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
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Space Vector Modulated – Direct Torque Controlled (DTC – SVM
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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)
2.2. Mathematical Model of Induction Motor
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
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.
3. Vector Control Methods of Induction Motor
60
54004792
4567 4333 35082750 2208 2367 2333
0
5000
10000
15000
20000
25000
0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 H m [Nm]
f sw [Hz]
9,65
11,0611,97 11,00 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
3.4. Direct Flux and Torque Control (DTC)
61
The classical DTC method can be characterized as follows:
Advantages:
• simple structure:
o no coordinate transformation,
o no separate voltage modulation block,
o no current control loops,
• very good flux and torque dynamic performance,
Disadvantages:
• variable switching frequency,
• problems during starting and low speed operation,
• high torque ripples,
• flux and current distortion caused by stator flux vector sector position change
• high sampling frequency is required for digital implementation.
3.4.3. Direct Self Control (DSC) – Hexagon Flux Path
The block diagram of the direct self control method proposed by M. Depenbrock [31,
32] is presented in Fig. 3.21. This method was mainly applied in high power
applications, which required fast torque dynamic and low switching frequency [96].
Based on the command stator flux scΨ and the actual phase components sAΨ , sBΨ ,
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)
3. Vector Control Methods of Induction Motor
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.
3.4. Direct Flux and Torque Control (DTC)
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
3. Vector Control Methods of Induction Motor
64
angle [109]. Also solutions based on fuzzy logic and neural networks solutions were
proposed [85, 90].
3.5. Summary
In this chapter review of significant vector control methods of IM has been
presented. The characteristic features for all control schemes were described.
The FLC structure guarantees exact decoupling of the motor speed and rotor flux
control in both dynamic and steady states. However, it is complicated and difficult to
implement in practice. This method requires complex computation and additionally it is
sensitive to changes of motor parameters. Because of these features this method was 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:
4.2. Structures of DTC-SVM – Review
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).
4.2. Structures of DTC-SVM – Review
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:
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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 with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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)
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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)
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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 −
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
74
Different control structures based on the above induction motor model are proposed
in literature [73, 111, 112]. One of them is a method with two PI controllers [111],
which is presented in Fig. 4.5.
Considering a simple model of IM (Fig. 4.7), Fig. 4.8 shows the flux and torque
control loops for the method shown in Fig. 4.5. In Fig. 4.8 the dashed line represents the
IM model.
∫ssΩ
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.
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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:
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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=
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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 %
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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.
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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.
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
80
Fig. 4.15. SISO Design Tool
Configuration of the system structure is possible by importing transfer functions of
each block from the workspace. This is shown in Fig. 4.16.
Fig. 4.16. Import system data
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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).
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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
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.
4.3. Analysis and Controller Design for DTC-SVM Method with Close – Loop Torque and Flux Control in Stator Flux Coordinates
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=
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
94
Fig. 4.31. Steady state operation. From the top: line to line voltage, line current
The features of the DTC-SVM method can be summarized as follows:
• good dynamic control of flux and torque,
• constant switching frequency,
• unipolar voltage thanks to use of PWM block (SVM),
• low flux and torque ripple,
• sinusoidal stator currents.
4.4. Speed Controller Design
If the stator flux is assumed constant, .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.
4.4. Speed Controller Design
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:
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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)
4.4. Speed Controller Design
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)
4. Direct Flux and Torque Control with Space Vector Modulation (DTC-SVM)
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,
5. Estimation in Induction Motor Drives
100
• Kalman filter.
The DTC-SVM method is based on the information about stator flux vector (see
section 4.3). Therefore, it is the most important variable of the motor. Measurement of
flux in motor is difficult and demands special sensor. This solution is very expensive
and complicated. Because of that a method of calculation motor flux was developed.
In vector control methods this part of algorithm is especially important. Estimation
algorithm uses as input signals values, which are simple to measure. There are current
and voltage signals. Obviously new methods aim at reducing number of sensors for
more reliable operation and lower price of a drive.
The motor flux is the main component to calculate torque and speed. Therefore,
accuracy of the estimation flux is very important. Flux estimation is a significant task in
implementing of high-performance motor drives.
The advanced state variables calculation algorithm is characterized by:
• accuracy in steady and dynamic states,
• robustness for motor parameters variation,
• minimal number of sensor,
• operation in whole speed range,
• low calculation demanded.
All estimation algorithms based on the motor parameters. These parameters change
in time work of the drive. For instance, with change the temperature. Therefore,
estimation algorithm have to be less sensitive to the parameters variations.
All presented flux estimation algorithms are shown as stator flux estimators, because
of these algorithms work with DTC-SVM structure. In some algorithm rotor flux
estimation is required, but in this case it is convert on stator flux.
5.2. Estimation of Inverter Output Voltage
Input signals for the estimators are measurements of stator currents and voltages
which are recreated from the switching signals. Switch signals for the each inverter
phase are obtained by control algorithm. The reference voltage vector is realized by
5.2. Estimation of Inverter Output Voltage
101
modulator (see section 2.4). However, duty times are modified by dead-time, which is
requisite for correct inverter operation (see section 2.3). Because of this modification
delivered to the motor voltage is different from reference. To eliminate dead-time effect
there is a special part for compensation of dead-time in control algorithms. Obtained by
vector modulator duty cycles, represented by switching signals SA, SB, SC are modified
to SA', SB
', SC' (Fig. 5.2). This modification depends on the phase current direction and is
realized for each phase. Many different dead-time compensation methods are presented
in literature [2, 3, 8, 29, 64, 76]. Thanks to this modification after change signals by
dead-time, a correct voltage vector obtained by controller is delivered to the motor.
Because of that signals SA, SB, SC are used to recreate voltage values. The voltage is
calculated form the equations:
( )( )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
5. Estimation in Induction Motor Drives
102
In Fig. 5.2 voltage calculation block diagram is shown. Simultaneously with dead-
time compensation a voltage drop compensation algorithm is realized. It is especially
important for low speed operation range, when voltage is very low.
The main assumption in voltage calculation method is that identical voltage vector,
which is calculated by a controller is delivered to the motor. It means, proper
information about voltage depends on correct implementation dead-time and voltage
drop compensation algorithms.
Dead – Time Compensation
In order to prevent shortcircuiting an inverter leg, there should be a dead-time (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
5.2. Estimation of Inverter Output Voltage
103
So the real voltage vector across the motor can be expressed as:
∆UUU scmot −= (5.2)
The voltage distortion ∆U can be written as:
( )sI∆U 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= .
5. Estimation in Induction Motor Drives
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)
5.3. Stator Flux Vector Estimators
105
This is a classical voltage model of stator flux vector estimation, which obtain flux
by integrating the motor back electromagnetic force (EMF). The block diagram of this
estimator is shown in the Fig. 5.5.
sU
sI
sΨ
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
5. Estimation in Induction Motor Drives
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.
5.3. Stator Flux Vector Estimators
107
Voltage Model with Reference Flux (VM-RF)
The block diagram of the estimator based on voltage model with reference flux is
presented in Fig. 5.8 [25].
sU
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)
5. Estimation in Induction Motor Drives
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)
5.3. Stator Flux Vector Estimators
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 − .
5. Estimation in Induction Motor Drives
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).
5. Estimation in Induction Motor Drives
112
5.6. Summary
In this chapter estimation algorithms of flux, torque and rotor speed are presented.
The estimators provide feedback signals for DTC-SVM control scheme. Algorithms
selected to the implementation in final structure are described and discussed.
The speed estimator is based on the estimated stator and rotor fluxes. The mechanical
speed can be calculated in a simple way if motor flux is properly estimated. Therefore,
flux estimation algorithm is the most important part of sensorless control scheme.
Selected flux estimator for the sensorless mode is based on the voltage model. Thus
algorithm is sensitive on accuracy of inverter output voltage calculation. The voltages
are reconstructed from switching signals. In this method dead-time compensation
algorithm is significant. The dead-time effect and compensation algorithm was
presented.
The presented estimation methods are implemented in final DTC-SVM control
structure. The experimental results, presented in Chapter 7 confirm proper operation of
selected estimation methods.
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
6.3. Laboratory Setup Based on DS1103
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
6. Configuration of the Developed IM Drive Based on DTC-SVM
116
In Fig. 6.3 view of the laboratory setup is shown. All parts of the laboratory setup
can be seen in this picture.
dSPACE DS1103 PPC Board
The dSPACE DS1103 PPC is a mixed RISC/DSP digital controller providing a very
powerful processor for floating point calculations as well as comprehensive I/O
capabilities. Here are the most relevant features of the controller:
• Motorola PowerPC 604e running at 333 MHz,
• Slave DSP TI's TMS320F240 Subsystem,
• 16 channels (4 x 4ch) ADC, 16 bit , 4 µs, ±10 V,
• 4 channels ADC, 12 bit , 800 ns, ± 10V,
• 8 channels (2 x 4ch) DAC, 14 bit , ±10 V,6 µs,
• Incremental Encoder Interface -7 channels
• 32 digital I/O lines, programmable in 8-bit groups,
• Software development tools (Matlab/Simulink, RTI, RTW, TDE, Control Desk)
The DS1103 PPC card is pluged in one of the ISA slot of the motherboard of a host
computer of the type PIII/900MHz, 512 MBRAM, 40GB HDD, Windows 2000. All the
connections are made through six flat cables (50 wires each) available at the backside of
the desktop computer.
The DS1103 PPC is a very flexible and powerful system featuring both high
computational capability and comprenhensive I/O periphery. The board can be
programmed in C language. Additionally, it features a software SIMULINK interface
that allows all applications to be developed in the Matlab/Simulink user friendly
environment. All compiling and downloading processes are carried out automatically in
the background. An experimenting software called Control Desk, allow real-time
management of the running process by providing a virtual control panel with
instruments and scopes.
The detailed parameters of the dSPACE DS1103 PPC board are given in Appendix
A5.
6.3. Laboratory Setup Based on DS1103
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.
6. Configuration of the Developed IM Drive Based on DTC-SVM
118
Using data acquisition instruments you can capture data from the model running on
the real-time hardware. Changing parameter values is performed by operating input
instruments. The integrated Parameter Editor allows you to read the current parameter
values from the hardware and to change a parameter set in one step.
6.4. Drive Based on TMS320LF2406
DTC-SVM control algorithm was implemented in the drive based on microcontroller
TMS320LF2406. Setup consists of 18 kVA IGBT inverter and 15 kW induction motor.
The view of inverter is shown in Fig. 6.5. In this picture main control board of the
inverter with microprocessor module can be seen.
Fig. 6.5. 18 kVA inverter controlled by TMS320FL2406 processor
6.4. Drive Based on TMS320LF2406
119
The motor set (Fig. 6.6), which was used in tests consists of 15 kW induction motor
and 22 kW DC motor. The induction motor data are given in appendix A.3. The DC
motor works as a load and it is supply from the controlled rectifier.
Fig. 6.6. Motor set. From the left 22 kW DC motor and 15 kW IM motor.
Fig. 6.7. TMS320LF2406 microprocessor board
6. Configuration of the Developed IM Drive Based on DTC-SVM
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
6.4. Drive Based on TMS320LF2406
121
Interface (SCI) or Serial Peripheral Interface (SPI). Therefore, program can be loaded
from the PC via standard serial port (RS232).
This way of programming was used during the implementation of DTC-SVM control
algorithm. Thus it was possible to work with the processor without using the expensive
tools like JTAG.
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)
7. Experimental Results
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.
7.3. Flux and Torque Controllers
Dynamic tests for the flux and torque controller were done for different sampling
frequencies values and the same condition like for simulation presented in section 4.3
(motor speed 0=mΩ ). The flux controller parameters were calculated according to
symmetric optimum criterion (see section 4.3.1) and torque controller parameters were
calculated according to root locus method (see section 4.3.2).
In Fig. 7.6 – 7.8 are presented stator flux step response at sampling frequency
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)
7. Experimental Results
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.
7.3. Flux and Torque Controllers
127
The experimental results of torque controller dynamic test are shown in Fig. 7.9 –
7.11. Presented results were obtain at sampling frequency 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)
7. Experimental Results
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
The results from Fig. 7.12 can be compared with simulation results presented in Fig.
4.29. From Fig. 7.12 can be seen that decoupling between flux and torque is correct.
7.4. DTC-SVM Control System
In this section the experimental result for three possible drive operation modes,
which are described in Chapter 6 are shown. Therefore, comparison of a system
behavior in different modes is possible.
In Fig. 7.13 – 7.16 results for scalar control mode are presented. Fig. 7.13 gives
result for system startup to frequency Hzf 40= (motor speed sradΩm /125= ).
7. Experimental Results
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).
7.4. DTC-SVM Control System
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= .
7. Experimental Results
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).
7.4. DTC-SVM Control System
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:
7. Experimental Results
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.
7.4. DTC-SVM Control System
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.
7. Experimental Results
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)
7.4. DTC-SVM Control System
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,
8. Summary and Conclusions
139
which are used in classical DTC. However, obtained dynamic (response time for
the torque 1.5-2ms) is sufficient for general purpose drives.
• High sampling frequency is not required. The DTC-SVM algorithm works
properly at sampling frequency 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.
8. Summary and Conclusions
140
The quality of regulation process depends on an accuracy of feedback signals. In the
vector control of induction motor those signals are provided by flux and torque
estimators and, in sensorless operation mode, by a speed estimator. The precision of
estimated signals depends on:
• exact knowledge of motor parameters,
• good dead-time and voltage drop compensation algorithms,
• well realized measurements,
• implementation of on-line adaptation of motor parameters.
Those features are common for all vector control methods. Therefore, if feedback
signals are estimated accurately, the control scheme should be as simple as possible.
The DTC-SVM has a simple structure and it can be analyzed and implemented in a
simple way. It is very important feature of DTC-SVM.
Estimation problems in a drive with induction motor were discussed in Chapter 5.
Following estimation algorithms, selected for implementation, were presented: voltage
estimator with dead-time compensation algorithm, stator flux estimator, torque
estimator and mechanical speed estimator.
All parts of control scheme were verified in simulation and experiment. The whole
scheme consists of: flux and torque controllers, speed controller, estimation of flux,
torque and speed and compensation algorithms. Those complete structure was presented
in Chapter 6. Proposed solution was implemented in 3 kW experimental and 15 kW
industrial drives. The laboratory setups were also presented in Chapter 6.
Presented in Chapter 7 experimental results confirm proper operation of developed
control system.
Thus, thesis shows the process to select and develop the most convenient control
scheme for voltage source inverter-fed induction motor drives. Whole problems of
direct flux and torque control with space vector modulation (DTC-SVM) were analyzed
and investigated in simulation and experiment.
Finally, it should be stressed that the developed system was brought into serial
production. Presented algorithm has been used in new family of inverter drives
produced by Polish company Power Electronic Manufacture – „TWERD”, Toruń.
References
[1] V. Ambrozic, G.S. Buja, R. Menis, "Band-Constrained Technique for Direct Torque Control of
Induction Motor", IEEE Transactions on Industrial Electronics, Vol. 51, Issue: 4, Aug. 2004,
pp.776 - 784.
[2] C. Attaianese, D. Capraro, G. Tomasso, "A low cost digital SVM modulator with dead time