Supervisory Genetic Evolution Control for Induction Machine
Using Fuzzy Design Technique
Rong-Jong Wai*, Jeng-Dao Lee, and Li-Jung Chang
Department of Electrical Engineering, Yuan Ze University, Chung Li 320, Taiwan, R.O.C.
*E-mail: rjwai@saturn.yzu.edu.tw
AbstractThis study presents a supervisory genetic
evolution control (SGEC) system for achieving highprecision position tracking performance of an indirect
field-oriented induction motor (IM) drive. Based on
fuzzy inference and genetic algorithm (GA)
methodologies, a newly design GA control law is
developed first for dominating the main control task.
However, the stability of the GA control can not be
ensured when huge unpredictable uncertainties occur in
practical applications. Thus, a supervisory control is
designed within the GA control so that the states of the
control system are stabilized around a predetermined
bound region. In addition, the effectiveness of the
proposed control scheme is verified by numerical
simulation and experimental results, and its advantages
are indicated in comparison with a feedback control
system.
I. INTRODUCTION
Nowadays, the field-oriented control technique has been
widely used in industry for high-performance IM drive [1,
2], where the knowledge of synchronous angular velocity is
often required in the phase transformation for achieving the
favorable decoupling control. However, the performance is
sensitive to the variations of motor parameters, especially
the rotor time-constant, which varies with the temperature
and the saturation of the magnetizing inductance. Recently,
much attention has been given to the possibility of
identifying the changes in motor parameters of an IM while
the drive is in normal operation. Some researchers have
proposed various IM drives with rotor-resistance or rotor
time-constant identification to produce better control
performance [3-5]. However, the control performance of the
IM is still influenced by the uncertainties, such as
mechanical parameter variation, external disturbance,
unstructured uncertainty due to nonideal field orientation in
transient state, and unmodelled dynamics, etc. In the control
fields, the acquirement of the uncertainty information is an
important research topic. From a practical point of view,
however, it is usually very difficult to get the complete
information of uncertainties. Therefore, the motivation of
this study is to design a suitable control scheme to confront
the uncertainties existing in practical applications of an
indirect field-oriented IM drive.
To deal with the mentioned uncertainties, much research
has been done in recent years to apply various approaches
to attenuate the effect of uncertainties. On the basic aspect,
the conventional proportional-integral-derivative (PID)-type
controllers are widely used in industry due to their simple
control structure, ease of design, and inexpensive cost.
However, the PID-type controller can not provide perfect
control performance if the controlled plant is highly
nonlinear and uncertain [6, 7]. On the other hand, computed
torque or inverse dynamics technique is a special
application of feedback linearization of nonlinear systems
[8, 9]. The computed torque controller is utilized to
linearize the nonlinear equation by cancellation of some, or
all, nonlinear terms such that a linear feedback controller is
designed to achieve the desired closed-loop performance.
However, since the computed torque approach is based on
perfect cancellation of the nonlinear dynamics, the
objection to the real-time use of such control scheme is the
lack of knowledge of uncertainties.
Genetic algorithm (GA), which uses the concept of
Darwin’s theory, has been widely introduced to deal with
nonlinear control difficulties and to solve complicated
optimization problems [10-17]. Darwin’s theory basically
stressed the fact that the existence of all living things is
based on the rule of “survival of the fittest”. In the theory of
evolution, different possible solutions to a problem are
selected first to a population of binary strings encoding the
parameter space. The selected solutions undergo a parallel
global search process of reproduction, crossover, and
mutation to create a new generation with highest fitness
function [10]. This process of production of a new
generation and its evaluation is repeated until there is
satisfactory convergence within a predefined fitness grade.
Since the GA simultaneously evaluates many points in the
parameter space, it is more likely to converge toward the
global solution [16]. Recently, this underlying GA-based
global optimization technique has been applied in several
fuzzy logic control applications [18-22]. In view of the
previous research results, the favorable control or
optimization performance can reach their destination owing
to the powerful global searching capability of GA. However,
the role of GA control is usually used as a minor
compensatory tuner in the open literatures because the
stability of the GA-based control scheme can not be
guaranteed until now. The aim of this study is to design an
on-line GA control scheme as a major controller, moreover,
the stability of this strategy can be ensured with the aid of
supervisory control during the whole control process.
II. INDIRECT FIELD-ORIENTATION INDUCTION MOTOR
DRIVE
The IM used in this drive system is a three-phase Yconnected four-pole 800W 60Hz 130V/5.6A type.
Moreover, the drive system is a ramp comparison currentcontrolled pulse width modulated (PWM) voltage source
inverter (VSI). The current-controlled VSI is implemented
by isolated gate bipolar transistor (IGBT) switching
components with a switching frequency of 15kHz. For the
position control system, the braking machine is driven by a
current source drive to provide braking torque. An inertia
varying mechanism is coupled to the rotor of the IM. The
mechanical equation of an IM drive can be represented as
(1)
Jr  Br  TL  Te
where J is the moment of inertia; B is the damping
coefficient;  r is the rotor position; TL represents the
external load disturbance; Te denotes the electric torque.
With the implementation of field-oriented control [1, 2], the
electric torque can be simplified as
(2)
Te  Kt iqs*
with the torque constant K t is defined as
(3)
Kt  (3n p 2)(L2m Lr )ids*
Substituting (2) into (1) as follows can represent the
mechanical dynamic of the IM drive system:
K
B
1
r ( t )   r ( t )  t iqs* ( t )  TL
(4)
J
J
J
 Apr ( t )  B p U ( t )  D p TL
where Ap   B J ; B p  K t J  0 ; D p  1 J , and
U (t )  iqs* (t ) is the control effort. Dynamic modeling based
on measurements [23] is applied to find the drive model offline at the nominal condition. The results are (on a scale of
50(rad/s)/V)
K t  0.4851 N  m/A
J  4.78  10 3 N  m  s 2 / rad
(5)
B  5.34  10 N  m  s/rad
The overbar symbol represents the system parameters in
nominal conditions.
3
unpredicted uncertainties for the actual IM drive system
r (t )  ( Ap  A) r (t )  ( B p  B) U (t )  D p TL  
 A pr (t )  B p U (t )  L(t )
(7)
where A and B denote the uncertainties introduced by
system parameters J and B;  represents the unstructured
uncertainty due to nonideal field orientation in transient
state, and the unmodelled dynamics in practical applications;
L(t ) is called the lumped uncertainty and is defined as
(8)
L(t )  A (t )  BU (t )  D T  
r
p
L
Here the bound of the lumped uncertainty is assumed to be
given; that is,
(9)
L(t )  
where  is a given positive constant. The control problem
is to find a control law so that the rotor position can track
any desired commands. To achieve this control objective,
define a tracking error as e   m   r and its derivative
e     , in which  represents a reference trajectory
m
r
m
specified by a reference model. The control law for a SGEC
system is assumed to take the following form:
U  U GA  U S
(10)
where U GA is a GA control that is a main tracking controller,
and U S is a supervisory control that is designed so that the
states of the control system are stabilized around a
predetermined bound region. The overall scheme of the
SGEC strategy is depicted in Fig. 1 and the detailed
descriptions of each control part are exhibited in the
following subsection.
A. GA Control
III. SUPERVISORY GENETIC EVOLUTION CONTROL
With the field-oriented method, the dynamic behavior of
the IM is rather similar to that of a separately excited dc
motor. The decoupled relationship is obtained by means of
a proper selection of state coordinates under the hypothesis
that the synchronous angular velocity is precise. Therefore,
the rotor speed is asymptotically decoupled from rotor flux,
and the speed is linearly related to torque current after the
slip angular velocity can be obtained precisely. However,
the control performance of the IM is still influenced by the
uncertainties of the plant, such as mechanical parameter
uncertainty, external load disturbance, unstructured
uncertainty due to nonideal field orientation in transient
state, and unmodelled dynamics in practical applications.
Therefore, a SGEC scheme is designed in the sense of fuzzy
inference and GA methodologies to increase the robustness
of the indirect field-oriented IM drive for high-performance
applications.
Consider the parameters in the nominal condition
without external load disturbance, rewriting (4) as follows
can represent the nominal model of the IM drive system:
(6)
r (t )  Apr (t )  B p U (t )
where Ap   B J and Bp  Kt J  0 are the nominal
values of
Ap
and B p , respectively. Consider (6)
parametric
variation,
external
load
disturbance
and
In the GA controller, the tracking error ( e ) and its
derivative ( e ) are chosen as the input signals, and U GA is
the output signal. In this study, the spirit of fuzzy inference
mechanism is utilized to design this GA controller. It can
divide three main parts: GA membership region,
quantization number/levels and GA lookup table
introducing in the following paragraphs.
GA Membership Region
The membership regions Re and Re denote some area,
where the tracking error and its derivative maybe varied in
practical applications. The selection of membership regions
usually depends on the expert’s experience and various
applications.
Quantization Number/Levels
According to the quantization number ne and ne , the
tracking error and its derivative can be separated into
several different levels. Note that, the selection of ne and
ne has a great influence with higher or lower accuracy of
system performance. If the selection of quantization number
is too large, it will cause heavy computation load, and the
learning speed of the GA controller will be reduced. On the
contrary, if the selection of quantization number is too small,
it may cause the chattering efforts in the controlled system,
even to be unstable. In the study, the quantization functions
are denoted as Qer (e) and Qer (e) , and each of them has
nine levels, which are composed of NE (Negative Extend),
NB (Negative Big), NM (Negative Medium), NS (Negative
Small), ZE (Zero), PS (Positive Small), PM (Positive
Medium), PB (Positive Big), and PE (Positive Extend).
Indirect field-oriented IM drive
TL
_
Kt
Te
1
Js  B
+
GA control F
fit
reproduction
crossover
mutation
Cr
Mb
U
wr
r
1
s
_
d
dt
+
m
r
U GA
GA lookup
table
+
US
ne
supervisory
control

V
e
e
Re
membership
regions
e
e
m
quantization
levels
Re
K
+
Q er (e )
Qer (e )
ne
 r*
d
dt
_
+
reference
model
supervisory genetic evolution control system
Fig. 1. Block diagram of SGEC system.
Table I. GA Lookup Table
e
PE
PB
PM
PS
ZE
NS
NM
NB
NE
NE
C11
 C12
 C13
 C14
 C15
 C16
 C17
 C18
 C19
NB
+ C 21
C22
 C23
 C24
 C25
 C26
 C27
 C28
 C29
NM
+ C 31
+ C32
C33
 C34
 C35
 C36
 C37
 C38
 C39
NS
+ C 41
+ C42
+ C43
C44
 C45
 C46
 C47
 C48
 C49
ZE
+ C 51
+ C52
+ C53
+ C54
C55
 C56
 C57
 C58
 C59
PS
+ C61
+ C62
+ C63
+ C64
+ C65
C66
 C67
 C68
 C69
PM
+ C71
+ C72
+ C73
+ C74
+ C75
+ C76
C77
 C78
 C79
PB
+ C81
+ C82
+ C83
+ C84
+ C85
+ C86
+ C87
C88
 C89
PE
+ C 91
+ C92
+ C93
+ C94
+ C95
+ C96
+ C97
+ C98
C99
e
GA Lookup Table
When the input signals are passed through the
quantization number/levels step, the GA lookup table shown
in Table I will be constructed on line with the genetic
evolution mechanism: reproduction, crossover and mutation
introduced later. Note that, based on the fuzzy inference
mechanism, the sign of the associated control efforts are
predefined in Table I such that it has more possibility to
search optimal control efforts. In this study, each control
effort in the GA lookup table can be represented as a
chromosome and can be expressed via binary string
representation as
Ci j  {g1i j g 2i j  g li j }
with i  {0, , ne }, j  {0, , ne }
(11)
where C i j is one chromosome that has l-bits binary string,
and g i j denotes a gene. On the other words, the values of
the C i j are converted into their binary equivalent values. In
order to evaluate the fitness grade of each chromosome, a
fitness function is chosen as
(12)
Ffit (i, j )  exp{[(Δ  (i, j )  (i, j))  1]2 }  [0, 1]
predetermined bound region and guarantee the system
stability.
B. Supervisory Control
where  (i, j ) is the evaluated tracking error induced by the
original control effort, and  (i, j ) denotes the evaluated
tracking error-change at two continuous iterations via a new
chromosome in (i, j) area of the GA lookup table. During
the on-line searching process, the chromosome with a
highest fitness grade will be saved on the GA lookup table.
The basic genetic operation used in this study is
summarized as follows:
Assume that the lumped uncertainty is available, there
exists an ideal control law as follows such that the favorable
control performance can be ensured:
1
(16)
U *  B pn
[ Apnr  L  m  KE ]
Reproduction
This reproduction procedure is used to decide which
chromosomes would be selected into the mating pool for
further genetic operations. First, an initial chromosome,
named as mother chromosome, is taken as a control input of
the IM drive. According to the running result, it will
produce new tracking error and its derivative such that a
corresponding chromosome, named as father chromosome,
can be detected via GA lookup table. Both of them are
selected to the crossover operation.
Crossover
The crossover operation combines the features of two
parent chromosomes to form one offspring by swapping
corresponding segments of the parents. In this study, the
crossover operation is performed with one crossover rate
defined as
(13)
C r  ROUND[ F fit (i, j )  l ]  {0, , l}
where ROUND( ) denote rounding the element to its
nearest integer. If the selection of the crossover rate C r is
bigger, then the offspring has more characteristics in the
father chromosome. This operation is repeated until there is
satisfactory convergence within a predefined fitness grade.
Mutation
In order to avoid chromosome trapping in local optimal
point, every gene is subject to random change with
probability of the pre-assigned mutation rate, M r , at each
iteration. In the binary string case, mutation operators just
to change the bit form 0 to 1 or vice versa. According to the
corresponding fitness value, the mutation rate M r can be
represented as
(14)
M r  ROUND [(l  Cr )  M b l ]  {0, , M b }
where M b is a given upper bound of mutation number. As
time goes by, the fitness grade will gradually increase, and
the crossover and mutation operators also tend to settle.
This evolution procedure progresses until the fitness grade
reaches the desired specification. Thus, the output of the
GA controller can be represented as
(15)
U GA  Table( Qer (e), Qer (e))
However, the stability of the GA control can not be ensured
when huge unpredictable uncertainties occur in practical
applications. Therefore, the auxiliary design of a
supervisory control is necessary for the condition of
divergence of states to pull the states back to the
where K  [k1
k 2 ] is a given positive constant vector and
E  [e e] is a tracking error vector. From (7), (10) and
(16), an error equation is then obtained as follows:
(17)
E  E  Bm [U *  U GA  U S ]
T
1 
 0
is a stable matrix


k

k 2 
 1
Bm  [0 B pn ] . Define a Lyapunov function as
where
and
(18)
VS  E T PE / 2
where P is a symmetric positive definite matrix which
satisfies the following Lyapunov equation:
(19)
T P  P  Q
and Q  0 is selected by the designer. Take the derivative
of the Lyapunov function and use (17) and (19), then
1
VS   E T QE  E T PBm [U *  U GA  U S ]
2
1 T
  E QE  E T PBm ( U *  U GA )  E T PBmU S
2
(20)

To satisfy V  0 , the supervisory control U is designed
S
S
as follows [8, 9]:
1
U S  I sgn(E T PBm )[ U GA  B pn
( Apnr    m  KE )]
(21)
where sgn() is a sign function;  is an absolute function; I
is an index function and is defined as
 I  1, if VS  V
I 
(22)
I  0, if VS  V
in which V is a positive constant designed by the user.
Substitute (21) into (20) and consider the I  1 case, then
1
VS   E T QE  E T PB m ( U *  U GA )  E T PB m U S
2
T
  E QE / 2  E T PB [ B 1 ( A   L    KE )
m
 U GA  U GA
pn
Pn
r
m
 B ( A pnr    m  KE )]
1
pn
1 T
1
1
E QE  E T PB m B pn
(   L )   E T QE  0
(23)
2
2
Using the designed supervisory control U S as shown in eqn.
28, the inequality V  0 can be obtained for non-zero

S
value of the tracking error vector E when V S  V . As a
result, the stability of the SGEC system can be guaranteed.
The effectiveness of the proposed control scheme is verified
by the following simulation and experimental results.
IV. SIMULATION AND EXPERIMENTAL RESULTS
The simulation of the proposed SGEC system is
implemented via the “Matlab” package based on the scheme
B  3  B , TL  1Nm occurring at 5.5s. The control
objective is to make the rotor position follow the periodic
step reference trajectory under the occurrence of
uncertainties.
reference
model
rad
K  [100 20 ] (24)
Mb 1,
  5,
V  0.3 ,
All the parameters in the proposed control system are
chosen to achieve the best transient control performance in
both simulation and experimentation considering the
requirement of stability. In order to let the GA controller
have the self-organizing property, the initial GA lookup
table in this study is set at a null table. The effect due to the
inaccurate selection of the initialized population can be
retrieved by the on-line searching methodology. The
parameter searching process remains continually active for
the duration of the simulation and experiments runs.
A second-order transfer function with rise time 0.5s is
chosen as the reference model for the periodic step
command:
w n2
57 .8
(25)

s 2  2w n s  w n2 s 2  15 .2s  57 .8
where  and w n are the damping ratio (set at one for
critical damping) and undamped natural frequency.
Moreover, two simulation cases including parameter
variations and external load disturbance in the shaft due to
periodic commands are addressed as Case 1: J  J ,
B  B , TL  1Nm occurring at 5.5s; Case 2: J  3  J ,
responses are resulted owing to parameter variations and
external load disturbance. Though a large control gain K
may solve the problem of delay or degenerate tracking
responses, it will result in impractical large control efforts.
Therefore, the control gains are difficult to determine due to
the unknown uncertainties in practical applications, and are
ordinarily chosen as a compromise between the stability and
control performance. Now, the SGEC system is considered
under the same simulated cases as the feedback control
system. The simulated results of SGEC system for periodic
step command at Case 1 and Case 2 are depicted in Fig. 3.
The tracking errors converge quickly, and the robust
tracking performance of the proposed control scheme can
be obtained under the occurrence of uncertainties.
reference
model
rotor
position
time (sec)
(a)
rad
shown in Fig. 1, and its control parameters are given as
follows:
l  3,
Re  0.15 , Re  1.25 ,
i  j  9,
reference
model
rotor
position
time (sec)
(b)
Fig. 3. Simulated responses of SGEC system at Case 1 and Case 2.
rad
rotor
position
2 rad
reference
model
0rad rotor
time (sec)
(a)
position
reference
model
1Nm
start
1sec
(a)
rad
rotor
position
reference
model
time (sec)
(b)
Fig. 2. Simulated responses of feedback control system at Case 1 and Case
2.
In the simulation, first the ideal control law in (16)
without considering lumped uncertainty ( L  0 ), which is
called a feedback control system, is demonstrated for
comparison. The simulated results of feedback control
system for periodic step command at Case 1 and Case 2 are
depicted in Fig. 2. From the simulation results, favorable
tracking response shown in the beginning of Fig. 2(a) only
can be obtained at the nominal condition, and poor tracking
0rad
rotor
position
2 rad
1Nm
start
1sec
(b)
Fig. 4. Experimental results of feedback control system at external
disturbance condition and parameter variation condition.
Some experimental results are provided here to further
demonstrate the effectiveness of the SGEC system via
“Turbo C” language. Two test conditions are given to verify
the robustness of the proposed control scheme. One is the
external disturbance condition, that is the nominal inertia
with 1Nm braking-load disturbance occurring at 5.5s, and
the other is the parameter variation condition, that is the
increasing of the rotor inertia to approximately three times
the nominal value with 1Nm braking-load disturbance
occurring at 5.5s. First, a feedback control system, which is
the ideal control law shown in (16) with L  0 , is
implemented to control the IM drive for testing the
influence of lumped uncertainty. The experimental results
due to periodic step command at the two test conditions are
depicted in Fig. 4. Though favorable tracking responses
shown in the beginning of Fig. 4(a) can be obtained at the
nominal condition, the degenerated tracking responses are
resulted under the occurrence of parameter variations and
external load disturbance. Then, the SGEC system is
implemented to control the rotor position of the IM drive
system. The experimental results due to periodic step
command at the two test conditions are depicted in Fig. 5.
From the experimental results, the robust tracking
performance of the proposed control scheme can be
obtained under the occurrence of parameter variations and
external load disturbance. Compared these results with the
ones of feedback control system, the proposed SGEC
scheme is more suitable to control the rotor position of an
indirect field-oriented IM drive system under the possible
occurrence of uncertainties.
2 rad
reference
model
0rad
rotor
position
1Nm
start
1sec
(a)
reference
model
0rad
rotor
position
2 rad
1Nm
start
1sec
(b)
Fig. 5. Experimental results of SGEC system at external disturbance
condition and parameter variation condition.
V. CONCLUSIONS
This study has been successfully implemented a SGEC
system for an indirect field-oriented IM drive. This control
scheme contains two parts: one is a GA control that was
utilized to dominate the main control task, and the other is a
supervisory control that was designed to further ensure the
stable control characteristic. The effectiveness of the
proposed control scheme was confirmed by numerical
simulation and experimental results, and its advantages
indicated in comparison with a feedback control system.
The major contribution of this study is: 1) the successful
utilization of the spirit of fuzzy inference mechanism to
design a GA control with self-organizing property, and 2)
the successful confirmation of the stability of SGEC system
at the aid of a supervisory control, and 3) the successful
implementation of a SGEC system to an indirect fieldoriented IM drive for high-precision position tracking under
the occurrence of uncertainties in practice.
ACKNOWLEDGMENTS
The authors would like to acknowledge the financial
support of the National Science Council in Taiwan, R.O.C.
through its grant NSC 90-2213-E-155-003.
REFERENCES
[1] LEONHARD, W.: ‘Control of electrical drives’ (SpringerVerlag, 1996)
[2] KRISHNAN, R.: ‘Electric motor drives: modeling, analysis,
and control’ (Prentice-Hall, 2001)
[3] VUKOSAVIC, S.N., and STOJIC, M.R.: ‘On-line tuning of
the rotor time constant for vector-controlled induction motor
in position control applications’, IEEE Trans. Ind. Electron.,
1993, 40, (1), pp. 130-138
[4] LIN, F.J., SU, H.M., and CHEN, H.P.: ‘Induction motor
servo drive with adaptive rotor time-constant estimation’,
IEEE Trans. Aerosp. and Electron. Syst., 1998, 34, (1), pp.
224-234
[5] WAI, R.J., LIU, D.C., and Lin, F.J.: ‘Rotor time-constant
estimation approaches based on energy function and sliding
mode for induction motor drive’, Electr. Power Syst.
Research, 1999, 52, pp. 229-239
[6] HANG, C.C., ASTROM, K.J., and HO, W.K.: ‘Refinements
of the Ziegler-Nichols tuning formula’, IEE Proc. Contr.
Theory Appl., 1991, 138, (2), pp. 111-118
[7] ASTROM, K.J., and HAGGLUND, T.: ‘PID controller:
theory, design and tuning’ (Research Triangle Park, NC: ISA,
1995)
[8] SLOTINE, J.J.E., and LI, W.: ‘Applied nonlinear control’
(Prentice-Hall, 1991)
[9] ASTROM, K.J., and WITTENMARK, B.: ‘Adaptive control’
(Addison-Wesley, 1995)
[10] GOLDBERG, D.: ‘Genetic algorithms’ (Addison-Wesley,
1989)
[11] VARSEK, A., URBANCIC, T., and FILIPIC, B.: ‘Genetic
algorithms in controller design and tuning’, IEEE Trans. Syst.,
Man, Cybern., 1993, 23, (5), pp. 1330-1339
[12] OMATU, S., and DERIS, S.: ‘Stabilization of inverted
pendulum by the genetic algorithm’. IEEE Conf.
Evolutionary Computation, 1996, pp. 700-705
[13] HA, K.J., and KIM, H.M.: ‘A genetic approach to the attitude
control of an inverted pendulum system’. IEEE Conf. Tools
with Artificial Intelligence, 1997, pp. 268-269
[14] CHANG, C.S., and SIM, S.S.: ‘Optimising train movements
through coast control using genetic algorithms’, IEE Proc.
Electr. Power Appl., 1997, 144, (1), pp. 65-73
[15] ALONGE, F., D'IPPOLITO, F., FERRANTE, G., and
RAIMONDI, F.M.: ‘Parameter identification of induction
motor model using genetic algorithms’, IEE Proc. Contr.
Theory Appl., 1998, 145, (6), pp. 587-593
[16] CHEN, B.S., and CHENG, Y.M.: ‘A structure-specified H 
optimal control design for practical applications: a genetic
approach’, IEEE Trans. Contr. Syst. Technol., 1998, 6, (6),
pp. 707-718
[17] MIURA, T., and TANIGUCHI, T.: ‘Open-loop control of a
stepping motor using oscillation-suppressive exciting
sequence tuned by genetic algorithm’, IEEE Trans. Ind.
Electron., 1999, 46, (6), pp. 1192-1198
[18] SURMANN, H.: ‘Genetic optimization of a fuzzy system for
charging batteries’, IEEE Trans. Ind. Electron., 1996, 43, (5),
pp. 541-548
[19] TZES, A., PENG, P.Y., and GUTHY, J.: ‘Genetic-based
fuzzy clustering for DC-motor friction identification and
compensation’, IEEE Trans. Contr. Syst. Technol., 1998, 6,
(4), pp. 462-472
[20] MOALLEM, M., MIRZAEIAN, B., MOHAMMED, O.A.,
and LUCAS, C.: ‘Multi-objective genetic-fuzzy optimal
design of PI controller in the indirect field oriented control of
an induction motor’, IEEE Trans. Magnetics: Part 1, 2001,
37, (5), pp. 3608-3612
[21] LEE, S.I., and CHO, S.B.: ‘Emergent behaviors of a fuzzy
sensory-motor controller evolved by genetic algorithm’, IEEE
Trans. Syst., Man, Cybern.: Part B, 2001, 31, (6), pp. 919929
[22] CAO, Y.D., HU, B.G., and GAO, D.J.: ‘Genetic-based robust
optimal design for one-input fuzzy PID controllers’. IEEE
Conf. Syst., Man, Cybern., 2001, pp. 2263-2268
[23] LIAW, C.M., OUYANG, M., and PAN, C.T.: ‘Reduced order
parameter estimation for continuous system from sampled
data’, ASME Trans., J. Dynamic System Measurement and
Control, 1990, 112, pp. 305-308