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Transcript
Expert System, Fuzzy Logic, and
Neural Network Applications in Power
Electronics and Motion Control
BIMAL K. BOSE, FELLOW, IEEE
Invited Paper
Artificial intelligence (AI) tools, such as expert system, fuzzy
logic, and neural network are expected to usher a new era in power
electronics and motion control in the coming decades. Although
these technologies have advanced significantly in recent years and
have found wide applications, they have hardly touched the power
electronics and mackine drives area. The paper describes these
Ai tools and their application in the area of power electronics
and motion control. The body of the paper is subdivided into
three sections which describe, respectively, the principles and
applications of expert system, fuzzy logic, and neural network.
The theoretical portion of each topic is of direct relevance to
the application of power electronics. The example applications
in the paper are taken from the published literature. Hopefully,
the readers will be able to formulate new applications from these
examples.
I. INTRODUCTION
Artificial Intelligence is machine emulation of the human
thinking processes. The term began to be systematically
used since the Dartmouth College conference in 1956
when “artificial intelligence” was defined as “computer
processes that attempt to emulate the human thought processes that are associated with activities that require the
use of intelligence.” Human brain is the most complex
machine on earth. For a long time, the neuro-biologists
have been taking the bottom-up approach to understand
the brain structure and its functioning, and the behavioral
scientists, such as psychologists and psychiatrists, the topdown approach to understand the human thinking process.
However, our knowledge about the brain is so inadequate at
present that it is expected to take another 50 to 100 years
to understand the human brain and its thinking process.
Since human brain is the ultimate intelligent machine, the
question is: Is it possible to generate such intelligence,
or at least a part of it, artificially with the help of a
computer so that it can solve our complex problems which
Manuscript received November 29, 1993.
The author is with the Department of Electrical Engineering, The
University of Tennessee, Knoxville, TN 37996 USA.
IEEE Log Number 9402594.
are difficult to solve in traditional way? In early age, it
was perceived that human brain takes decision on the basis
of “yes-no” or “true-false” reasoning. In 1854, George
Boole first published his article “Investigations on the
laws of thought,” and Boolean algebra and set theory
were born as a result. Gradually, the advent of electronic
logic and solid state IC’s ushered the modem era of Von
Neumann type digital computation. Digital computers were
defined as “intelligent” machines because of their capability
to process human thought-like yes ( I t n o (0) logic. Of
course, using the same binary logic, computers can solve
complex scientific, engineering, and other data processing
problems. Since the 1960’s and in the early 1970’s, it was
felt that computers have severe limitations being able to
handle only algorithmic-type problems. An entirely new
way of structuring software that closely matches the human
thinking process, called “Expert System” was bom. The
new branch of software engineering is called “Knowledge
Engineering.” This new breed of “Knowledge Engineers”
was responsible for the acquisition of knowledge from the
human experts in a particular domain and translating it into
software. In the 1980’s, expert system applications prolifereated in industrial process control, medicine, geology,
agriculture, information management, military science, and
space technology, just to name a few.
Since the mid 1960’s, a new theory called “Fuzzy Logic”
or fuzzy set theory was propounded which gradually helped
to supplement the expert system as an A I tool. L. A.
Zadeh [ 161, the originator of this theory, argued that most
of human thinking is fuzzy or imprecise in nature, and
therefore, Boolean logic (which is represented by crisp “0’
and “I”) cannot adequately emulate the thinking process.
However, the general methodology of reasoning remaining
the same, it was defined as “fuzzy expert system.” In recent
years, fuzzy logic has emerged as an important AI tool
to characterize and control a system whose model is not
known, or ill-defined. It has been widely applied in process
0018-9219/94$04.00 0 1994 IEEE
PROCEEDINGS OF THE IEEE. VOL. 82, NO. 8, AUGUST 1994
I303
control, estimation, identification, diagnostics, stock market
prediction, agriculture, military science, etc.
While the traditional digital computer is very efficient in
solving expert system problems and somewhat less efficient
in solving fuzzy logic problems, its inability to solve
pattem recognition and image processing type problems
was seriously felt since the beginnning of the 1990’s. In
fact, expert system techniques which held so much promise
in the 1980’s, could not fulfill the expected computational
needs. Therefore, people’s attention was recently focused
on a new branch of AI, called “artificial neural network”
(ANN) or “neural network.” Fundamentally, the human
brain is constituted of billions of nerve cells, called neurons,
and these neurons are interconnected to constitute the biological neural network. Our thinking process is generated
by the action of this neural network. The ANN tends to
simulate the neural network by electronic computational
circuits. The ANN technology is the most generic for
emulation of human thinking. It has been applied to process
control, diagnostics, identification, character recognition,
robot vision, flight scheduling, financial prediction, etc. The
history of ANN technology is not new. It was gradually
evolving since the 1950’s, but the glamor of modem
digital computer and expert system techniques practically
camouflaged the neural network evolution in the 1960’s and
1970’s. Since the beginning of the 1990’s, neural network
as AI tool has captivated the attention of practically the
whole scientific community. This new form of machine
intelligence has suddenly been elevated to transcendental
heights. Often, it is held as the greatest technological
advance since the invention of the transistor. It is predicted
to touch almost every scientific and engineering application
by the early 21st century. Of course, we need to wait and
see to what extent this is true.
This paper is concemed with the application of expert
system, fuzzy logic, and neural network techniques in
power electronics and motion control systems. With these
tools, a system is said to be “intelligent,” “learning,” or
have “self-organizing” capability. Traditionally, the design
of a control system is dependent on the explicit description
of its mathematical model and parameters. Often, the model
and the parameters are unknown, or ill-defined. The system,
again, may be complex with nonlinearity and parameter
variation problems. An intelligent or self-organizingcontrol
system can identify the model, if necessary, and give
predicted performance even with wide range of parameter
variation. The recent advancement of AI tools, coupled with
the availability of powerful personal computers, micro- controllers, digital signal processors, and high-density analog
and digital ASIC’s will provide significant capability for
high-performance control of power electronic and motion
control systems.
11. EXPERTSYSTEM
A . Expert System Principles
Expert system is basically a cluster of software routines
especially organized in a computer that tends to emulate
1304
the human expertise in a certain domain. Consider a power
electronics engineer or technician who has a special or
domain expertise in the fault diagnosis of a power electronic
system. He has learned or acquired this knowledge by
education and experience over a prolonged period of time.
The question is: Is it possible to embed this knowledge in a
computer program so that it can replace the human expert?
The answer is “yes,” but we need to recognize that human
thinking is so complex that no computer program, however
sophisticated, can ever replace human thinking. The expert
system, unlike conventional algorithmic programs which
can be described by flowcharts, or finite-state machine
programs, are specially structured to resemble the human
thinking process. Figure 1 shows the basic elements of the
expert system. The core of the expert system is the representation of knowledge transferred from the human domain
expert. The domain expert, say the power electronics engineer, may or may not have the requisite software expertise.
Knowledge engineering is a branch of computer science that
deals with the techniques of knowledge representation by
computer software. The knowledge engineer acquires the
knowledge from the domain expert and translates it into
expert system software. The knowledge, as shown, can be
classified into two types: the expert knowledge embedded
in the knowledge base, and the data, facts, and statements
that are normally embedded in database for supporting the
expert knowledge. The knowledge base basically consists
of a cluster of production rules, as shown in Fig. 2, where
each rule is given by an IF . . . THEN . . , statement. Often,
an expert system is defined as knowledge-based or rulebased system. A rule has the premise (or antecedent or
condition) part in the IF statement and the consequent
(or conclusion or action) part in the THEN statement.
Each rule is supported by parameters. The parameters
can have numerical, logical, or textual values. In the
example rule of Fig. 2, dc link voltage, ac line voltage, and
machine speed are the parameters. A rule is “fired” if the
premise is true, and then the action guided by the THEN
statement is executed. The rules can also be designed to
handle a limited amount of probability through certainty
factors and probability-based models, such as Bayesian
approach. The knowledge content can be easily altered,
updated as the technology changes, or enhanced on the basis
of “machine learning.” The inference engine (or control
system), as the name indicates, is essentially the executive
software that tests the rules in sequence and tries to draw
an inference or a conclusion. It also controls the user
interface, as shown. The inference engine tries to validate
rules by the forward- or backward-chaining method. In a
forward-chaining or antecedent rule, the premise part is
tested first, and if it is true then, the rule is fired. In a
backward-chaining or consequent rule, the inference engine
hypothesises the inference or consequent part of the rule,
and then tests backward for the premise part to be true
for the rule’s validity. This is analogous to the medical
doctor’s assumption of a disease, and then trying to match
the symptoms with it. In an expert system, both forwardand backward-chaining rules may be strategically mixed.
PROCEEDINGS OF THE IEEE, VOL. 82, NO.
a
AUGUST 1994
EXPLANATION
SUB-SYSTEM
- - - _ - - _KNOwL_EDGE- - ENGINE
-
- --
BASE
-A
KNOWLEDGE
ACOUl SI T ION
WORK SPACE
‘I
L
DOMAIN
EXPERT
-___-__
I
J
Fig. 1. Block diagram showing basic expert system elements
~
/
RULE I: IF Dc LINK VOLTAGE <2CQV AND AC LINE VOLTAGE
IS ZERO AND MACHINE SPEED >50% OF RATED
SPEED, THEN REDUCE MACHINE SPEED BY 20%
RULE N
Fig. 2. Expert system knowledge base showing a set of production rules.
The user interface of the expert system is very important
because often the user is an unskilled or semi-skilled person
trying to consult the expert system. He must communicate
in natural language because of his usual unfamiliarity with
the computer language. The expert system holds userfriendly dialog with the user and requests parameter values
for the relevant problem solving. The knowledge base is
then searched, appropriate rules are fired, and the solution
is given on the screen. In a real-time expert system-based
control, the input parameters are accessed from the sensors.
These signals are then processed and control signals for the
system are generated.
The user education is one of the most important features
of the expert system. For a problem to be solved, he
can get intense education and have understanding of how
the problem is solved and the conclusion reached by the
“HELP,” “WHY,” and “HOW’ commands. The HELP
command can explain to the user the in-depth technical
features of the problem with the help of texts and graphics.
The WHY command can explain why the expert system is
asking relevant information from the user, and the HOW
command explains how the expert system arrived at the
consultation conclusion.
Which computer language should be used for the development of expert system? Since the bulk of processing is
symbolic or non-numeric in nature, a symbolic processing
language, such as PROLOG or LISP is very convenient.
The LISP or its dialect has been traditionally accepted
as the expert system language because of its power and
flexibility. Of course, the numeric-computation-intensive
languages, such as Fortran, Pascal, C, etc., can also be
used in expert systems because they have limited symbolic
processing capability. For real-time control of the power
electronic system, a fast low-level language, such as C or
Assembly language, may be essential.
An expert system knowledge base can be structured in
the form of a tree with the help of a number of frames as
shown in Fig. 3. A frame essentially consists of a cluster
of characteristic rules and the associated parameters. The
frame-based architecture permits logical organization of a
large knowledge base into modular form. The root frame is
the core of the knowledge base. It may have child subframes
( A and B ) and grandchild subframes (C, D , and E ) , as
shown in the figure. Each subframe can be considered as
subdomain of expert knowledge. Assume, for example, the
problem of drive product selection for a certain application
which will be described later. The root frame corresponds
to the expertise of a general sales engineer, and subframes
A and B , respectively, correspond to application engineer’s
expertise in induction and synchronous motor drives. The
user interfaces the root frame in the beginning, and based
on user dialog, if induction motor drive appears to be the
choice, the subframe A will be “instantiated’ and conversation will begin with it. The subframes C and D can relate
to auxiliary features, and price and delivery considerations,
respectively. Any frame or subframe may access the central
database which may be the drive product catalog in this
case. For convenience, normally a frame can access the
rules of children and grandchildren frames, but not its
parent and grandparent frames. However, a frame normally
has access to the parameters in the parent and grandparent
frames, but not to the children and grandchildren frames.
A relatively small-size knowledge base can use the root
frame only. An expert system can track its own operation
and enhance efficiency of knowledge base operation which
is based on leaming. The term meta-knowledge means
knowledge about the knowledge base operation, and metarule means rule about the rules. The meta-rule can dictate
the most efficient order of rule search and thus increase
efficiency for reaching the conclusion.
The knowledge in an expert system can be defined as
“shallow” or “deep.” Shallow knowledge can result in
a set of rules directly derived from the technician’s or
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1305
USER
INTERFACE
m l
Fig. 3. Frame structure of knowledge base.
operating engineer’s knowledge (see Fig. 2), whereas the
rules for deep knowledge can be derived from the system
model that corresponds to the designer’s knowledge. The
knowledge can also be categorized as declarative or factlike knowledge and procedural or method-like knowledge.
B . Expert System Shell
A shell is a software environment for efficient and userfriendly development of an expert system. The developed or
client program can be operated within the shell or exported
to another computer. A large number of expert system
shells [3] based in mainframe, mini, and personal computers
is available for different applications. Recently, personal
computers have become very powerful, and a number of
PC-based shells [6], such as 1st Class (1st Class Expert
Systems, Inc.), Exsys (Exsys, Inc.), Guru (Micro Data Base
Systems), PC (Personal Consultant) Easy, and PC (Personal
Consultant) Plus (both by Texas Instruments) have become
available which are well-suited for application in power
electronics area. Since there are a lot of common elements
in the features of these shells, the PC Plus will be briefly
reviewed as an example in this paper.
The PC Plus development system [7], normally based
in IBM-compatible PC, operates in DOS environment and
uses the PC SCHEME language which is a dialect of LISP.
The program developer needs to have some familiarity
with PC SCHEME although English-like Abbreviated Rule
Language (ARL) is used for fast development of the rules
in the knowledge base. Rule 1 in Fig. 2 can be represented
in ARL as
IF : : DCVL < 200 AND ACLV
= NO AND MC-SPD > 0.5
THEN : : MC-SPD = MC-SPD * 0.8
where DCVL, ACLV, and MC-SPD are the corresponding
parameter names. The run-time version or client program
operates alone in DOS environment and the user dialog with
the program is in pure English. The client program can be
generated either in LISP for non-time-critical application
or in C for time-critical application. When the program
is resident in the shell, the developer can easily alter
or update it, but no program modification is possible
in client environment. The knowledge base is organized
in hierarchical frame-based structure, as indicated before.
The inference engine defaults to backward chaining unless
forward chaining is specifically instructed in the rule (antecedent rule). The extemal interface of the shell is shown
1306
PC SCHEME
Fig. 4.
Extemal interface of shell.
swLl
rmFRFACE
FOR
DOSFILE
WRITEDOS-FILE
DOSCAU-
D(KwABLE
Dos
READM)S-FILE
in Fig. 4. The rules can process simple arithmetic and
logical operations with the help of LISP, but for complex
calculation, such as solving differential equations, it can
interface the DOS program, as indicated in Fig. 5. When
a DOS calculation is needed, the expert system writes the
data in the DOS program, executes them, and then reads
the resulting data. A limited amount of data can be directly
embedded in the program, but for larger size of data, such
as product catalog consultation, dBASE files are consulted.
Similarly, LOTUS 1-2-3 spreadsheets can be linked with
the shell. One of the powerful features of the shell is
its capability to integrate pictures with the knowledge
base using a utility called SNAPSHOT. The picture is
first created with graphics editor, such as DR. HALO
(Media Cybernetics) or ORCAD (Orcad Systems). With the
compression tool of the SNAPSHOT, the created picture is
compressed into a file. The expansion tool automatically
expands the picture when the knowledge base needs it for
consultation.
C . Expert System Application
Although expert system techniques are almost in the
mature state of evolution, they have hardly touched the
power electronics area. They have the potential for application practically in all aspects of the power electronics
area, such as system analysis, design, simulation, control,
tests, diagnostics, assembling, marketing, shipping, etc. In
this section, a few applications which are described in the
literature, will be briefly reviewed.
I ) Fault Diagnosis and Monitoring f o r AC Drives [12],
(131: Fault diagnosis in an industrial plant is one of
PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8 AUGUST 1994
3-+
60H2
AC
Fig. 6. Fault diagnosis signals for a voltage-fed inverter ac drive.
the most popular applications of the expert system. The
diagnosis may be on the basis of off-line or on-line diagnostics. In off-line diagnostics (trouble-shooting), the plant
is shut down intentionally or by the protection system.
Then, the expert system that embeds the expertise of a
diagnostic technician, is used to identify the fault. The
procedure may be static or dynamic in nature. The expert
system communicates the trouble-shooting procedure to the
operator, and the observed symptoms are fed as input in
the form of a dialog. The rule base is then searched and
conclusions are drawn. The operator training, as indicated
before, is a very important feature of the expert system. In
complex problems, a trained operator can make intelligent
conversation with the expert system.
The expert system based on-line diagnostics may be
quite involved. Here, the objective is to maintain reliability
and safety of the operating plant avoiding unnecessary
shut-down. The monitoring, alarm processing and system
protection functions can be integrated with the diagnostic
system. Figure 6 shows a voltage-fed inverter ac drive
where the ac line voltages and currents, dc link voltage
and currents, transistor base drive signals, machine stator voltages and currents, and stator winding temperature
signals are fed to the microcomputer that embeds the
diagnostic program. The rule base of the program contains
the expertise of the operator and the designer. An example
of on-line diagnostic rule is given in Fig. 2, where the dc
link voltage is maintained by pumping in the regenerative
braking enery in case of ac line power failure. The expert
system may be designed to monitor the general health of
the drive, avoid preventable shut-down, and provide faulttolerant control of the system.
2) Drive Product Selection [9]: The expert system can
help a semi-skilled user to select a drive product best
suited for his application. Normally, the user determines
his preliminary application needs and then extensively
consults a company applications engineer. The applications
engineer with his knowledge of drive technology and
company products, makes some calculations, consults the
product catalog, and then makes recommendation of a drive
product. In the expert system, the application engineer’s
expertise and the product catalog are embedded in the
knowledge base. The user holds a dialog with the expert
system where application-based information is requested in
detail. Based on this information, the knowledge base and
database are searched and the appropriate drive product is
recommended. A typical rule in PC Plus using ARL can
be given as follows:
IF : : MOTOR = INDUCTION-TYPE AND
APPLICATION
= CENTRIFUGAL-PUMP AND
POWER = 10-HP AND
SUPPLY-VOLTAGE = 230-V AND
PHASE = THREE AND
SPEED-RANGE = 10&1750 r/min AND
AUTO-RESTURT = YES AND
SPEED-RESTART YES AND
SPEED-REVERSAL = YES
THEN : : SELECTED-PRODUCT
= COMPANY-A-MODEL-3TSO9
The knowledge base and database can be easily modified and updated as new products are introduced and
old produts are deleted. The systematic problem-solving
flowchart is given in Fig. 7. The system gets applicationrelated data from the user, searches the database, and the
candidate products are identified. The motor overheating
with the inverter is then checked, and if unsatisfactory,
a higher machine frame size is recommended. If the acceleration/deceleration time profile is needed, the inverter
oversizing factor is calculated by the LISP or DOS program,
and finally, the product type is selected with a check of
options and other features.
3) Converter Design, Simulation, and Optimization [ I 01,
[ l l ] :The expert system can help a semi-skilled designer
to automate the converter system design (as shown in
Fig. 6, for example), and then optimize the design based
on simulation. The designer holds consultation with the
expert system and supplies the details of load condition,
line power supply, and other specifications. Based on these,
the expert system designs the diode rectifier, filter, PWM
inverter, snubbers, and the cooling system in detail using the
knowledge base that incorporates the domain expertise of
the converter designer, and finally the solutions are given
on the screen. With user’s command, the expert system
simulates the converter system, iterates the design, checks
the critical variables to be within the safe limits. and then
BOSE: EXPERT SYSTEM, FUZZY LOGIC. AND NEURAL NETWORK APPLICATIONS
I307
I
I
I
Fig. 7. Problem-solving flowchart for drive product selection.
1
Fig. 8. Converter design, simulation, and optimization flowchart.
confirms the final design. A sample design rule in ARL is
given as
IF : :
OUTPUT-POWER IS KNOWN AND
OUTPUT-VOLT IS KNOWN
THEN : :
POWER-BJT-IDC = (7.733*OUTPUT
- POWER) * IOF *
msrry8Munlm
SUB M
E -1
HKFBRlDQE
SIYuUllON AND
SNUBBEROPTYIUTIOW
SUBFRAUEP
INV-OVERLOAD/OUTPUT-VOLT
where IOF is the inverter overloading factor. Note that
the arithmetic computation is done directly in LISP. The
development and consultation flowchart is given in Fig. 8,
and Fig. 9 gives the structure of the knowledge base. Note
that the database stores the numerical data for the power
semiconductor specifications sheets, but the graphical data
are converted to polynomial equations and embedded in
the knowledge base. Once the converter system is fully
designed, the half-bridge version of the inverter is simulated as a dc-to-dc converter to optimize the polarized
snubber with the worst case line current. Finally, the full
system, as shown in Fig. 6, is simulated to verify the safe
voltage and current levels. As indicated in Fig. 9, the root
frame performs design of the converter system. Subframe1 is responsible to interface the simulation program (in
SIMNON language), perform the simulation study, make
observation on voltage and current waves as well as their
critical values. Subframe-2 accepts the worst case inverter
1308
oBsEfwE~uE
I
oBsERvATw3NOFWAVES
ANDcRmcALvAwEs
OasERVATloNOF WAVES
Fig. 9. Structure of knowledge base for converter design.
load current (either from the root frame or from SubframeI), simulates the half-bridge inverter, and optimizes the
snubber parameters.
111. Fuzzy LOGIC
A. Fuzzy Logic Principles
Fuzzy logic, unlike Boolean or crisp logic, deals with
problems that have vagueness, uncertainty, or imprecision,
and uses membership functions (MF) with values varying
between 0 and 1. Fuzzy logic tends to mimic human
thinking that is often fuzzy in nature. In conventional
PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8 AUGUST 1994
't
MEDIUM
m z
z
0.0
0
800
400
1200
1600
2000
SPEED (rpm)
Fig, 10. Fuzzy sets of speed defined by membership functions
set theory based on Boolean logic, a particular object or
variable is either a member (logic 1) of a given set or it is
not (logic 0). On the other hand, in fuzzy set theory based on
fuzzy logic, a particular object has a degree of membership
in a given set that may be anywhere in the range of 0
(completely not in the set) to 1 (completely in the set). This
property allows fuzzy logic to deal with uncertain situations
in a fairly natural way. It may be mentioned that although
fuzzy logic deals with imprecise information, it is based on
sound quantitative mathematical theory. Of course, in this
section, fuzzy logic principles related to control, modeling,
and estimation applications will be emphasized.
A fuzzy variable has values which are expressed by
natural English language. For example, the speed of a
machine, as indicated in Fig. 10, can be defined by linguistic variables (fuzzy sets or subsets) LOW, MEDIUM, and
HIGH, where each is defined by a gradually varying bellshaped (Gaussian) membership function. The shape can
also be triangular or trapezoidal, and can be symmetrical or
asymmetrical. For example, if the speed is below 400 r/min,
it belongs completely to the set LOW, whereas for 700
r/min, it belongs to the set LOW by 50% (MF = O S ) , and to
the set MEDIUM by another 50% (MF = 0.5). The change
in Boolean logic is abrupt between 0 and 1, and in Fig. 10,
the low-to-medium transition may occur at 550 r/min, and
similarly, the medium-to-high transition may occur at 1350
r/min. In fuzzy set terminology, all the possible values
that a variable (speed) can assume are named universe of
discourse, and the fuzzy sets (characterized by membership
functions) cover the whole universe of discourse.
The basic properties of Boolean theory are also valid in
fuzzy set theory, and are given as follows:
Union: Given two fuzzy subsets A and B of a universe
of discourse X, the union A U B is also a fuzzy set of X
with membership function given as
PAUB(Z)
= max
[ P A ( z ) ,P B ( 5 ) ] .
(1)
This is equivalent to Boolean OR logic.
Intersection: The intersection of two fuzzy sets A and
B of the universe of discourse X, denoted by A nB has
the membership function given by
PAnB(5)
= min [ P A ( z ) P; B ( Z ) ] .
(2)
This is equivalent to Boolean AND logic.
Complement or Negation: The complement of a given
set A of the universe of discourse X , defined by ] A , has
the membership function
PA(Z)
= 1- P ] A ( 5 ) .
(3)
't
I .o
L
o
=l
0
1
2
3
4
5
6
0
1
2
3
4
5
6
x
x
(d)
Fig. 11. Basic operation involving fuzzy sets. (a) Fuzzy sets A
and B. (b) Union .4UB. (c) Intersection A n B . (d) Negation ] A .
This is equivalent to Boolean NOT logic.
Figure 11 illustrates the above operations with triangular
membership functions.
A process control algorithm that is based on fuzzy logic
is called fuzzy control. A fuzzy control essentially embeds
the intuition and experience of a human operator, and sometimes those of a designer and researcher. The conventional
control is normally based on mathematical model of a plant,
as mentioned before. If an accurate mathematical model
of a plant is available with known parameters, it can be
analyzed, for example, by a Bode or a Nyquist plot, and a
controller can be designed for the specified performance.
Often, the plant model is unknown or ill-defined. Even
if the plant model is known, there may be a parameter
variation problem. Sometimes, the model is multivariable,
complex, and nonlinear, such as the dynamic 0-Q model of
an induction motor. Various adaptive control theories, such
as self-tuning regulation (STR), model referencing adaptive
control (MRAC), and sliding mode control (SMC) have
been developed to combat such problems. It can be shown
that fuzzy control is basically adaptive in nature, and can
give improved robustness in such problems. Mamdani and
Assilian [ 181 first reported the application of fuzzy logic to
control a model laboratory steam engine. The purpose was
to control engine speed and boiler steam pressure by using
heat applied to the boiler and the throttle setting on the
engine. Afterwards, gradually, fuzzy control was applied to
cement plant, chemical reactor, blast fumace, robotics, and
electrical machine drives.
Fuzzy control, similar to the expert system based control,
is described by a set of IF . . . THEN . . . rules (called
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1309
RULE I
input signal condition and then computes the effective
control action. The composition operation is the method
by which such a control output can be generated. Several
composition methods, such as MAX-MIN (or SUP-MIN)
and MAX-DOT have been proposed in the literature. The
commonly used SUP-MIN method, as illustrated in Fig. 12,
is given as
kf
POS ITlVE
NEGAT 1VE
SMALL
RULE 2:
A
0
ERROR (E)
f
ERROR RATE (CElJ
I
FINAL FUZZY
VALUE FOR DU
*
DU
+lo
,’ ‘\ :d\
GRAVITY
CONTROL
Fig. 12. Fuzzy-rule-based composition indicating SUP-MIN
principle.
implication), where the rule has the following general
structure:
IF
3:
is A AND y is B THEN z is C
where x, TJ, and z are the fuzzy variables and A , B,
and C are the fuzzy subsets in the universe of discourses
X, Y , and 2,respectively. Fuzzy logic is often defined as
“fuzzy expert system” where the knowledge base is fuzzy
or imprecise in nature. However, compared to the expert
system, the fuzzy expert system has fewer rules.
Figure 12 illustrates the typical fuzzy control of a dc
motor drive where the two rules are derived from the
observed behavior of the plant. Rule 1 states that if the
speed loop error ( E ) is zero (ZE) and the rate of change
of speed (CE) is negative small (NS), then the control
signal increment (DU) is negative small (NS). The linguistic
variables ZE, NS, and DU are defined by symmetrical
membership functions, as shown. Graphically solving the
problem, the control output of Rule 1 is DUI. In practice,
more than one rule is fired at a time. If Rule 2 is fired, it will
give output DU2. The effective control output is given by
the weighted average of DUI and DU:!. The fuzzy control
can be implemented either by microcomputer or dedicated
hardware.
In general, a fuzzy rule base (see Table 1) is first
constructed by the designer and then all the fuzzy sets
of each variable are described by appropriate membership
functions (see Fig. 16). In general, a rule is n-dimensional
where n is the number of variables included in the rule.
The individual rules are combined to give an overall rule
R which is computed by the union operator as follows:
For the given rule base of a control system, the fuzzy
controller determines the rules to be fired for the specific
1310
u=x.R
or
P U ( P ) = SUP, b i n ( P X ( Z ) . P R ( T
.)I.
(5)
As indicated in Fig. 12, the output membership function of
each rule is given by MIN (minimum) operator whereas
the combined fuzzy output is given by SUP (supreme or
maximum) operator.
The general structure of a complete fuzzy control system
is given in Fig. 13. The plant control signal U is inferred
from the two state variables, error ( e ) and change in error
( d e l d t or ce for the sampling interval). The e and ce are
per unit (pu) signals derived from the actual E and C E
signals by dividing with the respective gain factors, as
shown. The “fuzzification” operation can be performed by
considering the crispy input values as “singletons” (fuzzy
sets that have membership value of 1 for a given input
value and 0 at other points) and taking the values of the
set’s membership function at the respective data value.
“Defuzzification” operation can be performed by a number
of methods of which center-of-gravity (or centroid) and
height methods are common. The centroid defuzzification
method, as indicated in Fig. 12, determines the output crisp
value from center of gravity of the output membership
function and is given by the expression
In the height method, the centroid of each output membership function for each rule is first evaluated. The final
output is then calculated as the average of the individual
centroids weighted by their heights (degree of membership)
as follows:
2vi P(ui>
2
U() = i = l
i= 1
P(ui>
(7)
‘
Finally, the database in Fig. 13 provides the operational
definitions of the fuzzy sets used in the control rules,
fuzzification, and defuzzification operations. Further details
of fuzzy control will be given in the application examples.
In spite of the advantages of fuzzy control, its main
limitations are the lack of systematic procedure for design
and analysis of the control system. The heuristic and
iterative approach to fine-tune the rule base and membership
functions may be very time-consuming. If the system can
be simulated on a computer, the tuning can be based on
the simulation results. A few other difficulties in fuzzy
PROCEEDINGS OF THE IEEE. VOL. 82, NO. 8 AUGUST 1994
u
u
C
+
Fig. 13. Basic structure of fuzzy control system.
PREMISES
CONSEWENTS
I
t
/MEDIUM
A
/
\
\
/MEDIUM
Tsl ‘A01 +AllW+A21H
W
DEFUZZ IF ICAT ION
THE LOWER OF THE
TWO IF CONDITION
OUTPUTS IS SELECTED
WIDTH (W)--
HEIGHT (HI-
Fig. 14. Principle of relational estimation (Sugeno’s method).
control are lack of completeness of the rule base and lack
of definite criteria for selection of the shape of membership
functions, their degree of overlapping, and the levels of
data quantization. Recently, fuzzy neural network (FNN)
techniques (described later) have been developed to solve
some of these problems.
Fuzzy logic can also be applied to modeling and estimation. A process, such as cement plant, is difficult to
describe by a reasonably good mathematical model, but
its operational behavior can be described by a set of fuzzy
rules. Such a fuzzy model can help to enhance the performance of fuzzy control, just as the mathematical-modelbased conventional control can give superior performance.
Similarly, the fuzzy estimation technique can be applied
to a process where mathematical model is not known, illdefined, or has a parameter variation problem. The fuzzy
modeling and estimation can use the rule base method,
as described above, or the relational method described by
Sugeno [30] that is also known as Sugeno’s method. Figure
14 illustrates the principle of relational estimation of rms
line current (Is)(described later) for a diode rectifier where
the current pulsewidth ( W ) and height ( H ) are given as
inputs. The idea behind the fuzzy relational approach is
to define the regions where the output can be expressed
as linear functions of the inputs. Basically, it is a hybrid
method that combines the fuzzy and mathematical methods.
As shown in Fig. 14, the premise portion of the rules
is identical with that in the rule-base approach, but the
consequents are described by equations. Rule 1 in the figure
can be stated as
IF W is MEDIUM AND H is MEDIUM
THENIS = A 0 1 + A l l . W + A 2 1 . H .
The consequents are linear functions of W and H and
the parameters Ai, are constant coefficients. The Aij can
be determined by multiregression linear analysis, and then
fine-tuned by observation or simulation. The linear equation
outputs are then defuzzified, i.e., weighted average of the
consequents is evaluated by the respective membership
values to determine the crisp output. The relational method
of estimation requires fewer rules, gives better accuracy,
and the algorithm development time is somewhat smaller
than for the rule base method.
B. Fuzzy Logic Application
Fuzzy logic can be applied to control, diagnostics, modeling, and estimation of power electronic system. In general,
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
I31 I
vac
CURRENT
CONTROLLER
DC
MACH INE
J
PHASE
-
CONMRTER
Y
Fig. 15. Fuzzy speed control block diagram of dc drive.
fuzzy expert system is applicable wherever the knowledge
base of an expert system contains fuzziness. In this section,
a few example applications will be discussed from the
literature.
I) Speed Control of DC Motor [22]: Fuzzy logic can be
applied in the closed-loop control of a drive system. With
nonlinearity, parameter variation, and load disturbance effects, it can provide fast and robust control, as mentioned
before. The drive system may be based on a dc or ac
machine. Since vector-controlled ac drive and dc drive
have identical dynamical models, the same fuzzy control
principle is valid in either case. Figure 15 gives the control
block diagram of a phase-controlled converter dc drive
using a separately excited constant field dc motor. Instead
of conventional PI control, the system uses fuzzy control
in the speed loop where E (error) and C E (change in
error) are the input signals and 1; is the output armature
current command. The drive system also uses fuzzy logic in
the current controller, and in the linearization of converter
characteristics at discontinuous conduction, but these will
not be discussed here. The rule base of the speed controller,
shown in matrix form in Table 1, has altogether 49 rules
which are developed by heuristics from the viewpoint of
practical system operation. A typical rule can be given as
IF the speed loop error (e) is positive small (PS) AND
change in error (ce) is negative small (NS)
THEN the control increment ( d U ) is zero (Z)
Figure 16 shows the plot of triangular membership functions for the variables e, ce, and dU which are expressed
in per unit (pu) quantities. Note that the membership
functions have asymmetrical shape with more crowding
near the origin. This permits precision control near steady
state without unduly increasing the number of sets. A
finer partitioning for dU was necessary because of higher
sensitivity of the variable. With the 50% overlap assumed
in Fig. 16, the four rules fired for the given inputs are
indicated in Table 1. Correspondingly, the fuzzy output (by
SUP-MIN composition) is shown in Fig. 16(c). The output
dU is determined by height defuzzification principle and
then integrated to get the current command 1;. It can be
shown that with fuzzy control the response is more robust
with inertia variation and load torque disturbance than with
conventional PI control.
2) Induction Motor EfSlciency Optimization Control 1271,
[28]: Induction motor drives are normally operated at rated
flux condition to give best transient response. However, at
light-load condition, this gives excessive core loss, impairing efficiency of the drive. The flux can be programmed
at light-load steady state in order to improve efficiency of
1312
Table 1 Rule Base for Speed Control
NB
I
NM
1 I@
NS
933
NK
NS
2
FW
PB
WB
W B W B
PB
F'VB
NE
NM
NS Z!'
W B
PS
PM
PE
PS
PM
PE
W B
(a)
NB
NM
NS '/Z
ce -I
(b)
NVB
-I
NE
-U,
NM NSP!Z
-U2-U30
PS PM
U3 U2
PB
PVB
U3
dU(pu)
L d U
(C)
Fig. 16. Membership functions for fuzzy speed controller.
the drive. Figure 17 explains the on-line search technique
of efficiency optimization by flux programming. Consider
the motor operation initially at rated flux and steady state
with the load, torque, and speed, as shown. The rotor
flux is decremented in steps by reducing the magnetizing
component of stator current i d s . This results in an increase
of the torque component of current i, (normally by the
speed loop), so that the developed torque remains the same.
As the core loss decreases with the decrease of flux, the
copper loss increases, but the system (converter and machine) loss decreases improving the overall efficiency. This
PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8 AUGUST 1994
OFERATlON
4
ITORQUE CURRENT
(rated)
>=
--p&"G
ROTOR FLUX
I
TIME
/-Lmss
COPPER toss
flux is controlled by the voltage and the torque is controlled
by the feedforward slip signal estimated from the machine
terminal voltages and currents.
3 ) Slip Gain Tuning Control of Induction Motor Drive
[25], [26]: Slip gain tuning of indirect vector-controlled
induction motor drive has been the subject of intense
research in recent years. Slip gain detuning, caused by
variation of machine parameters, gives undesirable transfer
characteristics for torque and flux, and unsatisfactory transient response characteristic of a higher order system that
might eventually result in instability of the drive system.
The fuzzy logic technique can be gainfully applied to tune
the slip gain. Figure 19 shows the block diagram of a fuzzy
on-line tuning of slip gain ( K , )using the model referencing
adaptive control (MRAC) technique (the plant and other
control elements are not shown). The scheme depends on
reference model computation of reactive power (Q*) and
D-axis voltage (v:,) at the machine terminal for ideally
tuned condition of K,. The expressions of these parameters
are given as
CONVERTER
Q* = w e ( L s z-~ L,i;:)
~
= Rsi:s - w,L,i;E,
Loss
LRON LOSS
TIME
Fig. 17. On-line search method of efficiency optimization control
by flux programming.
is reflected in the decrease of dc link power P d , as shown.
The search is continued until the system settles down at
the minimum input power point A. Figure 18 shows the
block diagram of an indirect vector-controlled induction
motor drive incorporating the fuzzy-logic-based efficiency
controller, as discussed above. The fuzzy controller has the
advantage that it adaptively decrements the step size of the
excitation current so that fast convergence is attained. The
steps are again programmable and depend on the operating
point of the torque-speed plane.The speed loop generates
the torque current command i q S ,as indicated. The fuzzy
efficiency controller detects the steady-state condition when
the speed loop error Aw, approaches zero, and then it
invokes the efficiency optimization control. A typical fuzzy
rule can be given as
IF
the power increment ( A p d )
is negative medium (NM)
AND the last ids(L- i d s ) is negative ( N )
THEN the excitation increment ( d z d s )
is negative medium (NM).
Note that as i d s is decremented, there will be loss of
torque which will be normally compensated by the sluggish
speed control loop. The resulting pulsating torque may be
objectionable. It can be compensated by a feedforwarded
torque compensator, as shown. When the speed command
or load torque is changed, the system can easily transition
to the fast transient response mode when the rated flux
is established and the torque is directly controlled by the
speed loop. The above fuzzy control can easily be translated
to open-loop volt-per-hertz controlled drive [29] where the
(8)
(9)
where L, = L, - ( L m 2 / L r ) and the other equation
elements are standard symbols. The reference models are
then compared with the respective estimate of the actual
quantities given by
Q = vqszds
Vds
- vdsiqs
= vbs sin 0,
+ vis cos 0,
(10)
(1 1)
where cose, and sine, are unit vectors. The respective
loop error is divided by a base value to convert into per
unit (pu) form for convenient manipulation in the fuzzy
controller. The base value is essentially the same as the
reference value. Note that the reverse polarity of AQ is due
to opposite behavior of v d s and Q with respect to K,. There
are, in fact, two fuzzy controllers in Fig. 19. The controller
FLC-I generates a weighting factor K f which permits
appropriate distribution of Q control and V d s control on
the sz: - we, i.e., the torque-speed plane. This is to ensure
high sensitivity to detuning control by assigning dominant
use of the Q control in the low-speed high-torque region,
and the v d s control in the high-speed low-torque region. An
example rule can be given as
IF
speed ( w e ) is low ( L ) and torque ( i q s )
is high ( H )
THEN weighting factor K f is high ( H ) .
The combined error signal is given as
E = AQ . K f
+
nvds(1
- Kj).
(12)
The second fuzzy controller FLC-2 generates the corrective
incremental slip gain A K , based on the combined detuning
error E and its slope. Basically, it is an adaptive feedbackloop controller, as discussed before, for fast convergence at
any operating point irrespective of the strength of E and
C E signals. Under an ideally tuned condition, the signals
AQ and A V & , and correspondingly, the E signal, will
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1313
I
-L
I’I’
0
1
1
I
l
l
Fig. IS. Vector-controlled drive with fuzzy efficiency optimizer.
IKf
AV&
I
FIXI-2
FLC-1
Fig. 19. Fuzzy-logic-based MRAC tuning control block diagram.
be zero and the slip gain K, will be set to the correct
value (K,o). If the system is detuned, for example due to
variation of rotor resistance, the actual Q and uds variables
will deviate from the respective reference variables, and
the resulting error will alter the K , value until the system
becomes tuned, i.e., E = 0.
4 ) Waveform Estimation [31]: Power electronic converters characteristically generate distorted voltage and current
waveforms. Electronic instrumentation techniques are extensively used to process these waves and determine the
quantities, such as total rms value, fundamental rms value,
active power, reactive power, displacement factor, and
power factor. Often, mathematical model (if available)
and look-up table methods are also used for the estimation. The computation-intensive approaches have the
disadvantage that the response is slow because integration
and averaging processes are involved. The look-up table
solves this demerit, but for good accuracy, the size of
the table (one or multi-dimensional) should be large or
interpolative calculation becomes necessary. Fuzzy-logic1314
based waveform estimation has the advantage of fast response, multiple outputs from a single premise of a rule,
and immunity of noise and drift from the sensors. Both
rule-based and relational methods, as discussed before,
can be applied for the estimation. Figure 20 illustrates
the rule-based estimation technique for line current of a
three-phase diode rectifier feeding a capacitive load. The
pattern of the current wave, as shown, is characterized
by the width ( W ) and height (H)parameters, and the
estimate is dependendent on their values. Both W and H
are defined by 6 and 11 fuzzy sets, respectively, giving
66 rules. The number of sets for rms current ( I s ) and
fundamental rms current (If)is 16, but the displacement
factor (DPF) has only 6 (same as W) sets. Note that the
membership functions are asymmetrical and nonidentical
for each variable because each output is different and has
different degree of nonlinearity. All the fuzzification and
defuzzification are done on pu basis, as indicated in the
figure. Since the values of the input variables have large
range, the implementation is made by the so-called “auto
range” normalization and denormalization.Of the four rules
valid in the figure, a typical rule is given as
IF
H is PMS AND W is PSB
THEN Is is PMM, I f is PSB, and DPF is PMS.
Once I s , I f , and DPF are estimated, the power factor (PF)
can be given by the simple relation
PF = DPF .If/Is.
(13)
For improved accuracy, the formulation of rule base and
membership functions and their iteration are based on
simulation results.
IV. NEURALNETWOW
A. Neural Network Principles
Neural network or artificial neural network (ANN), as the
name indicates, is the interconnection of artificial neurons
PROCEEDINGS OF THE IEEE. VOL. 82, NO. 8 AUGUST 1994
MF. FOR RMS
CURRENT
M F. FOR HEIGHT (HI
VZO PSS PSM PSB PMS PMM PMB PBS PBM
PBB
VB
I
P
I
0
//
I
PSS PSB PSVB
VZO.PSZO/PSM/
PBZO
ASPMMPMB
p
I.o
I
PBVB
PBSPBMPBB
I
VB
M.F. FOR FUND.
RMS CURRENT
M F. FOR WIDTH
MF. FOR OISP.
FACTOR
Fig. 20. Rule-based estimation of rectifier input current wave.
that tends to simulate the nervous system of a human brain.
It is also defined in literature as a neurocomputer or a
connectionist system. Neurocomputing is a more generic
form of artificial intelligence than expert system and fuzzy
logic. The human brain is said to have around 100 billions
neurons or nerve cells, and each neuron is interconnected
to IO00 to 10000 other neurons. A biological neuron is
a processing element that receives and combines signals
from other neurons through input paths called dendrites. If
the combined signal is strong enough, the neuron “fires,”
producing an output signal along the axon that connects to
dendrites of many other neurons. Each signal coming into a
neuron along a dendrite passes through a synaptic junction.
This junction is an infinitesimal gap in the dendrite which
is filled with neurotransmitter fluid that either accelerates
or retards the flow of electrical charges. The fundamental
actions of the neuron are chemical in nature, and this
neurotransmitter fluid produces electrical signals that go
to the nucleus or soma of the neurons. The adjustment of
the impedance or conductance of the synaptic gap leads to
“memory” or “learning” process of the brain. According
to this theory, we are led to believe that the brain has the
characteristics of “associative memory” and does not have
computer-like CPU and central storage memory.
“B
SYNAPSE
WEIGHTS
‘I\
INPUTS
E
X3
I)
1
SUMMING
,NEURON
OUTPUT Y:
SIGMOIDAL
FUNCTION
NODE
7
XN
Fig. 21. Structure of an artificial neuron.
The model of an artificial neuron that closely matches a
biological neuron is given by an op-amp summer-like configuration shown in Fig. 21. The artificial neuron (or simply
neuron) is also called a processing element (PE), a neurode,
a node, or a cell. The input signals XI,Xp,X 3 , . . . , X , are
normally continuous variables instead of discrete pulses
that occur in a natural neuron. Each of the input signals
flows through a gain or weight, called synaptic weight or
connection strength whose function is analogous to that of
the synaptic junction in a natural neuron. The weights can
be positive (excitory) or negative (inhibitory) corresponding
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1315
to acceleration or inhibition, respectively, of the flow of
electrical signals. The summing node accumulates all the
input-weighted signals and then passes to the output through
the transfer function which is usually nonlinear. The transfer function can be step- or threshold-type (that passes
logical 1 if the input exceeds a threshold, or else 0), signumtype (output is + I if the input exceeds a threshold, or else
- 1) or linear threshold type with the output clamped to 1.
The transfer function can also be nonlinear continuously
varying type, such as sigmoid (shown in Fig. 21), inversetan, hyperbolic, or Gaussian type. The sigmoidal transfer
function is most commonly used, and it is given by
+
Y =
1
1
+ e-ax
where a is the coefficient or gain which adjusts the slope
of the function that changes between the two asymptotic
values (0 and + l ) . Note that with high gain, it approaches
a step function. The sigmoidal function is nonlinear, monotonic, differentiable, and has the largest incremental gain
at zero signal, and these properties are of particular interest. All the above transfer functions are characterized
as “squashing function,” because they squash or limit the
output values between the two asymptotes. It should be
mentioned here that the linear transfer function removes
nonlinearity from the neuron and eliminates the capability
of neural network to emulate nonlinear phenomena.
How the biological neurons remain interconnected in the
brain still remains a mystery, but scientists have evolved
more than 60 neural network models. Whether any of these
models match that in the brain is not very important. What
is important is that these models help solve our scientific,
engineering, and many other problems. In general, neural
networks can be classified as feedforward and feedback
types depending on the interconnection of the neurons. At
present, the majority of the problems (roughly 90%) use
feedforward architecture, and it is of direct relevance to
power electronics and motion control applications. Therefore, this type of network will be emphasized in the paper.
Figure 22 shows the structure of a feedforward multilayer
network with three input and two output signals. The
topology is based on Perceptron which was proposed by
Rosenblatt in 1958 and was used to emulate the biological
vision system. The circles represent neurons and the dots
in the connections represent the weights. The transfer functions are not shown for simplicity. The back propagation
training, as indicated, will be discussed later. The network
has three layers, defined as input layer (a), hidden layer
(b), and output layer (c). The hidden layer functions as a
connection between the input and output layers. The input
and output layers (defined as buffers) have neurons equal to
the respective number of signals. The input-layer neurons
do not have transfer functions, but there are scale factors, as
shown, to normalize the input signals. There may be more
than one hidden layer. The number of hidden layers and
the number of neurons in each hidden layer depend on the
network design considerations. The input layer transmits the
1316
signals to the hidden layer, and the hidden layer, in tum,
transmits the signals to the output layer, as shown. There
is no self-, lateral, or feedback connection of neurons. The
network is “fully connected when each of the neurons in a
given layer is connected with each of the neurons in the next
layer, as shown in Fig. 22, or can be “partially connected”
when some of these connections are deleted. A neural
network input and output signals may be logical (0, l),
discrete bi-directional (& 1) or continuous variables. Often,
continuous-variable signals, such as sigmoid functions at
the output are clamped to convert to logical variables.
The vector and matrix notation is often convenient
in dealing with the inputs, outputs, and weights. In
Fig. 22, assume that the hidden-layer neuron outputs are
V4, V5,v6, V7, and Vg, as indicated. If the transfer functions
are assumed to be linear with unity gain, then the output
of the hidden layer in matrix form can be given as
w41
w42
w43
-w81
w82
w83
or
where % is the output vector of layer b which is given as
the dot product of the weight or connectivity matrix mba
and the input layer signal vector
Similarly, the network
output signals can be given in the matrix form as
x,.
[
Yl
y2]
=
[
w94
w95
w96
w97
w98
w10,4
w10,5
WlO, 6
WlO, 7
w10,8
1.
11
v,
V8
(17)
or
Combining (15) and (17)
w10,4
‘
w95
w96
w97
w10,5
w10,6
w10,7
w41
w42
w43
w51
w52
w53
Iw
w
7
61
w7
62
w7]
w63
Wai
Ws2
W83
’
E:]
w10,8
(19)
or
which indicates that the output vector
is the dot product
of combined weight matrix m c b a and the input vector
Note again that with the nonlinear transfer function, the
above calculations are strictly invalid.
xa.
PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8 AUGUST I994
HIDDEN
LAYER
INPUT
Fig. 22. Structure of feedforward neural network showing back propagation training.
E . Training of Neural Network
So far, the discussion has been confined to the operating
principle of a neural network, and that is also for the
feedforward or hierarchical type. One thing is obvious
that the neural network computes very fast in parallel and
distributed manner compared to the sequential computation
in a conventional computer that requires the help of centralized CPU and storage memory. It is more like analog
computation with which we are all familiar.
How does a neural network perform useful computational
function? Basically, it performs the function of nonlinear
mapping or pattem recognition. This means that if an input
set of data corresponds to a definite signal pattem, the
network can be “trained” to give correspondingly a desired
pattem at the output. The network has the capability to
“learn” because of the distributed intelligence contributed
by the weights. The input-output pattem matching is possible if appropriate weights are selected. In Fig. 22, there
are altogether 25 weights, and by altering these weights, we
can get 25 degrees of freedom for the output with a fixed
input pattem. The network will be initially “untrained” if
the weights are selected at random, and the output pattem
will then totally mismatch the desired pattem. The actual
output pattem can be compared with the desired output
pattem and the weights can be adjusted by an algorithm
until the pattem matching occurs, i.e., the error becomes
acceptively small. The training should be continued with
a large number of input-output example pattems. At the
completion of training, the network should be capable not
only to recall all the trained output patterns (look-up table
function) but also to interpolate and extrapolate the trained
pattems. This tests the leaming capability of the network.
This type of leaming is called supervised leaming (learning
by a teacher) compared to unsupervised or self-leaming and
reinforced leaming (leaming with a critic) described in the
literature.
With the leaming principle described above, the problem
can be solved satisfactorily but the accuracy of solution
is somewhat compromised. Again, compared to human
learning or expert system knowledge, the neural network
cannot explain why it gave a particular output.
The learning for pattem processing function will be
illustrated by alphabet character recognition problem, as
shown in Fig. 23. The problem here is to convert the
alphabet characters into a 5-bit code (can be considered
as data compression) so that altogether 2’ = 32 characters
can be coded. The letter “C” is represented by a 7x 5
matrix array of inputs consisting of logical 0’s and I ’s. The
input vector of 35 signals is connected to the respective
35 neurons at the input layer. The three-layer network
has five outputs corresponding to the five bits (in this
case lOOlO), as indicated. The network uses sigmoidal
transfer function which is clamped to logical outputs. The
mapping is performed by supervised leaming, i.e., altering
the large number of weights (800 altogether) to appropriate
values. If now the letter “B” is impressed at the input
and the desired output map is 10001, the output will be
totally distorted with the previous training weights. The
network undergoes another round of training until the
desired output pattem is satisfied. This is likely to deviate
the desired output for “C.” The back-and-forth training
rounds will satisfy output pattems for both “C” and “B.”
In this way, a large number of training exersises will
eventually train the network for all the 32 characters. It
is also possible to train the network for inverse mapping,
i.e., with the input vector of 10010, the output vactor maps
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1317
1
NEURAL
NETWORK
7x5
MATRIX
where d? is the desired output of the j t h neuron in the
output layer, y; is the corresponding actual output, S is the
dimension of the output vector, y p is the actual net output
vector, and d p is the corresponding desired output vector.
The total squared error E for the set of P patterns is then
given by
5x I
MATRIX
P
Ep =
E=
Fig. 23. Input-output mapping of the letter “C.”
p=l
the letter “C.” Again, it is possible to Wain the network so
that the output pattem is the same as the input pattem.
This is called auto-associative network compared to the
hetero-associative network discussed above. The benefit
of auto-associative mapping is that if the input pattem
is distorted, the output mapping will be clean and crisp
because the network is trained to reproduce the nearest
crisp output. This inherent noise filtering property of the
network is very important. The neural network is often
characterized as fault-tolerant. This means that if a few
weights are erroneous or several connections are destroyed,
the output remains virtually unaffected. This is because
of the distribution of knowledge throughout the network.
At the most, the output will degrade gracefully for larger
defects in the network compared to catastrophic failure
which is the characteristic of a conventional computer.
1)Back-Propagation Training: Back-propagation training algorithm is most commonly used in a feedforward
neural network, as mentioned before. For this reason,
a feedforward network is often defined as “back-prop’’
network. In the beginning, the network (see Fig. 22) is
assigned random positive and negative weights. For a given
input-signal pattem, step-by-step calculations are made in
the forward direction to derive the output pattem. A cost
functional given by the squared difference between the
net output and the desired net output for the set of input
pattems is generated and this is minimized by gradient
descent method altering the weights one at time starting
from the output layer. The equations for the output of a
single processing unit, shown in Fig. 21, are given as
N
W;jXi
Net; =
i=l
where j is the processing unit under consideration, p is the
input pattem number, X i is the output of the zth neuron
connected to the j t h neuron, W;j is the connection weight
between the ith and jth neurons, Net; is the output of
the summing node, i.e., the jth neuron activation signal,
N is the number of neurons feeding the j t h neuron, fj
is the nonlinear differentiable transfer function (usually a
sigmoid), and Y,p is the output of the corresponding neuron.
For the input pattern p , the squared output error for all the
output-layer neurons of the network is given as
c(d;-
1
l S
-(dp - yp)2= 2
p - 2
J=1
E -
1318
$)z
(23)
l P
x(q- $)’.
(24)
p = l j=l
The weights are changed to reduce the cost functional E to
a minimum value by gradient descent method, as mentioned
before. The weight update equation is then given as
+
where 77 is the learning rate, W z j ( t 1) is the new weight,
is the old weight. The weights are iteratively
and UTZ3(t)
updated for all the P training pattems. Sufficient learning
is achieved when the total error E summed over the P
pattems falls below a prescribed threshold value. The iterative process propagates the error backward in the network
and is therefore called a back-propagation algorithm, first
proposed by Rumelhart, Hinton, and Williams in 1986. To
be sure that the error converges to a global minimum but
does not get locked up in a local minimum, a momentum
term a[Wz,(t)- W2,(t- l)]is added to the right of (25).
Further improvement of the back-propagation algorithm is
possible by making the learning rate step size adaptive, i.e.,
~ (+ t1) = uq(t), with U > 1.0
(26)
so that the oscillation becomes minimal as it settles to the
global minimum point.
From the above discussion, it is evident that neural
network training is very time-consuming, and this time will
increase fast if the number of neurons in the hidden layer
or the number of hidden layers is increased. Normally, the
training is done off-line with the help of a computer simulator program. Examples of personal-computer-based simulation programs are BRAINMAKER by Califomia Scientific
Software, EXPLORER by Neuralware, and EXPLORENET
by HNC. The input-output example pattem data files can
be obtained separately by calculation, simulation or experiment. Once the network topology is designed and the
network is trained by simulation program, the weights are
then downloaded to the prototype network. The prototype
operation can be realized either by microcomputer software
(sequential implementation) or in parallel by dedicated
hardware. Various dedicated hardware IC chips, such as
Intel 80170NX ETANN (electrically trainable analog neural
network), Micro Device MDl220NBS (neural bit slice),
Neural Semiconductor NUSU32, etc., are already available
in the market.
C. Fuzzy Neural Network [321, (461
Fuzzy neural network (F”)
applies neural network
technique to fuzzy reasoning. Basically, it emulates a
fuzzy controller. This type of fuzzy control emulation
PROCEEDINGS OF THE IEEE. VOL. 82, NO. 8 AUGUST 1994
U:
for fuzzy control.
Fig. 24. Fuzzy neural network (F")
has the advantages that it permits automatic identification
of fuzzy rules and tunes the membership functions. The
F" topology can be either on rule based approach or
relational (Sugeno's) approach, which were discussed in
Section 111-A. The F" topology for closed-loop adaptive
speed control is shown in Fig. 24. The network has two
inputs (loop error ( E ) and change in error ( C E ) )and one
output (control signal (U)). Each premise has three membership functions (SMALL, MEDIUM, and BIG) which
are synthesized with the help of sigmoids (f) giving a
Gaussian-type shape. The weights W, and W, give spacing
and slope, respectively, for the membership functions. The
weights are determined by back-propagation method. The
premises are identical to both rule-based and relational
topologies. The nine outputs of the premises after product
( T ) operation indicate that there are nine rules. The inferred
value of the F" is obtained as sum of the products of the
truth values in the premises and the linear equations in the
consequences, as shown. A typical rule in Fig. 24 can be
read as
IF E is SM AND C E is ME THEN U =
+
UlPl UZP2
P1+ PZ
where
~1
= SM . SM
and
uz = SM . ME.
The generation of linear equations is shown in the lower
part of the figure where the weights Wuli,Wu2irand W,O~
are the trained parameters.
D.Feedback
Neural Network [34]
This section will remain incomplete without a brief
review of feedback neural network. In a feedback network,
the neural output of one layer is connected to the input of a
previous layer or to the same layer. Therefore, when a pattem is applied at the input, the signals reverberate back and
forth until they settle down to a stable condition. The design
and operation of a feedback network is definitely more
complex than a feedforward network. The convergence of
a network to a final answer is defined by a mathematical
function called computational energy. This energy function
reaches a minimum as the solution is reached. Figure 25
shows a few key types of a feedback neural network. A
typical Hopfield network, shown in Fig. 25(a), has one layer
of neurons (called the Hopfield layer) where the output of
each neuron is fed back to the inputs of each of the other
neurons, as indicated. The neuron transfer function is of
sigmoidal type with a resistor+apacitor delay (not shown).
The network is symmetrically connected (W;j = W,,), and
the input-output signals are normally bistable. The network
has self-organizing associative memory characteristics, i.e.,
for an input pattem of signals, a corresponding output signal
pattem is retrieved. The network can also recall a stored
pattem for the corresponding partial input pattem. It is interesting to note that the current large-scale interest in neural
networks started after John Hopfield presented his paper at
the National Academy Science in 1982. Figure 25(b) shows
the bidirectional associative memory (BAM) network which
was introduced by Kusko. It is essentially a generalization
of a Hopfield network. The BAM has two layers of neurons
and uses two sets of connections between the neurons, as
shown. The neurons are linear threshold type. Since BAM
is bidirectional, a signal pattem p l can be entered at the
terminal A and the corresponding stored pattem pz can be
retrieved at the terminal B, or the pattem pa can be entered
at B and the corresponding pattem p l can be retrieved at A .
Many such signal pattems can be stored in BAM. Grossberg
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1319
mtao
LAYER
INPUT
BUFFER
INPUTS
ic)
Fig. 25. Feedback neural networks. (a) Hopfield network.
(b) Kosko’s bidirectional associative memory (BAM) network.
(c) Grossberg’s adaptive resonance theory (ART) network.
and Carpenter proposed a more complex adaptive resonance theory (ART) feedback network, shown in Fig. 25(c),
which is based on psychological and mathematical theories.
The ART neurons are functionally clustered into “nodes.”
The two layers (storage and input layers) have modifiable
connections between every node in the input layer and
every node in the storage layer. There are two sets of
connections between the layers, and the storage layer has
lateral inhibition (competing) connection, as shown. An
input pattem is transmitted to the storage layer through
the weighted connections, and the corresponding output
pattern is sent back to the input layer through another set of
weighted connections. At stable state, the input and output
pattems are said to be resonant. The network is considered
very powerful, but the number of stored pattems is limited
to the number of nodes in the storage layer.
E. Neural Network Application
A neural network can be used for various control and
signal processing applications in power electronics and
1320
drives. Considering its simple input-output nonlinear mapping property, one straightforward application is one- or
multidimensional function generation. Figure 26 illustrates
a network that has been trained for Y = 0.8 sinX function generation [38]. The training has been carried out
with large Y versus X precomputed example data table
for the whole cycle. Although it appears like a look-up
table implementation, the trained network can interpolate
between the example data values. Another example of
similar application is the selected harmonic elimination
method of PWM control where the notch angles of a
wave can be generated by a neural network for a given
modulation index (m). As before, the network can be
trained from a precomputed notch angle table with the
modulation index.
A network can be trained for on-line or off-line diagnostics of a power electronic system. Consider, for example,
an ac drive where the essential sensor signals relating to
the state of the system are fed to a neural network. The
network output can interpret the “health” of the system
for monitoring purposes. The drive may not be permitted
to be commissioned if the health does not appear good.
The diagnostic information can be used for appropriate
remedial control, such as shutdown or fault-tolerant control
of the system. Similarly, a network can receive FFT pattem
of a complex signal and be trained to draw important
conclusions from it. A neural network can receive timedelayed inputs of a distorted wave and perform adaptive
noise or harmonic filtering without any phase shift [37].
Although a feedforward network cannot incorporate any
dynamics within it, a nonlinear dynamical system can be
emulat6d [36] by time-delayed input and output signals
which will be discussed later. The feedback voltage and
current signals of a machine can be processed with a
network to estimate torque, flux, active power, etc. [47].
A fuzzy neural network, as discussed earlier, can be used
for adaptive feedback control [45] or estimation [32] in a
power electronic system. A few more application examples
from the literature will be briefly reviewed here.
Inverter Pulsewidth Modulation [42], [43]: Figure 27
shows a current-control PWM scheme with the help of
a neural network. The network receives the phase current
error signals through the scaling gain K and generates the
PWM logic signals for driving the inverter devices. The
sigmoidal function is clamped to 0 or 1 when the threshold
value is reached. The output signals (each with 0 and 1)
have eight possible states corresponding to the eight states
of the inverter. If, for example, the current in a phase
reaches the threshold value f0.O 1, the respective output
should be 1 which will tum on the upper device of the leg.
If, on the other hand, the error reaches -0.01, the output
should be 0 and the lower device will be switched on. The
network is trained with eight such input-output example
pattems.
In a modified scheme [43], the network is trained to
generate the optimum PWM pattem for a prescribed set of
current errors. The desired pattem is generated separately
by a PWM computer, as shown. The desired pattern and
PROCEEDINGS OF THE IEEE, VOL. 82, NO. 8 AUGUST 1994
HIDOEN LAYER
INPUT LAYER
OUTPUT LAYER
-0.0241
3 06
INPUT ( X I
- Tr< XSTT
- 0 989
0.0355
2 68
= sinX synthesis with neural network.
Fig. 26. lr
(FOR TRAINING1
Fig. 27. Neural-network-based PWM controller.
the actual output pattern can be compared and the resulting
errors can train the network. The training is very timeconsuming, but the performance tends to be good. In a
somewhat simpler scheme, the network is trained to minimize the current errors within the constraint of switching
frequency.
Identification and Control of DC Drive [44]: Figure 28
shows a neural-network-based indirect model referencing
adaptive control (MRAC) scheme of a dc drive where
it is desirable that the motor speed follows an arbitrary
command speed trajectory. The motor model with the load
is nonlinear and time-invariant, and the model is completely
unknown. However, the reference model which the motor is
to follow is given. Here, the unknown nonlinear dynamics
of the motor and the load are captured by a feedforward
neural netwoi The trained network identifier is then
combined with the reference model to achieve trajectory
control of speed.
The dc motor electrical and mechanical dynamics can
be given by the following set of equations:
K,w,(t) = v ( t )- R,i,(t)
dwr
di
dt
- La>
+
+ Bwr(t) TL(t)
dt
TL(t)= Kw,2(t)[Sign (wr(t))]
Kti,(t) = j-
(27)
(28)
(29)
where the common square-law torque characteristics have
been assumed. These equations can be combined and
BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS
1321
~(K-11
*-
Fig. 28. Model identification and adaptive control of a dc motor using a neural network.
or
v ( K ) = g [ w r ( K + 11, w,(K),
u,(K - I)]
(31)
where (see (32) at bottom of previous page) and where K is
the sampling instant. Equation (31) gives the discrete model
of the machine. A three-layer network with five hidden
layer neurons is trained off-line to emulate the unknown
nonlinear function g[.].The signals w,(K+l), w,(K), and
w,(K - 1) are the network inputs and the corresponding
output is g[.] or v [ K ] .This is basically an inverse model
of the machine. The signal E ( X - 1) is the identification
error which should approach zero after successful training.
After training, the network is placed in the forward path, as
shown, to cancel the motor dynamics. Since the reference
model is asymptotically stable, and assuming that the
tracking error E,(K) tends to be zero, the speed at ( K
1)th time step can be predicted from the expression
+
G,(K
+ 1) = 0.6w,(K) + 0.2w,(K + 1) + r * ( K ) . (33)
Therefore, for a command trajectory of wf(K), r * ( K )can
be solved from the reference model, and the corresponding
G,(K
l), w,(K), and w,(K - 1) signals can be
impressed on the neural network controller to generate
the estimated v ( K ) signal for the motor, as shown. The
parameter variation problem cannot be incorporated in
the network with off-line training. The model emulation
and adaptive control, as described above, can be extended
for ac drive application [47].
+
1322
V. CONCLUSION
The paper gives a brief but comprehensive review of the
three branches of artificial intelligence, i.e., expert system,
fuzzy logic, and neural network. The theoritical principles
of each that are relevent to power electronics and motion
control applications are described in a simple manner in
order to make them comprehensible to the readers with
power electronics background. Then, several applications
in each topic are described to supplement the concepts.
Fuzzy logic and neural network technologies are in the
process of fast evolution. The frontier of power electronics
and motion control, which is already so complex and
interdisciplinary, will be definitely extended far and wide
by the AI techniques, and will provide a great challenge to
the community of power electronic engineers.
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Bimal K. Bose (Fellow, IEEE) received the
B.E. degree from Bengal Engineering College,
India, the M.S. degree from the University of
Wisconsin, Madison, and the Ph.D. degree from
Calcutta University, India, in 1956, 1960, and
1966, respectively.
Early in his career, he served as a faculty
member in Calcutta University (Bengal Engineering College) for 11 years. In 1971, he joined
Rensselaer Polytechnic Institute, Troy, NY, and
in 1976, he came to General Electric Corporate
Research and Development, Schenectady, NY, as Electrical Engineer and
also served there for 11 years. His research interests are power converters,
ac drives, microcomputer control, and application of expert systems,
fuzzy logic, and neural network in power electronics. He has published
more than 100 papers and holds 18 U.S. patents. He authored/edited 4
books in power electronics: Power Electronics and AC Drives (Englewood
Cliffs, NJ: Prentice-Hall, 1986). Adjusrable Speed AC Drive Systems (
New York: IEEE Press, 1981), Microcompufer Control of Power Electronics and Drives (New York: IEEE Press, 1987). and Modern Power
Elecfronics (New York: IEEE Press, 1992). In addition, he contributed
to the Systems and Confrol Encyclopedia (New York: Pergamon, 1987),
Electrical Engineering Handbook (Boca Raton, FL: CRC Press, 1987).
and Encyclopedia of Applied Physics (VCH, to be published). For his
research contributions at the Bengal Engineering College he was awarded
the Premchand Roychand scholarship and the Mouat Gold Medal by the
Calcutta University in 1968 and 1970. respectively. In 1993, he received
the IEEE Industry Applications Society Outstanding Achievement Award
for “outstanding contributions to the application of electricity to industry”
and in 1994 he was awarded IEEE Region 3 Outstanding Engineer
Award for “outstanding achievements in power electronics and drives
technology.”
Dr. Bose has served the IEEE in various capacities that include Chairman of IAS Industrial Power Converter Committee, IAS member in the
Neural Netweork Council, Chairman of the Industrial Engineering Society
Power Electronics Council, and the Power Electronics Committee, Associate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,
and Distinguished Lecturer of the IEEE Industrial Electronics and Industry
Applications Societies.
APPLICATIONS
I323