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8 IEEE INDUSTRIAL ELECTRONICS MAGAZINE FALL 2007 1932-4529/07/$25.002007IEEE
DIGITALVISION
LECH M. GRZESIAK AND
MARIAN P. KAZMIERKOWSKI
Exploring the Problems
and Remedies
Digital Object Identifie r 10.1109/MIE.2007.901483
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H
IGH-PERFORMANCE
control methods for
converter-fed ac motors
such as field-oriented
control (FOC), direct
torque control (DTC),adaptive, and nonlinear
or sliding mode control [1][5], [42]
require complete information about
state and output variables. However,
sensors used in feedback loops
increase costs and decrease reliability
and immunity of the drive system;
therefore, they should be avoided.
Since the late 1980s, many efforts have
been made to reconstruct such state
variables of ac motors as rotor or stator
flux vectors and rotor angular speed,
e.g. [6][12].Artificial neural networks (ANNs)
are well suited for ac drive control and
estimation, because of their known
advantages, such as the ability to
approximate any nonlinear functions to
a desired degree of accuracy, learning
and generalization, fast parallel compu-
tation, robustness to input harmonic
ripples, and fault tolerance [3], [4].
These aspects are important in the case
of nonlinear systems, like converter-fed
ac drives, where linear control theory
cannot be directly applied. Additionally,
high-efficiency power electronic con-
verters used for ac motors operate in
switch mode, which results in very
noisy signals. For these reasons, ANNs
are attractive for signal processing and
control of ac drives. The commonlyused feed-forward ANN (FF-ANN) [Fig-
ure 1(a)] as universal nonlinear func-
tion approximator is suitable only for
steady-state systems. For a system
dynamics approximation task, a few
modifications of the FF-ANN architec-
ture are commonly used (Figure 1):
placement of tapped delay lines
(TDLs) at inputs of the FF-ANN [see
Figure 1(b)]
recurrent ANNs (RANNs) [see Figure
1(c)(d)].
All presented dynamic models[Figure 1(b)(d)] are widely applied as
nonlinear models of plants, estimators,
and controllers. The motivation for
using such an architecture is simple
mathematical description and avail-
ability of a very efficient training
method (e.g., available in the MATLAB
Neural Networks Toolbox).
However, presented schemes are
marked by serious limitations inher-
ited from TDLs and recurrent archi-
tecture, which requires that the
initially selected sampling time is
applied to the data in learning and
working phases.
The tapped delay neural architec-
ture [Figure 1(b)] has several limita-
tions caused by sampling and accuracy
of measurements [10]. These factorsinfluence rank of a matrix called the
input teaching matrix which is essen-
tial for neural network parameter tun-
ing. It is quite obvious that the ANN
with TDLs shown in Figure 1(b) (also
used in an ac drive control system) has
to act between two domains marked by
very different frequency spectra, at
inputs and at output. For instance, a
neural speed estimator works in steady
state at constant speed, which must be
reconstructed from periodical sinu-
soidal input signals (stator voltage andstator current). Limitations of certain
neural schemes based on time
instances of periodic signals are dis-
cussed in detail in [13] and [14].
The sampling time selected for a
continuous signal must fulfil Shannons
condition, so it is bounded from the
top as T < (1/2fmax) , but it is also
bounded from below. If a very small
sampling time is selected, then two
neighboring columns (each column
representing data at given time) of the
input teaching matrix become very
FIGURE 1 Example of ANNs used as models of static or dynamic plant: (a) a simple static FF-ANN, (b) adynamic model comprised of TDLs and static FF-ANN, (c) a Jordan network, and (d) a recurrent network with
TDLs on input and output signals.
ANN
Output
Input
DUDU
DU
DU
ANN
DU
DU
DU
DU
DU
DU
Output
OutputOutput
Input
InputInput
ANN
ANN
(a) (b)
(c) (d)
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close. So if their differences are within
the accuracy of measurement, then the
input teaching matrix may loose its fea-
ture of being full column rank, reducing
the dimension of the approximation
space. The lower bound of sampling
time, below which two sinusoidal sig-
nals shifted by the sampling time are
fully located within accuracy of themeasurement, has been determined.
Using the concept of indistinguishable
signals, it was demonstrated in [10],
[14], and [26] that the range of allowed
sampling is related to maximal and
minimal useful frequencies of the signal
and accuracy of the measurement in
the following manner:
fmax
fmin
100
p, (1)
wherep is the accuracy of measurement
signal in %. This equation expresses thatthe useful frequency band of every
input signal is limited. One has to
acknowledge that one value of the sam-
pling time must be selected for all
inputs and the output signal. So, if there
are signals with different spectrumi.e.,
different fmin and fmax parametersand
the spectrum of one signal is not includ-
ed in another, then according to (1) it is
impossible to select just one T parame-
ter (sampling time) as being appropriate
for all the inputs and the output. To
avoid such limitation, it is necessary to
select either different physical signals or
use a nonlinear (or dynamic) transfor-
mation (called here preprocessing) of
existing signals to achieve the inputs
and output spectra confinement. In such
cases, new structures for modelingdynamic systems using a neural archi-
tecture can be created.
This article presents selected exam-
ples of ANN-based flux vector and
mechanical speed estimators. By using
appropriate preprocessing of input sig-
nals, the performances of flux vector
and speed estimators are considerably
improved (compared to estimators
based on TDL FF-ANN and RANN) in
terms of accuracy and sensitivity to
parameter changes. The properties of
the discussed estimators are illustratedin an example of the induction motor
drive system with the direct torque con-
trol and space vector modulation (DTC-
SVM) scheme, as shown in Figure 2.
This system has been selected as a
very practical high-performance
scheme that can be used for induction
and/or permanent magnet synchronous
motor drives [3]. All presented experi-
mental oscillograms have been meas-
ured using the laboratory set-up (Figure
B) described in the Appendix.
Stator Flux Estimation
Based on ANN
Overview
Operation of high-performance ac motor
drives (DTC or FOC) depends stronglyon stator (or rotor) flux estimation accu-
racy. Several approaches are used for
flux vector estimation: model-based [15],
[16], using Kalman filters [17], Luenberg-
er observers [8], [18], [19], and many
other closed-loop estimators (e.g., [6],
[20]). Nevertheless, in many applica-
tions the stator flux is calculated from
the so-called voltage model
s(t) =
s(t0)+
tt0
(vs(t)
Rsis
(t))dt,(2)
where s
denotes stator flux space vec-
tor, vs, is denote stator voltage and cur-
rent space vectors, respectively, and R sdenotes the estimated stator resistance.
Accurate knowledge of stator resist-
ance is important for speed sensorless
drives operating at a wide speed con-
trol range including zero speed in
steady states and transients. In order to
implement (2), numerous improved
FIGURE 2 Block scheme of a DTC-SVM induction motor drive apply-ing flux and speed estimators based on ANN.
M
Control System (DTC SVM)
refs
Tes s
Load
ANN-a ANN-b
Vdc
LPF
m
refm
FIGURE 3 RANN architecture for stator flux estimation.
(k)us
(k)is
(k)is
(k)us
DU
ANN
DU
s(k+1)
s(k+1)
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integration algorithms have been pro-
posed [6], [7], [21], [22]. These deal with
drift and initial condition problems relat-
ed to pure integration. However, any sta-
tor flux estimator which includes back
electromotive force integration requires
an additional algorithm for Rs adapta-
tion. This is because even relatively
small modeling errors due to motor tem-perature rise can lead to large errors in
flux estimation accuracy [6].
Simple RANN Architecture
for Estimating Stator Flux VectorTo reconstruct flux directly from stator
currents and voltages (instead of back
EMF), a nonlinear transformation
between stator flux and stator voltage
and current will be reflected via neural
model. From a basic ac motor mathe-
matical model, stator voltage and flux
current equations can be written as[24], [25]
d
dt
s(t) = Rsis(t)+ vs(t) .
(3)
Now, if is and vs are assumed to be
measurable and the model parameters
Rs, Lm, and Lr are constant, then the
system becomes linear and no typical
neural network attributes are needed.
Having collected enough data points
in time and using a simple linear
autoregressive moving average model
(ARMA), one can find a linear approxi-
mation [is(k), vs(k)] s(k+ 1) as
a direct pseudo-inverse calculation.
However, if some of the parameters
change in time, they will influence is;therefore, a nonlinear approximation
is necessary.
The stator resistance variations
should be included in a training set;
thus, some level of robustness could
be achieved. Note that the relationship
between (vs(k), is(k)), and s(k) is
not a static one. This in turn implies
that there is no such function f1 that
satisfies s
(k) = f1(vs(k), is(k)). One
can expand the approximation space
to turn the problem into a static one
s
(k+ 1) = f2(v s(k), is(k),
s(k)) . (4)
To build a neural estimator using
(4), it is necessary to write down (3) in
stationary orthogonal coordinates.
Now the mathematical model of flux
components is given by
d
dts(t) = vs(t) Rsis(t)
d
dts (t) = vs (t) Rsis (t), (5)
where v(k)s , v
(k)s , i
(k)s , i
(k)s ,
(k )s , and
(k)s denote real and imaginary com-
ponents of the stator voltage, stator
current, and stator and rotor flux
space vectors, respectively.A neural architecture for stator
flux vector estimation is presented in
Figure 3. The ANN estimates stator
flux from the stator voltage and cur-
rent data. Mathematically, the prob-
lem can be classified as a nonlinear
dynamic system approximation. The
ANN can use only a single-hidden-
layer architecture. Training data can
be generated from a simulated mathe-
matical model operated in various
working conditions or from the data
collected from motor measurements.To train the network, many different
methods can be applied. Mostly, back-
propagation methods are used. For
such a training method, the architec-
ture of the network (number of hid-
den layers and neurons) must be set
up in advance. One can also use incre-
mental learning methods (originated
in [27] and [28]), presented for exam-
ple in [10] and [26], to design an FF-
ANN for function approximation. If an
incremental learning method is cho-
sen for ANN design and training (Fig-
ure 3), the number of hidden sigmoid
neurons is not fixed in advance. At
FIGURE 4 Illustration of incremental approximation concept shown in sequence situation when first, second, and nth neuron are added.
f1
f2
fm
x1
x2
g1 g1
g2 g2
xd
g1x1
x2
xd
x1
x2
xd
f1
f2
fm
f1
f2
fmgn
(a) (b) (c)
Artificial neural networks are well suited
for ac drive control and estimation.
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each iteration, one hidden neuron isoptimized and added to the network,
but all other hidden neuron parame-
ters remain unchanged. Then all out-
put weights are recalculated. The red
lines in Figure 4 indicate connection
parameters being recalculated when a
neuron is added to the network. The
iterative process is terminated when
final conditions such as error level or
number of hidden neurons are met.This type of ANN can approximate
any continuous function with any
accuracy, provided that one may use
as many hidden neurons as needed
[10], [27], [28].
However, this ANN architecture
(Figure 3) is marked by serious limita-
tions inherited from recurrent ANN.
First, it requires that initially selected
sampling time is applied to the data in
learning and recall phases, as dis-
cussed earlier. Second, there is no
guarantee of an ANN estimators stable
operation when it is trained in a series-
parallel identification scheme (during
the learning process, inputs and out-
puts signals of plant have been used)
and then works in a parallel configura-tion (only real input signals are avail-
able) using an estimated output signal.
FF-ANN with Dynamical Preprocessing
as a Stator Flux Estimator
To improve stator flux estimation accu-
racy, it is possible to use, rather than
the FF-ANN with TDLs or RANN, a sim-
ple dynamical preprocessing method
FIGURE 5 An FF-ANN-based stator flux estimator with dynamic signal preprocessing: (a) with ortogonal (, ) components of voltage and currentspace vector on input and (b) with natural (a, b, c) terminal voltage and phase current on input.
vab0v1vs
vs
is
K1u T1u
FF-ANN FF-ANN
K2u T2u
K3u T3u
K1i T1i
K2i T2i
K3i T3i
is
K1u T1uK0u T0u
K2u T2u
K3u T3u
vab
vbc
ia
K1i T1i
K2i T2i
K3i T3i
ib
v1
i1
s
s
s
si1
(a) (b)
Considerable improvement of flux vector estimation
can be achieved using FF-ANN with dynamic signal
preprocessing.
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[29]. It was shown in [29] and [30] that
dynamical filtering of ANNs input sig-
nals can turn a believed nonfunction
modeling problem into a function mod-
eling one. The natural evaluations of
FF-ANN with TDLs on the input signals
(vs, vs, is, is) conduct to the
solution presented in [29], which is
shown in Figure 5(a). Input signals
(vs, vs, is, is) prompt different
low-pass filters (first-order dynamic
units). Outputs of filters are connected
to FF-ANN. Vector flux components
have been achieved on two outputs of
the FF-ANN. Time constants can be
chosen by trial and error. The best
results are when two filters act roughly
as integrators, whereas the third one
FIGURE 6 Performance of DTC-SVM drive: (a) results for programmable LPF as flux estimator, (b) results for neural flux estimator, and (c) s com-ponents, speed, and torque signals.
1.6 1.7 1.8 1.9 2 2.1 2.2
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
1.7 1.8 1.9 2 2.1 2.21.6
1.6 1.7 1.8 1.9 2 2.1 2.2
0 2 4 6 8 10
0 2 4 6 8 10
0 2 4 6 8 10
1.7 1.8 1.9 2 2.1 2.21.6
1
0.5
0
0.5
0.5
0
0.5
50
0
50
20
0
20
20
0
20
1
Te
[Nm]
T
load[Nm]
m
[Nm]
1
0.8
0.6
0.4
0.2
0.2
0.4
0.5 0 0.5 1
0.6
0.8
11 0.5 0 0.5 11
0
s[Vs] s[Vs]
s
[Vs]
s
[Vs]
Error[Vs]
1
0.5
0
0.5
0.5
0
0.5
50
0
50
20
0
20
20
0
20
1
Te
[Nm]
T
load[Nm]
m
[rad/s]
1
0.8
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1
0
s
[Vs]
s
[Vs]
Error[Vs]
s
s-sest
s -sest
sest
m
Tload
Te
s-sest
s -sest
sest
m
Tload
Te
s
t [s] t [s]
Time (s) Time (s)
(a)
(b)
(c)
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has a very small time constant and
performs only the duty of noise attenu-
ation. The similar flux estimator based
on FF-ANN and dynamic signal prepro-
cessing, but uses direct stator electri-
cal signals (a, b, c phase current and
terminal voltage), is shown in Figure
5(b) [30]. Note that measured stator
voltages and currents are not trans-formed into components, whereas
estimated flux components are
expressed in . The Clark transform
is automatically formed within the FF-
ANN during the learning process. Each
stator electrical signal, (vab, vbc, ia, ib),
excites three different first-order
dynamical systems. As shown in [29],
those almost dynamically unprocessed
signals, combined with others, span an
approximation space that turns a mod-
eling problem into a static one. It was
found that there exists such a functionf3 that satisfies
s
(t) = f3(v1(t), . . . ,v6(t),
i1(t), . . . , i6(t)) . (6)
There are several advantages related
to that scheme:
It is a very simple learning algo-
rithm because a typical feed for-
ward architecture of neural network
is used.
The resultant estimator is stable
(stable dynamics and static nonlin-
earity connected in series).
Contrary to an uncompensated pure
integrator, there is no drift problem
due to LPFs presence.
There are different sampling times
available in learning and recall
mode (contrary to the tapped delay
or recurrent architecture).
A significant level of robustness to sta-
tor resistance variations is achieved.The Matlab/Simulink model of the
DTC-SVM drive is shown in Figure A in
the Appendix. The performance of the
DTC-SVM drive with ANN stator flux
estimator (Figure 5) is compared with
the programmable low-pass filter (PLPF)
algorithm presented in [22], [43], and
[44]. After off-line supervised training,
ANN estimators have been implemented
in the DTC drive. Figure 6 shows select-
ed signals in the DTC-SVM drive. A sta-
tor resistance rise in the amount of 30%
has been used. Figure 6(a) (with PLPFestimator) shows clearly that such iden-
tification error leads to significant
dynamics deterioration and even nonex-
clusion of unstable behavior.
A contrary ANN-based estimator with
dynamic signal preprocessing with the
same conditions assures stable opera-
tion and decent dynamics [Figure 6(b)].
Experimental Verification
The block diagram of the experimen-
tal system is shown in the Appendix
(Figure B). The ANN was learned with
the help of patterns taken from tested
drives equipped with a conventional
PLPF-based estimator.
Estimated resistancethe one pres-
ent in the algorithmic estimatorwas
updated simultaneously with imposed
stator resistance variations. If there is
an error in the stator resistance (Rs) of
about 30%, a response of the system to
step change of reference speed visiblydeteriorates [Figure 7(a)]. Under simi-
lar conditions, the drive that takes
advantage of feedback signals provided
by the ANN estimator with dynamic
signal preprocessing reverses smooth-
ly [Figure 7(b)]. So the idea of dynami-
cal preprocessing at the inputs of the
neural approximator was successfully
implemented and shows that common
problems related to recurrent and
tapped delayed ANNs can be avoided.
Selected Problemsof ANN-Based Speed Estimation
Overview
In the past few years, many speed-sen-
sorless techniques have been pro-
posed to cope with the speed sensing
problem [5]. Developed speed estima-
tion algorithms are more or less
parameter dependent and/or computa-
tionally time-consuming, so further
investigation is justified. Speed estima-
tors are designed on the basis of the
very common belief that information
about actual speed is contained in
FIGURE 7 Performance of the experimental drive: (a) with incorrect stator resistance (Rs) identification (PLPF estimator) and (b) with ANN-basedestimator (visible improvement compare to the PLPF estimator).
0
50
0
50
20
0
20
20
0
20
50
0
50
20
0
20
20
0
20
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0
Test [Nm]
Tref
[Nm]
[rad/s]
Test [Nm]
Tref
[Nm]
[rad/s]
0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
e e
m
Tref
Teste
m
Tref
Teste
Time (s) Time (s)
(a) (b)
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easily accessible electrical signals.
Available solutions can be divided into
two main groups. The first group
includes methods that should be
regarded as algorithmic ones. These
methods exploit a mathematical model
of an induction motorextended Luen-
berger observer [18], sliding-mode
observers [33], extended Kalman filter(EKF) [17], model reference adaptive
systems (MRAS) [16], indirect flux
detection by online reactance meas-
urement (INFORM) [2], high-frequency
signal injection [34], low-frequency sig-
nal injection [12], slip calculation [16],
pseudoinversion [10], and their muta-
tions. Unfortunately, any mathematical
modelings introduce some simplifica-
tion, which in turn entails deteriora-
tion of estimation. On the other hand,
there is a set of solutions that does not
take advantage of any mathematicalmodel of discussed plant. This group
consists of estimators based on ANN.
In such a case, only inputs and outputs
are known, whereas nonlinear relation-
ships between them are not. ANN solu-
tions can incorporate online trained
nets [11], [31], [35] or off-line trained
ones [36], [37]. These estimators natu-
rally possess robustness to noise and
parameter disturbances.
However, most popular ANNs dedi-
cated to system dynamics approxima-
tion, consisting of a multilayer FF-ANN
with additional TDLs or recurrences
[Figure 1(b)(d)], cause problems and
limitations that have been briefly
discussed earlier. Therefore, the speed
reconstruction problem using as
inputs current and voltage signals has
exactly the same limitation like flux
vector estimation. Therefore, it is also
necessary to use a nonlinear transfor-
mation (called here preprocessing) of
existing signals to achieve the inputs
and output spectra confinement.
Speed Estimators
with Nonlinear Preprocessing
and Neural Function Approximator
Nonlinear preprocessing of the elec-
trical signals should be applied to
solve problems occurring with TDLs.
Its task is to provide input signals
with a spectrum similar to the speed
signal. At the same time, a dimension
of the approximation space is
enlarged and the number of delay
units can be reduced even to zero
[10], [13]. There is a large number ofnonlinear functions useful at this
stage of preprocessing [see (7)]. The
nonlinear preprocessing is performed
in order to create a set of signals
marked by suitable spectrum. These
transformations are designed with
the aid of cross and dot products of
stator voltage vs and current is space
vectors, giving for instance the fol-
lowing equations:
u1 = abs(v s) =v2s + v
2s
u2 = abs(is) =
i2s + i
2s
u3 = Re(v s i
s )
= isvs + isvs
u4 = Im(vs i
s )
= isvs isvs
u5 = Re
v s
is
=isvs + isvs
i2s + i
2s
u6 = Imvs
is
=isvs isvs
i2s + i
2s
...
un = f(is, vs , is , vs) . (7)
Given the first set of six signals
(7), one can enlarge this set by
including their product ratios and
powers [13]. The basic structure of
the neural speed estimator with non-
linear input signal preprocessing is
shown in Figure 8. It is a difficult task
to take the best of the signal results(including most of the important
FIGURE 8 Speed estimator for ac motor with nonlinear preprocessing of input signals and neuralfunction approximator.
FF-ANN
Nonlinear
Preprocessing
vs
vs
is
is
m
FIGURE 9 Improved speed estimator for acmotor with nonlinear preprocessing, neural(PCA) linear preprocessing and neural func-tion approximator.
NonlinearPreprocessing
isa isb vsa vsb
is is vs vs
Self-Organizing
PCA
FF-ANN
Transformationabc/
Online
Offline
m
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information) from preprocessing. In
[13] and [32], few methods of final
selection from candidate signals have
been described and discussed.
Speed Estimator with Nonlinear
Preprocessing and NeuralImplementation of Principal
Component Analysis andFunction ApproximatorFurther improvement of the speed esti-
mator can be achieved by adding an
extra system that can automatically
select the best signals from the large
number of candidates [29].
The structure of such a speed esti-
mator (Figure 9) consists of three
stages connected in series: a nonlinear
preprocessing, a linear preprocessing
(self-organizing principal component
analysis, or PCA) and nonlinear func-tion approximator (FF-ANN) stage. The
second stage is designed to supply
optimal signals for the neural function
approximator. The goal of the second
stage is to decorrelate variables and to
maximize eigenvalues of the autocorre-
lation matrix at the same time. Such a
problem can be solved by PCA [32].
The PCA model generates a new set of
a few decorrelated variables called
principal components (PCs). The pur-
pose of the PCA is to derive a smallnumber of decorrelated linear combi-
nations of a set of zero-mean variables
while retaining as much of the
APPENDIX
FIGURE A Simulink model of a DTC-SVM drive with neural flux and neural speed estimators.
PITorque Controller
PISpeed Controller
k2k1
gamma
U_s_d
U_s_q
U_s_alfa_r
U_s_beta_r
Transformation
Visualization_Data.mat
Training_Data.mat
To File1
Load Torque
Signal Builder
Reference SpeedSignal Builder
In
U1
U2
U3
U4
U5
U6
NonlinearPreprocessing
y{1}p{1}
Neural Network 2Speed Estimator
y{1}p{1}
Neural Network 1Stator Flux Estimator
MS3
MS2
MS1
In
U1
U2
U3
U4
U5
U6
Linear DynamicPrprocessing
U_s_alfa_r
U_s_beta_r
U_s_alfa
U_s_beta
Inverter
[abs_Psi_s]
[gamma]
[Speed_est]
[Psi_s_est]
[Psi_s]
[Psi_r]
[Speed]
[Us_Is]
[Torque]
[Psi_s]
[Psi_r]
[Us_Is]
[gamma]
[Us_Is]
[abs_Psi_s]
[Speed_est]
[Torque]
[Speed_est]
[Psi_s_est]
[Torque]
[Speed]
[Psi_s_est]
[Psi_s]
[Us_Is]
[Us_Is]
[Psi_s]
[Speed]
[Speed]
PIFlux Controller
Reference_Flux
In
gamma
abs(Psi_s)
Calculation
Us_alfa
Us_beta
T_load
I_s_alfa
I_s_ beta
Torque
Speed
Psi_r_alfa
Psi_r_beta
Psi _s_alfa
Psi _s_beta
ac Motor
To File2
+
+
+
The Simulink simulation model of a DTC-SVM drive with neural flux
and speed estimators is shown in Figure A.
The block scheme of the laboratory set-up used for experimental
verification is shown in Figure B. It consists of a 1.5-kW, six-pole ac
motor which is fed by an IGBT voltage source inverter. For control
tasks, a dSpace DS1103 card programmed in the Matlab/Simulink
Real-Time Workshop and monitored via the ControlDesk interface
has been used. The control and estimation algorithms run at a com-
putation time of 0.5 ms. The angular speed of the drive is measured
with an encoder.
16 IEEE INDUSTRIAL ELECTRONICS MAGAZINE FALL 2007
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information from the original variables
as possible [38]. This, in turn, implies
reduction of a number of signals in
comparison to the number of nonlinear
transformations. The dimensionality
reduction is one of the basic features of
PCA. The PCA model involves second-
order statistics and guarantees data
decorrelation with simultaneousdenoising [38]. PCA is normally done
by analytically solving an eigenvalue
problem of the input correlation func-
tion. The eigenvectors must be put indecreasing order with respect to eigen-
values. However, in [38] it was demon-
strated that PCA can be accomplished
by a single-layer, linear self-organizingneural network trained with a modified
Hebbian learning rule [37], [39], [40].
Several different types of stopping
rules have been developed to deter-
mine the number of extracted compo-
nents from a given analysis.
One of the most popular is a per-
centage of variance criterion in which
successive eigenvectors are extracted
until some absolute percentage of the
total variance has been explained (com-
monly used with typical threshold set
to 95%). Such a type of PCA implemen-tation is shown in Figure 9 as the sec-
ond stage of signal preprocessing for a
neural speed estimator. Computer test
results of a DTC-SVM drive operated
with a feedback signal from a neural
speed estimator is shown in Figure 10.
One can see the very good performance
of drive systems.
Experimental Verification
The experimental has been performed
on drive system shown in Figure B
with data given in the Appendix. The
control and estimation algorithms
have been running with a sampling
time of 0.5 ms. The drive was tested at
random speed and load profiles.
The speed of the drive was meas-
ured additionally with an encoder.
After offline training, the nonlinear
ANN was implemented in the DSP
board. Figure 11 shows some experi-
mental results of a drive operated with
speed estimator of Figure 9(b).
Conclusions
This article presented problems and
selected improvements related to the
application and implementation of
ANN-based flux vector and mechani-
cal speed estimators for control of
high-performance pulse width modu-
lated (PWM) inverter-fed induction
motor drives. Key conclusions include
the following:
The tapped delay neural architecture
has several limitations caused by sampling and
accuracy of measurements.
FIGURE B Block diagram of experimental set-up DTC-SVM drive for testing of flux and speed estimators.
acGrid
M
Rectifier Inverter
ac Motor
dSPACEDS1103
Visualization
Power Circuit
Load
Encoder
PC Computer(ControlDesk)
Speed
Calculation
Flux EstimatorPLPF
NeuralFlux Estimator
NeuralSpeed Estimator
us,
is
S1
S2
is
SpeedController
PWM-SVM
DTCTorque and Flux
Controller
Input: Keyboard Output: Screen
CurrentandVoltage
Measurement
M ENC
Parameters Set UpConfiguration Set Up
est
est m
ref
ref
est
MOTOR DATA:
Induction cage motor Sf100L6K:
PN= 1.5 kW, UN= 220 V, IN= 6.8 A, fN= 50 Hz, cos N= 0.75, N= 0.76,
nN= 930 rpm, Rs = 1.54 , Rr= 1.29 , Xs = 31.56 , Xr= 30.43 ,
Xm = 28.74
INVERTER DATA:
IPM-IGBT module:Vdc = 330 V, switching frequency= 10 kHz, Iout = 50A
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Recurrent ANNs can be used for flux
vector estimation only under the
assumption of very fast sampling
equal in learning and recall mode.
Considerable improvement of flux
vector estimation can be achieved
using FF-ANN with dynamic signal
preprocessing (Figure 5). This estima-
tor poses the following advantages:very simple learning algorithm, sta-
ble operation, no drift problems due
to LPFs presence, different sampling
times available in learning and recall
mode (contrary to the tapped delay
or recurrent architecture), and some
level of robustness to stator resist-
ance variations.
For reliable mechanical speed esti-
mation, an FF-ANN with nonlinear
signal preprocessing has been
described. Two-stage preprocessing
(nonlinear preprocesing and linearPCA) of four terminal signals is com-
bined with FF-ANN. The first one
guarantees enlarged approximation
space using a linearly independent
set of input signals based on cross
and dot products of motor voltage
and current vectors. The second one
(linear stage, PCA) takes advantage
of self-organizing principal compo-
nent analysis to optimize the
approximation space without loss of
information. Proposed estimators
are very convenient to implement.
The presented experimental oscillo-
grams measured in a 1.5-kW labora-
tory induction motor drive verify
estimators based on ANN with non-
linear preprocessing of input signals.
Achieved results can be easily
extended to DTC-SVM permanent
magnet synchronous motor drives.
It is expected that, thanks to contin-
uous developments in digital signal
processing technology, ANN-based
techniques will have a strong impacton drive control, estimation, and
monitoring in the coming decades.
BiographiesLech M. Grzesiak graduated from the
Electrical Engineering Faculty of
Warsaw University of Technology in
1976. He received the Ph.D. in 1985 and
the Dr.Sc. degree in 2002, respectively,
from the same university. Since 1977, he
18 IEEE INDUSTRIAL ELECTRONICS MAGAZINE FALL 2007
FIGURE 10 Simulation results of DTC-SVM drive with speed feedback signal taken from a neuralspeed estimator (as shown in Figure 8).
100
0
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10 12 14 16 18 20
0 2 4 6 8 10
Time (s)
12 14 16 18 20
100
5
0
5
20
0
20
10
0
Tload
[Nm]
Te
[Nm
]
Errorm
[%]
m
[rad/s]
10
FIGURE 11 Experimental waveforms of speed estimation based on seven principal components(estimator structure shown in Figure 9).
0
50
0
50
50
0
50
5
0
5
10 20 30 40 50 60 70 80
0 10 20 30 40 50 60 70 80
0 10 20 30 40
Time (s)
50 60 70 80
[
rad/s]
m
[rad/s]
es
[rad/s]
By using appropriate preprocessing of input signals,
the performances of flux vector and speed estimators
are considerably improved in terms of accuracy and
sensitivity to parameter changes.
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has been employed at Warsaw Universi-
ty of Technology, currently as a profes-
sor. He was also codirector of the Centre
of Excellence on Power Electronics Intel-
ligent Control for Energy Conservation
(PELINCEC) from 20032005. He is an
associate editor ofIEEE Transactions on
Industrial Electronics since 2004. His
main research interests and publica-tions are in the theory and application
of control, generally dedicated for elec-
tric drives, power electronics, and ener-
gy generating systems. From 1994, his
research interest has focused on devel-
opment and applications of neural sys-
tems. He is an author and coauthor of a
variety of papers related to this subject.
He is a Senior Member of the IEEE.
Marian P. Kazmierkowski re-
ceived the M.S., Ph.D., and Dr.Sci.
degrees in electrical engineering from
the Institute of Control and IndustrialElectronics (ICIE), Warsaw University of
Technology, Warsaw, Poland, in 1968,
1972, and 1981, respectively. Since
1987, he has been a professor and
director of ICIE. He was also head of
PELINCEC from 20032005 (European
Framework Program V) at ICIE, Warsaw
University of Technology, Poland. He
coedited (with R. Krishnan and F.
Blaabjerg) and coauthored the com-
pendium Control in Power Electronics
(Academic Press, 2002). He received an
Honorary Doctorate degree from Aal-
borg University in 2004 and the Dr.
Eugene Mittelmann Achievement
Award from the IEEE Industrial Elec-
tronics Society in 2005. He was the edi-
tor-in-chief of IEEE Transactions on
Industrial Electronics (20042006). He is
past-chair of the IEEE Poland Section.
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