Expert system, fuzzy logic, and neural network ... network/4.pdf · Expert System, Fuzzy Logic, and Neural Network Applications in Power Electronics and Motion Control BIMAL K. BOSE,

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 top- down 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

IEEE Log Number 9402594. University of Tennessee, Knoxville, TN 37996 USA.

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 pro- lifereated 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

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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-organizing control 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- con- trollers, 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. EXPERT SYSTEM

A . Expert System Principles Expert system is basically a cluster of software routines

especially organized in a computer that tends to emulate

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 rule- based 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 forward- and backward-chaining rules may be strategically mixed.

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EXPLANATION SUB-SYSTEM

- - - _ - - _KNOwL_EDGE - - - - - - -

ENGINE BASE

-A WORK SPACE

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. tion rules.

Expert system knowledge base showing a set of produc-

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 user- friendly 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

KNOWLEDGE ACOUl SI T ION

‘ DOMAIN I EXPERT I L - _ _ _ - _ _ J

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 meta- rule 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

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m l

swLl rmFRFACE

FOR

DOSFILE

Fig. 3. Frame structure of knowledge base.

D(KwABLE WRITEDOS-FILE

DOSCAU- Dos

READM)S-FILE

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 fact- like knowledge and procedural or method-like knowledge.

B . Expert System Shell

A shell is a software environment for efficient and user- friendly 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

THEN : : MC-SPD = MC-SPD * 0.8 = NO AND MC-SPD > 0.5

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

USER INTERFACE

PC SCHEME

Fig. 4. Extemal interface of shell.

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

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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 fault- tolerant 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 application- related 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

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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 POWER-BJT-IDC = (7.733*OUTPUT - POWER) * IOF * INV-OVERLOAD/OUTPUT-VOLT

THEN : :

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. Subframe- 1 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

- HKFBRlDQE msrry8Munlm SIYuUllON AND

SUBFRAUEP SNUBBEROPTYIUTIOW

o B s E f w E ~ u E

SUB M E -1

I

oBsERvATw3NOFWAVES OasERVATloN OF WAVES ANDcRmcALvAwEs

Fig. 9. Structure of knowledge base for converter design.

load current (either from the root frame or from Subframe- I ) , 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


MEDIUM

m z

z 0.0 0 400 800 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 bell- shaped (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

(1) P A U B ( Z ) = max [ P A ( z ) , P B ( 5 ) ] .

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

P A n B ( 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

(3) P A ( Z ) = 1 - P ] A ( 5 ) .

' t

I .o 't L 0 1 2 3 4 5 6 x

lo= 0 1 2 3 4 5 6 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


RULE I

RULE 2:

kf POS ITlVE NEGAT 1 VE SMALL

f I ERROR (E)

A 0 DU

ERROR RATE (CElJ FINAL FUZZY * + l o VALUE FOR DU ,’ ‘\ :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

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

u = x . R

or

PU(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 (de ldt 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:

2 vi P(ui> (7) U() = i= l

2 P ( u i > ‘ i= 1

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

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u u

C +

Fig. 13. Basic structure of fuzzy control system.

PREMISES CONSEWENTS I \ / A

\

t /MEDIUM /MEDIUM

Tsl ‘A01 +AllW+A21H

W DEFUZZ I F ICAT I ON

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-model- based conventional control can give superior performance. Similarly, the fuzzy estimation technique can be applied to a process where mathematical model is not known, ill- defined, 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 =A01 + 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, model-

ing, and estimation of power electronic system. In general,

BOSE: EXPERT SYSTEM, FUZZY LOGIC, AND NEURAL NETWORK APPLICATIONS I31 I

vac DC MACH I NE

CURRENT PHASE - J

CONTROLLER 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 ef- fects, 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, impair- ing efficiency of the drive. The flux can be programmed at light-load steady state in order to improve efficiency of

Table 1 Rule Base for Speed Control

NB I NM 1 NS I @

PB

933 NK NS 2

FW PB WB

W B W B

F'VB W B W B

NE NM NS '!Z PS PM PE

(a)

NB NM NS '/Z PS PM PE

ce -I

(b)

NVB NE NM NSP!Z PS PM PB PVB

-I - U , - U 2 - U 3 0 U3 U2 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


OFERATlON 4

(rated)

I

I- TORQUE CURRENT

=>

--p&"G

ROTOR FLUX

TIME

/ - L m s s

COPPER toss

CONVERTER Loss LRON LOSS

TIME

Fig. 17. by flux programming.

On-line search method of efficiency optimization control

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 )

is negative medium (NM). THEN the excitation increment ( d z d s )

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

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

Q* = w e ( L s z ~ ~ - L,i;:) (8) = Rsi:s - w,L,i;E, (9)

where L, = L, - (Lm2/Lr ) 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 = v q s z d s - v d s i q s (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 z:s - 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

speed ( w e ) is low ( L ) and torque ( iq s ) is high ( H ) weighting factor K f is high ( H ) .

V d s = vbs sin 0, + vis cos 0,

IF

THEN The combined error signal is given as

E = AQ . K f + n v d s ( 1 - K j ) . (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 feedback- loop 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


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-logic-

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 THEN Is is PMM, I f is PSB, and DPF is PMS.

H is PMS AND W is PSB

Once Is , 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. NEURAL NETWOW

A. Neural Network Principles

Neural network or artificial neural network (ANN), as the name indicates, is the interconnection of artificial neurons


M F. FOR HEIGHT (HI

VZO PSS PSM PSB PMS PMM PMB PBS PBM PBB VB

P

0

M F. FOR WIDTH

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.

MF. FOR RMS CURRENT

I

I

PSS PSB PSVB PBZO PBVB // VZO.PSZO/PSM/ A S P M M P M B I PBSPBMPBB I VB I .o

M.F. FOR FUND. RMS CURRENT

I p

MF. FOR OISP. FACTOR

SYNAPSE ‘I\ WEIGHTS

INPUTS X 3 “B E ,NEURON OUTPUT Y:

SIGMOIDAL 1 SUMMING FUNCTION I)

NODE

XN 7 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 con- figuration 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


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), signum- type (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), inverse- tan, hyperbolic, or Gaussian type. The sigmoidal transfer function is most commonly used, and it is given by

1 1 + e-ax

Y =

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, mono- tonic, 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. There- fore, 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

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 x,. Similarly, the network output signals can be given in the matrix form as

v, Yl w94 w95 w96 w97 w98 1 . 1 1 [ y2] = [ w10, 4 w10, 5 WlO, 6 WlO, 7 w10, 8

V8 (17)

or

Combining (15) and (17)

w95 w96 w97

w10,4 w10,5 w10,6 w 1 0 , 7 w10,8

w41 w 4 2 w43

w51 w52 w53

‘ Iw71 w61 w72 w62 w63 w7] ’ E:] (19)

Wai Ws2 W83

or

which indicates that the output vector is the dot product of combined weight matrix mcba and the input vector xa. Note again that with the nonlinear transfer function, the above calculations are strictly invalid.

1316 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 cen- tralized 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


1

7x5 NEURAL 5x I MATRIX NETWORK MATRIX

Fig. 23. Input-output mapping of the letter “C.”

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

Net; = W ; j X i 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 th 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 th 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

1 l S E - - ( d p - y p ) 2 = 2 c(d; - $)z (23) J = 1

p - 2

where d? is the desired output of the j th neuron in the output layer, y; is the corresponding actual output, S is the dimension of the output vector, yp 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

l P P

E = Ep = x(q - $)’. (24)

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

p = l p = l j=l

where 77 is the learning rate, Wzj(t + 1) is the new weight, and UTZ3(t) is the old weight. The weights are iteratively 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.,

~ ( t + 1) = 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 simula- tor 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


Fig. 24. Fuzzy neural network (F") for fuzzy control.

U:

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 (CE) ) 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

UlPl + UZP2

P1+ PZ IF E is SM AND CE is ME THEN U =

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, Wu2ir and 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 inter- esting 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


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

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 time- delayed 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


INPUT LAYER HIDOEN LAYER OUTPUT LAYER

-0.0241

3 06

- 0 989 INPUT ( X I - Tr< XSTT

0.0355

2 68

Fig. 26. lr = sinX synthesis with neural network.

(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 time- consuming, but the performance tends to be good. In a somewhat simpler scheme, the network is trained to min- imize 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:

d i K,w,(t) = v ( t ) - R,i,(t) - La> dt (27)

dwr dt Kti,(t) = j- + Bwr(t) + TL(t) (28)

(29) TL(t) = Kw,2(t)[ Sign (wr(t ) )]

where the common square-law torque characteristics have been assumed. These equations can be combined and


~ ( K - 1 1 *-

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].

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.

REFERENCES

B. K. Bose, “Variable frequency drives-Technology and applications,” in Proc. of IEEE Int. Symp. on Industrial Electronics, (Budapest, Hungary, 1993), pp. 1-18. -, “Power electronics-Recent advances and future per- spective,” in IEEEIIECON Conf. Rec., pp. 14-16, 1993. M. W. Firebaugh, Artificial Intelligence. Boston, MA: Boyed and Fraser, 1988. D. A. Waterman, A Guide to Expert Systems. Reading, MA: Addison-Wesley, 1986. D. Chorafas, Knowledge Engineering. New York: Van Nos- trand, 1990. R. G . Vedder, “PC based expert system shells: some desirable and less desirable characteristics,” Expert Syst., vol. 6, pp. 28-42, Feb. 1989. PC PLUS User’s Reference Manual, Texas Instruments Inc., Dallas, TX, , Nov. 1988. K. S . Tam, “Application of AI techniques to the design of static power converters,” in IEEEIIAS Annu. Meet. Con5 Rec., pp. 960-966, 1987. C. Daoshen and B. K. Bose, “Expert system based automated selection of industrial ac drives,” in IEEEIIAS Annu. Meet. Conf. Rec., pp. 387-392, 1992.

1322 PROCEEDINGS OF THE IEEE, VOL. 82. NO. 8 AUGUST 1994

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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 Engi- neering 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 Elec- tronics 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 Chair- man 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, Asso- ciate Editor of the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, and Distinguished Lecturer of the IEEE Industrial Electronics and Industry Applications Societies.

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