space vector modulated – direct torque controlled (dtc – svm

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

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.

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 28 2.4.5. 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 53 3.4.3. 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

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 110 5.6. 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 122 7.3. 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

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,

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.

VariableFrequency Control

Scalar basedcontrollers

Vector basedcontroller

U/f=const.Volt/Hertz

( )rs fi ω= Field Oriented FeedbackLinearization

Scalar basedcontrollers

Direct TorqueControl

Rotor FluxOriented

Stator FluxOriented

Direct TorqueSpace - Vector

Modulation

Passivity BasedControl

Circle fluxtrajectory

(Takahashi)

Hexagon fluxtrajectory

(Takahashi)

Direct(Blaschke)

Indirect(Hasse)

Closed LoopFlux & Torque

Control

Open LoopNFO (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.

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

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

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.

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:

dtdΨRIU A

sAA += (2.1a)

dtdΨRIU B

sBB += (2.1b)


7

dtdΨ

RIU CsCC += (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 is

defined as:

( ) ( ) ( )[ ]tktktk CBA ⋅+⋅+⋅= 2aa1k32 (2.2)

where: ( ) ( ) ( )tktktk CBA ,, – arbitrary phase quantities in a system of natural

coordinates, satisfying the condition ( ) ( ) ( ) 0=++ tktktk CBA ,

1, a, a2 – complex unit vectors, with a phase shift

2/3 – normalization factor.

Im

)(2 tka C

)(takB

)(tkA

Re

k

k23

A

B

C

a

2a

1

Fig. 2.1. Construction of space vector according to the definition (2.2)


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:

dtdRs

sss

ΨIU += (2.3a)

dtdRr

rrr

ΨIU += (2.3b)

rss IIΨ mjs MeL γ+= (2.4a)

srr IIΨ mjr MeL 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 KΩ .

KKK

KsK Ωdt

dR ss

ss ΨΨIU j++= (2.5a)

( ) KmbKK

KrK ΩpΩdt

dR rr

rr ΨjΨIU −++= (2.5b)

KMKsK LL rss IIΨ += (2.6a)

KMKrK LL srr IIΨ += (2.6b)

The equation of the dynamic rotor rotation can be expressed as:

[ ]mLem BΩMM

JdtdΩ

−−=1 (2.7)

where: eM – electromagnetic torque,

LM – load torque,

B – viscous constant.

In further consideration the friction factor will be negated ( )0=B .

The electromagnetic torque eM can be expressed by the following formulas:


9

( )rs II*Im2 M

sbe LmpM −= (2.8)

( )ss IΨ*Im2

sbe

mpM = (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:

KKK

KsK Ωdt

dR ss

ss ΨΨIU j++= (2.10a)

( ) KmbKK

Kr ΩpΩdt

dR rr

r ΨΨI −++= j0 (2.10b)

KMKsK LL rss IIΨ += (2.11a)

KMKrK LL srr IIΨ += (2.11b)

( )

−= L

sb

m MmpJdt

dΩss IΨ*Im

21 (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) βα −

in this case angular speed of the reference frame is zero 0=KΩ . The complex space

vector can be resolved into components α and β .

βα ssK UU j+=sU (2.13a)

βα ssK II j+=sI , βα rrK II j+=rI (2.13b)

βα ssK ΨΨ j+=sΨ , ββ rrK ΨΨ j+=rΨ (2.13c)

In βα − coordinate system the motor model equation can be written as:

dtdΨIRU s

sssα

αα += (2.14a)


10

dtdΨ

IRU ssss

βββ += (2.14b)

βα

α rmbr

rr ΨΩpdt

dΨIR ++=0 (2.14c)

αβ

β rmbr

rr ΨΩpdt

dΨIR −+=0 (2.14d)

ααα rMsss ILILΨ += (2.15a)

βββ rMsss ILILΨ += (2.15b)

ααα sMrrr ILILΨ += (2.15c)

βββ sMrrr ILILΨ += (2.15d)

( )

−−= Lssss

sb

m MIΨIΨmpJdt

dΩαββα2

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 βα − coordinate system that the

input signal to the motor is the stator voltage, the equations (2.14-2.16) can be

transformed into:

ααα

ssss IRU

dtdΨ

−= (2.17a)

βββ

ssss IRU

dtdΨ

−= (2.17b)

βαα

rmbrrr ΨΩpIR

dtdΨ

−−= (2.17c)

αββ

rmbrrr ΨΩpIR

dtdΨ

+−= (2.17d)

ααα σσ rrs

Ms

ss Ψ

LLLΨ

LI −=

1 (2.18a)

βββ σσ rrs

Ms

rs Ψ

LLLΨ

LI −=

1 (2.18b)


11

ααα σσ srs

Mr

rr Ψ

LLLΨ

LI −=

1 (2.18c)

βββ σσ srs

Mr

rr Ψ

LLLΨ

LI −=

1 (2.18d)

( )

−−= Lssss

sb

m MIΨIΨmpJdt

dΩαββα2

1 (2.19)

These equations can be represented in the block diagram as shown in Fig. 2.2.

βsΨ

mΩ

bp

αsI

αrI

αsΨαsU

sRsR

∫∫

∫

sLσ1

rs

M

LLL

σrs

M

LLL

σ

rLσ1

rR

αrΨ

∫rR

rLσ1βrI

∫sR

sLσ1

rs

M

LLL

σ rs

M

LLL

σ

βrΨ

βsU

2s

bmp eM

∫

LM

βsI

J1

Fig. 2.2. Block diagram of an induction motor in the stationary coordinate system βα −

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. From

the control point of view this system is complicated. That is the reason why there are a


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. 2.2

can 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 IGBT

transistors, 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

C2dcU

2dcU

C

0

SB+

SB-

SA+

SA-

SC+

SC-

T1

T2

T5

T6

T3

T4

DC side

UABA B C

N

IA IB IC

UA

RA

LA

EA

UB

RB

LB

EB

UC

RC

LC

EC

AC side

IM

PWM Converter

Fig. 2.3. Topology of the voltage source inverter


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

UB0

ωt2π

dcU21

dcU21

−

π

0

UA0

ωt2π

1 2 3 4 5 6

dcU21

dcU21

−

π

0

UC0

ωt2π

dcU21

dcU21

−

π

dcU32

dcU32

−

0

UAB

ωt2π

dcU31

dcU31

−

dcU

dcU−

π

dcU32

dcU32

−

0

UA

ωt2π

dcU31

dcU31

−

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]:

( ) ( ) ( )∑∑∞

=

∞

=

==11sinsin12

nnm

ndcA tnUtn

nUU ωω

π (2.20)

where:

dcU - dc supply voltage,


14

( ) dcnm Un

Uπ2

= - 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

Udc

U2 (110)

A B C

Udc

U3 (010)

A B C

Udc

U4 (011)

A B C

Udc

U5 (001)

A B C

Udc

U6 (101)

A B C

Udc

U0 (000)

A B C

Udc

U7 (111)

A B C

Udc

Fig. 2.5. Switching states for the voltage source inverter

From the equation (2.20) the fundamental peak value is given as:

( ) dcm UUπ2

1 = (2.21)


15

This value will be used to define the modulation index M 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...132 3)1(

v

veU vjdc

v

π

U (2.22)

The output voltage vectors are shown in Fig. 2.6.

U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (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


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 be

inserted. During this delay time, the dead-time TD transistors cease to conduct. Two

control signals SA+, SA- for transistors T1, T2 with dead-time TD are presented in Fig.

2.7. The duration of dead-time depends of the used transistor. Most of them it takes 1-

3µs.

t

t

Ts

TD TD

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

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.


2.4.1. 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 the

carrier based PWM methods the Zero Sequence Signals (ZSS) [46] are added to extend


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 PWM

method 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 UAc, UBc, UCc are

compared with triangular carrier signal Ut, 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.


19

Udc

A B C

N

Carrier

UAc

UBc

UCc

Ut

SA

SB

SC

Fig. 2.8. Block scheme of carrier based sinusoidal PWM

Ut UAc UBc

UCc

0

1

0

1

0

1

0

SB

SC

0dcU32dcU31

dcU32−dcU31−0

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


20

The modulation index m is defined as:

)(tm

m

UU

m = (2.23)

where:

mU - peak value of the modulating wave,

)(tmU - 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 2dcU , 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

UUπ

78.5

90.7

100

SPWM

SVPWMor SPWM with ZSS OM

Six stepoperation

Fig. 2.10. Output voltage of VSI versus modulation index for different PWM techniques


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

Udc

A B C

SA

SB

SC

Carrier

UtCalculationof ZSS

UAc

UBc

UCc

UAc*

UBc*

UCc*

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 to 2dcU . Therefore,

2dcU

± 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


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

Time0 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

Time0 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

UA

UN0

UA0

UA=UA0

UN0UN0

UA

UA0

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

Time0 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

Time0 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

UN0UN0

UN0

UA0UA0UA0

UA UA

UA

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


23

divide a plane for the six sectors I - VI. In the each sector the reference voltage vector

Uc is obtained by switching on, for a proper time, two adjacent vectors. Presented in

Fig. 2.13 the reference vector Uc can be implemented by the switching vectors of U1, U2

and zero vectors U0, U7.

I

II

III

IV

V

VI

U7 (111)

U0 (000) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (101)

α

Uc

(t1 /Ts )U1

(t 2 /T

s )U

2

Fig. 2.13. Principle of the space vector modulation

The reference voltage vector Uc is sampled with the fixed clock frequency ss Tf 1= ,

and next a sampled value ( )sTcU is used for calculation of times t1, t2, t0 and t7. The

signal flow in space vector modulator is shown in Fig. 2.14.

Udc

Sectorselection

SA

SB

SC

Calculation

t1 t2 t0 t7

fs

Uc

A B C

N

Uc(Ts)

Fig. 2.14. Block scheme of the space vector modulator


24

The times t1 and t2 are obtained from simple trigonometrical relationships and can be

expressed in the following equations:

( )αππ

−= 3sin321 sMTt (2.24a)

( )απ

sin322 sMTt = (2.24b)

Where M is a modulation index, which for the space vector modulation is defined as:

dc

c

stepsix

c

U

UU

UM

π2)(1

==−

(2.25)

where:

cU - vector magnitude, or phase peak value,

)(1 stepsixU − - fundamental peak value ( )πdcU2 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 dcU33 .

This is a radius of the circle inscribed of the hexagon in Fig. 2.13. At this condition the

modulation index is equal:

907.0233

==

dc

dc

U

UM

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 t1 and t2 from equations (2.24) the residual sampling time is

reserved for zero vectors U0 and U7.

70217,0 )( ttttTt s +=+−= (2.27)


25

The equations for t1 and t2 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 t0 and t7 are equal:

( ) 22170 ttTtt 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

Ts

U7

t0 t2/2

SA

SB

SC

U1 U2 U2 U1

t1/2t1/2 t2/2

0

0 0

0

00

0 1 1

0 1

0

01

0

Ts

U0 U1 U2 U1 U0

t2 t1/2 t0/2t0/2 t1/2

SA

SB

SC

0

0 0

0 0 0

0

00

000

1 1 1

1 1

1

111

11

1

Ts

U0 U1 U2 U7 U7 U2 U1 U0

t0/4 t1/2 t2/2 t0/4t0/4 t1/2 t2/2 t0/4

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


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) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001)U6 (101)

t7= 0

t7= 0

t7= 0

t0= 0

t0= 0

t0= 0

DPWM1

U7 (111)U0 (000) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001)U6 (101)

t7= 0

t7= 0

t7= 0

t0= 0

t0= 0

t0= 0

t0= 0

t7= 0

t0= 0

t7= 0

t7= 0

t0= 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

UN0

UA0

UA

DPWM2

U7 (111)

U0 (000) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001)U6 (101)

t7= 0

t7= 0t7= 0

t0= 0 t0= 0

t0= 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

UN0

UA0

UA

DPWM3

U7 (111)U0 (000) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001)U6 (101)

t7= 0

t7= 0

t7= 0

t0= 0

t0= 0

t0= 0

t0= 0

t7= 0

t0= 0

t7= 0

t7= 0

t0= 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

UN0

UA0

UA

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

UAUA0

UN0

a)

b)

c)

d)

Fig. 2.16. The discontinuous space vector modulation


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).


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 t0 and t7.

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 UAc*, UBc

*, UCc* are compared

with triangular carrier signal Ut, and in this way logical signals SA, SB, SC are generated.

In the space vector modulation duration time of active (t1, t2) and zero (t0, t7) 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 t1 and t2 equations are identically for all space

vector modulation methods. But every method demand suitable equation for the zero

vectors t0 and t7.

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.


29

0

0 0

0 0 0

0

00

000

0 1 1

0 1

0

011

01

0

Ts

U0 U1 U2 U1 U0

t2 t1/2 t0/2t0/2 t1/2

SA

SB

SC

UAc*

UBc*

UCc*

SA

SB

SC

b)

Car

rir b

ased

PW

MSp

ace

vect

or P

WM

UAc*

0

0 0

0 0 0

0

00

000

1 1 1

1 1

1

111

11

1

Ts

U0 U1 U2 U7 U7 U2 U1 U0

t0/4 t1/2 t2/2 t0/4t0/4 t1/2 t2/2 t0/4

UBc*

UCc*

SA

SB

SC

SA

SB

SC

a)

Car

rir b

ased

PW

MSp

ace

vect

or P

WM

Fig. 2.18. Comparison of carrier based PWM with space vector PWM a) SVPWM, b) DPWM1

UA

UB UC

UN0

A

B C

N0

2dcU

2dcU

UB0 =U

C0

U A0

Fig. 2.19. Equivalent circuit of VSI for the U1 vector


30

Taking into consideration the electrical circuit in Fig. 2.19 the voltage distribution

can be obtained. The voltages can be written as:

dcA UU32

= ; dcB UU31

−= ; dcC UU31

−= (2.32)

dcA0 UU21

= ; dcB0 UU21

−= ; dcC0 UU21

−= (2.33)

dcANA0N0 UUUU61

−=−= (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 CUC0U N0U

0U

1U

2U

3U

4U

5U

6U

7U

dcU21

dcU21

− dcU32

dcU31

−dcU21

− dcU31

− dcU61

−

dcU21

dcU32

−dcU31

dcU21

− dcU61

dcU21

dcU21

− dcU32

dcU31

−dcU21

− dcU31

− dcU61

−

dcU21

dcU31

dcU21

dcU21

− dcU32

− dcU31

dcU21

dcU31

dcU61

dcU21

− dcU21

− dcU32

dcU31

−dcU21

dcU31

− dcU61

dcU21

dcU21

− dcU31

dcU31

dcU21

dcU32

− dcU61

dcU21

− dcU21

− 0 0 dcU21

−0dcU21

−

dcU21

dcU21

0 0 dcU21

0dcU21

The average value for sampling time of UNO voltage can be written as follows:

++−−= 7210

dc

sN0 ttttU

TU

31

31

21 for the sectors I, III, V (2.35)

and

++−−= 7120

dc

sN0 ttttU

TU

31

31

21 for the sectors II, IV, VI (2.36)


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 (t0, t7) times equations for the most significant

modulation methods.

Table 2.2. Relation between carrier based and SVM methods

−= α

πcos41

2MTt s

0

( )

+−= αα

πsin3cos21

2MTt s

0

Calculation of t0 and t7

for sectors I, III, V

for sectors II, IV, VI

210s7 tttTt −−−=

Waveform of theZSS (Fig. 2.13)

( )0=N0U

Modulationmethod

SPWM

Sinusoidal with1/4 amplitude

no signal

THIPWM

−−= αα

π3cos

41cos41

2MTt s

0

−+−= ααα

π3cos

21sin3cos21

2MTt s

0

for sectors II, IV, VI

210s7 tttTt −−−=

for sectors I, III, V

Triangular with1/4 amplitude

Discontinuous

SVPWM

DPWM1

( ) 221s70 ttTtt −−==

0=0t

21s7 ttTt −−=

0=7t

21s0 ttTt −−=

when ( )1263

+<≤ nn παπ

when ( ) ( )13

126

+<≤+ nn παπ

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


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

dcU33 . 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) U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (101)

α

Uc

(t1 /Ts )U1

(t 2 /T

s )U

2 Overmodulation range0.907 < M < 1

Six-step modeM = 1

Linear rangeM ≤ 0.907

Fig. 2.20. Definition of the overmodulation range


33

If the value of the reference voltage beyond maximal value in the linear range vector

Uc can not be realized for whole range of α angle. However, average voltage value can

be obtained for modification of the reference voltage vector. Because of the modified

reference voltage vector overmodulation algorithms are not widely used in vector

control methods of drive. To modify the reference voltage vector different algorithm

may be applied. Overmodulation range can be considered as one region [33], or it can

be divided into two regions [16, 55, 75, 89].

In the algorithm where overmodulation region is considered as two regions two

modes depending on the reference voltage value were defined. In mode I the algorithm

modifies only the voltage vector amplitude, in mode II both the amplitude and angle of

the voltage vector.

Overmodulation mode I is shown in Fig. 2.21.

U0 (000)

U7 (111)

α

Uc

Uc*

U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (101)

θ

Fig. 2.21. Overmodulation mode I

In this mode voltage vector Uc crosses the hexagon boundary at two points in each

sector. There is a loss of fundamental voltage in the region where reference vector

exceeds the hexagon boundary. To compensate for this loss, the reference vector

amplitude is increased in the region where the reference vector is in hexagon boundary.

A modified reference voltage trajectory proceeds partly on the hexagon and partly on

the circle. This trajectory is shown in Fig. 2.21.


34

In the hexagon trajectory part only active vectors are used. The duration of these

vectors t1 and t2 are obtained from trigonometrical relationships and can be expressed in

the following equations:

αααα

sincos3sincos3

+−

= s1 Tt (2.37a)

1s2 tTt −= (2.37b)

0== 70 tt (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

UcUc

*

U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (101)

hα

hα

∗α

Fig. 2.22. Overmodulation mode II where both amplitude and angle is changed


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

3for66

00

πααππ

απααπαπ

αα

αα

α

h

hhh

h

h

(2.38)

where: αh – 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 αh, the algorithm holds the vector Uc* at the vertex (U1). Next part is for α from

αh to hαπ −3 . In this angle range the reference vector moves along the hexagon. In the

last range, from hαπ −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 αh 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


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 Ts and realized in the next switching time Tsw 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( −ncU )1( +n

cU)(ncU

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( −ncU )1( +n

cU)(ncU

a)

b)

sws TT =

sws TT =

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


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 sTα 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

Ts Ts Ts Ts

sTα sTα sTα sTα

SA

SB

SC

Ts Ts Ts Ts

Lead Lag Lag Lead

SA

SB

SC

Ts Ts Ts Ts

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)


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( −ncU )1( +n

cU)(ncU

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:

srTt =∆ (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

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 voltage

drop 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.

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 srK ΩΩ = ,

which is defined as follows:

dtdγΩ 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.

sqsdK UU j+=sU (3.2a)

sqsdK II j+=sI , rqrdK II j+=rI (3.2b)

sqsdK ΨΨ j+=sΨ , rrdK ΨΨ ==rΨ (3.2c)


41

α

β

rΨ

dq sI

βsI

αsI

sdIsqI

srγ

δ

srΩ

Fig. 3.1. Vector diagram of induction motor in stationary βα − and rotating qd − coordinates

In qd − coordinate system the induction motor model equations (2.10-2.12) can be

written as follows:

sqsrsd

sdssd ΨΩdt

dΨIRU −+= (3.3a)

sdsrsq

sqssq ΨΩdt

dΨIRU ++= (3.3b)

dtdΨIR r

rdr +=0 (3.3c)

( )mbsrrrqr ΩpΩΨIR −+=0 (3.3d)

rdMsdssd ILILΨ += (3.4a)

rqMsqssq ILILΨ += (3.4b)

sdMrdrr ILILΨ += (3.4c)

sqMrqr ILIL +=0 (3.4d)

−= Lsqr

r

Msb

m MIΨLLmp

JdtdΩ

21 (3.5)

The equations 3.3c and 3.4c can be easy transformed to:


42

rr

rsd

r

rMr ΨLRI

LRL

dtdΨ

−= (3.6)

The motor torque can by expressed by rotor flux magnitude rΨ and stator current

component sqI as follows:

sqrr

Msbe IΨ

LLmpM

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.

rΨ

mΩ

∫

2s

bmp eM

∫

LM

J1

r

rM

LRL

r

r

LR

r

M

LL

sdI

sqI

eM

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 βα − .

Therefore, current components αsI , βsI must be transformed to the rotating system

qd − . Similarly, the reference stator voltage vector components csU α , csU β , must be

transformed from the system qd − to βα − . These transformations requires a rotor

flux angle srγ . 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.


43

For DFOC an estimator or observer calculates the rotor flux angle srγ . 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

SCsqcI

FluxEstimator

Udc

αsU

βsU

sI

csU α

csU β

αsI

βsI

srγ

rcΨ

ecM

sdI

sqI

sdcI

PIβα −

qd −

βα −

qd −

3

2

Motor

rcM

r

sb ΨLL

mp12

ML1

VoltageCalculation

Fig. 3.3. Block diagram of the Direct Field Oriented Control (DFOC)

For the IFOC rotor flux angle srγ is obtained from reference sdcI , sqcI currents. The

angular speed of the rotor flux vector speed can be calculated as follows:

mbslrs ΩpΩΩ += (3.8)

where slΩ is a slip angular speed. It can be calculated from (3.3d) and (3.4d).

sqcr

r

sdcsl I

LR

IΩ 1

= (3.9)

In Fig. 3.4 a block diagram of the IFOC is shown.


44

PI

SVM

SA

SB

SCsqcI

Udc

sI

csU α

csU β

αsI

βsI

srγ

rcΨ

ecM

sdI

sqI

sdcI

PIβα −

qd −

βα −

qd −

Motor

rcM

r

sb ΨLL

mp12

ML1

3

2

mΩsrΩ

slΩ

sdcr

r

ILR 1

∫

bp

Fig. 3.4. Block diagram of the Indirect Field Oriented Control (IFOC)

In both presented examples reference currents in rotating coordinate system sdcI , sqcI

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:

rM

sdc ΨL

I 1= (3.10)

ecrcM

r

sbsqc M

ΨLL

mpI 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,

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.


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:

ββαα gg)x(x ss UUf ++=& (3.12)

where:


46

−−

−+−−+

+−+−−

=

JMIΨIΨ

IΨΨΩpIΨΩpΨILΨΨΩpILΨΩpΨ

f

Lsrsr

srrmb

srmbr

sMrrmb

sMrmbr

)(

)(

αββα

ββα

αβα

ββα

αβα

µ

γαββγβαβ

αααα

x (3.13)

T

g

= 00100 ,,,,

sLσα (3.14)

T

g

= 01000 ,,,,

sLσβ (3.15)

[ ]Tx mssrr ΩIIΨΨ ,,,, βαβα= (3.16)

and

r

r

LR

=α (3.17)

rs

M

LLL

σβ = (3.18)

2

22

rs

Mrrs

LLLRLR

σγ +

= (3.19)

JLmp Ms

b 2=µ (3.20)

Because βα rrm ΨΨΩ ,, are not dependent on βα ss UU , it is possible to chose variable

dependent on x:

2221 )x( rrr ΨΨΨ =+= βαφ (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 φfLz = (3.23b)


47

)x(23 φ=z (3.23c)

)x(24 φfLz = (3.23d)

=

α

β

r

r

ΨΨ

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

φφ

s

s

f

f

UU

LL

zz

D2

21

2

3

1

&&

&& (3.24)

where

=

22

11

φφφφ

βα

βα

fgfg

fgfg

LLLLLLLL

D (3.25)

If 01 ≠φ (the amplitude of flux is not zero) then 0D) ≠det( and it is possible to

define the linearization feedback as:

+

−−

=

2

1

22

12

vv

LL

UU

f

f

s

s

φφ

β

α 1-D (3.26)

Then the resulting system is described by the equations:

21 zz =& (3.27a)

12 vz =& (3.27b)

43 zz =& (3.27c)

24 vz =& (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.


48

mΩ

LM

eM2ν∫ 4z

J

∫

rΨ1ν2z 2

rΨ∫∫

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 zkzzkv ref −−= (3.28)

( ) 42233212 zkzzkv 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 switching

frequency,

3.4. Direct Flux and Torque Control (DTC)

49

• the stator currents are sinusoidal except of high frequency switching harmonics.

SpeedController

FluxController Vector

Modulator

ControlSignals

Transfor-mation

FeedbackSignals

Transfor-mation

1ν

2ν

βsIαsI

rαΨ

rβΨ

FluxEstimator

mΩ

2rcΨ

5z

SA

SB

SC

VoltageCalculation

mcΩ

1z

2z

3z

4z

csU β

Motor

sU

sI

csU α

dcU

Fig. 3.6. Block scheme of the feedback linearization control method


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 sqI in accordance with equation

(3.7). This equation can also be written as:

δsin2 sr

r

Msbe IΨ

LLmpM = (3.30)

where:

δ - angle between rotor flux vector and stator current vector.

The formula (3.30) can be transformed into the equation:

ΨrsMsr

Msbe ΨΨ

LLLLmpM δsin

2 2−= (3.31)

where:

Ψδ - angle between rotor and stator flux vectors.


50

It can be noticed that the torque depends on the stator and rotor flux magnitude as

well as the angle Ψδ . The vector diagram of IM is presented in Fig. 3.7. The two angels

δ and Ψδ are also shown in Fig. 3.7. The angle δ is important in FOC algorithms,

whereas Ψδ in DTC techniques.

α

β

δ

sI

sΨ

rΨδΨ

ssγ

srγ

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:

ss U

Ψ=

dtd

(3.32)

Taking into consideration the output voltage of the inverter in the above equation it

can be written as:

∫=t

vdt0

UΨs (3.33)

where:

=

==

−

7,00

6...132 3)1(

v

veU vjdc

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.


51

U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (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

Ψδ 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 Ψδ 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.


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


53

U1 (100)

U2 (110)U3 (010)

U4 (011)

U5 (001) U6 (101)

U7 (111)

U0 (000)

β

α

voltage U3 applied

voltage U2 applied

voltage U3 applied

voltage U3 applied

voltage U4 applied

voltage U4 applied

voltage U3 applied

voltage U4 applied

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

SA

SB

SC

Udc

Motor

TorqueController

FluxController

scΨ Ψd

Md

VoltageCalculation

VectorSelection

Table

(N)ssγ

SectorDetection

Flux andTorque

Estimator

Mec

UsIs

eM αsΨ βsΨ

Me

Ψe

Fig. 3.12. Block scheme of the direct torque control method


54

The stator flux amplitude scΨ and the electromagnetic torque cM are the reference

signals which are compared with the estimated sΨ and eM values respectively. The

flux Ψe and torque Me errors are delivered to the hysteresis controllers. The digitized

output variables Ψd , Md and the stator flux position sector ( )Nssγ 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)

Ψe

Ψd

ΨH

b)

Md

Me

MH

Fig. 3.13. The hysteresis controllers a) two-level, b) three-level

The output signals Ψd , Md are defined as:

1=Ψd for ΨΨ He > (3.35a)

0=Ψd for ΨΨ He −< (3.35b)

1=Md for MM He > (3.36a)

0=Md for 0=Me (3.36b)

1−=Md for MM He −< (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,

6ππγ ss (3.37a)

Sector 2:

+∈

2,

6ππγ ss (3.37b)

Sector 3:

++∈

65,

2ππγ ss (3.37c)


55

Sector 4:

−+∈

65,

65 ππγ ss (3.37d)

Sector 5:

−−∈

2,

65 ππγ ss (3.37e)

Sector 6:

−−∈

6,

2ππγ ss (3.37f)

U7 (111)U0 (000) U1 (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 Ψδ 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.


56

α

β

sΨ

rΨ

δΨ Sector 1

U2U3

U1U4

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

Ψd Md Sector 1 Sector 2 Sector 3 Sector 4 Sector 5 Sector 6

1

0

1

-1

1

0

1

-1

0

U4U3U2 U1U6U5

U7 U0 U7 U0 U7 U0

U6 U1 U2 U3 U4 U5

U4U3 U2U1U6U5

U7 U0 U7 U0 U7U0

U4U3U2U1U6U5

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.


57

a)

b)

Fig. 3.16. Steady state operation for the classical DTC method ( )kHzf 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.


58

cM

mc HM +

mc HM −t1 t2 t3 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

ss T

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 lower

sampling frequency kHzf 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

kHzf 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 fs = 20kHz (Fig. 3.19) the switching frequency and torque error are

not sensitive for hysteresis band. However, at the high sampling frequency fs = 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

scs

ΨΨΨ

s

−=ψε (3.38a)


59

%100ˆ

eN

eceM M

MM −=ε (3.38b)

where: sNΨ - nominal stator flux, eNM - nominal torque

Fig. 3.18. Steady state operation for the classical DTC method operating with lower sampling frequency ( )kHzf s 15=

The average value of the flux and torque errors are calculated in a period of the

fundamental frequency.


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 11,00 10,17

9,43 9,93 10,6812,03

02468

101214

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 of the torque hysteresis band at sampling frequency fs = 20kHz

5666545054926142666674008233

1331719750

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

3,062,43

2,6402468

101214

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 of the torque hysteresis band at sampling frequency fs = 80kHz


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 ,

sCΨ , the flux comparators generate digital variables Ad , Bd , Cd , 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:

CA dS = , AB dS = , BC dS = for 1=md (3.39a)

0=AS , 0=BS , 0=CS for 0=md (3.39b)


62

sI

Udc

Motor

TorqueController

ecM

FluxComparators

sU

VoltageCalculation

scψ

Flux andTorque

Estimator

sBψ

sAψ

sαψ

sβψ

Ad

Cd

Bd

mdSA

SB

SC

sCψ

eMβα −

ABC

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.


63

a)

b)

Fig. 3.22. Steady state operation for the DSC method a) 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


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 not

chosen for implementation.

Table 3.2 Comparison of control methods

FOC DTC DTC-SVM Advantages Modulator

Constant switching frequency Unipolar inverter output voltage Low switching losses Low sampling frequency Current control loops

Structure independent on rotor parameters, universal for IM and PMSM

Simple implementation of sensorless operation

No coordinate transformation

No current control loops

Disadvantages • Coordinate transformation

• A lot of control loops

• Control structure depended on rotor parameters

• No modulator • Bipolar inverter

output voltage • Variable switching

frequency • High switching

losses • High sampling

frequency

Structure independent on rotor parameters, universal for IM and PMSM

Simple implementation of sensorless operation

No coordinate transformation

No current control loops

Modulator Constant switching frequency Unipolar inverter output 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

3.5. Summary

65

methods. Table 3.2 summarizes features of analyzed control methods. It can be seen a

combination of DTC and FOC leads to the direct torque control with space vector

modulation (DTC-SVM) method which is an effect of this search. In Table 3.2 also

characteristic performance of DTC-SVM was given.

The disadvantages of classical DTC are caused by hysteresis controllers and

switching table used in a structure. Therefore, new DTC-SVM method replaces

switching table by space vector modulator and linear PI controllers are used like in the

FOC scheme. However, the current control loops are eliminated. The DTC-SVM

methods are widely discussed in the Chapter 4 where a detailed description of those

features can be found.

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:


67

+=

dtdΨ

RLΨ

LLΨ rc

r

rrc

M

ssdc σ (4.1a)

rc

ecs

M

r

sbsqc Ψ

MLLL

mpΨ σ2

= (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

222

2

+

=

rc

ec

M

rs

sbrc

M

ssc Ψ

MLL

Lmp

ΨLL

Ψ σ (4.2)

The commanded value of stator flux sdcΨ , sqcΨ after transformation to stationary

coordinate system βα − are compared with the estimated values αsΨ , βsΨ .

rcΨ

ecMEgs (4.1)

sdcΨ

sqcΨscΨ

RotorFlux

Estimator

StatorFlux

Estimator

sΨ

srγ

SVM

SA

SB

SC

VoltageCalculation

sT1s∆Ψ

βα −

qd −

sR

scU

sU

sI

dcU

βα −

ABC

AI

BI

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 sR :

ss

sc I∆ΨU ss

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

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

ecMEg. (4.4)ψδ∆ scΨ

PI

Flux andTorque

Estimator

sΨssγ

SVM

SA

SB

SC

VoltageCalculation

sT1s∆Ψ

sR

scU

sU

sI

dcU

βα −

ABC

AI

BI

TorqueController

eM

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 angle Ψ∆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:

( )Ψss ∆jsceΨ δγ += 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).


69

α

β

ssγ

srγ

Ψ∆δ sΨ

rΨΨδ

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

ecMEg. (4.7)

PI

Flux andTorque

Estimator

Ψk

ssγ

SVM

SA

SB

SC

VoltageCalculation

sT1s∆Ψ

sR

scU

sU

sI

dcU

βα −

ABC

AI

BI

TorqueController

eM

P

FluxController

sd∆γ s∆γ

ss∆γ

sΨ

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 Ψk and s∆γ

of the flux and torque controllers as follows:


70

( ) ( ) ( )1−−= kkk sss ΨΨ∆Ψ

( )[ ] ( )( ) ( )111 −⋅−⋅+= kekk kj∆Ψ

ssΨγ (4.5)

With the approximation

( ) ( )kj∆e skj∆ s γγ +≅1 (4.6)

The equation (4.5) can be written in the form

( ) ( ) ( )[ ] ( )1−⋅+= kkj∆kkk 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 ( yx − ).

scΨ

ecMPI

Flux andTorque

Estimator

sxcU

ssγTorqueController

PI

FluxController

sycU

yx −

βα −

eM

sΨ

SVM

SA

SB

SC

scU

sI βα −

ABC

AI

BI

VoltageCalculation

sUdcU

Fig. 4.5. DTC-SVM scheme operated in stator flux cartesian coordinates

4.3. Analysis and Controller Design for DTC-SVM Method

71

These dc voltage commands are then transformed into stationary frame ( βα − ), the

commanded values csU α , csU 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 yx − . This system of coordinates yx − rotates with the stator flux angular

speed ssK ΩΩ = . This angular speed is defined as follows:

dtdΩ ss

ssγ

= (4.8)

where: ssγ is a stator flux vector angle.

The complex space vector can be resolved into components x and y .

sysxK UU j+=sU (4.9a)

sysxK II jI +=s , ryrxK II j+=rI (4.9b)


72

ssxK ΨΨ ==sΨ , ryrxK ΨΨ j+=rΨ (4.9c)

The motor model equations (2.10-2.12) in yx − coordinate system can be written as:

dtdΨIRU s

sxssx += (4.10a)

ssssyssy ΨΩIRU += (4.10b)

( )ssmbryrx

rxr ΩΩpΨdt

dΨIR −++=0 (4.11a)

( )mbssrxry

ryr ΩpΩΨdt

dΨIR −++=0 (4.11b)

rxMsxss ILILΨ += (4.12a)

ryMsys ILIL +=0 (4.12b)

sxMrxrrx ILILΨ += (4.12c)

syMryrry ILILΨ += (4.12d)

−= Lsys

sb

m MIΨmpJdt

dΩ2

1 (4.13)

The electromagnetic torque can be expressed by the following formula:

syss

be IΨmpM2

= (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:

sxssxs IRU

dtdΨ

−= (4.15)

( )ssssyss

bs

e ΨΩUΨm

pR

M −=2

1 (4.16)


73

ssΩ

sxI

sΨsxU

sR

∫∫

sR

syU

syI

21

mrs LLL −

bp

rxI

∫rLσ

1rR

rxΨ

∫rR

rLσ1ryI

ryΨ

s

M

LL

÷ ML

rL

2mrs

M

LLLL−

mΩ2

sb

mp eM∫

LM

J1

sΨ

Fig. 4.6. Complete block diagram of an induction motor in the stator flux oriented coordinates yx −

The block diagram of induction motor based on equations (4.15) and (4.16) is shown

in Fig. 4.7.

∫ssΩ

sΨsxU

sxs IR

syU eM

s

sb R

mp 12

Fig. 4.7. Simplified (rotor equation omitted) induction motor block diagram in the stator flux oriented coordinates yx −


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

sΨsxU

sxs IR

syUecMPI eM

PIscΨ

s

sb R

mp 12

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

ip

ipR sT

sTK

sTK

sEsUsG

+=

+==

111 (4.17)

where: pK - controller gain, iT - controller integrating time.

The PI controller scheme is presented in Fig. 4.9.


75

( )sU( )sE

sTi

1

1

pK

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.

s1 sΨsxU

PIscΨ11

1sT+

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

sTsTeKsG

sτc

+=

−

(4.18)

where: 1=cK is the inverter gain, 0τ is dead time of the inverter ( 00 =τ ideal

converter), 12 =T , and sTT =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:


76

( ) scpΨ TTK

TK21

2 01

2 =+

=τ

(4.19)

( ) siΨ TTT 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, nΨt - time when the actual flux is first time equal reference value and Ψp -

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) kHzf s 10= , b) kHzf s 5= , c) kHzf s 5.2=


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.

syUecMPI eM

ssT+11

ss

sb Ψ

Rmp 12

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=pMK , siM TT 4= the proportional gain pMK is

increasing cyclically as it is shown in Fig. 4.13. From these oscillograms the best value

of pMK 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=pMK and for 10kHz 24=pMK .

The finally obtained in this way parameters of the torque controller are shown in

Table 4.2. There are also shown parameters of the step torque response obtained in

simulation, nMt - time when the actual torque achieves first time reference value and

Mp - 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 %


78

a)

4=pMK

10=pMK 10=pMK

24=pMK17=pMK

4=pMK

b)

Fig. 4.13. Torque response for selected controller gain pMK values, at different sampling frequency

a) kHzf s 5= ( )sTiM µ800= , b) kHzf s 10= ( )sTiM µ400=

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.


79

Re

Im

αα

damping

damping

settlingtime

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.


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


81

The plant (G) is a transfer function of the motor torque or flux and the compensator

(C) is a transfer function of the PI controller.

In the cases of flux and torque control, the open-loop consists of a PI controller and

plant transfer function, according to scheme (Fig. 4.8). The plant transfer function for

the flux and the torque are calculated separately based on the motor model equation in

the stator flux reference frame (4.10 - 4.12).

Flux Controller Design

Based on the motor model equations (4.10 - 4.12), the following equation can be

obtained:

( ) srsrssrrssxrssr ΨdtdLLLRLR

dtdRRU

dtdLLLR

+++=

+

2

σσ

( )mbssrssys ΩpΩLLIR −+ σ (4.21)

where: rs

M

LLL 2

1−=σ

Under the assumption that the last term in the equation (4.21) is very small:

( ) 0≈− mbssrssys ΩpΩLLIR σ (4.22)

the equation (4.21) becomes:

( ) srsrssrrssxrssr ΨdtdLLLRLR

dtdRRU

dtdLLLR

+++=

+

2

σσ (4.23)

Based on the equations (4.23) the open-loop flux transfer function can be obtained as

follows:

( )ΨΨ

Ψ

sx

sΨ CsBs

sAUΨsG

+++

== 2 (4.24)

where: r

rΨ L

RA

σ= ;

rs

rssrΨ LL

LRLRB

σ+

= ;rs

rsΨ LL

RRC

σ=

The flux control loop is shown in Fig. 4.17, where ( )sGRΨ is a transfer function of

the PI controller given by equation (4.17).


82

sxUscΨ ( )sGΨ( )sGRΨsΨ

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

Imag

Axi

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=pΨK , 00074.0=iΨT .

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.


83

Fig. 4.19. Simulated (SABER) flux response for controller parameters designed according to root locus method

Torque Controller Design

Based on motor model equations (4.10 - 4.12), the following equation can be

obtained:

( ) ( )mbssrssxmbsrsyrsyrssrrs ΩpΩLLIΩpΨLULIdtdLLLRLR −+−=

++ σσ

(4.25)

where: rs

M

LLL 2

1−=σ

Under the assumption that the last term in equation (4.25) is very small:

( ) 0≈− mbssrssx ΩpΩLLI σ (4.26)

the equation (4.25) becomes:

( ) mbsrsyrsyrssrrs ΩpΨLULIdtdLLLRLR −=

++ σ (4.27)

The additional assumption is that the motor is not loaded 0=LM .

Under those assumptions the rotor speed can be expressed:


84

syss

bm IΨ

mp

JdtdΩ

21

= (4.28)

From equation (4.14) current syI can be expressed as follows:

ssbesy Ψmp

MI 2= (4.29)

If both sides of equation (4.27) are differentiated, this equation becomes:

( )dt

dΩpΨL

dtdU

LIdtdLL

dtdLRLR m

bsrsy

rsyrssrrs −=

++

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:

( )MM

M

sy

eM CsBs

sAUMsG

++== 2 (4.31)

where: s

ssbM L

ΨmpAσ2

= ; rs

srrsM LL

LRLRBσ+

= ; JLΨmpCs

ssbM σ2

22

=

The torque control loop is shown in Fig. 4.20, where ( )sGRM is a transfer function of

the PI controller given by equation (4.17).

syU eM( )sGM( )sGRMecM

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=pMK , 00045.0=iMT .


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

Imag

Axi

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

pMMMMpMM

iMiM

pMM

ec

eMc

TKA

CsBKAs

sTTKA

MMsG

++++

+==

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=pMK , 00045.0=iMT .

Step Response

Time (sec)

Ampl

itude

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

To: y

Fig. 4.22. Simulated (Matlab) step response of the system from Fig. 4.20 described by transfer function given by equation (4.32)


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 MC , in equation

(4.32) normally is several order lower in comparison with ( )iMpMM TKA . 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:

( )1

1+

=sT

sGF

FM (4.33)

The time constant of the prefilter is equal time constant of the torque controller

iMF TT = .

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.

syUecM eM( )sGM( )sGRM( )sGFM

Fig. 4.23. Torque control loop with prefilter

Step Response

Time (sec)

Ampl

itude

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

To: y

Fig. 4.24. Simulated (Matlab) step response of the system from Fig. 4.23


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=pΨK , 00076.0=iΨT and torque controller

8492.1=pMK , 00046.0=iMT .

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).


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.


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

ecMPI

Flux andTorque

Estimator

sxcU

ssγTorqueController

PI

FluxController

sycU

yx −

βα −

eM

sΨ

SVM

SA

SB

SC

scU

sI βα −

ABC

AI

BI

VoltageCalculation

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 flux

magnitude 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: pΨK , iΨT , pMK and iMT . 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 iMT (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.


90

a)

b)

Fig. 4.29. Dynamic tests a) torque step change, b) flux step change. From the top: reference and estimated torque, 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

kHzf 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.


91

Sym

met

ryC

riter

ion

Met

hod

Con

trolle

r par

amet

ers

Torq

ue

Mod

el p

aram

eter

s

Flux

Torq

ueFl

ux

Dyn

amic

par

amet

ers

Torq

ueFl

ux

Tabl

e 4.

3. S

umm

ary

of c

ontro

ller d

esig

n

1=

TsT pure

inte

grat

or

Roo

t Loc

usM

etho

drr

ΨLR

Aσ

=

rs

rs

sr

ΨL

LL

RL

RB

σ+

=

rs

rs

ΨL

LRR

Cσ

=

rs

ss

br

ML

LΨ

mp

LA

σ2=

rs

sr

rs

ML

LL

RL

RB

σ+

=

JL

LL

Ψm

pC

rs

rs

sb

Mσ2

22

=

21.33

=pM

K

0004

5.0

=iMT

2531

=pΨ

K

0007

4.0

=iΨT

ss

sb

RΨ

mp

,,

,sT

%49.1

=Ψp

st nΨ

0019

.0=

%04.1

=Mp

st nM

0009

.0=

%6.1=

Ψp

st nΨ

0015

.0=

%39.8

=Mp

st nM

0007

.0=

00.24

=pM

K

0008

0.0

=iMT

5000

=pΨ

K

0004

0.0

=iΨT


92

All simulation results for root locus method presented in section 4.3.2 were done at

sampling frequency kHzf 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 the

input 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: kHzf s 10= , kHzf s 5= and kHzf 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 0.000455.0 kHz 0.0030 1% 15.88 0.000982.5 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.


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) kHzf s 10= , b) kHzf s 5= , c) kHzf s 5.2=


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, .constΨ s = , that based on the equations (4.13)

and (4.14) dynamic of IM can be described as:

[ ]Lem MM

JdtdΩ

−=1 (4.34)

A block diagram of the speed control loop is shown in Fig. 4.32, where ( )sGRS is a

transfer function of PI controller (see equation 4.17) and ( )sGM' 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. fT is a time constant of the filter.

The low pass filter is necessary in hardware setup.


95

ecM eMmcΩ

LM

J1( )sGRS ( )sGM

'

s1 mΩ

11+sTf

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:

( ) ( ) ( )sGsGMMsG McFM

ec

eM ⋅==' (4.35)

where: ( )sGMc - torque control loop transfer function given by equation (4.32),

( )sGFM - prefilter transfer function given by equation (4.33).

The transfer function ( )sGM' can by expressed as:

( )1'2'

''

++=

sCsBAsG

MM

MM (4.36)

where: pMMiMM

pMMM KATC

KAA

+=' ;

pMMiMM

iMM KATC

TB+

=' ; ( )

pMMiMM

MpMMiMM KATC

BKATC

+

+='

The torque control loop can be approximate by first order integrating part, because

of:

0' ≈MB (4.37)

The simplified transfer function can be written as:

( )1'

''

+=

sCAsG

M

MM (4.38)

For the torque controller parameters 87.15=pMK , 00087.0=iMT obtained in section

4.3.3 at the sampling frequency kHzfs 5= the transfer function parameters have values:


96

9944.0' =MA , 007563.3' −= eBM , 0009329.0' =MC . 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 transferfunction

simplifiedtransfer 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

sTsTeKsG

sτc

+=

−

(4.39)

where: 'Mc AK = is gain of the plan, 0τ is dead time of the inverter ( 0 0τ = ideal

converter), JT =2 , and fTCT +=1 is a sum of small time constants. The optimal

controller parameters can be calculated as:

( ) ( )fcps TC

JTKTK

+=

+=

22 01

2

τ (4.40)

( ) ( )fis TCTT +=+= 44 01 τ (4.41)

For the filter frequency Hzf f 25= where:

ff f

Tπ21

= (4.42)


97

the speed controller parameters are obtained as follows: 33.1=psK ; 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 sradΩm /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 sradΩm /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)


98

a) b)

Fig. 4.36. Load torque step change at sradΩm /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.

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 variablescalculation methods

Physicalmethods

Neural networkmethods

Estimators ofstate variables

Observer ofstate variables Kalman Filter

Mathematicalmodels

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,


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


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:

( )( )CBAdcsα DDDUU +−= 5.032 (5.1a)

( )CBdcs DDUU −=33

β (5.1b)

where DA, DB, DC are duty cycles corresponding to the switching signals SA, SB, SC

and dcU is the voltage of inverter dc-link.

VectorModulator

VoltageCalculation

Motor

DeadTime

&Voltage

DropCompen-

sation

SA

SB

SC

SA'

SB'

SC'

DeadTime

SA+SA-SB+SB-SC+SC-

csU β

csU α

sI

αsUdcU

dcU

sI

βsU

Fig. 5.2. Input signals for the estimators


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 (TD)

between the turn-off one switch (IGBT) and the turn-on of the next one (from the same

leg). TD 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>AI

D1

D2

C2dcU

2dcU

C

0

SA+

SA-

T1

T2

A 0<AI

b)a)

t

t

SA-

SA+

SA

TD

TD

0

UA0

dcU21

dcU21

−

t

t

t

t

SA-

SA+

SA

TD

TD

0

UA0

dcU21

dcU21

−

t

t

0>AI 0<AI

Fig. 5.3. Dead-time effect for different current sing a) 0>AI , b) 0<AI


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 signUfT dcsD= (5.3)

where: sf - sampling frequency,

( )sign - signum function.

The dead-time compensation can be implemented by adjusting the phase duty cycles

as following:

( )ksDkk IsignfTDD +=' (5.4)

where: CBAk ,,= .

This means that the on-time of the upper bridge arm switch is shortened by TD 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 ( )levelI is defined, which describes zone around the zero current as:

levelklevel III >>− (5.5)

If the condition (5.6) is performed the duty cycles are modified as follows:

( )ksDlevel

kkk IsignfTIIDD +=' (5.6)

In the other cases the duty cycles are modified according to the equation (5.4).

The value of the current level ( )levelI depends on the motor power and can be

deducted experimentally. For 3kW drive the optimal value of current level was

AIlevel 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 Hzf 2= .


104

a)

b)

Fig. 5.4. Simulated U/f=const. control method at frequency Hzf 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:

( )∫ −= dtRs sss IUΨ (5.7)


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

sR

∫

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:

( ) ssss ΨIU

Ψ ˆ1ˆˆ

Fs TR

dtd

−−= (5.8)

The block diagram of the method with low-pass filter is presented in Fig. 5.6.

s1sU

sI

sΨ

sR FT1

Fig. 5.6. Flux estimator based on voltage model with low-pass filter


106

The estimator stabilization time depends on the low-pass filter time constant TF.

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.

sUλΩ ss

ˆs +1

sΨ

ssγ

)ˆ(signj ssΩλ−1

s

sΨ

ssγ

ssΩ

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

ΩsΩsignj

ˆ)ˆ(1ˆ

λ

λ

+

−=

s

s

EΨ

(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.


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

sIsΨ

srγ

rcΨ

rΨ

s

ττs+1

τs+11

M

r

LL

srje γ

r

M

LL

sI

σsL

σsL

sR

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

ˆsrjrceΨK

dtd γ−+= rr

r ΨEΨ (5.10)

where K is the gain factor and rE is the rotor back EMF defined as:

)(dtd

LRLL

ssm

r sssr

IIUE σ−−= (5.11)

Then assuming τ1

−=K the equation (5.10) can be rewritten yielding:

srjrceΨ

ssγ

τττ ˆ

11

1ˆ

++

+= rr EΨ (5.12)

where:

dtds = (5.13)


108

From the equation describing the IM in βα − coordinate system (2.15) formulas for

calculation stator flux vector sΨ are obtained.

srs IΨΨ sr

m LLL

σ+= 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:

dtdγ

Ω mm = (5.15)

Taking into consideration number of pole pairs bp angular speed of the coordinate

system qd ′−′ is equal mbK ΩpΩ = .

The voltage, currents and fluxes complex space vector can be resolved into

components d ′ and q′ .

qsdsK UU ′′ += jsU (5.16a)

qsdsK II ′′ += jsI , qrdrK II ′′ += jrI (5.16b)

qsdsK ΨΨ ′′ += jsΨ , qrdrK ΨΨ ′′ += jrΨ (5.16c)


109

The complete set of equations for IM (2.10-2.12) can be transformed to the qd ′−′

coordinate system. In this coordinate system the motor model equation can be written as

follows:

qsmbds

dssds ΨΩpdtdΨIRU ′

′′′ −+= (5.17a)

dsmbqs

qssqs ΨΩpdtdΨ

IRU ′′

′′ ++= (5.17b)

dtdΨIR dr

drr′

′ +=0 (5.17c)

dtdΨ

IR qrqrr

′′ +=0 (5.17d)

drMdssds ILILΨ ′′′ += (5.18a)

qrMqssqs ILILΨ ′′′ += (5.18b)

dsMdrrdr ILILΨ ′′′ += (5.18c)

qsMqrrqr ILILΨ ′′′ += (5.18d)

( )

−−= ′′′′ Ldsqsqsds

sb

m MIΨIΨmpJdt

dΩ2

1 (5.19)

From the equations (5.17-5.17) formulas for the estimated rotor flux can be obtained

[66].

( )drdsMr

dr ΨILTdt

Ψd′′

′ −= ˆ1ˆ (5.20a)

( )qrqsMr

qr ΨILTdt

Ψd′′

′ −= ˆ1ˆ (5.20b)

where: r

rr R

LT =

The current vector is measured in stationary coordinate βα − . Therefore, current

components αsI , βsI must be transformed to the system qd ′−′ . Similarly, the

estimated rotor flux vector rΨ , must be transformed from the system qd ′−′ to βα − .


110

Stator flux vector sΨ is calculated from the equation (5.14).

Block diagram of the whole stator flux estimator is shown in Fig. 5.9.

αsI

βsI

dsI ′

qsI ′

ML

ML

rT1

∫

drΨ ′ˆ

qrΨ ′ˆ

rT1

∫βα −

qd ′−′ βα −

qd ′−′

mγ

αsI

αrΨ

βrΨ

βsI

r

M

LL

σsL

r

M

LL

σsL

αsΨ

βsΨ

Fig. 5.9. Block diagram of the current model flux estimator in rotor coordinates

This flux estimator model ensures good accuracy over the entire frequency range. It

has a very good behavior in steady and dynamic state. Also it has resistant to wrong

initial conditions. Its disadvantage is sensitive on change motor parameters.

This estimator was selected for the implementation DTC-SVM control structure in

sensor operation mode (see section 6.2).

5.4. Torque Estimation

The induction motor output torque is calculated based on the equation (2.9), which

for stationary coordinate system βα − can be written as follows:

( ) ( )αββα sssss

bs

be IΨIΨmpmpM ˆˆ2

ˆIm2

* −== ss IΨ (5.21)

It can be seen that the calculated torque is depended on the current measurement

accuracy and stator flux estimation method.

5.5. Rotor Speed Estimation

If a flux estimator works properly and rotor flux is accurately calculated mechanical

speed can be obtained from simple motor model equation [87]. If in control structure the

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:

( )slsrb

m ΩΩp

Ω −=1 (5.22)

where: srΩ - rotor synchronous speed,

slΩ - slip frequency,

bp - number of pole pairs.

The rotor synchronous speed is equal angular speed of the rotor flux vector and can

be calculated as:

dtdΩ sr

srγ

= (5.23)

The slip frequency of induction motor is defined as follows [66]:

mbsrsl ΩpΩΩ −= (5.24)

Based on the equations (3.3d) and (3.4d) in rotor flux coordinate system the slip

frequency can be expressed:

sqrr

Mrsl I

ΨLLRΩ 1

= (5.25)

Taking into consideration the torque equations (3.7) and (5.25) the estimated sleep

frequency can be calculated as follows:

( )αββα ssssr

rsl IΨIΨ

ΨRΩ ˆˆˆ 2 −= (5.26)

Finally mechanical motor speed is calculated from the equation (5.22).


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.

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.

6. Configuration of the Developed IM Drive Based on DTC-SVM

114

SVM

ScalarControl

Torqueand Flux

Controller

Switch 1ReferenceFrequency

ReferenceSpeed

ReferencesValue

EstimationsValue

Torqueand FluxEstimator

SpeedEstimator

SpeedController

Inverter

MeasurementsSignals

Switch 2 EstimationSpeed

MeasurmentSpeed

MotorSpeedSensor

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 with

estimated 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.

6.3. Laboratory Setup Based on DS1103

115


The basic structure of the laboratory setup is depicted in Fig. 6.1. The motor setup

consist of induction motor and DC motor, which is used for the loading. The induction

motor is fed by the frequency inverter controlled directly by the DS1103 board. The

dSPACE DS1103 PPC is plugged in the host PC. The DC motor is supplied by a torque

controlled rectifier. The encoder is used for the measure mechanical speed. The DSP

Interface – a set of eurocards mounted in a 19” rack with the main purpose to provide

galvanic isolation to all signals connected to the DS1103 PPC controller.

Measurement

DSPInterface

measuredDC line voltage

PC

3 32

gridRectifier Inverter

SA

measuredphase

currentSCSB

encoder

AC motor DC motorDS1103 dSPACE

Master : PowerPC 604eSlave: DSP TMS320F240

Rectifier

Fig. 6.2. Structure of the laboratory setup

Fig. 6.3. Laboratory setup


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.


117

Experimenting Software – Control Desk

Control Desk experiment software provides all the functions for controlling,

monitoring, and automation of real-time experiments and makes the development of

controllers more effective. A Control Desk experiment layout for controlling an

induction motor with DTC-SVM control methods is shown in Fig. 6.5.

Fig. 6.4. Control Desk experiment layout

Control Desk package consists of the following modules:

• The Experiment Management - assures a consistent data management controlling

all the data relevant for an experiment. The experiment can be loaded as a

complete set of data with a single operation. The content of the experiment can

be defined by the user.

• The Hardware Management - allows you to configure the dSPACE hardware and

to handle real-time applications with a graphical user interface.

• The Instrumentation Kits - offer a variety of virtual instruments to build and

configure virtual instrument panels according to your special needs.


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


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


120

The microprocessor board shown in the Fig. 6.7 was used to control the inverter. The

sizes of the processor module are 53x56mm. This board contains microcontroller

TMS320LF2406 and required equipment. The communication with main inverter board

by three connectors (2x20pins and 1x26pins) is provided.

The TMS320Lx240xA series of devices are members of the TMS320 family of

digital signal processors (DSPs) designed to meet a wide range of digital motor control

(DMC) and other embedded control applications [99, 100]. This series is based on the

C2xLP 16-bit, fixed-point, low-power DSP CPU, and is complemented with a wide

range of on-chip peripherals and on-chip ROM or flash program memory, plus on-chip

dual-access RAM (DARAM).

The TMS320 family consists of fixed-point, floating-point, multiprocessor digital

signal processors (DSPs), and fixed-point DSP controllers. TMS320 DSPs have an

architecture designed specifically for real-time signal processing. The 240xA series of

DSP controllers combine this real-time processing capability with controller peripherals

to create an ideal solution for control system applications. There are short characteristics

of the TMS320 family:

• flexible instruction set,

• operational flexibility,

• high-speed performance

• Innovative parallel architecture,

• cost effectiveness.

Devices within a generation of a TMS320 platform have the same CPU structure but

different on-chip memory and peripheral configurations. Spin-off devices use new

combinations of on-chip memory and peripherals to satisfy a wide range of needs in the

worldwide electronics market. By integrating memory and peripherals onto a single

chip, TMS320 devices reduce system costs and save circuit board space.

The detailed parameters of the TMS320FL2406 microprocessor are given in

Appendix A6.

The important feature of the TMS320FL246 microprocessor is the bootloader.

Thanks to that it is possible to program the device using Serial Communications


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.

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 Hzf 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 Hzf 40= 1) switching signal SA, 2) pole voltage UA0 (150 V/div), 3) phase voltage UA (150 V/div), 4) output current IA (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.

7.2. Pulse Width Modulation

123

Fig. 7.2. Discontinuous modulation (DPWM2) at frequency Hzf 40= 1) switching signal SA, 2) pole voltage UA0 (150 V/div), 3) phase voltage UA (150 V/div), 4) output current IA (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 Hzf 40= 1) switching signal SA, 2) pole voltage UA0 (150 V/div), 3) phase voltage UA (150 V/div), 4) output current IA (5 A/div)


124

Fig. 7.4. Overmodulation mode II at frequency Hzf 40= 1) switching signal SA, 2) pole voltage UA0 (150 V/div), 3) phase voltage UA (150 V/div), 4) output current IA (5 A/div)

The results for six-step mode are presented in Fig. 7.5.

Fig. 7.5. Six-step mode at frequency Hzf 40= 1) switching signal SA, 2) pole voltage UA0 (150 V/div), 3) phase voltage UA (150 V/div), 4) output current IA (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

7.3. Flux and Torque Controllers

125

Hzf 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.


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

kHzfs 10= , kHzfs 5= , kHzf 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 kHzf s 10= 1) reference flux (0.15 Wb/div), 2) estimated flux (0.15 Wb/div)


126

Fig. 7.7. Stator flux response at sampling frequency kHzf 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 kHzf 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.


127

The experimental results of torque controller dynamic test are shown in Fig. 7.9 –

7.11. Presented results were obtain at sampling frequency kHzfs 10= (Fig. 7.9),

kHzfs 5= (Fig. 7.10), kHzf s 5.2= (Fig. 7.11).

Fig. 7.9. Torque response at sampling frequency kHzf s 10= 1) reference torque (4.5 Nm/div), 3) estimated torque (4.5 Nm/div)

Fig. 7.10. Torque response at sampling frequency kHzf s 5= 1) reference torque (4.5 Nm/div), 3) estimated torque (4.5 Nm/div)


128

Fig. 7.11. Torque response at sampling frequency kHzf s 5.2= 1) reference torque (4.5 Nm/div), 3) estimated torque (4.5 Nm/div)

The result from Fig. 7.9 – 7.11 can be compared with simulation results presented in

Fig. 4.30. Experimental results presented in Fig. 7.9 – 7.11 confirm proper operation of

the torque control loop at different sampling frequency.

The decoupling between flux and torque control loops is presented in Fig. 7.12. The

torque step response (Fig. 7.12a) and magnitude stator flux step response (Fig. 7.12b)

are shown.

a)

7.4. DTC-SVM Control System

129

b)

Fig. 7.12. Dynamic tests a) torque step change, b) flux step change 1) 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.


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 Hzf 40= (motor speed sradΩm /125= ).


130

Fig. 7.13. Scalar control mode - Startup from 0 to Hzf 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 Hzf 25= is shown in Fig. 7.14.

Fig. 7.14. Scalar control mode - Load torque step change from 0 to NL MM = at frequency Hzf 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 ( Hzf 25±= ). The reverse

time is 0.5s (Fig. 7.15) and 5s (Fig. 7.16).


131

Fig. 7.15. Scalar control mode - Speed reversal Hzf 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 Hzf 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 sradΩm /120= .


132

Fig. 7.17. Vector control mode with speed sensor - Startup from 0 to sradΩm /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 sradΩm /75= is shown in Fig. 7.18.

Fig. 7.18. Vector control mode with speed sensor - Load torque step change from 0 to NL MM = at speed sradΩm /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 ( sradΩm /75±= ). The

reverse time is 0.5s (Fig. 7.19) and 5s (Fig. 7.20).


133

Fig. 7.19. Vector control mode with speed sensor - Speed reversal sradΩm /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)

Fig. 7.20. Vector control mode with speed sensor - Speed reversal sradΩm /75±= (reverse time 5s) 1) reference speed (30 (rad/s)/div), 2) actual speed (30 (rad/s)/div), 4) phase current (10 A/div)

In sensorless vector control mode the accuracy of the speed estimation algorithm

is important. Therefore, static and dynamic error of estimated speed were

investigated. The error of estimated speed can be written as:


134

%100ˆ

m

mmΩ Ω

ΩΩεm

−= (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]

erro

r_om

ega

[%]

[%]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.


135

Fig. 7.22. Dynamic test of the speed estimation - Speed reversal sradΩm /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 sradΩm /120= .

Fig. 7.23. Sensorless vector control mode - Startup from 0 to sradΩm /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 sradΩm /75= is shown in Fig. 7.24.


136

Fig. 7.24. Sensorless vector control mode - Load torque step change from 0 to NL MM = at speed sradΩm /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 ( sradΩm /75±= ). The

reverse time is 0.5s (Fig. 7.25) and 5s (Fig. 7.26).

Fig. 7.25. Sensorless vector control mode - Speed reverse sradΩm /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)


137

Fig. 7.26. Sensorless vector control mode - Speed reverse sradΩm /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. 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,


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 kHzfs 5= whereas DTC requires sampling

frequency at least kHz4025 − .

• Low flux and torque ripple than in classical DTC. The torque ripples in DTC-SVM

at sampling frequency kHzfs 5= are ten times lower than presented in section

3.4.2 torque ripples for classical DTC at sampling frequency kHzfs 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.


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.

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List of Symbols

23j

21e 3π2j +−==a

B - viscous constant

f - frequency

sf - sampling frequency

swf - switching frequency

I - current, absolute value

AI , BI , CI - instantaneous values of stator phase currents

rI - rotor current space vector

sI - stator current space vector

βα ss II , - stator voltage vector components in stationary βα − coordinate

system

βα rr II , - rotor voltage vector components in stationary βα − coordinate system

k - space vector, generally

pK - controller gain

pMK - torque controller gain

pΨK - flux controller gain

L - inductance, absolute value

ML - main, magnetizing inductance

sL - stator winding self-inductance

rL - rotor winding self-inductance

M - mutual inductance, absolute value

List of symbols

152

M - torque, absolute value

eM - electromagnetic torque

LM - load torque

M , m - modulation index

sm - number of phase windings

bp - number of pole pairs

SA, SB, SC - switching states for the voltage source inverter

R - resistance, absolute value

rR - rotor phase windings resistance

sR - stator phase windings resistance

iT - controller integrating time

iMT - torque controller integrating time

iΨT - flux controller integrating time

DT - dead time of inverter

r

rr R

LT = - rotor time constant

sT - sampling time

swT - switching time

U - voltage, absolute value

AU , BU , CU - instantaneous values of the stator phase voltages

sU - stator voltage space vector

rU - rotor voltage space vector

νU - inverter output voltage space vectors, 70,...,ν =

cU - reference voltage vector

List of symbols

153

βα ss UU , - stator voltage vector components in stationary βα − coordinate

system

cscs UU βα , - reference stator voltage vector components in stationary βα −

coordinate system

sqcsdc UU , - reference stator voltage vector components in rotating qd −

coordinate system

dcU - inverter dc link voltage

( )nmU - peak value of the n-th harmonic, n = 1, 2, 3,…

AcU , BcU , CcU - reference stator phase voltages

tU - triangular carrier signal

ABU , BCU , CAU - line to line voltages

Ψ - flux linkage, absolute value

AΨ , BΨ , CΨ - flux linkages of the stator phase windings

sΨ - space vector of the stator flux linkage

rΨ - space vector of the rotor flux linkage

sΨ - stator flux amplitude

rΨ - rotor flux amplitude

βα ss ΨΨ , - stator flux vector components in stationary βα − coordinate system

ββ rr ΨΨ , - rotor flux vector components in stationary βα − coordinate system

mγ - motor shaft position angle

srγ - rotor flux vector angle

ssγ - stator flux vector angle

Ω - angular speed, absolute value

List of symbols

154

KΩ - angular speed of the coordinate system

mΩ - angular speed of the motor shaft dt

dΩ mm

γ=

srΩ - angular speed of the rotor flux vector dt

dΩ srsr

γ=

ssΩ - angular speed of the stator flux vector dt

dΩ ssss

γ=

slΩ - slip frequency

rs

M

LLL 2

1−=σ - total leakage factor

Superscript

^ - estimated value

Subscripts

..c - reference value

Rectangular coordinate systems

βα − - stator oriented, stationary coordinate system

'' qd − - rotor oriented, rotated coordinate system

yx − - stator flux oriented, rotated coordinate system

qd − - rotor flux oriented, rotated coordinate system

Abbreviations

IM – Induction Motor

MMF – Magnetomotive Force

PWM – Pulse Width Modulation

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

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 tnbtf ωω (A.1.1)

where, for n = 1, 2, 3, …

( ) ( ) ( )∫=π

ωωωπ 0

sin2 tdtntfbn (A.1.2)

Function which describes phase inverter voltage is shown in the Fig. A.1.1

dcU32

dcU32

−

0

UA

ωt

dcU31

dcU31

−

π3π

32π

34π

35π π2

Fig. A.1.1. Phase voltage of the inverter

Taking into consideration this function coefficient bn can be written as follows:

( ) ( ) ( )∫=π

ωωπ 0

sin2 tdtntUb An

( ) ( ) ( ) ( ) ( ) ( )

++= ∫∫∫π

π

π

π

π

ωωωωωωπ

32

32

3

3

0

sin31sin

32sin

312 tdtnUtdtnUtdtnU dcdcdc

( ) ( ) ( )

−−−= π

π

π

π

π

ωωωπ 3

232

3

30

coscos2cos132 tntntnUn dc

( )

−

+−= πππ

π 32cos

3coscos11

32 nnnUn dc (A.1.3)

Appendices

157

for even n:

( )

−

+− πππ

32cos

3coscos1 nnn

03

cos3

cos11 =

−−

+−=

πππ nnn (A.1.4)

and for uneven n:

( ) ( )

−−+−

++=

−

+−

31cos

3cos11

32cos

3coscos1 πππππππ nnnnnn

+=

3cos12 πn (A.1.5)

From above formulas the Fourier series for UA is given by:

( )∑∞

=

+=

1sin

3cos11

34

ndcA tnn

nUU ωπ

π

( )∑∞

=

=1

sin12n

dc tnn

U ωπ

(A.1.6)

where:

n=1+6k, k=0, ±1, ±2,…

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 from

library.

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 βα − coordinates system are written in properly form in

“motor.sin” SABER file. The content of this file is shown in Fig. A.2.3

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.

Appendices

160

#motor.sintemplate 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*irafsb = ls*isb + lm*irbfra = lr*ira + lm*isafrb = 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)+=it1it1: it1=isai(t2->t0)+=it2it2: it2=0.5*(-isa + sqrt(3)*isb)i(t3->t0)+=it3it3: it3=0.5*(-isa - sqrt(3)*isb)

Fig. A.2.3. SABER file „motor.sin”

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

MN = 20 Nm

PN = 3 kW

UN = 380 V

IN = 6.9 A

fN = 50 Hz

= 1415 rpm

pb = 2

= 0.98 Wb

NΩ

sNΨ

Power


Moment of inertia

Voltage

Current

Nominal torque

Base speed

Frequency

Nominal stator flux

J = 0.007 kgm2

MN = 20 Nm

PN = 3 kW

UN = 380 V

IN = 6.9 A

fN = 50 Hz

= 1415 rpm

pb = 2

= 0.98 Wb

NΩ

sNΨ

Table A.3.2. Parameters of 3 kW induction motor

Rotor winding resistance

Stator inductance

Mutual inductance

Rotor inductance

Rs = 1.85Stator winding resistance Ω

ΩRr = 1.84

Ls = 170 mH

Lr = 170 mH

LM = 160 mH


Power


Moment of inertia

Voltage

Current

Nominal torque

Base speed

Frequency

Nominal stator flux

J = 0.875 kgm2

MN = 98 Nm

PN = 15 kW

UN = 380 V

IN = 28.9 A

fN = 50 Hz

= 1460 rpm

pb = 2

= 0.98 Wb

NΩ

sNΨ

Appendices

162



Stator inductance

Mutual inductance

Rotor inductance


ΩRr = 0.26

Ls = 63.5 mH

Lr = 63.5 mH

LM = 58.1 mH


Power


Moment of inertia

Voltage

Current

Nominal torque

Base speed

Frequency

Nominal stator flux

J = 1.50 kgm2

MN = 580 Nm

PN = 90 kW

UN = 380 V

IN = 158 A

fN = 50 Hz

= 1483 rpm

pb = 2

= 0.98 Wb

NΩ

sNΨ



Stator inductance

Mutual inductance

Rotor inductance


ΩRr = 0.016

Ls = 16.36 mH

Lr = 16.74 mH

LM = 16 mH

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

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.

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

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).

Appendices

167

A.6. Processor TMS320FL2406

Fig. A.6.1 gives overview of the TMS320FL2406 structure.

C2xxDSPCore

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 Timers/ 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,

Appendices

168

• 544 Words of Dual-Access RAM,

• 2K Words of Single-Access RAM.

• Boot ROM:

• SCI/SPI Bootloader,

• Two Event-Manager (EV) Modules (EVA and EVB), Each Includes:

• Two 16-Bit General-Purpose Timers,

• Eight 16-Bit Pulse-Width Modulation (PWM) Channels Which Enable:

• Three-Phase Inverter Control,

• Center- or Edge-Alignment of PWM Channels,

• Emergency PWM Channel Shutdown With External PDPINTx\

Pin,

• Programmable Deadband (Deadtime) Prevents Shoot-Through Faults,

• Three Capture Units for Time-Stamping of External Events,

• Input Qualifier for Select Pins,

• On-Chip Position Encoder Interface Circuitry,

• Synchronized A-to-D Conversion.

• Watchdog (WD) Timer Module,

• 10-Bit Analog-to-Digital Converter (ADC):

• 16 Multiplexed Input Channels,

• 375 ns or 500 ns MIN Conversion Time,

• Selectable Twin 8-State Sequencers Triggered by Two Event Managers,

• Controller Area Network (CAN) 2.0B Module,

• Serial Communications Interface (SCI),

• 16-Bit Serial Peripheral Interface (SPI),

• Phase-Locked-Loop (PLL)-Based Clock Generation,

Appendices

169

• 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,

• Scan-Based Self-Emulation (XDS510™),

• Broad Third-Party Digital Motor Control Support,

Package 100-Pin LQFP PZ.

space vector modulated – direct torque controlled (dtc – svm

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