 s7 t t t T t −−−=
for sectors I, III, V
Triangular with
1/4 amplitude
Discontinuous
SVPWM
DPWM1
( ) 221 s7 0 t t T t t −−==
0=0t
21 s7 t t T t −−=
0=7 t
21 s0 t t T t −−=
when ( )1263
+<≤ nn π α
π
when ( ) ( )13
126 +<≤+ nn π α π
5,4,3,2,1,0=n
Waveforms of the ZSS presented in Table 2.2 are shown in Fig. 2.12.
2.4.5. Overmodulation (OM)
At the end of the linear range (Fig. 2.10) the inverter output voltage is 90.7% of the
maximum output peak voltage in six-step mode (see equation 2.21). The nonlinear
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 38/175
2. Voltage Source Inverter Fed Induction Motor Drive
32
range between this point and six-step mode is called overmodulation. This part of the
modulation techniques is not so important in vector controlled drives methods for the
sake of big distortion current and torque. For example, the overmodulation can be
applied in drives working in open loop control mode to increase the value of inverter
output voltage.
The overmodulation has been widely discussed in the literature [16, 33, 55, 75, 89].
Some of methods are proposed as extensions of the carrier based modulation and others
as extensions of space vector modulation. In the carrier based methods overmodulation
algorithm is realized by increasing reference voltage beyond the amplitude of the
triangular carrier signal. In this case some switching cycles are omitted and each phase
is clamped to one of the dc busses.
The overmodulation region for space vector modulation is shown in Fig. 2.20. The
maximum length of vector Uc possible to realization in whole range of α angle is equal
dcU 3
3. It is a radius of the circle inscribed of the hexagon. This value corresponds to
the modulation index equal to 0.907 (see equation 2.26). To realize higher values a
voltage overmodulation algorithm has to be applied. At the end of the overmodulation
region is a six-step mode (at M = 1).
U7 (111)
U0 (000) U
1(100)
U2(110)U
3 (010)
U4 (011)
U5 (001) U
6 (101)
α
Uc
(t 1 /T s )U1
( t 2 / T s
) U 2 Overmodulation range
0.907 < M < 1
Six-step mode
M = 1
Linear range
M ≤ 0.907
Fig. 2.20. Definition of the overmodulation range
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 39/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 40/175
2. Voltage Source Inverter Fed Induction Motor Drive
34
In the hexagon trajectory part only active vectors are used. The duration of these
vectors t 1 and t 2 are obtained from trigonometrical relationships and can be expressed in
the following equations:
α α
α α
sincos3
sincos3
+−= s1 T t (2.37a)
1 s2 t T t −= (2.37b)
0== 7 0 t t (2.37c)
The output voltage waveform is given approximately by linear segments for the
hexagon trajectory and sinusoidal segments for the circular trajectory. Boundary of the
segments is determined by a crossover angle θ which depends on the reference voltage
value. As known from Fig. 2.21 the upper limit in mode I is when θ = 0°. Then the
voltage trajectory is fully on the hexagon. The fundamental peak value generated in this
way voltage is 95% of the peak voltage of the square wave [75]. It gives modulation
index M = 0.952.
For the modulation index higher then 0.952 the overmodulation mode II is applied.
The overmodulation mode II is shown in Fig. 2.22. In this mode not only the reference
vector amplitude is modified but also an angle. The reference angle from α to α * is
changed.
U0 (000)
U7 (111)
α
Uc
Uc*
U1(100)
U2(110)U
3 (010)
U4 (011)
U5 (001) U
6 (101)
hα
hα
∗
α
Fig. 2.22. Overmodulation mode II where both amplitude and angle is changed
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 41/175
2.4. Pulse Width Modulation (PWM)
35
The trajectory of Uc* is maintained on the hexagon which defines amplitude of the
reference voltage vector. The angle is calculated from the following equations:
≤≤−
−<<−
−
≤≤
=∗
333
3for 66
00
π α α π π
α π α α π
α π
α α
α α
α
h
hh
h
h
h
(2.38)
where: α h – hold-angle.
This angle uniquely controls the fundamental voltage. It is a nonlinear function of the
modulation index [16, 55].
In Fig. 2.22 is shown the reference vector trajectory generated for the first sector.
This trajectory is obtained in three steps. First part, if angle α is less than the respective
value of α h, the algorithm holds the vector Uc* at the vertex (U1). Next part is for α from
α h to hα π −3 . In this angle range the reference vector moves along the hexagon. In the
last range, from hα π −3 to hα , the vector Uc* is held until the next vertex (U2).
The overmodulation mode II works up to the six-step mode for α h equal zero. The
six-step mode characterized by selection of the switching vector for one-sixth of the
fundamental period. In this case the maximum possible inverter output voltage is
generated.
2.4.6. Random Modulation Techniques
The pulse width modulation technique is important for drive performance in respect
to voltage and current harmonics, torque ripple, acoustic noise emitted from an
induction motor and also electromagnetic interference (EMI). Different approaches
were used in PWM techniques for reduction of these disadvantages. One of the
proposed methods is random pulse width modulation (RPWM) [5, 7, 11, 14, 61, 68,
104].
Previously presented modulation methods were named deterministic pulse width
modulation (DEPWM), because of constant sampling and switching frequency and all
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 42/175
2. Voltage Source Inverter Fed Induction Motor Drive
36
cycles the switching sequence is deterministic. In RPWM methods the switching
frequency or the switching sequence change randomly.
One of the proposed random modulation techniques is a method with randomly
varied lengths of coincident switching and sampling time of the modulator. This method
was named RPWM 1. The sampling and switching cycles in DEPWM with RPWM 1 is
comparable shown in Fig. 2.23. The reference voltage vectors Uc, which are calculated
in one sampling time T s and realized in the next switching time T sw are shown. In drive
systems the controller mostly operates in synchronism with modulator and in RPWM 1
arises problems in the control system, when it works with variable sampling frequency.
An additional control algorithm with variable sampling frequency is difficult tin a
digital implementation.
1 2 3 ... n-1 n ...sampling cycles
switching cycles 1 2 3 ... n-1 n ...
)1(
cU)2(
cU)3(
cU)(K
cU)1( −n
cU)1( +n
cU)(n
cU
sampling cycles
switching cycles ...1 2 ... n-1 n
...1 2 ... n-1 n
3
3
)1(
cU)2(
cU)3(
cU)(K
cU )1( −n
cU)1( +n
cU)(n
cU
a)
b)
sw s T T =
sw s T T =
Fig. 2.23. Sampling and switching cycles a) DEPWM, b) RPWM 1
For elimination of these disadvantages random modulation techniques were
proposed, which operate with a fixed switching and sampling frequency. These methods
randomly change switching sequence in the interval. Three of these methods are shown
in Fig. 2.24 [6].
First of them (Fig. 2.24a) is random lead-lag modulation (RLL). In this method pulse
position is either commencing at the beginning of the switching interval (leading-edge
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 43/175
2.4. Pulse Width Modulation (PWM)
37
modulation) or its tailing edge is aligned with the end of the interval (lagging-edge
modulation). A random number generator controls the choice between leading and
legging edge modulation.
In Fig. 2.24b is shown a random center pulse displacement (RCD) method. In this
technique pulses are generated identically as in the SVPWM method (Fig. 2.15), but
common pulse center is displaced by the amount sT α from the middle of the period.
The parameter α is varied randomly within a band limited by the maximum duty cycle.
The last presented method (Fig. 2.24c) is random distribution of the zero voltage
vector (RZD). Additionally distribution of the zero vectors can by different, until only
one zero vector in switching cycle in the discontinuous methods (Fig. 2.15b, c). This
fact is utilized in the random distribution of the zero voltage vector, where the
proportion between the time duration for the two zero vectors U0(000) and U7(111) is
randomized in the switching cycles.
SA
SB
SC
T s
T s
T s
T s
sT α sT α sT sT
SA
SB
SC
T s
T s
T s
T s
Lead Lag Lag Lead
SA
SB
SC
T s
T s
T s
T s
a)
b)
c)
Fig. 2.24. Different fixed switching random modulation schemes a) Random lead-leg modulation (RLL),
b) Random center displacement (RCD), c) Random zero vector distribution (RZD)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 44/175
2. Voltage Source Inverter Fed Induction Motor Drive
38
The main disadvantage of the RPWM 1 method (Fig. 2.23b) is variable switching
frequency. For elimination of this disadvantage RPWM 2 [119] was proposed, which
operates with fixed sampling frequency and variable switching frequency. The principle
of this method is shown in Fig. 2.25.
1 2 3 ... n-1 n ...
...1 2 3 ... n-1 n
sampling cycles
switching cycles
)1(
cU)2(
cU)3(
cU)(K
cU)1( −n
cU)1( +n
cU)(n
cU
swT
sT
t ∆
Fig. 2.25. Sampling and switching cycles in RPWM 2 technique
In this method the start of each switching cycles is delayed with respect to that of the
coincident sampling cycle by a random varied time interval t ∆ . It is given as:
srT t =∆ (2.39)
where r denotes a random number between 0 and 1. Time interval t ∆ is limited for
the sake of minimum switching time of inverter.
Fig. 2.26. The output line to line voltage harmonics content a) RPWM 1, b) RPWM 2
Corresponding spectra for the RPWM 1 and RPWM 2 techniques are shown in Fig.
2.26a and 2.26b respectively. It can be seen that the harmonic clusters typical for the
determination modulation (compared to Fig. 2.17) are practically eliminated by the
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 45/175
2.5. Summary
39
random modulation techniques. Simulation result presented in both figures (Fig. 2.17
and Fig. 2.26) was done at the same conditions: sampling frequency 5 kHz, output
frequency 50 Hz.
2.5. Summary
In this chapter mathematical description of IM based on complex space vectors was
presented. The complete equations set is the basis of further consideration of control
and estimation methods.
The structure of two levels voltage source inverter was presented. The main features
and voltage forming methods were described. For the sake of dead-time and voltagedrop on the semiconductor devices the inverter has nonlinear characteristic. Therefore,
in control scheme compensation algorithms are needed.
The inverter is controlled by pulse width modulation (PWM) technique. The
modulation methods are divided into two groups: triangular carrier based and space
vector modulation. Between those two groups there are simple relations. All the carrier
based methods have equivalent to the space vector modulation methods. The type of
carrier based method depends on the added ZSS and type of the space vector
modulation depends on the placement of zero vectors in the sampling period. Presented
modulation methods will be used in the final drive.
This chapter contains compete review of the modulation techniques, including some
random modulation methods. Those methods have very interesting advantages and can
be implemented in special application of IM drives. Currently they have not been
implemented in a presented serially produced drive. However, it will be offered as an
option in a near future. Some experimental results for the implemented modulation
methods are shown in Chapter 7.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 46/175
3. Vector Control Methods of Induction Motor
3.1. Introduction
In this chapter review of the most significant IM vector control method is presented.
According to the classification presented in Chapter 1. The theoretical basis and short
characteristic for all methods are given. The direct torque control (DTC) method creates
a base for further analyze of DTC-SVM algorithms. Therefore, DTC is more detailed
discussed (see section 3.4).
3.2.
Field Oriented Control (FOC)
The principle of the field oriented control (FOC) is based on an analogy to the
separately excited dc motor. In this motor flux and torque can be controlled
independently. The control algorithm can be implemented using simple regulators, e.g.
PI-regulators.
In induction motor independent control of flux and torque is possible in the case of
coordinate system is connected with rotor flux vector. A coordinate system qd − is
rotating with the angular speed equal to rotor flux vector angular speed sr K ΩΩ = ,
which is defined as follows:
dt
d γΩ sr
sr = (3.1)
The rotating coordinate system qd − is shown in Fig. 3.1.
The voltage, current and flux complex space vector can be resolved into components
d and q.
sq sd K U U j+=sU (3.2a)
sq sd K I I j+=sI , rqrd K I I j+=rI (3.2b)
sq sd K Ψ Ψ j+=sΨ , r rd K Ψ Ψ ==rΨ (3.2c)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 47/175
3.2. Field Oriented Control (FOC)
41
α
β
rΨ
d
q sI
β s I
α s I
sd I sq I
sr γ
δ
sr Ω
Fig. 3.1. Vector diagram of induction motor in stationary β α − and rotating qd − coordinates
In qd − coordinate system the induction motor model equations (2.10-2.12) can be
written as follows:
sq sr sd
sd s sd Ψ Ωdt
d Ψ I RU −+= (3.3a)
sd sr
sq
sq s sq Ψ Ωdt
d Ψ I RU ++= (3.3b)
dt
d Ψ I R r
rd r +=0 (3.3c)
( )mb sr r rqr Ω pΩΨ I R −+=0 (3.3d)
rd M sd s sd
I L I LΨ += (3.4a)
rq M sq s sq I L I LΨ += (3.4b)
sd M rd r r I L I LΨ += (3.4c)
sq M rqr I L I L +=0 (3.4d)
−= L sqr
r
M sb
m M I Ψ L
Lm p
J dt
d Ω
2
1 (3.5)
The equations 3.3c and 3.4c can be easy transformed to:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 48/175
3. Vector Control Methods of Induction Motor
42
r
r
r sd
r
r M r Ψ L
R I
L
R L
dt
d Ψ −= (3.6)
The motor torque can by expressed by rotor flux magnitude r Ψ and stator current
component sq I as follows:
sqr
r
M sbe I Ψ
L
Lm p M
2= (3.7)
Equations (3.6) and (3.7) are used to construct a block diagram of the induction
motor in qd − coordinate system, which is presented in Fig. 3.2.
r Ψ
mΩ
∫
2
s
b
m
p
e M
∫ L M
J
1
r
r M
L
R L
r
r
L
R
r
M
L
L
sd I
sq I
e M
Fig. 3.2. Block diagram of induction motor in qd − coordinate system
The main feature of the field oriented control (FOC) method is the coordinate
transformation. The current vector is measured in stationary coordinate β α − .
Therefore, current components α s I , β s I must be transformed to the rotating system
qd − . Similarly, the reference stator voltage vector components c sU α , c sU β , must be
transformed from the system qd − to β α − . These transformations requires a rotor
flux angle sr γ . Depending on calculations of this angle two different kind of field
oriented control methods maybe considered. Those are Direct Field Oriented Control
(DFOC) and Indirect Field Oriented Control (IFOC) methods.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 49/175
3.2. Field Oriented Control (FOC)
43
For DFOC an estimator or observer calculates the rotor flux angle sr γ . Inputs to the
estimator or observer are stator voltages and currents. An example of the DFOC system
is presented in Fig. 3.3.
PI
SVM
SA
SB
SC sq c I
FluxEstimator
U dc
α sU
β sU
s I
c sU α
c sU
β
α s I
β s I
sr γ
rcΨ
ec M
sd I
sq I
sd c I
PI β α −
qd −
β α −
qd −
3
2
Motor
rc M
r
sb Ψ L
L
m p
12
M L
1
VoltageCalculation
Fig. 3.3. Block diagram of the Direct Field Oriented Control (DFOC)
For the IFOC rotor flux angle sr γ is obtained from reference sdc I , sqc I currents. The
angular speed of the rotor flux vector speed can be calculated as follows:
mb sl rs Ω pΩΩ += (3.8)
where sl Ω is a slip angular speed. It can be calculated from (3.3d) and (3.4d).
sqc
r
r
sdc
sl I L
R
I Ω
1= (3.9)
In Fig. 3.4 a block diagram of the IFOC is shown.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 50/175
3. Vector Control Methods of Induction Motor
44
PI
SVM
SA
SB
SC sq c I
U dc
s I
c sU α
c sU
β
α s I
β s I
sr γ
rcΨ
ec M
sd I
sq I
sdc I
PI β α −
qd −
β α −
qd −
Motor
rc M
r
sb Ψ L
L
m p
12
M L
1
3
2
mΩ sr Ω
sl Ω
sdcr
r
I L
R 1
∫
b p
Fig. 3.4. Block diagram of the Indirect Field Oriented Control (IFOC)
In both presented examples reference currents in rotating coordinate system sdc I , sqc I
are calculated from the reference flux and torque values. Taking into consideration the
equations describing IM in field oriented coordinate system (3.6) and (3.7) at steady
state the formulas for the reference currents can be written as follows:
r
M
sdc Ψ L
I 1
= (3.10)
ec
rc M
r
sb
sqc M Ψ L
L
m p I
12= (3.11)
The property of the FOC methods can be summarized as follows:
• the method is based on the analogy to control of a DC motor,
• FOC method does not guarantee an exact decoupling of the torque and flux
control in dynamic and steady state operation,
•
relationship between regulated value and control variables is linear only for
constant rotor flux amplitude,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 51/175
3.3. Feedback Linearization Control (FLC)
45
•
full information about motor state variable and load torque is required (the
method is very sensitive to rotor time constant),
• current controllers are required,
•
coordinate transformations are required,
• a PWM algorithm is required (it guarantees constant switching frequency),
• in the DFOC rotor flux estimator is required,
•
in the IFOC mechanical speed is required,
• the stator currents are sinusoidal except of high frequency switching harmonics.
3.3. Feedback Linearization Control (FLC)
The transformation of the induction motor equations in the field coordinates has a
good physical basis because it corresponds to the decoupled torque production in a
separately excited DC motor. However, from the theoretical point of view, other types
of coordinates can be selected to achieve decoupling and linearization of the induction
motor equations.
In [28] it is shown that a nonlinear dynamic model of IM can be considered as
equivalent to two third-order decoupled linear systems. In [70] a controller based on a
multiscalar motor model has been proposed. The new state variables have been chosen.
In result the motor speed is fully decoupled from the rotor flux. In [82] the authors
proposed a nonlinear transformation of the motor states variables, so that in the new
coordinates, the speed and rotor flux amplitude are decoupled by feedback. Others
proposed also modified methods based on Feedback Linearization Control like in [93,
94].
In the example given new quantities for control of rotor flux magnitude and
mechanical speed were chosen [93]. For this purpose the induction motor equations
(2.10-2.12) can be written in the following form:
β β α α gg)x(x s s U U f
& (3.12)
where:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 52/175
3. Vector Control Methods of Induction Motor
46
=
J
M I Ψ I Ψ
I Ψ Ψ Ω p
I Ψ Ω pΨ
I LΨ Ψ Ω p
I LΨ Ω pΨ
f
L sr sr
sr r mb
sr mbr
s M r r mb
s M r mbr
)(
)(
α β β α
β β α
α β α
β β α
α β α
µ
γ αβ β
γ β αβ
α α
α α
x (3.13)
T
g
=
001
00 , , , , s Lσ
α (3.14)
T
g
=
01
000 , , , , s Lσ
β (3.15)
[ ]
Tx m s sr r Ω I I Ψ Ψ , , , , β α β α
(3.16)
and
r
r
L
R=
α (3.17)
r s
M
L L
L
σ β =
(3.18)
2
22
r s
M r r s
L L
L R L R
σ γ
=
(3.19)
J
Lm p M s
b2
=µ (3.20)
Because β α r r m Ψ Ψ Ω ,, are not dependent on β α s s U U , it is possible to chose variable
dependent on x:
222
1 )x( r r r Ψ Ψ Ψ = β α φ (3.21)
mΩ)x(2φ (3.22)
If it is assumed that )x(1φ , )x(2φ are output variables, the full definition of new
coordinates can be given by:
)x(11 φ z (3.23a)
)x(12 φ f L z =
(3.23b)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 53/175
3.3. Feedback Linearization Control (FLC)
47
)x(23 φ z (3.23c)
)x(24 φ f L z =
(3.23d)
=
α
β
r
r
Ψ Ψ z arctan5 (3.23e)
It should be mentioned that the goal of the control is to obtain constant flux
amplitude and to follow the reference angular speed.
The fifth variable cannot be fully linearized. Additionally, it is not controllable (the
fifth variable correspond to slip in the motor). Therefore, the last equation is not
considered. Then the dynamics of the system are given by:
=
β
α
φ
φ
s
s
f
f
U
U
L
L
z
z D
2
2
1
2
3
1
&&
&& (3.24)
where
=
22
11
φ φ
φ φ
β α
β α
f g f g
f g f g
L L L L
L L L LD (3.25)
If 01 ≠
φ (the amplitude of flux is not zero) then 0D) ≠
det( and it is possible todefine the linearization feedback as:
=
2
1
2
2
1
2
v
v
L
L
U
U
f
f
s
s
φ
φ
β
α 1-D (3.26)
Then the resulting system is described by the equations:
21 z z =
& (3.27a)
12 v z =
& (3.27b)
43 z z =
& (3.27c)
24 v z =
& (3.27d)
and the final block diagram of the induction motor with the new defined control
signals can be shown as in Fig. 3.5.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 54/175
3. Vector Control Methods of Induction Motor
48
mΩ
L M
e M 2ν
∫ 4 z
J
∫
r Ψ 1ν 2 z 2
r Ψ
∫∫
Fig. 3.5. Block diagram of the induction motor with new 1v and 2v control signals
The control signals 1v , 2v are calculated by using linear feedback as follows:
21211111 z k z z k v ref (3.28)
42233212 z k z z k v ref (3.29)
where coefficients 11k , 12k , 21k , 22k are chosen to receive reference close loop
system dynamics.
An example of a FLC system for PWM inverter-fed induction motor is presented in
Fig. 3.6.
The property of the FLC can be summarized as follows:
• it guarantees exactly decoupling of the motor speed and rotor flux control in both
dynamic and steady state,
• the method is implemented in a state variable control fashion and needs complex
signal processing,
• full information about motor state variables and load torque is required,
•
there are no current controllers,
•
a PWM vector modulator is required, what further guarantee constant switchingfrequency,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 55/175
3.4. Direct Flux and Torque Control (DTC)
49
•
the stator currents are sinusoidal except of high frequency switching harmonics.
Speed
Controller
FluxController Vector
Modulator
Control
Signals
Transfor-
mation
Feedback
Signals
Transfor-mation
1ν
2ν
β s I
α s I
r αΨ ˆ
r β Ψ ˆ
Flux
Estimator
mΩ
2
rcΨ
5 z
SA
SB
SC
Voltage
Calculation
mcΩ
1 z
2 z
3 z
4 z
c sU β
Motor
sU ˆ
s I
c sU α
dcU
Fig. 3.6. Block scheme of the feedback linearization control method
3.4. Direct Flux and Torque Control (DTC)
3.4.1. Basics of Direct Flux and Torque Control
As it was mentioned in section 3.2 in the classical vector control strategy (FOC) the
torque is controlled by the stator current component sq I in accordance with equation
(3.7). This equation can also be written as:
δ sin2
sr
r
M sbe I Ψ
L
Lm p M = (3.30)
where:
δ - angle between rotor flux vector and stator current vector.
The formula (3.30) can be transformed into the equation:
Ψ r s
M sr
M sbe Ψ Ψ
L L L
Lm p M δ sin
22
−= (3.31)
where:
Ψ δ - angle between rotor and stator flux vectors.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 56/175
3. Vector Control Methods of Induction Motor
50
It can be noticed that the torque depends on the stator and rotor flux magnitude as
well as the angle Ψ δ . The vector diagram of IM is presented in Fig. 3.7. The two angels
δ and Ψ δ are also shown in Fig. 3.7. The angle δ is important in FOC algorithms,
whereas Ψ δ in DTC techniques.
α
β
δ
sI
sΨ
rΨ
δ Ψ
ssγ
sr γ
Fig. 3.7. Vector diagram of induction motor
From the motor voltage equation (2.10a), for the omitted voltage drop on the stator
resistance, the stator flux can by expressed as:
s
s UΨ
=dt
d (3.32)
Taking into consideration the output voltage of the inverter in the above equation it
can be written as:
∫=t
vdt 0
UΨs (3.33)
where:
=
==
−
7,00
6...13
2 3)1(
v
veU v j
dc
v
π
U (3.34)
Equation (3.33) describe eight voltage vectors which correspond to possible inverter
states. These vectors are shown in Fig. 3.8. There are six active vectors U1-U6 and two
zero vectors U0, U7.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 57/175
3.4. Direct Flux and Torque Control (DTC)
51
U1
(100)
U2
(110)U3 (010)
U4 (011)
U5 (001) U
6 (101)
Im
ReU7 (111)
U0 (000)
Fig. 3.8. Inverter output voltage represented as space vectors
It can be seen from (3.33), that the stator flux directly depends on the inverter voltage
(3.34).
By using one of the active voltage vectors the stator flux vector moves to the
direction and sense of the voltage vector. It can be observed by simulation of six-step
mode (Fig. 3.9) and PWM operation (Fig. 3.10). In Fig. 3.9 is well shown how stator
flux changes direction for the cycle sequence of the active voltage vectors. Obviously,
the same effect is for the PWM operation (Fig. 3.10). However, in this case the control
algorithm choose correct voltage vectors, thanks to that waveform is close to be
sinusoidal. In this simulation a low sampling frequency is used (0.5kHz) for better
presenting the effect. A zoom part of the flux vector trajectory is shown in Fig. 3.11.
In induction motor the rotor flux is slowly moving but the stator flux can be changed
immediately. In direct torque control methods the angle between stator and rotor flux
Ψ δ can be used as a variable of torque control (3.31). Moreover stator flux can be
adjusted by stator voltage in simple way. Therefore, angle Ψ δ as well as torque can be
changed thanks to the appropriate selection of voltage vector.
There are the general bases of the direct flux and torque control methods. Those
consideration and above equations can be used in analysis of the classical DTC
algorithms as well as in new proposed methods. It is also bases of the DTC-SVM
methods, which are presented in Chapter 4.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 58/175
3. Vector Control Methods of Induction Motor
52
a)
b)
Fig. 3.9. IM under six-step mode a) voltage and stator flux waveforms, b) stator flux trajectory
a)
b)
Fig. 3.10. IM under PWM operation a) voltage and stator flux waveforms, b) stator flux trajectory
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 59/175
3.4. Direct Flux and Torque Control (DTC)
53
U1(100)
U2(110)U
3 (010)
U4 (011)
U5 (001) U6 (101)
U7 (111)
U0 (000)
β
α
voltage U3
applied
voltage U2applied
voltage U3
applied
voltage U3applied
voltage U4
applied
voltage U4
applied
voltage U3
applied
voltage U4applied
Fig. 3.11. Forming of the stator flux trajectory by appropriate voltage vectors selection
3.4.2. Classical Direct Torque Control (DTC) – Circular Flux Path
The block diagram of classical DTC proposed by I. Takahashi and T. Nogouchi [97]
is presented in Fig. 3.12.
sΨ ˆ
SA
SB
SC
U dc
Motor
Torque
Controller
Flux
Controller
scΨ Ψ d
M d
Voltage
Calculation
Vector
Selection
Table
(N) ssγ
Sector
Detection
Flux and
Torque
Estimator
M ec
U s
I s
e M ˆ α sΨ ˆ β sΨ ˆ
M e
Ψ e
Fig. 3.12. Block scheme of the direct torque control method
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 60/175
3. Vector Control Methods of Induction Motor
54
The stator flux amplitude scΨ and the electromagnetic torque c M are the reference
signals which are compared with the estimated sΨ ˆ and e M ˆ values respectively. The
flux Ψ e and torque M e errors are delivered to the hysteresis controllers. The digitized
output variables Ψ d , M d and the stator flux position sector ( ) N ssγ selects the
appropriate voltage vector from the switching table. Thus, the selection table generates
pulses SA, SB, SC to control the power switches in the inverter.
For the flux is defined two-level hysteresis controller, for the torque three-level, as it
is shown in Fig. 3.13.
a)
Ψ e
Ψ
d
Ψ H
b)
M
d
M e
M H
Fig. 3.13. The hysteresis controllers a) two-level, b) three-level
The output signals Ψ d , M d are defined as:
1=Ψ d for Ψ Ψ H e > (3.35a)
0=Ψ d for Ψ Ψ H e −< (3.35b)
1= M d for M M H e > (3.36a)
0= M d for 0= M e (3.36b)
1−= M d for M M H e −< (3.36c)
In the classical DTC method the plane is divided for the six sectors (Fig. 3.14),
which are defined as:
Sector 1:
+−∈
6,
6
π π γ ss (3.37a)
Sector 2:
+∈
2,
6
π π γ ss (3.37b)
Sector 3:
++∈
65,
2π π γ ss (3.37c)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 61/175
3.4. Direct Flux and Torque Control (DTC)
55
Sector 4:
−+∈
6
5,
6
5 π π γ ss (3.37d)
Sector 5:
−−∈
2
,
6
5 π π γ ss (3.37e)
Sector 6:
−−∈
6,
2
π π γ ss (3.37f)
U7 (111)
U0 (000) U
1(100)
U2(110)
U3 (010)
U4 (011)
U5 (001)
U6 (101)
Sector 1
Sector 2Sector 3
Sector 4
Sector 5 Sector 6
α
β
Fig. 3.14. Sectors in the classical DTC method
For the stator flux vector laying in sector 1 (Fig. 3.15) in order to increase its
magnitude the voltage vectors U1, U2, U6 can be selected. Conversely, a decrease can be
obtained by selecting U3, U4, U5. By applying one of the zero vectors U0 or U7 the
integration in equation (3.33) is stopped. The stator flux vector is not changed.
For the torque control, angle between stator and rotor flux Ψ δ is used (equation
3.31). Therefore, to increase motor torque the voltage vectors U2, U3, U4 can be selected
and to decrease U1, U5, U6.
The above considerations allow construction of the selection table as presented in
Table 3.1.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 62/175
3. Vector Control Methods of Induction Motor
56
α
β
sΨ
rΨ
δ Ψ
Sector 1
U2
U3
U1
U4
U5
U6
Fig. 3.15. Selection of the optimum voltage vectors for the stator flux vector in sector 1
Table 3.1. Optimum switching table
Ψ d M d Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6
1
0
1
-1
1
0
1
-1
0
U4
U3
U2
U1
U6
U5
U7
U0
U7
U0
U7
U0
U6
U1
U2
U3
U4
U5
U4
U3
U2
U1
U6
U5
U7
U0
U7
U0
U7
U0
U4
U3
U2
U1
U6
U5
The signal waveforms for steady state operation of classical DTC method are shown
in Fig. 3.16.
The DTC was proposed as an analog control method. The implementation of the
hysteresis controller in the analog setup is easy and the control system works properly.
When the hysteresis controller is implemented in a digital signal processor (DSP), its
operation is quite different from that of the analog scheme [19]. The digital
implementation of the hysteresis controller is also called sampled hysteresis.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 63/175
3.4. Direct Flux and Torque Control (DTC)
57
a)
b)
Fig. 3.16. Steady state operation for the classical DTC method ( )kHz f s 40=
a) signals in time domain, b) stator flux trajectory
In Fig. 3.17 are presented typical switching sequences of the torque hysteresis
controller for the analog (Fig. 3.17a) and for the digital (Fig. 3.17b) implementation.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 64/175
3. Vector Control Methods of Induction Motor
58
c M
mc H M +
mc H M −t 1
t 2
t 3
T s
T s
T s
S/H
a) b)
Fig. 3.17. Operating of the torque hysteresis controller a) analog, b) digital
In the analog implementation the torque ripple are kept exactly within the hysteresis
band and the switching instants are not equally spaced. The digital system operates at
fixed sampling time sT and works like analog only for high sampling frequencies
s
sT
f 1
= .
For the lower sapling frequency the switching instants are not when the estimated
torque crosses the hysteresis band but on the sampling time. This situation is presented
in Fig. 3.17b. The simulation results illustrated control system behavior at lowersampling frequency kHz f s 15= are given in Fig. 3.18. It can be seen that current and
torque ripples are bigger compare to this one operate with sampling frequency
kHz f s 40= (see Fig. 3.16).
The influence of the torque hysteresis band for the torque error and switching
frequency at different sampling frequencies is shown in Fig. 3.19 and Fig. 3.20. At low
sampling frequency f s = 20kHz (Fig. 3.19) the switching frequency and torque error are
not sensitive for hysteresis band. However, at the high sampling frequency f s = 80kHz
(Fig. 3.20) when the hysteresis band is increased the switching frequency decreases and
the torque error increases. Simulated results show that the hysteresis controllers need a
high sampling frequency to obtain a proper operation.
The torque and flux errors are calculated according to equations:
%100ˆ
sN
sc s
Ψ
Ψ Ψ s
−=ψ ε (3.38a)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 65/175
3.4. Direct Flux and Torque Control (DTC)
59
%100ˆ
eN
ece M
M
M M −=ε (3.38b)
where: sN Ψ - nominal stator flux, eN M - nominal torque
Fig. 3.18. Steady state operation for the classical DTC method operating with lower
sampling frequency ( )kHz f s 15=
The average value of the flux and torque errors are calculated in a period of the
fundamental frequency.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 66/175
3. Vector Control Methods of Induction Motor
60
54004792
4567 4333 35082750 2208 2367 2333
0
5000
10000
15000
20000
25000
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 H m [Nm]
f sw [Hz]
9,65
11,0611,97
11,0010,17
9,43 9,9310,68
12,03
0
2
4
6
8
10
12
14
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 H m [Nm]
ε Μ _avr [%]
a)
b)
Fig. 3.19. Simulated results for classical DTC a) switching frequency and b) torque error as a function ofthe torque hysteresis band at sampling frequency f s = 20kHz
5666545054926142666674008233
13317
19750
0
5000
10000
15000
20000
25000
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 H m [Nm]
f sw [Hz]
10,27
8,947,77
6,565,364,21
3,06
2,43
2,640
2
4
6
8
10
12
14
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 H m [Nm]
ε Μ _avr [%]
a)
b)
Fig. 3.20. Simulated results for classical DTC a) switching frequency and b) torque error as a function ofthe torque hysteresis band at sampling frequency f s = 80kHz
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 67/175
3.4. Direct Flux and Torque Control (DTC)
61
The classical DTC method can be characterized as follows:
Advantages:
• simple structure:
o no coordinate transformation,
o no separate voltage modulation block,
o no current control loops,
• very good flux and torque dynamic performance,
Disadvantages:
•
variable switching frequency,
• problems during starting and low speed operation,
• high torque ripples,
• flux and current distortion caused by stator flux vector sector position change
• high sampling frequency is required for digital implementation.
3.4.3. Direct Self Control (DSC) – Hexagon Flux Path
The block diagram of the direct self control method proposed by M. Depenbrock [31,
32] is presented in Fig. 3.21. This method was mainly applied in high power
applications, which required fast torque dynamic and low switching frequency [96].
Based on the command stator flux scΨ and the actual phase components sAΨ , sBΨ ,
sC Ψ , the flux comparators generate digital variables Ad , Bd , C d , which corresponds to
active voltage vectors (U1 – U6). The hysteresis torque controller generates the signal
md , which determines zero states. For the constant flux region, the control algorithm is
as follows:
C A d S = , A B d S = , BC d S = for 1=md (3.39a)
0= AS , 0= BS , 0=C S for 0=md (3.39b)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 68/175
3. Vector Control Methods of Induction Motor
62
s I
U dc
Motor
Torque
Controller
ec M
Flux
Comparators
sU
Voltage
Calculation
scψ
Flux and
TorqueEstimator
sBψ ˆ
sAψ ˆ
sαψ ˆ
s β ψ ˆ
Ad
C d
Bd
md
SA
SB
SC
sC ψ ˆ
e M ˆ β α −
BC
Fig. 3.21. Block diagram of Direct Self Control method
The signal waveforms for steady state operation of DSC method are shown in Fig.
3.22. It can be seen that the flux trajectory is identical with that for the six-step mode(Fig. 3.9). This follows from the fact that the zero voltage vectors stop the flux vector,
but do not affect its trajectory. The dynamic performances of torque control for the DSC
are similar as for the classical DTC.
The property of the DSC can be summarized as follows:
• hexagonal trajectory of the stator flux vector for PWM operation,
• block type of PWM (not sinusoidal),
• non-sinusoidal current waveforms,
• switching selection table is not required,
• low (minimum) inverter switching frequency (depended on hysteresis torque
band),
• very good torque and flux control dynamics.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 69/175
3.4. Direct Flux and Torque Control (DTC)
63
a)
b)
Fig. 3.22. Steady state operation for the DSC methoda) signals in time domain, b) stator flux trajectory
Several solutions have been proposed to improve the conventional DSC. For
instance, reduction of the current distortion has been achieved by introducing 12 stator
flux sectors [110] or by processing not only the stator flux value , but also the stator flux
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 70/175
3. Vector Control Methods of Induction Motor
64
angle [109]. Also solutions based on fuzzy logic and neural networks solutions were
proposed [85, 90].
3.5. Summary
In this chapter review of significant vector control methods of IM has been
presented. The characteristic features for all control schemes were described.
The FLC structure guarantees exact decoupling of the motor speed and rotor flux
control in both dynamic and steady states. However, it is complicated and difficult to
implement in practice. This method requires complex computation and additionally it is
sensitive to changes of motor parameters. Because of these features this method was notchosen for implementation.
Table 3.2 Comparison of control methods
FOC DTC DTC-SVM
Advantages Modulator
Constant switching
frequency Unipolar inverter
output voltage
Low switchinglosses
Low samplingfrequency
Current controlloops
Structure
independent on
rotor parameters,universal for IM
and PMSM
Simpleimplementation of
sensorlessoperation
No coordinatetransformation
No current control
loops
Disadvantages • Coordinatetransformation
• A lot of control
loops• Control structure
depended on rotor
parameters
• No modulator
• Bipolar inverteroutput voltage
•
Variable switchingfrequency
• High switching
losses
• High samplingfrequency
Structure
independent on
rotor parameters,universal for IM
and PMSM
Simpleimplementation of
sensorlessoperation
No coordinatetransformation
No current control
loops Modulator
Constant switchingfrequency
Unipolar inverteroutput voltage
Low switching
losses Low sampling
frequency
Due to above mentioned facts the FOC and DTC methods were considered next.
Analysis of advantages and disadvantages of FOC and DTC methods resulted in a
search for method which will eliminate disadvantages and keep advantages of those
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 71/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 72/175
4. Direct Flux and Torque Control with Space Vector
Modulation (DTC-SVM)
4.1. Introduction
Direct flux and torque control with space vector modulation (DTC-SVM) schemes
are proposed in order to improve the classical DTC. The DTC-SVM strategies operate
at a constant switching frequency. In the control structures, space vector modulation
(SVM) algorithm is used. The type of DTC-SVM strategy depends on the applied flux
and torque control algorithm. Basically, the controllers calculate the required stator
voltage vector and then it is realized by space vector modulation technique.
In the DTC-SVM methods several classes have evolved:
• schemes with PI controllers [111],
• schemes with predictive/dead-beat [74],
• schemes based on fuzzy logic and/or neural networks [40],
• variable-structure control (VSC) [72, 73, 112].
Different structures of DTC-SVM methods are presented in the next section. For
each of the control structures, different controller design methods are proposed.
The classical DTC algorithm is based on the instantaneous values and directly
calculated the digital control signals for the inverter. The control algorithm in DTC-
SVM methods are based on averaged values whereas the switching signals for the
inverter are calculated by space vector modulator. This is main difference between
classical DTC and DTC-SVM control methods.
4.2. Structures of DTC-SVM – Review
4.2.1. DTC-SVM Scheme with Closed – Loop Flux Control
In the control structure of Fig. 4.1 the rotor flux is assumed as a reference [24]. The
reference stator flux components defined in the rotor flux coordinates sdcΨ , sqcΨ can be
calculated from the following equations:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 73/175
4.2. Structures of DTC-SVM – Review
67
+=
dt
d Ψ
R
LΨ
L
LΨ
rc
r
r rc
M
s sdc σ (4.1a)
rc
ec s
M
r
sb
sqc
Ψ
M L
L
L
m p
Ψ σ 2
= (4.1b)
Formulas (4.1) can be derived from the equations (3.3), (3.4) and (3.7). The
equations (3.3), (3.4) and (3.7) describe the motor model in the rotor flux coordinate
system qd − .
The amplitude of the reference stator flux, using equations (4.1) can by expressed as:
( )2
2
22
2
+
=
rc
ec
M
r
s sb
rc M
s
sc Ψ
M
L
L L
m pΨ
L
LΨ σ (4.2)
The commanded value of stator flux sdcΨ , sqcΨ after transformation to stationary
coordinate system β α − are compared with the estimated values α sΨ , β sΨ ˆ .
rcΨ
ec M
Egs (4.1)
sdcΨ
sqcΨ
scΨ
Rotor
Flux
Estimator
Stator
Flux
Estimator
sΨ
sr γ
SVM
SA
SB
SC
Voltage
Calculation
sT
1s∆Ψ
β α −
qd −
s R
scU
sU
sI
dcU
β α −
ABC
A I
B I
Fig. 4.1. DTC-SVM scheme with closed flux control
The reference voltage vector depends on the increment stator flux s∆Ψ and voltage
drop on the stator winding resistance s R :
ss
sc I∆Ψ
U s
s
RT
+= (4.3)
In this DTC-SVM structure the rotor flux magnitude is regulated. Thanks of them
increase the torque overload capability is possible [19, 24]. However, the drawback of
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 74/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
68
this algorithm is that it requires all the motor parameters and moreover it is very
sensitive to their variation.
4.2.2. DTC-SVM Scheme with Closed – Loop Torque Control
The method with close-loop torque control was originally proposed for the
permanent magnet synchronous motor (PMSM) [35, 36, 37]. However, the DTC basics
for both IM and PMSM are identical and therefore the method can also be used for the
IM [126]. The block scheme of the control structure DTC-SVM with close-loop torque
control is presented in Fig. 4.2.
scΨ
ec M Eg. (4.4)
ψ δ ∆ scΨ
PI
Flux and
Torque
Estimator
sΨ ssγ
SVM
SA
SB
SC
Voltage
Calculation
sT
1s∆Ψ
s R
scU
sU
sI
dcU
β α −
ABC
A I
B I
Torque
Controller
e M ˆ
Fig. 4.2. DTC-SVM scheme with closed-loop torque control
For the torque regulation a PI controller is applied. Output of this PI controller is an
increment of torque angleΨ
∆δ (Fig. 4.3). In this way the torque is controlled by
changing the angle between stator and rotor fluxes according to the basics of DTC (see
section 3.4.2).
The reference stator flux vector is calculated as follows:
( )Ψ ss ∆ j
sceΨ δ γ += ˆ
scΨ (4.4)
Next, reference stator flux vector is compared with the estimated value. The error of
the flux s∆Ψ is used, for calculation of the reference voltage vector, according to the
equation (4.3).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 75/175
4.2. Structures of DTC-SVM – Review
69
α
β
ssγ
sr γ
Ψ ∆δ sΨ
rΨ
Ψ δ
scΨ
Fig. 4.3. Vector diagram
The presented method has simple structure and only one PI torque controller. It
makes the tuning procedure easier. The flux is adjusted in open-loop fashion.
4.2.3. DTC-SVM Scheme with Close – Loop Torque and Flux Control
Operating in Polar Coordinates
When both torque and flux magnitudes are controlled in a closed-loop way, the
strategies provide further improvement. The method operating in polar coordinates is
shown in Fig. 4.4 [49].
scΨ
ec M Eg. (4.7)
PI
Flux and
Torque
Estimator
Ψ k
ssγ
SVM
SA
SB
SC
Voltage
Calculation
sT
1s∆Ψ
s R
scU
sU
sI
dcU
β α −
ABC
A I
B I
Torque
Controller
e M ˆ
P
Flux
Controller
sd ∆γ s ∆γ
ss ∆γ
sΨ ˆ
Fig. 4.4. DTC-SVM scheme operated in stator flux polar coordinates
The error of the stator flux vector s∆Ψ is calculated from the outputs Ψ k and s ∆γ
of the flux and torque controllers as follows:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 76/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
70
( ) ( ) ( )1−−= k k k sss ΨΨ∆Ψ
( )[ ] ( ) ( )111 −⋅−⋅+= k ek k k j ∆
Ψ
s
sΨγ
(4.5)
With the approximation
( ) ( )k j ∆e s
k j ∆ s γ γ +≅1 (4.6)
The equation (4.5) can be written in the form
( ) ( ) ( )[ ] ( )1−⋅+= k k j ∆k k k sΨ ss Ψ∆Ψ γ (4.7)
The commanded stator voltage vector is calculated according to equation (4.3). To
improve the dynamic performance of the torque control, the angle increment s ∆γ is
composed of two parts: the dynamic part sd ∆γ delivered by the torque controller and
the stationary part ss ∆γ generated by a feedforward loop.
4.2.4. DTC-SVM Scheme with Close – Loop Torque and Flux Control
in Stator Flux Coordinates
A block diagram of the method with close-loop torque and flux control in stator flux
coordinate system [111] is presented in Fig. 4.5. The output of the PI flux and torque
controllers can be interpreted as the reference stator voltage components sxcU , sycU in
the stator flux oriented coordinates ( y x − ).
scΨ
ec M
PI
Flux and
Torque
Estimator
sxcU
ssγ Torque
Controller
PI
Flux
Controller
sycU
y x −
β α −
e M ˆ
sΨ ˆ
SVM
SA
SB
SC
scU
sI β α −
ABC
A I
B I
Voltage
Calculation
sUdcU
Fig. 4.5. DTC-SVM scheme operated in stator flux cartesian coordinates
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 77/175
4.3. Analysis and Controller Design for DTC-SVM Method
71
These dc voltage commands are then transformed into stationary frame ( β α − ), the
commanded values c sU α , c sU β are delivered to SVM.
4.2.5. Conclusions from Review of the DTC-SVM Structures
In the three first presented structures (Fig. 4.1, Fig. 4.2 and Fig. 4.4) the calculation
of reference voltage vector is based on demanded s∆Ψ according to equation (4.3).
This differentiation algorithm is very sensitive to disturbances. In case of errors in the
feedback signals the differentiation algorithm may not be stable. This is very serious
drawback of these methods.
The methods presented in Fig. 4.1 and Fig. 4.2 do not have close-loop flux control.
In these methods stator flux magnitude is only adjusted.
The last presented method (Fig. 4.5) eliminates problems with differentiation
algorithm. Moreover, this method controls torque and flux in close-loop fashion.
Therefore, this scheme will be selected for experimental realization. In the next sub-
section controller design for flux and torque closed loops will be discussed.
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop
Torque and Flux Control in Stator Flux Coordinates
The compete set of motor model equations can be written in stator flux coordinate
system y x − . This system of coordinates y− rotates with the stator flux angular
speed ss K ΩΩ = . This angular speed is defined as follows:
dt
d Ω
ss ss
γ = (4.8)
where: ssγ is a stator flux vector angle.
The complex space vector can be resolved into components x and y .
sy sx K U U j+=sU (4.9a)
sy sx K
I I jI +=s
,ryrx K
I I j+=r
I (4.9b)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 78/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
72
s sx K Ψ Ψ ==sΨ , ryrx K Ψ Ψ j+=rΨ (4.9c)
The motor model equations (2.10-2.12) in y− coordinate system can be written as:
dt
d Ψ I RU s sx s sx += (4.10a)
s ss sy s sy Ψ Ω I RU += (4.10b)
( ) ssmbryrx
rxr ΩΩ pΨ dt
d Ψ I R −++=0 (4.11a)
( )mb ssrx
ry
ryr Ω pΩΨ dt
d Ψ I R −++=0 (4.11b)
rx M sx s s I L I LΨ += (4.12a)
ry M sy s I L I L +=0 (4.12b)
sx M rxr rx I L I LΨ += (4.12c)
sy M ryr ry I L I LΨ += (4.12d)
−=
L sy s
s
b
m
M I Ψ
m
p J dt
d Ω
2
1
(4.13)
The electromagnetic torque can be expressed by the following formula:
sy s s
be I Ψ m
p M 2
= (4.14)
Based on the equations (4.10-4.14) the block diagram of induction motor can be
constructed (Fig. 4.6).
The block scheme presented in Fig. 4.6 is a full model of an induction motor. As can
be seen, this model is quite complicated and therefore difficult to analyze. However,
taking into consideration the stator voltage equations (4.10) and torque equation (4.14),
the motor can be described as follows:
sx s sx s I RU
dt
d Ψ −= (4.15)
( ) s ss sy s
s
b s
e Ψ Ω
U Ψ
m
p R M −= 2
1
(4.16)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 79/175
4.3. Analysis and Controller Design for DTC-SVM Method
73
ssΩ
sx I
sΨ
sxU
s R
∫∫
s R
syU
sy I
2
1
mr s L L L −
b p
rx I
∫
r Lσ
1r R
rxΨ
∫
r Rr Lσ
1ry I
ryΨ
s
M
L
L
÷ M L
r L
2
mr s
M
L L L
L
−
mΩ
2
sb
m p
e M
∫
L M
J
1
sΨ
Fig. 4.6. Complete block diagram of an induction motor in the stator flux oriented coordinates y x −
The block diagram of induction motor based on equations (4.15) and (4.16) is shown
in Fig. 4.7.
∫ ssΩ
sΨ sxU
sx s I R
syU e M
s
sb
R
m p
1
2
Fig. 4.7. Simplified (rotor equation omitted) induction motor block diagram in the stator flux oriented
coordinates y x −
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 80/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
74
Different control structures based on the above induction motor model are proposed
in literature [73, 111, 112]. One of them is a method with two PI controllers [111],
which is presented in Fig. 4.5.
Considering a simple model of IM (Fig. 4.7), Fig. 4.8 shows the flux and torque
control loops for the method shown in Fig. 4.5. In Fig. 4.8 the dashed line represents the
IM model.
∫ ssΩ
sΨ sxU
sx s I R
syU ec M
PI e M
PI scΨ
s
sb
R
m p
1
2
Fig. 4.8. Control loops with two PI controllers and simplified IM model of Fig. 4.7
In the next parts two approaches to a controller design will be presented and
compared. Both of them are based o the assumption that control loop can be considered
as quasi-continuous (fast sampling). The first method is based on simple symmetric
criterion [66], the second one uses root locus technique [34, 86].
PI Controllers
The transfer function of PI controllers is given as follows:
( ) ( )
( ) i
i p
i
p R sT
sT K
sT K
s E
sU sG
+=
+==
111 (4.17)
where: p K - controller gain, iT - controller integrating time.
The PI controller scheme is presented in Fig. 4.9.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 81/175
4.3. Analysis and Controller Design for DTC-SVM Method
75
( ) sU ( ) s E
sT i
1
1
p K
Fig. 4.9. Block diagram of PI controller
Presented above model of the controller was used in DTC-SVM control method with
two PI controllers.
4.3.1.
Torque and Flux Controllers Design – Symmetry Criterion Method
Flux Controller Design
The block diagram of the flux control loop is shown in Fig. 4.10. This control loops
is based on the model presented in Fig. 4.8. The voltage drop on the stator resistance is
neglected. In the stator flux control loop the inverter delay is taken into consideration.
s
1 sΨ sxU PI
scΨ
1
1
1
sT +
Fig. 4.10. Stator flux magnitude control loops
For the flux controller parameter design the symmetry criterion can by applied [66].
In accordance with the symmetry criterion the plant transfer function can be written as:
( )( )12 1
0
sT sT
e K sG
sτ
c
+=
−
(4.18)
where: 1=c K is the inverter gain, 0τ is dead time of the inverter ( 00 =τ ideal
converter), 12 =T , and sT T =1 is a sum of small time constants, which includes
statistical delay of the PWM generation and signal processing delay. The optimal
controller parameters can be calculated as:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 82/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
76
( ) sc
pΨ T T K
T K
2
1
2 01
2 =+
=τ
(4.19)
( ) siΨ T T T 44 01 =+= τ (4.20)
In Table 4.1 are shown flux controller parameters calculated according to equations
(4.19) and (4.20). The considered range of the sampling frequency was form 2.5kHz to
10kHz. In Table 4.1 are also shown parameters of the step flux response obtained in
simulation, nΨ t - time when the actual flux is first time equal reference value andΨ
p -
overshoot. The results of simulation are presented in Fig. 4.11.
Table 4.1. Flux controller parameters calculated according to symmetric optimum criterion
f s K p Ψ T i Ψ t n Ψ p Ψ
10.0 kHz 5000 0.00040 0.00150 s 1.60 %
5.0 kHz 2500 0.00080 0.00180 s 2.37 %
2.5 kHz 1250 0.00160 0.00200 s 9.33 %
a)
b)
c)
Fig. 4.11. Simulated flux response for controller parameters calculated according to symmetric optimum
criterion at different sampling frequency a) kHz f s 10= , b) kHz f s 5= , c) kHz f s 5.2=
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 83/175
4.3. Analysis and Controller Design for DTC-SVM Method
77
Presented in Fig. 4.11 simulation results confirm proper operation of the flux
controller for the different sampling frequency. The symmetric optimum criterion can
be apply to tune flux controller in analyzed DTC-SVM structure.
Torque Controller Design
The block diagram of the torque control loop is shown in Fig. 4.12. The same like for
flux this control loops is based on the model presented in Fig. 4.8. However, coupling
between torque and flux is omitted. Because of that very simple model is obtained and
for this model any criterion cannot be applied.
syU ec
M PI e
M
s sT +1
1 s
s
sb Ψ R
m p
1
2
Fig. 4.12. Block diagram of the torque control loops
In this case the simple (practical) way to design torque controller can be used.
Starting from the initial values e.g. 1= pM K , siM T T 4= the proportional gain pM K is
increasing cyclically as it is shown in Fig. 4.13. From these oscillograms the best value
of pM K for the fast torque response without oscillation and small overshoot can be
selected. In Fig. 4.13 the chosen simulation results for 5kHz and 10kHz sampling
frequencies are shown. For the sampling frequency 5kHz the best value of proportional
gain is 17= pM K and for 10kHz 24= pM K .
The finally obtained in this way parameters of the torque controller are shown inTable 4.2. There are also shown parameters of the step torque response obtained in
simulation, nM t - time when the actual torque achieves first time reference value and
M p - overshoot.
Table 4.2. Torque controller parameters
f s K pM T iM t nM p Μ
10.0 kHz 24 0.0004 0.0007 s 8.39 %
5.0 kHz 17 0.0008 0.0008 s 18.53 %
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 84/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
78
a)
4= pM K
10= pM K 10= pM K
24= pM K 17= pM K
4= pM K
b)
Fig. 4.13. Torque response for selected controller gain pM K values, at different sampling frequency
a) kHz f s 5= ( ) sT iM µ 800= , b) kHz f s 10= ( ) sT iM µ 400=
4.3.2. Torque and Flux Controllers Design – Root Locus Method
A root-locus analysis is used for tuning the flux and torque controllers. This
technique shows how the changes in the system’s open-loop characteristics influences
the closed-loop dynamic characteristics. This method allows to plot the locus of the
closed-loop roots in s-plane as an open-loop parameters varies, thus producing a root
locus.
The damping factor, overshoot and settling time [106] limit the allowable area of
existence of the close-loop roots. The border of each of these parameters can be
represented in s-plane as a straight line.
The allowable area of existence for the close-loop roots limited by dumping and
settling time is shown in Fig. 4.14.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 85/175
4.3. Analysis and Controller Design for DTC-SVM Method
79
Re
Im
α
α
damping
damping
settling
time
Fig. 4.14. Allowable area of existence for the close-loop roots in s-plane
To plot and analyze the locus of the root in s-plane SISO Design Tool Control
System Toolbox v 5.0 the MathWorks, Inc. was used [84].
The SISO Design Tool is a Graphical User Interface (GUI) that allows to analyze
and tune the Single Input Single Output (SISO) feedback control systems. Using the
SISO Design Tool, it is possible to graphically tune the gains and dynamics of the
compensator (C) and prefilter (F), using a mix of root locus and loop shaping
techniques. The example window of the SISO Design Tool is shown in Fig. 4.15. In the
upper right area of the window, the currently tested control structure is displayed. More
on the left the values of the compensator parameters are visible, and below them the
resulting root-locus of the system is shown. In the root locus diagram, two lines
corresponding to the inserted values of settling time and the overshoot are also visible.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 86/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
80
Fig. 4.15. SISO Design Tool
Configuration of the system structure is possible by importing transfer functions of
each block from the workspace. This is shown in Fig. 4.16.
Fig. 4.16. Import system data
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 87/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 88/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
82
sxU scΨ ( ) sG
Ψ ( ) sG RΨ
sΨ
Fig. 4.17. Flux control loop
The input data to the SISO Design Tool are obtained based on equations (4.17) and
(4.24). The parameter values are calculated for a 3 kW motor. The motor data are given
in appendix A.3. Required control parameters are set as follows: settling time < 0.003,
overshoot < 4.33%. For these parameters a root loci of the close-loop is obtained, see
Fig. 4.18.
-4500 -4000 -3500 -3000 -2500 -2000 -1500 -1000 -500 0
-1500
-1000
-500
0
500
1000
1500
2e+003 1e+003
0.992
0.97
0.46
0.64 0.24
3e+003
0.78
0.93 0.46
0.97
0.992
0.93
4e+003
0.240.64
0.87
0.87
0.78
Root Locus Editor (C)
Real Axis
I m a g A x i s
Fig. 4.18. Root loci of the close-loop stator flux control system
From the position of the poles, the parameters of the PI flux controller are obtained:
2531= pΨ K , 00074.0=iΨ T .
The behaviour of the flux control loop with parameters like above was tested using
SABER simulation package. The model created in SABER takes into account the full
control system, including the models of inverter and induction motor (see appendix
A.2). The flux step response is presented in Fig. 4.19. The simulation result confirms a
good dynamics of the flux and proper operation in the steady state.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 89/175
4.3. Analysis and Controller Design for DTC-SVM Method
83
Fig. 4.19. Simulated (SABER) flux response for controller parameters designedaccording to root locus method
Torque Controller Design
Based on motor model equations (4.10 - 4.12), the following equation can be
obtained:
( ) ( )mb ssr s sxmb sr syr syr s sr r s
Ω pΩ L L I Ω pΨ LU L I dt
d L L L R L R −+−=
++ σ σ
(4.25)
where:r s
M
L L
L2
1−=σ
Under the assumption that the last term in equation (4.25) is very small:
( ) 0≈− mb ssr s sx Ω pΩ L L I σ (4.26)
the equation (4.25) becomes:
( ) mb sr syr syr s sr r s Ω pΨ LU L I dt
d L L L R L R −=
++ σ (4.27)
The additional assumption is that the motor is not loaded 0= L M .
Under those assumptions the rotor speed can be expressed:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 90/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
84
sy s s
bm I Ψ
m p
J dt
d Ω
2
1= (4.28)
From equation (4.14) current sy I can be expressed as follows:
s sb
e syΨ m p
M I 2
= (4.29)
If both sides of equation (4.27) are differentiated, this equation becomes:
( )dt
d Ω pΨ L
dt
dU L I
dt
d L L
dt
d L R L R m
b sr
sy
r syr s sr r s −=
++
2
σ
(4.30)
Based on the equations (4.30), (4.28) and (4.29) the open-loop torque transfer
function can be obtained as follows:
( ) M M
M
sy
e M
C s B s
s A
U
M sG
++==
2 (4.31)
where: s
s sb M
L
Ψ m p A
σ 2= ;
r s
sr r s M
L L
L R L R B
σ
+= ;
J L
Ψ m pC
s
s sb M
σ 2
22
=
The torque control loop is shown in Fig. 4.20, where ( ) sG RM is a transfer function of
the PI controller given by equation (4.17).
syU e M
( ) sG M ( ) sG RM
ec M
Fig. 4.20. Torque control loop
The input data to the SISO Design Tool are obtained in the same way like for the
flux. The transfer functions are calculated for the 3 kW motor from the equation (4.17)
and (4.31). The required control parameters are set as follows: settling time < 0.0015,
overshoot < 2%. For these parameters a root loci of the close-loop is obtained, see Fig.
4.21. From the position of the poles (Fig. 4.21), the parameters of the PI torque
controller are obtained: 21.33= pM K , 00045.0=iM T .
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 91/175
4.3. Analysis and Controller Design for DTC-SVM Method
85
-7000 -6000 -5000 -4000 -3000 -2000 -1000 0
-2500
-2000
-1500
-1000
-500
0
500
1000
1500
2000
2500
6e+003
0.66
0.78
0.992
0.24
0.480.93
5e+003
0.78
4e+003
0.48
3e+003 2e+0037e+003 1e+003
0.66
0.992
0.87
0.97
0.97
0.93 0.87
0.24
Root Locus Editor (C)
Real Axis
I m a g A x i s
Fig. 4.21. Root loci of the close-loop torque control system
The transfer function of the close loop torque control shown in Fig. 4.20 is given as:
( )( )
( )iM
pM M
M M pM M
iM
iM
pM M
ec
e Mc
T
K AC s B K A s
sT T
K A
M
M sG
++++
+
==2
1
(4.32)
The SISO Design Tool enables to observe the step response of the investigated
control system. In the Fig. 4.22 is shown the step response of the torque control system
from Fig. 4.20 described by equation (4.32), with the PI controller parameters setting as:
21.33= pM K , 00045.0=iM T .
Step Response
Time (sec )
A m p l i t u d e
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4From: r
T o : y
Fig. 4.22. Simulated (Matlab) step response of the system from Fig. 4.20 described by transferfunction given by equation (4.32)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 92/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
86
It should be note that moment of inertia J can change during drive operation (for
example in still industry systems). However, the value of coefficient M C , in equation
(4.32) normally is several order lower in comparison with iM pM M T K A . Therefore,
it’s influence on torque close loop dynamic can be neglected.
Because of the forcing element in transfer function (4.32) the step response presented
in Fig. 4.22 characterized much higher overshoot then the assumed 2%.
To compensate the forcing element in the numerator (4.32) a prefilter is inserted into
the reference channel of the torque controller. The transfer function of the prefilter is
given as:
( ) 11+= sT
sG F
FM (4.33)
The time constant of the prefilter is equal time constant of the torque controller
iM F T T = .
The full control loop of torque with prefilter is shown in Fig. 4.23. The step response
of this control loop is presented in Fig. 4.24.
syU ec M e M ( ) sG M ( ) sG RM ( ) sG FM
Fig. 4.23. Torque control loop with prefilter
Step Response
Time (sec)
A m p l i t u d e
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
x 10-3
0
0.2
0.4
0.6
0.8
1
1.2
1.4From: r
T o : y
Fig. 4.24. Simulated (Matlab) step response of the system from Fig. 4.23
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 93/175
4.3. Analysis and Controller Design for DTC-SVM Method
87
Figure 4.24 shows that the torque control loop with a prefilter incorporated into the
reference channel reduces considerably the overshoot.
The behaviour of the torque control loop with the same settings of the parameters
was also tested in SABER simulation model. The torque step response is presented in
Fig. 4.25. The result of simulation confirms a good dynamics of the torque and proper
operation in the steady state.
Fig. 4.25. Simulated (SABER) torque response
Torque Controller Design for High Power Motor
The same method of tuning the controllers was used for a 90 kW motor. The
parameters of this motor can be found in appendix A.3. The required control parameters
are set as follows: for the flux settling time < 0.003, overshoot < 4.33% and for the
torque settling time < 0.0015, overshoot < 2%. The parameters of the controllers are
obtained as follows: flux controller 2592= pΨ K , 00076.0=
iΨ T and torque controller
8492.1= pM K , 00046.0=iM T .
The simulation model of drive with a 90 kW motor was also build in the SABER
package.
The flux step response is presented in Fig. 4.26. The control loop of the flux is
identical for both motors (Fig. 4.8) and does not depend on the motor parameters.
Therefore, the parameters of the flux controller and the result of simulation (Fig. 4.26)
is very similar to the result for the 3 kW motor (Fig. 4.19).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 94/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
88
The torque response for the 90 kW motor is presented in Fig. 4.27. The results of the
simulations (Fig. 4.26, 4.27), similarly like in the case of the small power ratting motor,
confirm a good dynamics of the torque and a proper operation in the steady state.
Fig. 4.26. Simulated (SABER) flux response for 90 kW motor
Fig. 4.27. Simulated (SABER) torque response for 90 kW motor
4.3.3. Summary of Flux and Torque Controllers Design
In the Fig. 4.28 a full control structure of the DTC-SVM scheme is shown. This
scheme is completed on the prefilter, compared to the basic scheme form Fig. 4.5.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 95/175
4.3. Analysis and Controller Design for DTC-SVM Method
89
The presented above controller tuning algorithm is based on the open-loop transfer
function for the flux (equation 4.24) and for the torque (equation 4.31). These transfer
functions are obtained under the assumptions (4.22) and (4.26) respectively. Because of
the assumed simplifications, the results of full model simulations are slightly differ form
the initially expected values.
scΨ
ec M PI
Flux and
Torque
Estimator
sxcU
ssγ
Torque
Controller
PI
Flux
Controller
sycU
y x −
β α −
e M ˆ
sΨ ˆ
SVM
SA
SB
SC
scU
sI β α −
ABC
A I
B I
Voltage
Calculation
sUdcU
F
Prefilter
Fig. 4.28. Full scheme of the DTC-SVM control method
Additional assumption for the torque controller analysis is that the stator fluxmagnitude is constant. Therefore, decoupling between flux and torque control loops is
important. In Fig. 4.29 the torque step response (Fig. 4.29a) and magnitude stator flux
step response (Fig. 4.29b) are shown. From Fig. 4.29 can be seen that both controllers
are very fast and decoupling between flux and torque is correct.
The full control structure (Fig. 4.28) is different from the basic scheme, which can be
seen in Fig. 4.8. In the torque reference channel a prefilter is incorporated. The basic
structure assumed four controllers parameters: pΨ K , iΨ T , pM K and iM T . The addition
of the prefilter does not introduce any additional parameters, because the time constant
of the prefilter is equal to the torque controller integrating time iM T (see equation 4.33).
Thus the control methods needs only four parameters.
Additionally, if a very fast torque response is not required, the prefilter time constant
can be increased independently from the torque controller parameters in order to
improve the stability of the system.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 96/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
90
a)
b)
Fig. 4.29. Dynamic tests a) torque step change, b) flux step change. From the top: reference and estimatedtorque, reference and estimated stator flux
In section 4.3 two methods of flux and torque controller design for DTC-SVM are
presented. The comparison of the result obtained in two methods is summarized in
Table 4.3. The summary is done for the 3kW motor and sampling frequency
kHz f s 10= . The first method uses simplified IM model and is based on symmetric
optimum criterion. However, this approach gives good results only for flux control loop.
The second approach uses dynamic model of IM including rotor parameters and is
based on root locus method. The results obtained in simulation are good for both flux
and torque controllers. However, it is much more complicated than first method.
The dynamic of the flux control loop is very similar in both cases. Therefore, to tune
flux controller symmetry criterion should be used because it is simpler.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 97/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 98/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
92
All simulation results for root locus method presented in section 4.3.2 were done at
sampling frequency kHz f s 10= . However, presented controller design method
provides to obtain controller parameters for different sampling frequency. This aspect
will be presented for the torque controller. When the sampling frequency is changed theinput parameters: settling time and overshoot must be modified. For lower sampling
frequency the dynamic of control loop is decreasing [34]. Thus, for the continuous
analysis, which is used in root locus method, the settling time should be increased and
overshoot reduced.
Table 4.4 shows torque controller parameters calculated for three sampling frequency
values: kHz f s 10= , kHz f s 5= and kHz f s 5.2= .
Table 4.4. Torque controller parameters for different sampling frequency
f s settling time overshoot K p Μ T i Μ
10.0 kHz 0.0015 2% 33.21 0.00045
5.0 kHz 0.0030 1% 15.88 0.00098
2.5 kHz 0.0060 1% 7.12 0.00180
Simulated results obtained for parameters presented in Table 4.4 are shown in Fig.
4.30. The result of simulation confirms a good behavior of the system for all three
sampling frequencies.
The root locus method gives proper results for different motor type. It confirms
results obtained for the 90 kW motor.
The very important features of the DTC-SVM in comparison with classical DTC are
performance in steady state. In the Fig. 4.31 the steady state operation of the DTC-SVM
control system is shown. It can be seen that the line current is sinusoidal and voltage has
an unipolar waveform. Presented in Fig. 4.31 can be compared with simulation results
for classical DTC from Fig. 3.16, where controller just select voltage vectors to reduce
instantaneous flux and torque errors, and does not implement the true PWM. Therefore,
inverter output voltage is not unipolar. This increase switching losses of the
semiconductor power devices.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 99/175
4.3. Analysis and Controller Design for DTC-SVM Method
93
b)
c)
a)
Fig. 4.30. 3 kW motor torque response for controller parameters calculated according to root locus
method at different sampling frequency a) kHz f s 10= , b) kHz f s 5= , c) kHz f s 5.2=
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 100/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
94
Fig. 4.31. Steady state operation. From the top: line to line voltage, line current
The features of the DTC-SVM method can be summarized as follows:
• good dynamic control of flux and torque,
• constant switching frequency,
• unipolar voltage thanks to use of PWM block (SVM),
• low flux and torque ripple,
• sinusoidal stator currents.
4.4. Speed Controller Design
If the stator flux is assumed constant, .const Ψ s = , that based on the equations (4.13)
and (4.14) dynamic of IM can be described as:
[ ] Lem M M
J dt
d Ω−=
1 (4.34)
A block diagram of the speed control loop is shown in Fig. 4.32, where ( ) sG RS is a
transfer function of PI controller (see equation 4.17) and ( ) sG M
' is a transfer function of
full torque control loop. In the speed controller design process the filter for the
measured value should be taken into consideration. f T is a time constant of the filter.
The low pass filter is necessary in hardware setup.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 101/175
4.4. Speed Controller Design
95
ec M e M mcΩ
L M
J
1( ) sG RS ( ) sG M
'
s
1 mΩ
1
1
+ sT f
Fig. 4.32. Block diagram of the speed control loop
The transfer function of the full torque control loop (Fig. 4.23) can be calculated as:
( ) ( ) ( ) sG sG M M sG Mc FM
ec
e M ⋅==
' (4.35)
where: ( ) sG Mc - torque control loop transfer function given by equation (4.32),
( ) sG FM - prefilter transfer function given by equation (4.33).
The transfer function ( ) sG M
' can by expressed as:
( ) 1'2'
''
++= sC s B
A sG
M M
M M (4.36)
where: pM M iM M
pM M
M K AT C
K A A
+=
';
pM M iM M
iM M
K AT C
T B
+=
';
pM M iM M
M pM M iM
M K AT C
B K AT C
+
+=
'
The torque control loop can be approximate by first order integrating part, because
of:
0'≈ M B (4.37)
The simplified transfer function can be written as:
( )1
'
''
+=
sC
A sG
M
M M (4.38)
For the torque controller parameters 87.15= pM K , 00087.0=iM T obtained in section
4.3.3 at the sampling frequency kHz f s 5= the transfer function parameters have values:
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 102/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
96
9944.0'= M A , 007563.3
'−= e B M , 0009329.0
'= M C . Those parameters confirm that
assumption (4.37) is correct.
The step response of the full and simplified transfer function are shown in Fig. 4.33.
0 0.005 0.01 0.015 0.02 0.025 0.03-5
0
5
10
15
20
25
Time
full transfer
function
simplified
transfer function
Fig. 4.33. Torque response for full and simplified transfer function
For the speed controller parameter design the symmetry criterion can by applied [66].In accordance with the symmetry criterion the plant transfer function can be written as:
( )( )12 1
0
sT sT
e K sG
sτ
c
+=
−
(4.39)
where: ' M c A K = is gain of the plan, 0τ is dead time of the inverter ( 0 0τ = ideal
converter), J T =2 , and f T C T +=1 is a sum of small time constants. The optimal
controller parameters can be calculated as:
( ) ( ) f c
psT C
J
T K
T K
+=
+=
22 01
2
τ (4.40)
( ) f is T C T T +=+= 44 01 τ (4.41)
For the filter frequency Hz f f 25= where:
f f f
T π 2
1= (4.42)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 103/175
4.4. Speed Controller Design
97
the speed controller parameters are obtained as follows: 33.1= ps K ; 0292.0=isT .
Fig. 4.34, 4.35 and 4.36 show simulation and experimental results for the system
operated with speed controller parameters obtained above. The speed reversals are
presented in Fig. 4.34 and 4.35 for high and small reference speed differences
respectively. The step change of the load torque at constant speed is presented in Fig.
4.36. All presented in Fig. 4.34, 4.35 and 4.36 results confirm proper operation of the
speed control loop.
a) b)
Fig. 4.34. Speed reversal srad Ωm /100±= a) simulated (SABER), b) experimental 1) reference speed
(75 (rad/s)/div), 2) actual speed (75 (rad/s)/div), 3) reference torque (20 Nm/div)
a) b)
Fig. 4.35. Speed reversal - small signal srad Ωm /5±= a) simulated (SABER), b) experimental 1)
reference speed (7.5 (rad/s)/div), 2) actual speed (7.5 (rad/s)/div), 3) reference torque (20 Nm/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 104/175
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
98
a) b)
Fig. 4.36. Load torque step change at srad Ωm
/100= a) simulated (SABER), b) experimental
1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div), 3) estimated torque (20 Nm/div)
4.5. Summary
This chapter gives review of DTC-SVM control methods. To analysis and
implementation was chosen DTC-SVM method with close-loop torque and flux control
in stator flux coordinates. Full mathematical analysis of IM drive working with this
control method is presented. Two different flux and torque controllers design algorithm
are analyzed and discussed. Furthermore, speed controller tuning methods is shown.
The flux and torque controller design methods for sampling frequency changes and
different motor power are discussed. The analysis presented in this chapter give
complex knowledge about control structure and controller design methods. Obtained
parameters provide good dynamic and steady state operation of a drive. It is confirmed
by simulation and experimental results presented in this chapter and in Chapter 7.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 105/175
5. Estimation in Induction Motor Drives
5.1. Introduction
The vector control methods of induction motor require feedback signals. This is an
information about flux, torque and mechanical speed in drives operated without
mechanical sensor (sensorless operation mode).
There are many different method to obtain these state variables of induction motor.
Basic methods can be divided into three main group [87]:
• physical methods – based on nonlinear construction of IM [60, 77, 113],
•
mathematical models – used mathematical description of IM and control theory,
• neural network methods – based on the artificial intelligence techniques [9, 91,
95].
The general classification of the state variables calculation methods is presented in
Fig. 5.1 [87].
Induction motor state variables
calculation methods
Physical
methods
Neural network
methods
Estimators of state variables Observer of state variables Kalman Filter
Mathematical
models
Fig. 5.1. Classification of induction state variables calculation methods
The mathematical models is based on the space vector equations, which describe
induction motors. Fig. 5.1 shows division of these methods into three groups:
• estimators of state variables,
• observer of state variables,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 106/175
5. Estimation in Induction Motor Drives
100
•
Kalman filter.
The DTC-SVM method is based on the information about stator flux vector (see
section 4.3). Therefore, it is the most important variable of the motor. Measurement of
flux in motor is difficult and demands special sensor. This solution is very expensive
and complicated. Because of that a method of calculation motor flux was developed.
In vector control methods this part of algorithm is especially important. Estimation
algorithm uses as input signals values, which are simple to measure. There are current
and voltage signals. Obviously new methods aim at reducing number of sensors for
more reliable operation and lower price of a drive.
The motor flux is the main component to calculate torque and speed. Therefore,
accuracy of the estimation flux is very important. Flux estimation is a significant task in
implementing of high-performance motor drives.
The advanced state variables calculation algorithm is characterized by:
•
accuracy in steady and dynamic states,
• robustness for motor parameters variation,
• minimal number of sensor,
• operation in whole speed range,
• low calculation demanded.
All estimation algorithms based on the motor parameters. These parameters change
in time work of the drive. For instance, with change the temperature. Therefore,
estimation algorithm have to be less sensitive to the parameters variations.
All presented flux estimation algorithms are shown as stator flux estimators, because
of these algorithms work with DTC-SVM structure. In some algorithm rotor flux
estimation is required, but in this case it is convert on stator flux.
5.2. Estimation of Inverter Output Voltage
Input signals for the estimators are measurements of stator currents and voltages
which are recreated from the switching signals. Switch signals for the each inverter
phase are obtained by control algorithm. The reference voltage vector is realized by
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 107/175
5.2. Estimation of Inverter Output Voltage
101
modulator (see section 2.4). However, duty times are modified by dead-time, which is
requisite for correct inverter operation (see section 2.3). Because of this modification
delivered to the motor voltage is different from reference. To eliminate dead-time effect
there is a special part for compensation of dead-time in control algorithms. Obtained by
vector modulator duty cycles, represented by switching signals SA, SB, SC are modified
to SA', SB
', SC' (Fig. 5.2). This modification depends on the phase current direction and is
realized for each phase. Many different dead-time compensation methods are presented
in literature [2, 3, 8, 29, 64, 76]. Thanks to this modification after change signals by
dead-time, a correct voltage vector obtained by controller is delivered to the motor.
Because of that signals SA, SB, SC are used to recreate voltage values. The voltage is
calculated form the equations:
( )( )C B Adc sα D D DU U +−= 5.03
2 (5.1a)
( )C Bdc s D DU U −=3
3 β
(5.1b)
where D A, D B, DC are duty cycles corresponding to the switching signals SA, SB, SC
anddcU is the voltage of inverter dc-link.
Vector
Modulator
Voltage
Calculation
Motor
Dead
Time
&
Voltage
Drop
Compen-
sation
SA
SB
SC
SA
'
SB
'
SC
'
Dead
Time
SA+
SA-
SB+
SB-
SC+
SC-
c sU β
c sU α
sI
α sU
dcU
dcU
sI
β sU
Fig. 5.2. Input signals for the estimators
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 108/175
5. Estimation in Induction Motor Drives
102
In Fig. 5.2 voltage calculation block diagram is shown. Simultaneously with dead-
time compensation a voltage drop compensation algorithm is realized. It is especially
important for low speed operation range, when voltage is very low.
The main assumption in voltage calculation method is that identical voltage vector,
which is calculated by a controller is delivered to the motor. It means, proper
information about voltage depends on correct implementation dead-time and voltage
drop compensation algorithms.
Dead – Time Compensation
In order to prevent shortcircuiting an inverter leg, there should be a dead-time (T D)
between the turn-off one switch (IGBT) and the turn-on of the next one (from the same
leg). T D should be larger than the maximum storage time of the switching device. The
effect of the dead-time is a voltage distortion delivered to the motor. The voltage
distortion ∆U is depending on current sign, as can be seen in Fig. 5.3.
D1
D2
C2dcU
2dcU
C
0
SA+
SA-
T1
T2
A
0> A I
D1
D2
C2dcU
2dcU
C
0
SA+
SA-
T1
T2
A
0< A I
b)a)
t
t
SA-
SA+
SA
T D
T D
0
U A0
dcU 2
1
dcU 2
1
t
t
t
t
SA-
SA+
SA
T D
T D
0
U A0
dcU 2
1
dcU 2
1
t
t
0> A I 0< A I
Fig. 5.3. Dead-time effect for different current sing a) 0> A
I , b) 0< A
I
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 109/175
5.2. Estimation of Inverter Output Voltage
103
So the real voltage vector across the motor can be expressed as:
∆UUU scmot −= (5.2)
The voltage distortion ∆U can be written as:
( )sI∆U signU f T dc s D= (5.3)
where: s f - sampling frequency,
( ) sign - signum function.
The dead-time compensation can be implemented by adjusting the phase duty cycles
as following:
( )k s Dk k I sign f T D D +='
(5.4)
where: C B Ak ,,= .
This means that the on-time of the upper bridge arm switch is shortened by T D and
for positive current it is increased by the same amount for negative current.
Because of the current has ripple around zero-crossing the algorithm should be
modified. One of the possible solutions is method with current level. In this method the
current level ( )level I is defined, which describes zone around the zero current as:
level k level I I I >>− (5.5)
If the condition (5.6) is performed the duty cycles are modified as follows:
( )k s D
level
k k k I sign f T
I
I D D +='
(5.6)
In the other cases the duty cycles are modified according to the equation (5.4).
The value of the current level ( )level I depends on the motor power and can be
deducted experimentally. For 3kW drive the optimal value of current level was
A I level 1.0= .
The simulated results for the dead-time compensation algorithms are presented in
Fig. 5.4. In this test drive operates with scalar control (U/f=const.) algorithm at
fundamental frequency Hz f 2=
.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 110/175
5. Estimation in Induction Motor Drives
104
a)
b)
Fig. 5.4. Simulated U/f=const. control method at frequency Hz f 2= a) without dead-time compensation,
b) with dead-time compensation
From Fig. 5.4a it can be seen that without dead-time compensation the output
currents are considerably distorted and has reduced value. Fig. 5.4b shown simulated
result with dead-time compensation algorithm. Thanks of the compensation proper
voltage is delivered to the motor. Therefore, currents have correct value and currents
waveforms are sinusoidal.
Presented dead-time compensation algorithm was implemented in final control
system.
5.3. Stator Flux Vector Estimators
The flux vector estimator algorithms can be divided into two groups in terms of the
input signal. The currents and voltages are the input signals to the voltage models (VM),
while the currents and speed or position information are input signals to the current
models (CM). Obviously, for sensorless control structures general voltage models with
many different modifications and improvements are used.
The stator flux can be directly obtained from the motor model equation (2.10a) as
follows:
( )∫ −= dt R s sss IUΨ (5.7)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 111/175
5.3. Stator Flux Vector Estimators
105
This is a classical voltage model of stator flux vector estimation, which obtain flux
by integrating the motor back electromagnetic force (EMF). The block diagram of this
estimator is shown in the Fig. 5.5.
sU
sI
sΨ
s R
∫
Fig. 5.5. Voltage model based estimator with pure integrators
This method is sensitive for only one motor parameter, stator resistance. However,
the implementation of pure integrator is difficult because of dc drift and initial value
problems. Moreover, when estimator based on pure integrator in control structure are
additional disadvantages. Using a pure integrator to estimate the stator flux it is not
possible to magnetize the machine if a zero torque command is applied [25]. Moreover,
the dynamic performance is lower and torque oscillations are bigger than in another
stator flux estimation method. Because of that many different stator flux estimation
algorithms based on the voltage model were proposed, which does not approach to the
pure integrator [15, 53, 54, 57, 58].
Voltage Model with Low – Pass Filter (VM-LPF)
The simplest method, which eliminates problems with initial conditions and dc drift,
which appear in pure integrator, is a method with low-pass filter. In this case the
equation (5.7) can be transformed as follows:
( ) sss
sΨIU
Ψ ˆ1ˆˆ
F
sT
Rdt
d −−= (5.8)
The block diagram of the method with low-pass filter is presented in Fig. 5.6.
s
1sU
sI
sΨ
s R F T
1
Fig. 5.6. Flux estimator based on voltage model with low-pass filter
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 112/175
5. Estimation in Induction Motor Drives
106
The estimator stabilization time depends on the low-pass filter time constant T F .
Obviously, the low-pass filter produces some errors in phase angle and a magnitude of
stator flux, especially when the motor frequency is lower than the cutoff frequency of
the filter. Therefore, flux estimator with low-pass filter can be used successfully only in
a limited speed range.
Voltage Model with Compensated Low – Pass Filter (VM-CLPF)
One way to overcome the errors introduced by low-pass filter is compensated
algorithm [48]. The block diagram of flux estimator based on a voltage model with
compensated low-pass filter is presented in Fig. 5.7.
sUλ Ω ss
ˆ s +
1
sΨ
ssγ
)ˆ ( sign j ssΩ λ −1
s
sΨ
ssγ
ssˆ Ω
Fig. 5.7. Flux estimator based on voltage model with compensated low-pass filter
In presented method the compensation is carried out before low-pass filtering. The
stator flux is given by equation:
ss
ss
Ω s
Ω sign j
ˆ
)ˆ(1ˆ
λ
λ
+
−=
s
s
E
Ψ (5.9)
where: λ is a positive constant.
The complex-valued gain, instead of calculating the phase error and the gain error, is
used to compensation. Moreover, due to shifting the poles of pure integration from the
origin to ssΩλ − , the drift problems are avoided. The λ factor can be selected in range
from 0.1 to 0.5. For lower λ the transient performance is better, but a higher value of λ
allows bigger system inexactness.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 113/175
5.3. Stator Flux Vector Estimators
107
Voltage Model with Reference Flux (VM-RF)
The block diagram of the estimator based on voltage model with reference flux is
presented in Fig. 5.8 [25].
sU
sI
sΨ
sr γ
rcΨ
rΨ
s
τ
τ
s+1
τ s+
1
1
M
r
L
L
sr j
e γ
r
M
L
L
sI
σ s L
σ s
L
s R
Fig. 5.8. Flux estimator based on voltage model with rotor flux assumed as reference
This estimator calculates rotor and stator flux vector on the basis of stator voltages
and currents, and simultaneously the difference between reference and estimated rotor
flux magnitude is utilizing to correction estimated values.
In this estimator first a rotor flux vector is calculated based on the equation:
)ˆ(ˆ
sr j
rceΨ K dt
d γ −+= rrr
ΨEΨ
(5.10)
where K is the gain factor and r E is the rotor back EMF defined as:
)(dt
d L R
L
L
s sm
r s
ssr
IIUE σ −−= (5.11)
Then assumingτ
1−= K the equation (5.10) can be rewritten yielding:
sr j
rceΨ s s
γ
τ τ
τ ˆ
1
1
1ˆ
++
+= rr EΨ (5.12)
where:
dt d s = (5.13)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 114/175
5. Estimation in Induction Motor Drives
108
From the equation describing the IM in β α − coordinate system (2.15) formulas for
calculation stator flux vector sΨ are obtained.
srs
IΨΨ s
r
m L L
Lσ += ˆˆ (5.14)
This estimator works correctly for a wide speed range, ensures good dynamic
performance, eliminates influence of non correct initial values of the flux level.
Moreover, in this algorithm rotor flux is calculated, which is necessary for rotor speed
calculation (see section 5.5). It is important advantage of this estimator.
The flux estimator based on voltage model with reference flux was selected for the
implementation DTC-SVM control structure in sensorless operation mode (see section
6.2). Presented algorithm is compromise between precision of rotor and stator flux
estimation and computing demand.
Current Model in Rotor Coordinated (CM-RC)
The measured currents and mechanical speed are the input signals for the flux
estimator based on the current model in rotor coordinate.
Coordinate system qd ′−′ rotates with the angular speed of the motor shaft mΩ ,
which can be defined as follows:
dt
d γΩ m
m = (5.15)
Taking into consideration number of pole pairs b p angular speed of the coordinate
system qd ′−′ is equal mb K Ω pΩ = .
The voltage, currents and fluxes complex space vector can be resolved into
components d ′ and q′ .
q sd s K U U ′′ += jsU (5.16a)
q sd s K I I ′′ += jsI , qr d r K I I ′′ += jrI (5.16b)
q sd s K Ψ Ψ ′′ += jsΨ , qr d r K Ψ Ψ ′′ += jrΨ (5.16c)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 115/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 116/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 117/175
5.5. Rotor Speed Estimation
111
stator flux estimator is applied rotor flux can be calculated based on the equations
(5.14).
In the IM mechanical speed is defined as difference between synchronous speed and
sleep frequency:
( ) sl sr
b
m ΩΩ p
Ω −=1
(5.22)
where: sr Ω - rotor synchronous speed,
sl Ω - slip frequency,
b p - number of pole pairs.
The rotor synchronous speed is equal angular speed of the rotor flux vector and can
be calculated as:
dt
d Ω sr
sr
γ = (5.23)
The slip frequency of induction motor is defined as follows [66]:
mb sr sl Ω pΩΩ −= (5.24)
Based on the equations (3.3d) and (3.4d) in rotor flux coordinate system the slip
frequency can be expressed:
sq
r r
M r sl I
Ψ L
L RΩ
1= (5.25)
Taking into consideration the torque equations (3.7) and (5.25) the estimated sleep
frequency can be calculated as follows:
( )α β β α s s s s
r
r sl I Ψ I Ψ
Ψ
RΩ ˆˆ
ˆ 2 −= (5.26)
Finally mechanical motor speed is calculated from the equation (5.22).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 118/175
5. Estimation in Induction Motor Drives
112
5.6. Summary
In this chapter estimation algorithms of flux, torque and rotor speed are presented.
The estimators provide feedback signals for DTC-SVM control scheme. Algorithms
selected to the implementation in final structure are described and discussed.
The speed estimator is based on the estimated stator and rotor fluxes. The mechanical
speed can be calculated in a simple way if motor flux is properly estimated. Therefore,
flux estimation algorithm is the most important part of sensorless control scheme.
Selected flux estimator for the sensorless mode is based on the voltage model. Thus
algorithm is sensitive on accuracy of inverter output voltage calculation. The voltages
are reconstructed from switching signals. In this method dead-time compensation
algorithm is significant. The dead-time effect and compensation algorithm was
presented.
The presented estimation methods are implemented in final DTC-SVM control
structure. The experimental results, presented in Chapter 7 confirm proper operation of
selected estimation methods.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 119/175
6. Configuration of the Developed IM Drive Based on
DTC-SVM
6.1. Introduction
In this chapter a whole implemented control system will be presented. In the first
part, the configuration of the system and operation modes are described. In the next
parts, two hardware setups, which were used to verify DTC-SVM control structure are
presented. To development work was used laboratory setup based on dSPACE company
control board DS1103 PPC. This board has powerful microprocessor and special input-
output interface. The laboratory setup and control board DS1103 will be widely
described in section 6.3. The control algorithm was also implemented in a setup based
on a microcontroller TMS320LF2406 from Texas Instruments company. The
TMS320LF2406 is a 16-bits, fixed point microcontroller devoted for drive application
(see section 6.4).
6.2. Block Scheme of Implemented Control System
The IM drive based on DTC-SVM control structure can operate in three modes:
• scalar control,
• sensor vector control,
• sensorless vector control.
The inverter operate in a mode which is required by application. The system
configuration depends on the switches position, see Fig. 6.1. The most advanced is the
sensorless vector control mode.
In the scalar control mode algorithm obtains command voltage vector based on the
reference frequency. The command voltage vector is realized by space vector modulator
(SVM).
The reference speed in the command signal in the vector control modes. Depending
on mode the reference speed is compared with measured (sensor vector control mode)
or estimated (sensorless vector control mode) speed signal.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 120/175
6. Configuration of the Developed IM Drive Based on DTC-SVM
114
SVM
Scalar
Control
Torque
and Flux
Controller
Switch 1Reference
Frequency
Reference
Speed
References
Value
Estimations
Value
Torque
and Flux
Estimator
SpeedEstimator
Speed
Controller
Inverter
Measurements
Signals
Switch 2 Estimation
Speed
Measurment
Speed
Motor Speed
Sensor
Fig. 6.1. Block scheme of implemented control algorithm
Based on the speed error speed controller calculates reference torque value. The
commanded flux is obtained from the reference speed and selected characteristic, which
depends on the application. The reference values of torque and flux are compared withestimated values. Based on the errors flux and torque controllers calculate command
voltage vector. The command voltage vector is realized by the same space vector
modulator (SVM) algorithm, which is used in scalar control mode. Therefore, depended
on application requirements change between scalar and vector mode is simple.
The measured current and reconstructed voltage are input signals for the estimation
algorithms (see Chapter 5).
An inverter control structure presented in Fig. 6.1 was implemented for IM.
However, this structure can be also used for Permanent Magnet Synchronous Motor
(PMSM) [129].
All presented in Fig. 6.1 blocks are described in previous chapter of the thesis. The
torque, flux and speed controllers are discussed in Chapter 4. The estimation algorithms
are shown in Chapter 5 and different modulation techniques are presented in Chapter 2.
The experimental results for all three operating modes are presented in Chapter 7.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 121/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 122/175
6. Configuration of the Developed IM Drive Based on DTC-SVM
116
In Fig. 6.3 view of the laboratory setup is shown. All parts of the laboratory setup
can be seen in this picture.
dSPACE DS1103 PPC Board
The dSPACE DS1103 PPC is a mixed RISC/DSP digital controller providing a very
powerful processor for floating point calculations as well as comprehensive I/O
capabilities. Here are the most relevant features of the controller:
• Motorola PowerPC 604e running at 333 MHz,
• Slave DSP TI's TMS320F240 Subsystem,
•
16 channels (4 x 4ch) ADC, 16 bit , 4 µs, ±10 V,
• 4 channels ADC, 12 bit , 800 ns, ± 10V,
• 8 channels (2 x 4ch) DAC, 14 bit , ±10 V,6 µs,
• Incremental Encoder Interface -7 channels
• 32 digital I/O lines, programmable in 8-bit groups,
•
Software development tools (Matlab/Simulink, RTI, RTW, TDE, Control Desk)
The DS1103 PPC card is pluged in one of the ISA slot of the motherboard of a host
computer of the type PIII/900MHz, 512 MBRAM, 40GB HDD, Windows 2000. All the
connections are made through six flat cables (50 wires each) available at the backside of
the desktop computer.
The DS1103 PPC is a very flexible and powerful system featuring both high
computational capability and comprenhensive I/O periphery. The board can be
programmed in C language. Additionally, it features a software SIMULINK interface
that allows all applications to be developed in the Matlab/Simulink user friendly
environment. All compiling and downloading processes are carried out automatically in
the background. An experimenting software called Control Desk, allow real-time
management of the running process by providing a virtual control panel with
instruments and scopes.
The detailed parameters of the dSPACE DS1103 PPC board are given in Appendix
A5.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 123/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 124/175
6. Configuration of the Developed IM Drive Based on DTC-SVM
118
Using data acquisition instruments you can capture data from the model running on
the real-time hardware. Changing parameter values is performed by operating input
instruments. The integrated Parameter Editor allows you to read the current parameter
values from the hardware and to change a parameter set in one step.
6.4. Drive Based on TMS320LF2406
DTC-SVM control algorithm was implemented in the drive based on microcontroller
TMS320LF2406. Setup consists of 18 kVA IGBT inverter and 15 kW induction motor.
The view of inverter is shown in Fig. 6.5. In this picture main control board of the
inverter with microprocessor module can be seen.
Fig. 6.5. 18 kVA inverter controlled by TMS320FL2406 processor
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 125/175
6.4. Drive Based on TMS320LF2406
119
The motor set (Fig. 6.6), which was used in tests consists of 15 kW induction motor
and 22 kW DC motor. The induction motor data are given in appendix A.3. The DC
motor works as a load and it is supply from the controlled rectifier.
Fig. 6.6. Motor set. From the left 22 kW DC motor and 15 kW IM motor.
Fig. 6.7. TMS320LF2406 microprocessor board
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 126/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 127/175
6.4. Drive Based on TMS320LF2406
121
Interface (SCI) or Serial Peripheral Interface (SPI). Therefore, program can be loaded
from the PC via standard serial port (RS232).
This way of programming was used during the implementation of DTC-SVM control
algorithm. Thus it was possible to work with the processor without using the expensive
tools like JTAG.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 128/175
7. Experimental Results
7.1. Introduction
In this chapter selected experimental results obtained in the system described in
Chapter 6 are shown. All tests was done for 3 kW induction motor, which parameters
are given in Appendix A3.
7.2. Pulse Width Modulation
In Fig. 7.1 – 7.5 different modulation method are presented. All test was measured at
frequency Hz f 40= .
In Fig. 7.1 space vector modulation method with symmetrical zero vectors placement
– SVPWM is shown (see section 2.4.3).
Fig. 7.1. Space vector modulation (SVPWM) at frequency Hz f 40= 1) switching signal SA,
2) pole voltage U A0 (150 V/div), 3) phase voltage U A (150 V/div), 4) output current I A (5 A/div)
In Fig. 7.2 discontinuous pulse width modulation – DPWM2 is shown (see section
2.4.3). It can be observe differences in pole voltage waveforms and switching signal in
Fig. 7.1 and 7.2. DPWM2 modulation method has 60º no switch sectors. However,
phase voltage and output current have sinusoidal waveforms.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 129/175
7.2. Pulse Width Modulation
123
Fig. 7.2. Discontinuous modulation (DPWM2) at frequency Hz f 40= 1) switching signal SA,
2) pole voltage U A0 (150 V/div), 3) phase voltage U A (150 V/div), 4) output current I A (5 A/div)
In Fig. 7.3 and 7.4 overmodulation (OM) algorithm is shown (see section 2.4.5).
Fig. 7.3. Overmodulation mode I at frequency Hz f 40= 1) switching signal SA, 2) pole voltage
U A0 (150 V/div), 3) phase voltage U A (150 V/div), 4) output current I A (5 A/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 130/175
7. Experimental Results
124
Fig. 7.4. Overmodulation mode II at frequency Hz f 40= 1) switching signal SA, 2) pole voltage
U A0 (150 V/div), 3) phase voltage U A (150 V/div), 4) output current I A (5 A/div)
The results for six-step mode are presented in Fig. 7.5.
Fig. 7.5. Six-step mode at frequency Hz f 40= 1) switching signal SA, 2) pole voltage U A0 (150 V/div),
3) phase voltage U A (150 V/div), 4) output current I A (10 A/div)
Results presented in Fig. 7.3 – 7.5 ware obtained at decreased dc-link voltage.
Therefore, overmodulation and six-step operation modes can be shown with frequency
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 131/175
7.3. Flux and Torque Controllers
125
Hz f 40= like the other results. Thanks to it, current and voltage waveforms can be
better compared.
Experimental results presented in Fig. 7.1 – 7.5 confirm proper operation all type
modulation algorithms.
7.3. Flux and Torque Controllers
Dynamic tests for the flux and torque controller were done for different sampling
frequencies values and the same condition like for simulation presented in section 4.3
(motor speed 0=mΩ ). The flux controller parameters were calculated according to
symmetric optimum criterion (see section 4.3.1) and torque controller parameters were
calculated according to root locus method (see section 4.3.2).
In Fig. 7.6 – 7.8 are presented stator flux step response at sampling frequency
kHz f s 10= , kHz f s 5= , kHz f s 5.2= respectively. Those results can be compared
with simulation results presented in Fig. 4.11.
Fig. 7.6. Stator flux response at sampling frequency kHz f s 10= 1) reference flux (0.15 Wb/div),
2) estimated flux (0.15 Wb/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 132/175
7. Experimental Results
126
Fig. 7.7. Stator flux response at sampling frequency kHz f s 5= 1) reference flux (0.15 Wb/div),
2) estimated flux (0.15 Wb/div)
Fig. 7.8. Stator flux response at sampling frequency kHz f s 5.2= 1) reference flux (0.15 Wb/div),
2) estimated flux (0.15 Wb/div)
Presented in Fig. 7.6 – 7.8 experimental results confirm proper operation of the flux
control loop at different sampling frequency.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 133/175
7.3. Flux and Torque Controllers
127
The experimental results of torque controller dynamic test are shown in Fig. 7.9 –
7.11. Presented results were obtain at sampling frequency kHz f s 10= (Fig. 7.9),
kHz f s 5= (Fig. 7.10), kHz f s 5.2= (Fig. 7.11).
Fig. 7.9. Torque response at sampling frequency kHz f s 10= 1) reference torque (4.5 Nm/div),
3) estimated torque (4.5 Nm/div)
Fig. 7.10. Torque response at sampling frequency kHz f s 5= 1) reference torque (4.5 Nm/div),
3) estimated torque (4.5 Nm/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 134/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 135/175
7.4. DTC-SVM Control System
129
b)
Fig. 7.12. Dynamic tests a) torque step change, b) flux step change1) reference torque (9 Nm/div), 2) estimated torque (9 Nm/div),
3) reference flux (0.3 Wb/div), 4) estimated flux (0.3 Wb/div)
The results from Fig. 7.12 can be compared with simulation results presented in Fig.
4.29. From Fig. 7.12 can be seen that decoupling between flux and torque is correct.
7.4. DTC-SVM Control System
In this section the experimental result for three possible drive operation modes,
which are described in Chapter 6 are shown. Therefore, comparison of a system
behavior in different modes is possible.
In Fig. 7.13 – 7.16 results for scalar control mode are presented. Fig. 7.13 gives
result for system startup to frequency Hz f 40= (motor speed srad Ωm
/125= ).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 136/175
7. Experimental Results
130
Fig. 7.13. Scalar control mode - Startup from 0 to Hz f 40= 1) reference frequency (25 Hz/div),
2) actual speed (30 (rad/s)/div, 4) phase current (10 A/div)
The load torque step change at frequency Hz f 25= is shown in Fig. 7.14.
Fig. 7.14. Scalar control mode - Load torque step change from 0 to N L M M = at frequency Hz f 25=
1) reference frequency (25 Hz/div), 2) actual speed (30 (rad/s)/div), 3) torque (20 Nm/div),4) phase current (10 A/div)
In Fig. 7.15 and 7.16 result of speed reverses are shown ( Hz f 25±= ). The reverse
time is 0.5s (Fig. 7.15) and 5s (Fig. 7.16).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 137/175
7.4. DTC-SVM Control System
131
Fig. 7.15. Scalar control mode - Speed reversal Hz f 25±= (reverse time 0.5s) 1) reference frequency
(25 Hz/div), 2) actual speed (30 (rad/s)/div), 4) phase current (10 A/div)
Fig. 7.16. Scalar control mode - Speed reversal Hz f 25±= (reverse time 5s) 1) reference frequency
(25 Hz/div), 2) actual speed (30 (rad/s)/div), 4) phase current (10 A/div)
In Fig. 7.17 – 7.20 results for sensor vector control mode are presented. Fig. 7.17
gives result for system startup to speed srad Ωm /120= .
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 138/175
7. Experimental Results
132
Fig. 7.17. Vector control mode with speed sensor - Startup from 0 to srad Ωm /120= 1) reference speed
(30 (rad/s)/div), 2) actual speed (30 (rad/s)/div, 4) phase current (10 A/div)
The load torque step change at speed srad Ωm /75= is shown in Fig. 7.18.
Fig. 7.18. Vector control mode with speed sensor - Load torque step change from 0 to N L M M = at
speed srad Ωm /75= 1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div),
3) torque (20 Nm/div), 4) phase current (10 A/div)
In Fig. 7.19 and 7.20 result of speed reverses are shown ( srad Ωm /75±= ). The
reverse time is 0.5s (Fig. 7.19) and 5s (Fig. 7.20).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 139/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 140/175
7. Experimental Results
134
%100ˆ
m
mmΩ
Ω
ΩΩε
m
−= (7.1)
where:
mΩ - actual speed, mΩ - estimated speed.
In Fig. 7.21 speed estimation error as the function of mechanical speed in steady
state is presented.
0 5 10 15 20 25 30 35 40 45 500
5
10
15
20
25
30
35
40
45
50
omega_m [rad/s]
e r r o r_ o m e g a [ % ]
[%]εmΩ
[rad/s]Ωm
Fig. 7.21. Estimated speed error as the function of mechanical speed in steady state.
The results of speed estimator dynamic test are presented in Fig. 22. In this test speed
controller operates with the sensor and speed estimator work in open loop fashion.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 141/175
7.4. DTC-SVM Control System
135
Fig. 7.22. Dynamic test of the speed estimation - Speed reversal srad Ωm /50±= 1) reference speed
(30 (rad/s)/div), 2) actual speed (30 (rad/s)/div), 3) estimated speed (30 (rad/s)/div),
4) error of estimated speed (25 %/div)
In Fig. 7.23 – 7.26 results for sensorless vector control mode are presented. Fig. 7.23
gives result for system startup to speed srad Ωm /120= .
Fig. 7.23. Sensorless vector control mode - Startup from 0 to srad Ωm /120= 1) reference speed
(30 (rad/s)/div), 2) actual speed (30 (rad/s)/div, 4) phase current (10 A/div)
The load torque step change at speed srad Ωm /75= is shown in Fig. 7.24.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 142/175
7. Experimental Results
136
Fig. 7.24. Sensorless vector control mode - Load torque step change from 0 to N L M M = at speed
srad Ωm /75= 1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div),
3) torque (20 Nm/div), 4) phase current (10 A/div)
In Fig. 7.25 and 7.26 result of speed reverses are shown ( srad Ωm /75±= ). The
reverse time is 0.5s (Fig. 7.25) and 5s (Fig. 7.26).
Fig. 7.25. Sensorless vector control mode - Speed reverse srad Ωm
/75±= (reverse time 0.5s)
1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div), 4) phase current (10 A/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 143/175
7.4. DTC-SVM Control System
137
Fig. 7.26. Sensorless vector control mode - Speed reverse srad Ωm
/75±= (reverse time 5s)
1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div), 4) phase current (10 A/div)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 144/175
8. Summary and Conclusions
In this thesis the most convenient industrial control scheme for voltage source
inverter-fed induction motor drives was searched for, based on the existing control
methods. This method should provide: operation in wide power range, guarantee good
and repeatable parameters of drive. It is required by a serial production of a drive. To
achieve a low costs the control system should be implemented in simple
microprocessor. The analysis of existing methods were done in order to chose the
industrial oriented universal scheme.
The most important control techniques of IM were presented in Chapter 3: Field
Oriented Control (FOC), Feedback Linearization Control (FLC) and Direct Torque
Control (DTC). The FLC structure guarantees exact decoupling of the motor speed and
rotor flux control in both dynamic and steady states. However, it is complicated and
difficult to implement in practice. This method requires complex computation and
additionally it is sensitive to changes of motor parameters. Because of these features
this method was not chosen for implementation. In next step FOC and DTC methods
were analyzed. Characteristics of those methods were done on the basis of the literature,
simulation and experimental investigation. The conclusions of those consideration were
shown in section 3.5.
Analysis of advantages and disadvantages of FOC and DTC methods resulted in a
search for method which will eliminate disadvantages and keep advantages of those
methods. The direct torque control with space vector modulation (DTC-SVM) is an
effect of this search. The main features of this method can be summarized as:
• Space vector modulator,
• Constant switching frequency,
• Unipolar voltage thanks to use of PWM block (SVM),
• Sinusoidal waveform of stator currents,
• Algorithm operates with torque and flux value – implementation in
manufacturing process is easier,
•
Good dynamic control of flux and torque. The step responses are slower than in
classical DTC, because PI controllers are slower than hysteresis controllers,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 145/175
8. Summary and Conclusions
139
which are used in classical DTC. However, obtained dynamic (response time for
the torque 1.5-2ms) is sufficient for general purpose drives.
• High sampling frequency is not required. The DTC-SVM algorithm works
properly at sampling frequency kHz f s 5= whereas DTC requires sampling
frequency at least kHz 4025 − .
• Low flux and torque ripple than in classical DTC. The torque ripples in DTC-SVM
at sampling frequency kHz f s 5= are ten times lower than presented in section
3.4.2 torque ripples for classical DTC at sampling frequency kHz f s 40= .
The DTC-SVM scheme is based only on the analysis of stator equations like classical
DTC, therefore control algorithm is not sensitive to rotor parameters changes. This
method can be applied also for surface mounted permanent magnet (PM) synchronous
motors [129]. The PM synchronous motors of this type are more frequently used in
standard speed drives as interior PM. Hence, DTC-SVM method allows universal drive
building for both types of AC motors.
The very important part of DTC-SVM scheme is a space vector modulator. The
different modulation techniques can be applied in the system. Therefore, a drive has
additional advantages. The most important is full range of voltage control and reduction
of switching losses. For instance, reduction of switching losses can be obtained by
implementation of discontinuous PWM methods. These modulation techniques were
described and characterized in section 2.4. The experimental results for the
implemented modulation methods were shown in Chapter 7.
The short review of DTC-SVM methods proposed in literature were given in section
4.2. For further consideration the DTC-SVM method with close-loop torque and flux
control in stator flux Cartesian coordinates have been chosen. In author opinion this
method is best suited for commercial manufactured drives. For chosen scheme two
controller design procedures were proposed. Those analysis were presented in Chapter 4.
Also correction of controllers parameters for sampling frequency changes was discussed.
In adjustable speed drive superior speed controller is used. The analysis of speed
control loop and controller tuning were presented in section 4.4. Correctness of used
method was confirmed by simulation and experimental results.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 146/175
8. Summary and Conclusions
140
The quality of regulation process depends on an accuracy of feedback signals. In the
vector control of induction motor those signals are provided by flux and torque
estimators and, in sensorless operation mode, by a speed estimator. The precision of
estimated signals depends on:
• exact knowledge of motor parameters,
• good dead-time and voltage drop compensation algorithms,
• well realized measurements,
• implementation of on-line adaptation of motor parameters.
Those features are common for all vector control methods. Therefore, if feedback
signals are estimated accurately, the control scheme should be as simple as possible.
The DTC-SVM has a simple structure and it can be analyzed and implemented in a
simple way. It is very important feature of DTC-SVM.
Estimation problems in a drive with induction motor were discussed in Chapter 5.
Following estimation algorithms, selected for implementation, were presented: voltage
estimator with dead-time compensation algorithm, stator flux estimator, torque
estimator and mechanical speed estimator.
All parts of control scheme were verified in simulation and experiment. The whole
scheme consists of: flux and torque controllers, speed controller, estimation of flux,
torque and speed and compensation algorithms. Those complete structure was presented
in Chapter 6. Proposed solution was implemented in 3 kW experimental and 15 kW
industrial drives. The laboratory setups were also presented in Chapter 6.
Presented in Chapter 7 experimental results confirm proper operation of developed
control system.
Thus, thesis shows the process to select and develop the most convenient control
scheme for voltage source inverter-fed induction motor drives. Whole problems of
direct flux and torque control with space vector modulation (DTC-SVM) were analyzed
and investigated in simulation and experiment.
Finally, it should be stressed that the developed system was brought into serial
production. Presented algorithm has been used in new family of inverter drives
produced by Polish company Power Electronic Manufacture – „TWERD”, Toruń.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 147/175
References
[1] V. Ambrozic, G.S. Buja, R. Menis, "Band-Constrained Technique for Direct Torque Control of
Induction Motor", IEEE Transactions on Industrial Electronics, Vol. 51, Issue: 4, Aug. 2004, pp.776 - 784.
[2] C. Attaianese, D. Capraro, G. Tomasso, "A low cost digital SVM modulator with dead time
compensation", Power Electronics Specialists Conference, PESC. 2001 IEEE 32nd Annual, Vol. 1,
17-21 June 2001, pp.158-163.
[3] C. Attaianese, D. Capraro, G. Tomasso, "Hardware dead time compensation for VSI based
electrical drives", IEEE International Symposium on Industrial Electronics, Proceedings ISIE
2001, Vol. 2, 12-16 June 2001, pp.759-764.
[4]
U. Baader, M. Depenbrock, G. Gierse, "Direct Self Control (DSC) of Inverter-Fed-Inducktion
Machine - A Basis for Speed Control Without Speed Measurement", IEEE Trans. of Industry
Applications, Vol. 28, No. 3 May/June 1992, pp.581-588.
[5] M. M. Bech, "Analysis of Random Pulse-Width Modulation Techniques for Power Electronic
Converters", Alborg University, Denmark Institute of Energy Technology, August 2000.
[6] M.M. Bech, F. Blaabjerg, J.K. Pedersen, "Random modulation techniques with fixed switching
frequency for three-phase power converters", IEEE Transactions on Power Electronics, Vol. 15,
Issue: 4, July 2000, pp.753-761.
[7] M.M. Bech, J.K. Pedersen, F. Blaabjerg, A.M. Trzynadlowski, "A methodology for true
comparison of analytical and measured frequency domain spectra in random PWM converters",
IEEE Transactions on Power Electronics, Vol. 14, Issue: 3, May 1999, pp.578-586.
[8] L. Ben-Brahim, "The analysis and compensation of dead-time effects in three phase PWM
inverters", Industrial Electronics Society, 1998. IECON '98. Proceedings of the 24th Annual
Conference of the IEEE, Vol. 2d, 31 Aug.-4 Sept. 1998, pp.792-797.
[9] L. Ben-Brahim, R. Kurosawa, "Identification of induction motor speed using neural networks",
Record of the Power Conversion Conference, Yokohama 1993, 19-21 April 1993, pp.689-694.
[10] M. Bertoluzzo, G. Buja, R. Menis, "Analytical formulation of the direct control of induction motor
drives", Proceedings of the IEEE International Symposium on Industrial Electronics, ISIE '99, Vol.
1, 12-16 July 1999, pp.PS14-PS20.
[11] T. Biskup, J. Teluk, "Modulacja stochastyczna. Badania eksperymentalne wpływu rozk ładu
prawdopodobieństwa generatora losowego na efekty akustyczne", SENE'99, Łódź-Arturówek, 17-
19 Nov. 1999, pp.65-70.
[12] F. Blaschke, "The principle of fiels-orientation as applied to the Transvector closed-loop control
system for rotating-field machines", in Siemens Reviev 34, 1972, pp.217-220.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 148/175
References
142
[13] V. Blasko, "Analysis of a hybrid PWM based on modified space-vector and triangle-comparison
methods", IEEE Transactions on Industry Applications, Vol. 33, Issue: 3, May-June 1997, pp.756-
764.
[14] S. Bolognani, A. Di Bella, M. Zigliotto, "Random modulation and acoustic noise reduction in IM
drives: a case study", Ninth International Conference on Electrical Machines and Drives, (Conf.
Publ. No. 468), 1-3 Sept. 1999, pp.137 - 141.
[15] C.J. Bonanno, Li Zhen, Longya Xu, "A direct field oriented induction machine drive with robust
flux estimator for position sensorless control", Industry Applications Conference, 1995. Thirtieth
IAS Annual Meeting, IAS '95., Conference Record of the 1995 IEEE, Vol. 1, 8-12 Oct. 1995,
pp.166-173.
[16] B. K. Bose, "Modern Power Electronics and AC drives", Prentice-Hall, 2002.
[17] G. Buja, D. Casadei, G. Serra, "Direct stator flux and torque control of an induction motor:
theoretical analysis and experimental results", Proceedings of the 24th Annual Conference of the
IEEE Industrial Electronics Society, IECON '98, Vol. 1, 31 Aug.-4 Sept. 1998, pp.T50-T64.
[18] G. Buja, D. Casadei, G. Serra, "DTC-based strategies for induction motor drives", 23rd
International Conference on Industrial Electronics, Control and Instrumentation, IECON 97, Vol.
4, 9-14 Nov. 1997, pp.1506-1516.
[19] G.S. Buja, M.P. Kazmierkowski, "Direct Torque Control of PWM Inverter-Fed AC Motors-A
Survey", IEEE Transactions on Industrial Electronics, Vol. 51, Issue: 4, Aug. 2004, pp.744-757.
[20]
D. Casadei, F. Profumo, G. Serra, A. Tani, "FOC and DTC: two viable schemes for induction
motors torque control", IEEE Transactions on Power Electronics, Vol. 17, Issue: 5, Sept. 2002,
pp.779-787.
[21] D. Casadei, G. Grandi, G. Serra, A. Tani, "Effects of flux and torque hysteresis band amplitude in
direct torque control of induction machines", 20th International Conference on Industrial
Electronics, Control and Instrumentation, IECON '94, Vol. 1, 5-9 Sept. 1994, pp.299-304.
[22] D. Casadei, G. Grandi, G. Serra, A. Tani, "Switching Strategies in Direct Torque Control of
Induction Machines", Proc. of ICEM Conf., D8.11, 1994, pp.204-209.
[23] D. Casadei, G. Serra, A. Tani, "Analytical Investigation of Torque and Flux Ripple in DTC
Schemes for Induction Motors", Proceedings of the IECON Conference, 1997, pp. 552-556.
[24] D. Casadei, G. Serra, A. Tani, "Constant frequency operation of a DTC induction motor drive for
electric vehicle", Proc. of ICEM Conf., Vol. 3, 1996, pp. 224-229.
[25] D. Casadei, G. Serra, A. Tani, "Steady-state and transient performance evaluation of a DTC
scheme in the low speed range", IEEE Transactions on Power Electronics, Vol. 16, Issue: 6, Nov.
2001, pp.846-851.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 149/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 150/175
References
144
[40] P.Z. Grabowski, M.P. Kazmierkowski, B.K. Bose, F. Blaabjerg, "A simple direct-torque neuro-
fuzzy control of PWM-inverter-fed induction motor drive", IEEE Transactions on Industrial
Electronics, Vol. 47, Issue: 4, Aug. 2000, pp.863 - 870.
[41] Z. Grunwald, M. P. Kaźmierkowski, W. Koczara, J. Łastowiecki, G. Przywara, "Napę d
elektryczny", Wydawnictwa Naukowo-Techniczne WNT, Warszawa, 1978.
[42] T.G. Habetler, D.M. Divan, "Control strategies for direct torque control using discrete pulse
modulation", IEEE Transactions on Industry Applications, Vol. 27, Issue: 5, Sept.-Oct. 1991,
pp.893-901.
[43] T.G. Habetler, F. Profumo, M. Pastorelli, "Direct torque control of induction machines over a wide
speed range", Conference Record of the 1992 IEEE Industry Applications Society Annual
Meeting, Vol.14-9 Oct. 1992, pp.600-606.
[44] T.G. Habetler, F. Profumo, M. Pastorelli, L.M. Tolbert, "Direct torque control of induction
machines using space vector modulation", Conference Record of the 1991 IEEE Industry
Applications Society Annual Meeting, Vol.1, 28 Sept.-4 Oct. 1991, pp.428-436.
[45] K. Hasse, "Drehzahlregelverfahren fur schnelle Umkehrantriebe mit stromrichtergespeisten
Asynchron-Kurzschlusslaufermotoren", in Regelungstechnik 20, 1972, pp.60-66.
[46] A.M. Hava, R.J. Kerkman, T.A. Lipo, "A high performance generalized discontinuous PWM
algorithm", Applied Power Electronics Conference and Exposition, APEC '97 Conference
Proceedings 1997, Twelfth Annual, Vol. 2, 23-27 Feb. 1997, pp.886-894.
[47]
A.M. Hava, R.J. Kerkman, T.A. Lipo, "Simple analytical and graphical tools for carrier based
PWM methods", Power Electronics Specialists Conference, PESC '97 Record, 28th Annual IEEE,
Vol. 2, 22-27 June 1997, pp.1462-1471.
[48] M. Hinkkanen, J. Luomi, "Modified integrator for voltage model flux estimation of induction
motors", IEEE Transactions on Industrial Electronics, Vol. 50, Issue: 4, Aug. 2003, pp.818-820.
[49] F. Hoffman, M. Janecke, "Fast Torque Control of an IGBT-Inverter-Fed Tree-Phase A.C. Drive in
the Whole Speed Range - Experimental Result", Proc. EPE Conf., 1995, pp.3.399-3.404.
[50] D.G. Holmes, "A general analytical method for determining the theoretical harmonic components
of carrier based PWM strategies", Industry Applications Conference, Thirty-Third IAS Annual
Meeting. The 1998 IEEE, Vol. 2, 12-15 Oct. 1998, pp.1207-1214.
[51] D.G. Holmes, "The significance of zero space vector placement for carrier-based PWM schemes",
IEEE Transactions on Industry Applications, Vol. 32, Issue: 5, Sept.-Oct. 1996, pp.1122-1129.
[52] J. Holtz, "Pulsewidth modulation for electronic power conversion", Proceedings of the IEEE, Vol.
82, Issue: 8, Aug. 1994, pp.1194-1214.
[53] J. Holtz, "Sensorless control of induction motor drives", Proceedings of the IEEE, Vol. 90, Issue:
8, Aug. 2002, pp.1359-1394.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 151/175
References
145
[54] J. Holtz, Juntao Quan, "Sensorless vector control of induction motors at very low speed using a
nonlinear inverter model and parameter identification", IEEE Transactions on Industry
Applications, Vol. 38, Issue: 4, July-Aug. 2002, pp.1087-1095.
[55] J. Holtz, W. Lotzkat, A.M. Khambadkone, "On continuous control of PWM inverters in the
overmodulation range including the six-step mode", IEEE Transactions on Power Electronics, Vol.
8, Issue: 4, Oct. 1993, pp.546-553.
[56] K. B. Howell, "Principles of Fourier analysis", CHAPMAN & HALL/CRC, Boca Raton London
New York Washington, D.C., 2001.
[57] Jun Hu, Bin Wu, "New integration algorithms for estimating motor flux over a wide speed range",
IEEE Transactions on Power Electronics, Vol. 13, Issue: 5, Sept. 1998, pp.969-977.
[58] Hu Hu, Yong Dong Li, Yi Zeng, "Direct torque control of induction motor for railway traction in
whole speed range", IECON 02, Industrial Electronics Society, IEEE 2002 28th Annual
Conference, Vol. 3, 5-8 Nov. 2002, pp.2161-2166.
[59] K. D. Hurst, T. G. Habetler, "A Simple, Tacho-Less, I.M. Drive with Direct Torque Control Down
to Zero Speed", Proceedings of the IECON Conference, Vol.2, 1997, pp.563-568.
[60] K.D. Hurst, T.G. Habetler, G. Griva, F. Profumo, "Speed sensorless field-oriented control of
induction machines using current harmonic spectral estimation", Conference Record of the 1994
IEEE Industry Applications Society Annual Meeting, Vol.1, 2-6 Oct. 1994, pp.601-607.
[61] C.B. Jacobina, A.M.N. Lima, E.R.C. da Silva, A.M. Trzynadlowski, "Current control for induction
motor drives using random PWM", IEEE Transactions on Industrial Electronics, Vol. 45, Issue: 5,
Oct. 1998, pp.704-712.
[62] M. Jayne, I. Ludtke, Liang Yiqiang, T. Arias, "Evaluation of vector and direct torque controlled
strategies for cage rotor induction motor drives", The Third International Power Electronics and
Motion Control Conference, Proceedings PIEMC 2000, Vol. 1, 15-18 Aug. 2000, pp.452-457.
[63] F. Jenni, D. Wueest, "The optimization parameters of Space Vector Modulation", proc. EPE Conf.,
Vol. 4, 1993, pp. 376-381.
[64] Jong-Lick Lin, "A new approach of dead-time compensation for PWM voltage inverters", IEEE
Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 49, Issue: 4,
April 2002, pp.476-483.
[65] M.P. Kazmierkowski, A.B. Kasprowicz, "Improved direct torque and flux vector control of PWM
inverter-fed induction motor drives", IEEE Transactions on Industrial Electronics, Vol. 42, Issue:
4, Aug. 1995, pp.344-350.
[66] M. P. Kazmierkowski, H. Tunia, "Automatic Control of Converter Fed Drives", ELSEVIER
Amsterdam-London-New York-Tokyo, 1994.
[67]
M.P. Kazmierkowski, R. Krishnan, F. Blaabjerg, "Control in Power Electronics Selected
Problems", Academic Press, 2002.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 152/175
References
146
[68] R.L. Kirlin, A.M. Trzynadlowski, "A unified approach to analysis and design of random
pulsewidth modulation in voltage-source inverters", IEEE Transactions on Circuits and Systems-I:
Fundamental Theory and Applications, Vol. 44, Issue: 8, Aug. 1997, pp.763-766.
[69] Z. Krzemiński, "Cyfrowe sterowanie maszynami asynchronicznymi", Wydawnictwo Politechniki
Gdańskiej, Gdańsk 2001.
[70] Z. Krzemiński, "Nonlinear Control of Induction Motors", in Proc. of 10th IFAC World Congress,
Munich, Germany, 1997, pp.349-354.
[71] Y.-S. Lai, W.-K. Wang, Y.-C. Chen, "Novel Switching Techniques for Reducing the Speed Ripple
of AC Drives With Direct Torque Control", IEEE Transactions on Industrial Electronics, Vol. 51,
Issue: 4, Aug. 2004, pp.768-775.
[72] C. Lascu, A.M. Trzynadlowski, "Combining the principles of sliding mode, direct torque control,
and space-vector modulation in a high-performance sensorless AC drive", IEEE Transactions on
Industry Applications, Vol. 40, Issue: 1, Jan.-Feb. 2004, pp.170-177.
[73] C. Lascu, I. Boldea, F. Blaabjerg, "Variable-Structure Direct Torque Control-A Class of Fast and
Robust Controllers for Induction Machine Drives", IEEE Transactions on Industrial Electronics,
Vol. 51, Issue: 4, Aug. 2004, pp.785-792.
[74] Joong-Hui Lee, Chang-Gyun Kim, Myung-Joong Youn, "A dead-beat type digital controller for
the direct torque control of an induction motor", IEEE Transactions on Power Electronics, Vol. 17,
Issue: 5, Sept. 2002, pp.739-746.
[75]
Dong-Choon Lee, G-Myoung Lee, "A novel overmodulation technique for space-vector PWM
inverters", IEEE Transactions on Power Electronics, Vol. 13, Issue: 6, Nov. 1998, pp.1144-1151.
[76] D. Leggate, R.J. Kerkman, "Pulse based dead time compensator for PWM voltage inverters",
Proceedings of the 1995 IEEE IECON 21st International Conference on Industrial Electronics,
Control, and Instrumentation, Vol. 1, 6-10 Nov. 1995, pp.474-481.
[77] R.D. Lorenz "Sensorless, drive control methods for stable, high performance, zero speed
operation", proc. EPE-PEMC Conf., Kosice, 2000, pp. 1.1-1.11.
[78] I. Ludtke, M.G. Jayne, "A new direct torque control strategy", IEE Colloquium on Advances in
Control Systems for Electric Drives, 24 May 1995, pp.5/1-5/4.
[79] M. Malinowski "Adaptive modulator for three-phase PWM rectifier/inverter", in proc. EPE-PEMC
Conf., Kosice, 2000, pp.1.35-1.41.
[80] M. Malinowski, "Sensorless Control Strategies for Three-Phase PWM Rectifiers", PhD Thesis,
Warsaw University of Technology, 2001.
[81] R. Marino, P. Valigi, "Nonlinear control of induction motors: a simulation study", in European
Control Conference, Grenoble, France, 1991, pp.1057-1062.
[82]
R. Marino, S. Peresada, P. Valigi, "Adaptive input-output linearizing control of induction motors",
IEEE Transactions on Automatic Control, Vol. 38, Issue: 2, Feb. 1993, pp.208 - 221.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 153/175
References
147
[83] R. Marino, S. Peresada, P. Valigi, "Adaptive partial feedback linearization of induction motors", in
Proc. of the 29th Conference on Decision and Control, Honolulu, Hawaii, Dec. 1990, pp.3313-
3318.
[84] MathWorks, Inc, "Matlab® The Language of Technical Computing", Release 12, 2000.
[85] S.A. Mir, M.E. Elbuluk, D.S. Zinger, "Fuzzy implementation of direct self-control of induction
machines", IEEE Transactions on Industry Applications, Vol. 30, Issue: 3, May-June 1994,
pp.729-735.
[86] K. Ogata, "Modern control engineering", Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1990.
[87] T. Or łowska-Kowalska, "Bezczujnikowe uk łady napę dowe z silnikami indukcyjnymi", Officyna
Wydawnicza Politechniki Wrocławskiej, Wrocław 2003.
[88] R. Ortega, A. Loria, P. J. Nicklasson, H. Sira-Ramirez, "Passivity-based Control of Euler-Lagrange
Systems", Springer Verlag, London, 1998.
[89] J.O.P. Pinto, B.K. Bose, L.E.B. Da Silva, M.P. Kazmierkowski, "A neural-network-based space-
vector PWM controller for voltage-fed inverter induction motor drive", IEEE Transactions on
Industry Applications, Vol. 36, Issue: 6, Nov.-Dec. 2000, pp.1628-1636.
[90] K.L. Shi, T.F. Chan, Y.K, Wong, S.L. Ho, "Direct self control of induction motor based on neural
network", IEEE Transactions on Industry Applications, Vol. 37, Issue: 5, Sept.-Oct. 2001,
pp.1290-1298.
[91] M.G. Simoes, B.K. Bose, "Neural network based estimation of feedback signals for a vector
controlled induction motor drive", IEEE Transactions on Industry Applications, Vol. 31, Issue: 3,
May-June 1995, pp.620-629.
[92] D.L. Sobczuk, "Application of ANN for control of PWM inverter fed induction motor drives", PhD
Thesis, Warsaw University of Technology, 1999.
[93] D.L. Sobczuk, "Feedback linearization control of inverter fed induction motor-DSP
implementation", Proceedings of the 2002 IEEE International Symposium on Industrial
Electronics, ISIE 2002, Vol. 2, 8-11 July 2002, pp.678-682.
[94]
D.L. Sobczuk, "Feedback linearization control of inverter fed induction motor-with sliding modeflux observer", Electrical Drives and Power Electronics International Conference, Slovakia 2003,
pp.465-469.
[95] D.L. Sobczuk, P.Z. Grabowski, "DSP implementation of neural network speed estimator for
inverter fed induction motor", Proceedings of the 24th Annual Conference of the IEEE Industrial
Electronics Society, IECON '98, Vol. 2, 31 Aug.-4 Sept. 1998, pp.981-985.
[96] A. Steimel, "Direct Self-Control and Synchronous Pulse Techniques for High-Power Traction
Inverters in Comparison", IEEE Transactions on Industrial Electronics, Vol. 51, Issue: 4, Aug.
2004, pp.810-820.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 154/175
References
148
[97] I. Takahashi, T. Noguchi, "A new quick-response and high efficiency control strategy of an
induction machine", IEEE Trans. on Industrial Application, Vol. IA-22, no.5, Sept./Oct. 1986,
pp.820-827.
[98] I. Takahashi, T. Noguchi, "Take a Look Back upon the Past Decade of Direct Torque Control",
Proc. of IECON Conf., Vol. 2, 1997, pp.546-551.
[99] Texas Instruments Incorporated, "TMS320F/C24x DSP Controllers Reference Guide, CPU and
Instruction Set", Literature Number: SPRU160C, 1999.
[100] Texas Instruments Incorporated, "TMS320LF/LC240xA DSP Controllers Reference Guide,
System and Peripherals", Literature Number: SPRU357B, 2002.
[101] Texas Instruments Incorporated, "TMS320LF2407A, TMS320LF2406A, TMS320LF2403A,
TMS320LF2402A TMS320LC2406A, TMS320LC2404A, TMS320LC2402A DSP Controllers",
Literature Number: SPRS145I, 2003.
[102] P. Tiitinen, "The Next Generation Motor Control Method, Direct Torque Control, DTC", PEDES -
New Delhi Conf. Rec., 1996, pp.37-43.
[103] P. Tiitinen, M. Surandra, "The next generation motor control method, DTC direct torque control",
Power Electronics, Proceedings of the 1996 International Conference on Drives and Energy
Systems for Industrial Growth, Vol. 1, 8-11 Jan. 1996, pp.37-43.
[104] A.M. Trzynadlowski, F. Blaabjerg, J.K. Pedersen, R.L. Kirlin, S. Legowski, "Random pulse width
modulation techniques for converter-fed drive systems-a review", IEEE Transactions on Industry
Applications, Vol. 30, Issue: 5, Sept.-Oct. 1994, pp.1166-1175.
[105] A.M. Trzynadlowski, S. Legowski, "Minimum-loss vector PWM strategy for three-phase
inverters", IEEE Transactions on Power Electronics, Vol. 9, Issue: 1, Jan. 1994, pp.26-34.
[106] H. Tunia, M. P. Kazmierkowski, "Automatyka napę du przekształtnikowego", Warszawa PWN
1987.
[107] J.W. Umland, M. Safiuddin, "Magnitude and Symmetric Optimum Criterion for the Design of
Linear Control Systems: What Is It and How Does It Compare with the Others?", IEEE
Transactions on Industry Applications, Vol. 26, Issue: 3, May-June 1990, pp.489-497.
[108] P. Vas, "Sensorless Vector and Direct Torque Control", Oxford University Press, 1998.
[109] A.M. Walczyna, "Reduction of current distortions of VSI-fed induction machine controlled by
DSC method-generalized approach", IEEE International Symposium on Industrial Electronics,
Conference Proceedings, ISIE'93 - Budapest, 1-3 June 1993, pp.457-462.
[110] A.M. Walczyna, R.J. Hill, "Novel PWM strategy for direct self-control of inverter-fed induction
motors", IEEE International Symposium on Industrial Electronics, Conference Proceedings,
ISIE'93-Budapest, 1-3 June 1993, pp.610-615.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 155/175
References
149
[111] Y. Xue, X. Xu, T.G. Habetler, D.M. Divan, "A low cost stator flux oriented voltage source variable
speed drive", Conference Record of the 1990 IEEE Industry Applications Society Annual Meeting,
Vol.1, 7-12 Oct. 1990, pp.410-415.
[112] Z. Yan, C. Jin, V. Utkin, "Sensorless Sliding-Mode Control of Induction Motors", IEEE
Transactions on Industrial Electronics, Vol. 47, Issue: 6, Dec. 2000, pp.1286-1297.
[113] D.S. Zinger, F. Profumo, T.A. Lipo, D.W. Novotny, "A direct field-oriented controller for
induction motor drives using tapped stator windings", IEEE Transactions on Power Electronics,
Vol. 5, Issue: 4, Oct. 1990, pp.446-453.
Papers written during work on this thesis
[114] M. Żelechowski, P. Grabowski, "Universal board - ICG240 for induction motor control drives",
International XII Symposium on Micromachines and Servodrives, Kamień Ślą ski, Sep. 2000,
pp.475-479. (in Polish)
[115] M. Żelechowski, P. Grabowski, "SimTor – New Vector Controller for Energy-Efficient Inverter
Fed Induction Motor Drives", International Scientific Conference "Energy Saving in Electrical
Engineering", Proceedings 80th Anniversary of the Faculty of Electrical Engineering at the
Warsaw University of Technology, Warsaw, May 2001, pp.370-372.
[116] M. Żelechowski, M. P. Kaźmierkowski, P. Grabowski, "Practical implementation of direct torque
control of induction motor drive with space vector modulation", XXXVIII International
Symposium on Electrical Machines, Cedzyna-Kielce, June 2002, pp.237-243. (in Polish)
[117] D. Świerczyński, M. Żelechowski, "Direct torque and flux control of synchronous and
asynchronous motors", II Krajowa Konferencja MiS-2 Modelowanie i Symulacja, Kościelisko,
June 2002, pp.187-194. (in Polish)
[118] D. Świerczyński, M. Żelechowski, "Universal structure direct torque control for synchronous
permanent magnet and asynchronous motors", International XIII Symposium on Micromachines
and Servodrives, Krasiczyn, Sep. 2002, pp.333-340. (in Polish)
[119]
A. M. Trzynadlowski, Z. Wang, J. Nagashima, C. Stancu, M. Żelechowski, "Comparative
Investigation of PWM Techniques for General Motors’ New Drive for Electric Vehicles", Industry
Applications Conference, 37th IAS Annual Meeting, 2002, pp.2010-2015.
[120] M. Żelechowski, P. Kaczyński, M. P. Kaźmierkowski, "Parameters estimation of PWM inverter-
fed induction motor", 39th International Symposium on Electrical Machines, Gdańsk-Jurata, June
2003, pp.60.
[121] D. Świerczyński, M. Żelechowski, "Universal structure of direct torque control for AC motor
drives”, III Summer Seminar on Nordick Network for Multi Disciplinary Optimised Electric
Drives, Zegrze, Poland, June 2003, pp.23-27.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 156/175
References
150
[122] M. Żelechowski, D. Świerczyński, M. P. Kazmierkowski, J. Załę ski, "Universal inverter drives
controlled by new generation microprocessors", Elektroinfo Nr 6 (17) 2003, pp.26-28. (in Polish)
[123] M. Żelechowski, M. Malinowski, P. Kaczyński, W. Kołomyjski, M. Twerd, J. Załę ski, "DSP
Based Sensorless Direct Torque Control – Space Vector Modulated (DTC-SVM) for Inverter Fed
Induction Motor Drives", Problems of Automated Electrodrives Theory and Practice, Crimea,
Ukraine, Sep. 2003, pp.90-92.
[124] M. Jasiński, D. Świerczyński, M. P. Kaźmierkowski, M. Żelechowski, "Sensorless Direct Power
and Torque Control of Space Vector Modulated AC/DC/AC Converter - Fed Induction Motor",
Control in Power Electronics & Electrical Drives, SENE 2003, Łódź, Nov. 2003, pp.179-185.
[125] M. Żelechowski, P. Kaczyński, "Automatic measurement of induction motor parameters",
Przeglą d Elektrotechniczny, No. 1/2004, pp.6-10. (in Polish)
[126] D. Świerczyński, M. Żelechowski, "Universal structure of direct torque control for AC motor
drives", Przeglą d Elektrotechniczny, No. 5/2004, pp.489-492.
[127] M. Żelechowski, W. Kolomyjski, M. Twerd, "Industrial Application of Sensorless Direct Torque
Control – Space Vector Modulated (DTC-SVM) for Inverter Fed Induction Motor Drives", IV
Summer Seminar on Nordick Network for Multi Disciplinary Optimised Electric Drives, Tallinn,
Estonia, June 2004, pp.77-79.
[128] M. Cichowlas, M. Żelechowski, "PWM Rectifier with active filtering", IV Summer Seminar on
Nordick Network for Multi Disciplinary Optimised Electric Drives, Tallinn, Estonia, June 2004,
pp.101-107.
[129] M.P. Kaźmierkowski, M. Żelechowski, D. Świerczynski, "DTC-SVM an efficient method for
control both induction and PM synchronous motor”, In Proc. of the EPE- PEMC, Riga, Latvia,
Sep. 2004.
[130] M. Jasiński, M.P. Kaźmierkowski, M. Żelechowski, "Unified Scheme of Direct Power and
Torque Control for Space Vector Modulated AC/DC/AC Converter- Fed Induction Motor", In
Proc. of the EPE- PEMC, Riga, Latvia, Sep. 2004.
[131] M.P. Kaźmierkowski, M. Żelechowski, D. Świerczynski, "Simple DTC-SVM Control Scheme for
Induction and PM Synchronous Motor", XVI International Conference on Electrical Machines
ICEM’2004, Krakow, Poland, Sep. 2004.
[132] M. Jasiński, M. P. Kaźmierkowski, M. Żelechowski, "Direct Power and Torque Control Scheme
for Space Vector Modulated AC/DC/AC Converter- Fed Induction Motor", XVI International
Conference on Electrical Machines ICEM’2004, Krakow, Poland, Sep. 2004.
[133] M. Malinowski, W. Kołomyjski, M. Żelechowski, P. Wójcik, "New Space Vector Modulator in
Industrial Application", IX Sympozjum - Energoelektronika w Nauce i Dydaktyce ENID’2004,
Poznań, Sep. 2004, pp. 115-122.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 157/175
List of Symbols
2
3 j
2
1e
3π2 j+−==a
B - viscous constant
f - frequency
s f - sampling frequency
sw f - switching frequency
I - current, absolute value
A I , B I , C I - instantaneous values of stator phase currents
rI - rotor current space vector
sI - stator current space vector
β α s s I I , - stator voltage vector components in stationary β α − coordinate
system
β α r r I I , - rotor voltage vector components in stationary β α − coordinate system
k - space vector, generally
p K - controller gain
pM K - torque controller gain
pΨ K - flux controller gain
L - inductance, absolute value
M L - main, magnetizing inductance
s L - stator winding self-inductance
r L - rotor winding self-inductance
- mutual inductance, absolute value
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 158/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 159/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 160/175
List of symbols
154
K Ω - angular speed of the coordinate system
mΩ - angular speed of the motor shaftdt
d Ω
mm
γ =
sr Ω - angular speed of the rotor flux vectordt
d Ω
sr sr
γ =
ssΩ - angular speed of the stator flux vectordt
d Ω
ss ss
γ =
sl Ω - slip frequency
r s
M
L L
L2
1−=σ - total leakage factor
Superscript
^ - estimated value
Subscripts
..c - reference value
Rectangular coordinate systems
β α − - stator oriented, stationary coordinate system
'' qd − - rotor oriented, rotated coordinate system
y− - stator flux oriented, rotated coordinate system
qd − - rotor flux oriented, rotated coordinate system
Abbreviations
IM – Induction Motor
MMF – Magnetomotive Force
PWM – Pulse Width Modulation
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 161/175
List of symbols
155
ZSS – Zero Sequence Signals
SPWM – Sinusoidal (triangulation) Pulse Width Modulation
SVPWM – Space Vector Pulse Width Modulation
THIPWM – Third Harmonic Pulse Width Modulation
DPWM – Discontinues Pulse Width Modulation
SVM – Space Vector Modulation
OM – Overmodulation
RPWM – Random Pulse Width Modulation
RLL – Random Lead-Lag Modulation
RCD – Random Center Pulse Displacement
RZD – Random Distribution of the Zero Voltage Vector
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 162/175
Appendices
A.1. Derivation of Fourier Series Formula for Phase Voltage
If function f is a periodic, piecewise continuous and an odd, then its trigonometric
Fourier series is given by [56]:
( ) ( )∑∞
=
=1
sinn
n t nbt f ω ω (A.1.1)
where, for n = 1, 2, 3, …
( ) ( ) ( )
∫=
π
ω ω ω π 0
sin2
t d t nt f bn (A.1.2)
Function which describes phase inverter voltage is shown in the Fig. A.1.1
dcU 3
2
dcU 3
2
0
U A
ω t
dcU 3
1
dcU
3
1
π 3π
32π
34π
35π π 2
Fig. A.1.1. Phase voltage of the inverter
Taking into consideration this function coefficient bn can be written as follows:
( ) ( ) ( )∫=π
ω ω
π 0
sin2
t d t nt U b An
( ) ( ) ( ) ( ) ( ) ( )
++= ∫∫∫π
π
π
π
π
ω ω ω ω ω ω π
3
2
3
2
3
3
0
sin3
1sin
3
2sin
3
12t d t nU t d t nU t d t nU dcdcdc
( ) ( ) ( )
−−−=
π π
π
π
π
ω ω ω π 3
23
2
3
30
coscos2cos1
3
2t nt nt nU
n dc
( )
−
+−= π
π π
π 3
2cos
3
coscos11
3
2nnnU
n
dc (A.1.3)
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 163/175
Appendices
157
for even n:
( )
−
+− π
π π
3
2cos
3coscos1 nnn
03
cos3
cos11 =
−−
+−= π π π nnn (A.1.4)
and for uneven n:
( ) ( )
−−+−
++=
−
+−
31cos
3cos11
3
2cos
3coscos1
π π π
π π
π π nnnnnn
+=
3cos12 π
n (A.1.5)
From above formulas the Fourier series for U A is given by:
( )∑∞
=
+=
1
sin3
cos11
3
4
n
dc A t nnn
U U ω π
π
( )∑∞
=
=1
sin12
n
dc t nn
U ω π
(A.1.6)
where:
n=1+6k , k =0, ±1, ±2,…
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 164/175
Appendices
158
A.2. SABER Simulation Model
The control structures of IM were implemented in SABER v.2.4 Synopsys Inc.
package. SABER provides analysis behavior of the complete analog and mixed-signal
systems including electrical subsystem. SABER model scheme is presented in Fig.
A.2.1.
Fig. A.2.1. SABER model
The SABER package include the electrical and mechanical elements library. The
scheme of inverter (Fig. A.2.2) is based on the transistors and diodes models fromlibrary.
The user of SABER package can create own model using mathematical equation. In
this way is build model of induction motor. The equations (2.14-2.16) described
induction motor in β α − coordinates system are written in properly form in
“motor.sin” SABER file. The content of this file is shown in Fig. A.2.3
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 165/175
Appendices
159
Fig. A.2.2. Model of inverter
The control algorithm of induction motor has been written in MAST SABER
programming language. The code in MAST language is connected to “Control Block”,
which is shown in Fig. A.2.1. The MAST programming language is very similar to C
language. Therefore, implementation in laboratory setup of simulated structure is easier.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 166/175
Appendices
160
#motor.sin
template motor t1 t2 t3 t0 = rs,rr,ls,lr,lm,ml,,j
electrical t1, t2, t3, t0
<consts.sin
values
vt1=v(t1)-v(t0)
vt2=v(t2)-v(t0)
vt3=v(t3)-v(t0)
va=(1/3)*(2*vt1-vt2-vt3)
vb=(vt2-vt3)/sqrt(3)
fsa = ls*isa + lm*ira
fsb = ls*isb + lm*irb
fra = lr*ira + lm*isa
frb = lr*irb + lm*isb
equations
isb: vb - rs*isb = d_by_dt(fsb)
isa: va - rs*isa = d_by_dt(fsa)
irb: - rr*irb + p*omega_m*fra = d_by_dt(frb)
ira: - rr*ira - p*omega_m*frb = d_by_dt(fra)omega_m: (1/j ) * ( te - ml )= d_by_dt(omega_m)
i(t1->t0)+=it1
it1: it1=isa
i(t2->t0)+=it2
it2: it2=0.5*(-isa + sqrt(3)*isb)
i(t3->t0)+=it3
it3: it3=0.5*(-isa - sqrt(3)*isb)
Fig. A.2.3. SABER file „motor.sin”
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 167/175
Appendices
161
A.3. Data and Parameters of Induction Motors
Table A.3.1. Data of 3 kW induction motor
Power
Number of pole pairs
Moment of inertia
Voltage
Current
Nominal torque
Base speed
Frequency
Nominal stator flux
M N
= 20 Nm
P N
= 3 kW
U N = 380 V
I N
= 6.9 A
f N
= 50 Hz
= 1415 rpm
pb = 2
= 0.98 Wb
N Ω
sN Ψ
Power
Number of pole pairs
Moment of inertia
Voltage
Current
Nominal torque
Base speed
Frequency
Nominal stator flux
J = 0.007 kgm2
M N
= 20 Nm
P N
= 3 kW
U N = 380 V
I N
= 6.9 A
f N
= 50 Hz
= 1415 rpm
pb = 2
= 0.98 Wb
N Ω
sN Ψ
Table A.3.2. Parameters of 3 kW induction motor
Rotor winding resistance
Stator inductance
Mutual inductance
Rotor inductance
R s = 1.85Stator winding resistance Ω
Ω Rr = 1.84
L s = 170 mH
Lr = 170 mH
L M
= 160 mH
Table A.3.3. Data of 15 kW induction motor
Power
Number of pole pairs
Moment of inertia
Voltage
Current
Nominal torque
Base speed
Frequency
Nominal stator flux
J = 0.875 kgm2
M N
= 98 Nm
P N
= 15 kW
U N
= 380 V
I N
= 28.9 A
f N = 50 Hz
= 1460 rpm
pb = 2
= 0.98 Wb
N Ω
sN Ψ
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 168/175
Appendices
162
Table A.3.4. Parameters of 15 kW induction motor
Rotor winding resistance
Stator inductance
Mutual inductance
Rotor inductance
R s = 0.28Stator winding resistance Ω
Ω Rr = 0.26
L s = 63.5 mH L
r = 63.5 mH
L M
= 58.1 mH
Table A.3.5. Data of 90 kW induction motor
Power
Number of pole pairs
Moment of inertia
Voltage
Current
Nominal torque
Base speed
Frequency
Nominal stator flux
J = 1.50 kgm2
M N
= 580 Nm
P N
= 90 kW
U N
= 380 V
I N = 158 A
f N
= 50 Hz
= 1483 rpm
pb = 2
= 0.98 Wb
N Ω
sN Ψ
Table A.3.6. Parameters of 90 kW induction motor
Rotor winding resistance
Stator inductance
Mutual inductance
Rotor inductance
R s = 0.020Stator winding resistance Ω
Ω Rr = 0.016
L s = 16.36 mH
Lr = 16.74 mH
L M
= 16 mH
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 169/175
Appendices
163
A.4. Equipment
Table A.4.1. List of equipment
SABER 2002.4 Synopsys, Inc.
Matlab 6.1 MathWorks, Inc.
Digital oscilloscope
Analyzer
Voltage differential probe
Instrument Type
Tektronix TDS3034 300MHz
NORMA D6000 Lem
Tektronix P5200
Current probe Tektronix TCP A300
Simulation program
Simulation program
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 170/175
Appendices
164
A.5. dSPACE DS1103 PPC Board
Physically, DS1103 is built as a PC card that can be mounted into an ISA slot of a
regular PC. The I/O capability is rather impressive providing 300 signals. In order to
simplify the interface, 60 signals out of 300 are selected for further processing and then
connected to the SCU for signal conditioning. The selection is carried out in the
DEMUX card, which was fitted in a shielded box for EMC consideration.
The DS1103 is a single board system based on the Motorola PowerPC 604e/333MHz
processor (PPC), which forms the main processing unit.
I/O Units
A set of on-board peripherals frequently used in digital control systems has been
added to the PPC. They include: analog-digital and digital-analog converters, digital I/O
ports (Bit I/O), and a serial interface. The PPC can also control up to six incremental
encoders, which allow the development of advanced controllers for robots.
DSP Subsystem
The DSP subsystem, based on the Texas Instruments TMS320F240 DSP fixed-point
processor, is especially designed for the control of electric drives. Among other I/O
capabilities, the DSP provides 3-phase PWM generation making the subsystem useful
for drive applications.
CAN Subsystem
A further subsystem, based on Siemens 80C164 micro-controller (MC), is used for
connection to a CAN bus.
Master PPC Slave DSP Slave MC
The PPC has access to both the DSP and the CAN subsystems. Spoken in terms of
inter-processor communication, the PPC is the master, whereas the DSP and the CAN
MC are slaves.
Fig. A.5.14 gives an overview of the functional units of the DS1103 PPC.
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 171/175
Appendices
165
Fig. A.5.1. Block diagram of the dSPACE DS1103 board
The DS1103 PPC Controller Board provides the following features summarized in
alphabetical order:
A/D Conversion
• 4 parallel A/D-converters, multiplexed to 4 channels each, 16-bit resolution, 4 µs
sampling time, ± 10V input voltage range,
• 4 parallel A/D-converters with 1 channel each, 12-bit resolution, 800 ns sampling
time ± 10V input voltage range,
• Slave DSP ADC Unit providing.
• 2 parallel A/D converters, multiplexed to 8 channels each, 10-bit resolution, 6 µs
sampling time ± 10V input voltage range,
Digital I/O
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 172/175
Appendices
166
• 32-bit input/output, configuration byte-wise,
• Slave DSP Bit I/O-Unit providing,
• 19-bit input/output, configuration bit-wise,
CAN Support
• Slave MC fulfilling CAN Specifications 2.0 A and 2.0 B, and ISO/DIS 11898.
D/A Conversion
• 2 D/A converters with 4 channels each, 14-bit resolution ±10 V voltage range
Incremental Encoder Interface
• 1 analog channel with 22/38-bit counter range,
• 1 digital channel with 16/24/32-bit counter range,
• 5 digital channels with 24-bit counter range.
Interrupt Control - Interrupt Handling.
Serial I/O
• standard UART interface, alternatively RS-232 or RS-422 mode.
Timer Services
• 32-bit downcounter with interrupt function (Timer A),
• 32-bit upcounter with pre-scaler and interrupt function,
• 32-bit downcounter with interrupt function (PPC built-in Decrementer),
• 32/64-bit timebase register (PPC built-in Timebase Counter).
Timing I/O
• 4 PWM outputs accessible for standard Slave DSP PWM Generation,
• 3 x 2 PWM outputs accessible for Slave DSP PWM3 Generation and Slave DSP
PWM-SV Generation,
• 4 parallel channels accessible for Slave DSP Frequency Generation,
• 4 parallel channels accessible for Slave DSP Frequency Measurement (F2D) and
Slave DSP PWM Analysis (PWM2D).
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 173/175
Appendices
167
A.6. Processor TMS320FL2406
Fig. A.6.1 gives overview of the TMS320FL2406 structure.
C2xxDSP
Core
DARAM (B0)
256 Words
DARAM (B1)256 Words
DARAM (B2)32 Words
SARAM (2K Words)
Flash(32K Words)
Event Manager A
- Capture Inputs- Compare/PWM Outputs
- GP Timers/ PWM
Event Manager B
- Capture Inputs- Compare/PWM Outputs
- GP Time rs / PWM
JTAG Port
Digital I/O
Watchdog
CAN
SPI
SCI
PLL Clock
10 bit ADC
Fig. A.6.1. TMS320F2406 device overview
The features of the TMS320FL2406 processor [101] can be summarized as:
• High-Performance Static CMOS Technology:
• 25-ns Instruction Cycle Time (40 MHz),
• 40-MIPS Performance,
• Low-Power 3.3-V Design.
• Based on TMS320C2xx DSP CPU Core:
• Code-Compatible With F243/F241/C242,
• Instruction Set and Module Compatible With F240/C240.
• On-Chip Memory:
• 32K Words x 16 Bits of Flash EEPROM (4 Sectors),
• Programmable "Code-Security" Feature for the On-Chip Flash,
• 2.5K Words x 16 Bits of Data/Program RAM,
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 174/175
8/18/2019 PMSM Equation Mod Index Space Vector Modulated – Direct Torque Controlled (DTC – SVM) Inverter – Fed Inductio…
http://slidepdf.com/reader/full/pmsm-equation-mod-index-space-vector-modulated-direct-torque-controlled 175/175
Appendices
• 40 Individually Programmable, Multiplexed General-Purpose Input/Output
(GPIO) Pins,
• Five External Interrupts (Power Drive Protection, Reset, Two Maskable
Interrupts),
• Power Management:
• Three Power-Down Modes,
• Ability to Power Down Each Peripheral Independently,
• Real-Time JTAG-Compliant Scan-Based Emulation, IEEE Standard 1149.1
(JTAG),
• Development Tools Include:
• Texas Instruments (TI) ANSI C Compiler, Assembler/Linker, and Code
Composer Studio (CCS) Debugger,
• Evaluation Modules,