Fuzzy Logic Systems

Module 2

Fuzzy Control System Design

Prof. Marzuki Bin Khalid

CAIRO
Fakulti Kejuruteraan Elektrik
Universiti Teknologi Malaysia
UTM marzuki@utmkl.utm.my 1
www.cairo.utm.my

Fuzzy Control Systems Design

Module 2 Objectives

• To do a brief review on basics of control.

• To understand the need for fuzzy logic control.
• To understand how to design a fuzzy logic controller.
• Understanding the components of a fuzzy logic controller.
• To understand how inferencing is done in a fuzzy logic controller.
• To be able to understand how rules can be developed in a fuzzy logic
controller.
• To study several types of defuzzification techniques.
• To study the design procedure of a fuzzy logic controller.
• At the end of the module, the student should be able to understand the
basic components of a fuzzy logic controller and how they function.

2
 Module 2 Contents
• 2.1 Overview of fuzzy logic control
– 2.1.1 Review of Control System Basics
– 2.1.2 Why fuzzy logic control?

• 2.2 Designing a fuzzy logic control system (FLCS)

– 2.2.1 Components of the fuzzy controller
– 2.2.2 Operations of the fuzzy controller
– 2.2.2 Fuzzification
– 2.2.3 Knowledge base
– 2.2.4 Inference Mechanism
– 2.2.5 Defuzzification

• 2.3 Design procedure of the fuzzy logic controller

• 2.4 Summary of Module 2 3

2.1 Overview of Fuzzy Logic Control

2.1.1 Review of Control System Basics

2.1.2 Why fuzzy logic control?

2.1.3 Configuration of a fuzzy logic control system

4
 2.1.1 Review of Control System Basics
Example of control systems
– Cars, Aeroplanes, Trains, Ships, ...
– Nuclear Plants, Power Stations, ...
– Washing Machines, Refrigerators, ...
– Disk Drives, Stepper Motors, .......
– Chemical Processes, Food Processing Plants .....
– Robotic Manipulators, NC Machines, …

• Position • Pressure
• Speed • Turgidity
• Concentration
• Liquid level
• Intensity
• Temperature • Etc.
5

A Feedback (Closed-Loop) Control System

Error signal Control signal

+ Controller
Setpoint Process Output
-

Summer Feedback
(Op-Amp)

A Conventional Control Block Diagram

Control objective
• In many control systems, the objective is to design a controller such
that output can be controlled by giving the desired signals at the input.

Example of control
– Alignment of the front wheel of a vehicle follows that of the driver’s
steering wheel
– Rudders of a boat follow its steering wheel
– Concentration in liquids follows a given set-point
– Temperature of furnace follows a given set-point

6
 Control Systems Performance
• What are the factors affecting control systems?
– Choice of the Controllers (Algorithms)
– Tuning of Controllers
– Selection of Control Variables
– Selection of Performance Index
– Types of Sensors (Measurement Errors)
– Actuators
– Disturbances/Environment
– Noise
– Control Configuration
– Design Techniques
– Nonlinearity 7

• Several performance indices that can be used to

measure control system performance

– Integral Squared Error (ISE)

– Integral Absolute Error (IAE)
– Integral Time Absolute Error (ITAE)
– Integral Time Squared Error (ITSE)
– Minimum Fuel, Time, etc.

8
 Control system components

• A control system is made up of many sub-control systems

and components.

A military helicopter

A space shuttle
9

Analysis in Time Domain

• By observing the system time response we can measure
its performance.
• To measure the swiftness of system response: Check
rise-time and peak-time.
• To measure the closeness of system response to the
desired response: check overshoot, settling-time, rise-
time, steady-state error, ISE, etc.
• Other analysis can also be done.

10
 Example of Control Paradigms
Control Design Techniques and Control Paradigms

Modern
Classical

Artificial Intelligence
State Feedback
Root Locus State Estimation
Bode Plot Observers
Nichols Chart Optimal Control
Nyquist Plots Robust Control
H-Infinity
Internal Model Control
Adaptive Control
Neuro-Control
Fuzzy Control
Genetic Algorithms
Knowledge Based Systems
11

Example of Controllers
that can be applied in control systems

Conventional Controllers Predictive Controllers

• Bang-Bang (on-off) • Smith Predictor
• Proportional • Generalized Predictive Controllers
• PID Controller
Intelligent Controllers
Adaptive Controllers • Knowledge Based
• Self-Tuning Controller • Fuzzy Logic Controllers
• Self-Tuning PID Controller • Neuro-Controllers
• Auto-Tuning PID Controller • Adaptive Fuzzy
• Pole Placement

12
 Overview of Fuzzy Logic Control

2.1.2 Why Fuzzy Control?

• During the past decade, fuzzy logic control has emerged as one of the most active
and fruitful research areas in the application of fuzzy set theory, fuzzy logic and fuzzy
reasoning.

• The idea was first proposed by Mamdani and Assilian around 1972.

• Many industrial and consumer products using fuzzy logic technology have been built
and successfully sold worldwide.

• In contrast to conventional control techniques, fuzzy logic control is best utilized in

complex ill-defined processes that can be controlled by a skilled human operator
without much knowledge of their underlying dynamics.

13

Prof. E. H. Mamdani

Founder of Fuzzy
Logic Control
14
• The basic idea behind fuzzy logic control is to incorporate
the “expert experience” of a human operator in the design
of a controller in controlling a process whose input-output
relationship is described by a collection of fuzzy control
rules (e.g. IF-THEN rules) involving linguistic variables.

• This utilization of linguistic variables, fuzzy control rules,

and approximate reasoning provides a means to
incorporate human expert experience in designing the
controller.

15

Benefits of Fuzzy Control

• Suitable for Complex Ill-defined Systems where
mathematical modeling is difficult or Plant is too
abstract e.g. Complex chemical plant, cement-
kiln, etc.

• Able to design along linguistic lines – usage of

rules based on experience

• Better performance than Conventional PID

Controllers

• Simple to design

16
 Overview of Fuzzy Logic Control

2.2 Designing a Fuzzy

Logic Control System

Where do we start?
What are the Basics/Background needed?
What are the components of a Fuzzy
Controller?
Where can it be applied?

17

A fuzzy logic control system

Error Control Signal

Setpoint or InputTransducer Fuzzy Controller Process Output or

Reference + Controlled Variable
Defuzz
Fuzz

Ru le s
-

Rateof Change
of Error Output Transducer
or Sensor

18
 2.2.1 Components of the
fuzzy logic controller
• It generally comprises four principal components:
• fuzzifier
• knowledge base
• inference engine
• defuzzifier

• If the output from the defuzzifier is not a control action for a

process, then the system is a fuzzy logic decision support
system.

• The fuzzy controller itself is normally a two-input and a single-

output component. It is usually a MISO system. 19

Components of the Fuzzy logic

controller

Knowledge
Base

Fuzzy Fuzzy

Inference
Fuzzifier Defuzzifier
Engine

Process Output Crisp Control

& State Signal
Process

20
 Design Process
Identify controller Inputs and Outputs as the Fuzzy
variables
Break up Inputs and Outputs into several Fuzzy Sets
and label them according to the problem to be solved
and set up the fuzzy variables on the appropriate
universes of discourse <FUZZIFICATION>
Configure/develop RULES to solve the problem
Choose Inference Encoding procedure
Choose a DEFUZZIFICATION Strategy
Tune the adjustable parameters
21

Discuss how to design a fuzzy

controller for the following process?
• Hot shower system
• Automatic Fuzzy Car Wipers
• Rice Cooker
• Vacuum Cleaner
• Air conditioner
• Water Bath Temperature Control System

22
 Components of the Fuzzy Logic Controller

2.2.2 Operations of the fuzzy controller

• A fuzzy logic controller usually has 2 inputs

and 1 output for a SISO plant.

• The 2 inputs are used for accessing the

current conditions of the process such that the
necessary action can be taken by providing
the correct control signal (which is its output).

23

• The inputs to the fuzzy controller is usually the

error (e) which measures the system performance
and the rate at which the error changes (∆e). and
the output is the change of the control signal (∆u).

Inference Mechanism
Sensor
e readings
Control
signal
Defuzzification
Fuzzification

Rule base
∆u
IFXisAAND Yis B
∆e THEN Zis C

24
• A fuzzifier then transforms the crisp values of e and
∆e into corresponding fuzzy values (usually there are
several fuzzy values of e and ∆e).

• From the rule base, the fuzzy values of e and ∆e

determine which rules are to be fired through an
inferencing algorithm.

• Several values of ∆u will then be obtained and a

defuzzification mechanism will then transform these
values into one crisp value.

• The actual control signal is obtained by adding ∆u to

the past value of u which is send to the plant.

25

Components of the Fuzzy Logic Controller

2.2.2 Fuzzification

What is
Fuzzification?

26
 Fuzzification
• Involves the conversion of the input/output signals
into a number of fuzzy represented values (fuzzy
sets).
• Choose an appropriate Membership Function to
represent each Fuzzy Set
• Label the Fuzzy Sets appropriately such that they
reflect the problem to be solved
• Set up the Fuzzy Sets on appropriate Universes
of Discourse
• Adjust / tune the widths and centerpoints of
membership functions judiciously
27

Consider a Fuzzy Rice Cooker

• First, we need to identify the input and
output variables of the process, in this
case, the rice cooker.
• Study the control mechanism

28
 Input and Output Variables
of the Fuzzy Rice Cooker
"
#

29

Fuzzification
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. ( $)
+ %θ % * (

30
 Fuzzification

/
%µ∆ / 0 )/
1
2" , 3,
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5

+
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31

/
%µ" / 0 )/
1
2" , 3,
4(
5

-
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%µθ / 0 )/
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2" , 3,
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5

. ( + %
θ 32
 6 1
7 ' 6

Negative Medium NM
Negative Small NS
Zero ZE
Positive Small PS
Positive Medium PM

33

Consider an Air Conditioner

How do you design the fuzzification

component of the fuzzy Air-conditioner
system?

34
62/ -8-1
96628 )::96 .6 8 28.+21
• Usually fuzzy sets are overlapped by about 25%.

• It can be observed that in fuzzy logic control the transition

from one fuzzy set to another provides a smooth transition
from one control action to another.

• If there is no overlapping in the fuzzy sets then the control

action would resemble bivalent control (transition from one
error region to another is rather abrupt).

• On the other hand if there is too much overlap in the fuzzy

sets, there would be a lot of fuzziness and this blurs the
distinction in the control action.
35

• For simplicity we can choose the same (triangular)membership

functions for each of the fuzzy subsets of all the fuzzy variables.

• The example below shows membership functions chosen for 2 fuzzy

input variables and 1 output variable in controlling an inverted
pendulum.

mθ
NM NS ZE PS PM
1

0
0 Pendulum Angle,θ
m∆θ
NM NS ZE PS PM
1

0
0 Angular Velocity,∆θ
mv
NM NS ZE PS PM
1

0
0 Motor Voltage, v

Example of Fuzzification for an Inverted Pendulum Control 36

 Components of the Fuzzy Logic Controller

2.2.3Knowledge Base

• The knowledge base of a fuzzy logic controller consists of a data base and a rule
base.

• The basic function of the data base is to provide the necessary information for the
proper functioning of the fuzzification module, the rule base and the defuzzification
module.

• This information includes

– the meaning of the linguistic values of the membership functions of the
process state and the control output variables.
– physical domains and their normalized counterparts together with the
normalization, denormalization and scaling factors.
– the type of the membership function of a fuzzy set.
– the quantization look-up tables defining the discretization policy.
37

Fuzzy Control Rules

• The basic function of the rule base is to represented the expert
knowledge in a form of if-then rule structure.
• See C.C. Lee, "Fuzzy Logic Control: Part I", IEEE Transactions
on System, Man and Cybernetics, 1990
• These four methods of deriving the rule base can be described
as follows:
(i) Expert experience and control
engineering knowledge
(ii) Based on operator’s control actions
(iii) Based on fuzzy model of a process
(iv) Based on learning

38
 (i) Expert experience and control engineering knowledge
• This method is the least structured of the four methods and yet it is
one of the most widely used today.

• It is based on the derivation of rules from the experience based

knowledge of the process operator and/or control engineer.

39

(ii) Based on operator’s control actions

• This method tries to model an operator’s skilled actions or
control behavior in terms of fuzzy implications using the input-
output data connected with his control actions.

• The idea behind this technique is that it is easier to model an

operator’s actions than to model a process, since the input
variables of the model are likely found by asking the operator
the kind of information he uses in his control actions

40
(iii) Based on fuzzy model of a process
• In the linguistic approach, the linguistic description of the dynamic
characteristics of a controlled process may be viewed as a fuzzy
model of the process.

• Based on the fuzzy model, we can generate a set of fuzzy control

rules for attaining optimal performance of a dynamic system.

• The set of fuzzy control rules forms the rule base of the fuzzy logic
controller.

• Although this approach is somewhat more complicated, it yields better

performance and reliability and provides a more tractable structure for
dealing theoretically with the fuzzy logic controller.

41

(iv) Based on learning

• Many fuzzy logic controllers have been built to emulate human

decision making behavior.

• Currently, many research efforts are focused on emulating human

learning, mainly on the ability to create fuzzy control rules and to
modify them based on experience.

• There are now many examples of fuzzy controllers which have the
capability to learn and to compose the rules involving neural networks
and genetic algorithm.

• One example is given in the research at CAIRO on Self-Organizing

Neuro-fuzzy Control Systems (see Part II: Module 4).

42
 Example of Fuzzy Control Rules

Example of rules for traffic control

IF traffic from the north of the city is HEAVY

AND the traffic from the west is LESS
THEN allow movement of traffic from the north LONGER.

IF traffic from the north of the city is AVERAGE

AND the traffic from the west is AVERAGE
THEN allow NORMAL movement of traffic for both sides.

43

Example of a Rule for a

Temperature Control System
If the error in the temperature is positive and
large
and the rate of change of error is almost zero
then heater should be on positive and large.

This rule can be shorten as follows:

IF e is PL AND De is ZE THEN Du is PL

or (PL, ZE; PL)

44
 Example 2.1

• For simplification a matrix can be used for

presenting the rules which is called fuzzy rule
matrix.
• Many control rules are written in the form below:
( Antecedents) (Consequent)
IF X AND Y THEN Z
• Example of a fuzzy rule matrix for controlling a
temperature control process given as follows

45

• For the rule (P, Z; P)

• For the rule (N, Z; N)
• For the rule (Z, N; N)
Antecedents
e N Z P
De
Antecedents

N
Z

46
 Rules?

47

Derivation of fuzzy rules

based on observations

• Though fuzzy rules can be formulated through

observation of the process, they are, however,
could not be easily derived if one has not much
experience.

• A more systematic approach to formulate the fuzzy

control rules can be done following the approach
given by C.C. Lee.

• The fuzzy rules can be formulated based on the

conditions of error, E, and the rate of change of
error, ∆E, and the output is the change in the 48
control signal, ∆u.
• Mathematically, we can write:
for the error at the sampling instant k:

e(k ) = r (k ) − y (k )
de(t )
• For the derivative of the error in continuous time:
dt
• and in discrete time at sampling instant k:

∆e( k ) = (e( k ) − e( k − 1) )

Inference Mechanism
Sensor
e rea dings
Control
signal

Defuzzification
Fuzzification

Rule base

∆u
IF X is A AND Y is B
∆e TH EN Z is C

49

• The prototype of fuzzy control rules is tabulated in Table 1 and a

justification of fuzzy control rules is added in Table 2 (These are for only
3 quantizations P, Z and N).
• As an example, based on the underdamped 2nd order system response,
the corresponding rule of Region 2 can be formulated as rule R1 below
which decreases the system overshoot and for Region 3, Rule R2 has the
effect of shortening the rise time.

• More specifically,
R1: if (E is negative and ∆E is positive )
then ∆U is positive,
R2: if (E is negative and ∆E is negative)
then ∆U is negative.

• Tables 3 and 4 provide the selection of the consequents for 7

quantizations of the fuzzy control variables (i.e. NB, NM, NS, ZE, PS,
PM, PB).

50
 Observation of system response
for deriving fuzzy control rules
k ) = (e(k ) − e(k − 1))
∆e(e(k)=r(k)-y(k)

e- e-
∆e+ ∆e- e-
Setpoint ∆e+

e+
∆e+

e+ e+ e- e+ e+ e- e- e+
∆e- ∆e+ ∆e- ∆e- ∆e+ ∆e+ ∆e- ∆e-

a1
1 2 3 4 5 6 7 8 9 10 11 12 51

TABLE I
PROTOTYPE OF FUZZY CONTROL RULES WITH TERM SETS
(NEGATIVE, ZERO, POSITIVE)

Rule No. E ∆E ∆U Reference Point

1 P Z P a1, a2, a3
2 Z N N d1, d2, d3
3 N Z N c1, c2, c3
4 Z P P b1, b2, b3
5 Z Z Z set point

TABLE 2
P ROTOTYPE OF F UZZY C ONTROL R ULES W ITH T ERM S ETS
( N EGATIVE, Z ERO, P OSITIVE)

Rule No. E ∆E ∆U Reference Point

6 P N P 1 (rise time), 5
7 N N N 2 (overshoot), 6
8 N P N 3, 7
9 P P P 4, 8
10 P N Z 9
11 N P Z 10
52
 TABLE 3
PROTOTYPE OF FUZZY CONTROL RULES WITH TERM SETS
{NB, NM, NS, ZE, PS, PM, PB}

Rule No. E ∆E ∆U Reference Point

1 PB ZE PB a1
2 PM ZE PM a2
3 PS ZE PS a3
4 ZE NB NB b1
5 ZE NM NM b2
6 ZE NS NS b3
7 NB ZE NB c1
8 NM ZE NM c2
9 NS ZE NS c3
10 ZE PB PB d1
11 ZE PM PM d2
12 ZE PS PS d3
13 ZE ZE ZE set point

53

TABLE 4
PROTOTYPE OF FUZZY CONTROL RULES WITH TERM SETS
{NB, NM, NS, ZE, PS, PM, PM}

Rule No. E ∆E ∆U Reference Point

14 PB NS PM 1 (rise time)
15 PS NB NM 2 (overshoot)
16 NB PS NM 3
17 ND PB PM 3
18 PS NS ZE 9
19 NS PS ZE 10

54
 2.2.4 The Inference Mechanism

What is an Inference
Procedure in FLCS?

Knowledge
Base

Fuzzy Fuzzy

Inference
Fuzzifier Defuzzifier
Engine

Process Output Crisp Control

& State Signal
Process
55

Some Notes on the Inference Mechanism

• The Inference Mechanism provides the mechanism for invoking or
referring to the rule base such that the appropriate rules are fired.

• There are several methodologies but in Module 1 we have discussed

four methods (the compositional operators - Section 1.3.3).

• Two most common methods used in fuzzy logic control are the max-
min composition and the max-(algebraic) product composition.

• The inference or firing with this fuzzy relation is performed via the
operations between the fuzzified crisp input and the fuzzy relation
representing the meaning of the overall set of rules.

• As a result of the composition, one obtains the fuzzy set describing

the fuzzy value of the overall control output.

56
 Several Inference Procedures that
can be used in FLCS….
Max-Min
Max-Algebraic Product (or Max-Dot)
Max-Drastic Product
Max-bounded Product
Max-bounded sum 2 most commonly
Max-algebraic sum used
Max-Max
Min-Max
57

Example 2.2

• Consider a simple system where each rule comprises two antecedents and
one consequent. A fuzzy system with two non-interactive inputs x1 and x2
(antecedents) and a single output y (consequent) is described by a collection
of n linguistic if-then propositions:

• IF x1 is A1(k) and x2 is A2(k) THEN y(k) is B(k), k = 1,2,...n.

where A1(k) and A2(k) are fuzzy sets representing the kth antecedent pairs and
B(k) are the fuzzy sets representing the kth consequent.
• Based on the Mamdani implication method of inference, and for a set of
disjunctive rules, the aggregated output for the n rules will be given by

µB(k)(y) = Max Min[µA1(k)(input(i)), µA2(k)(input(j))]

• The equation above has a simple graphical interpretation, as seen in the

accompanying figure.

58
 Example of fuzzy inferencing using
Mamdani’s max-min compositional operator

Rule 1

µ µ µ
A 11 A 12 1 B1
1 1
min
0 x1 0 x2 y
input( i) input( j)

Rule 2
µ µ µ
A 21 1 A 22 1 B2
1
min

0 x1 x2 y
input( i) input( j)

Defuzzification
µ
1

y
y*
59

Some notes on the max-min inferencing method of Example 2.2

• The figure illustrates the graphical analysis of two rules, where the
symbols A11 and A12 refer to the first and second fuzzy antecedents of
the first rule, respectively, and the symbol B1 refers to the fuzzy
consequent of the first rule.

• The symbols A21 and A22 refer to the first and second fuzzy
antecedents, respectively, of the second rule, and the symbol B2
refers to the fuzzy consequent of the second rule.

• The minimum function arises because the antecedent pairs given in

the general rule structure for this system are connected by a logical
“and” connective.

• The minimum membership value for the antecedents propagates

through to the consequent and truncates the membership function for
the consequent of each rule.
60
 • This graphical inference is done for each rule.
• Then the truncated membership functions for each rule are
aggregated.
• The aggregation operation max results in an aggregated
membership function comprised of the outer envelope of the
individual truncated membership forms from each rule.
• Then, a crisp value for the aggregated output y* can be
obtained through the defuzzification technique which will be
discussed later in the next section.

61

Example 2.3

• In this example we show how another compositional operation results

which is based on the Larsen’s Max-product inference technique.
• Based on the max-product implication technique, for a set of
disjunctive rules, the aggregated output for the n-th rule would be
given by

µB(k)(y) = Max [µA1(k)(input(i))• µA2(k)(input(j))]

• The resulting graphical equivalent of the equation above is shown in

the following figure.
• The effect of the max-product implication is shown by the consequent
membership functions as scaled triangles.
• This figure also shows the aggregated consequent resulting from a
disjunctive set of rules and a defuzzified value, y*, resulting from the
defuzzification method.

62
 Example of fuzzy inferencing using
Larsen’s Max-product compositional operator

Rule 1
µ µ µ
A 11 A 12 1 B1
1 1

0 x1 0 x2 y
input( i) input( j)

Rule 2
µ µ µ
A 21 1 A 22 1 B2
1

0 x1 x2 y
input( i) input( j)

Defuzzification
µ
1

y
y* 63

2.2.5 Defuzzification

Knowledge
Base

Fuzzy
Fuzzy Crisp
Inference
Fuzzifier Defuzzifier`
Engine

Process Output Crisp Control

& State Signal
Process

64
 Some Notes on Defuzzification

• Defuzzification is a mapping from a space of fuzzy control actions

defined over an output universe of discourse into a space of non-
fuzzy (crisp) control action.
• This process is necessary because in many practical applications
crisp control action is required to actuate the plant.
• The defuzzifier also performs an output denormalization if a
normalization is performed in the fuzzification module.
• There are many methods of defuzzification that have been proposed
in recent years.
• Unfortunately, there is no systematic procedure for choosing a
defuzzification strategy.

65

Four most common defuzzification

methods:

• Max membership method

• Center of gravity method
• Weight average method
• Mean-max membership method

66
(i) Max membership method
• This scheme is limited to peaked output functions.
• This method is given by the algebraic expression:
µz(z*) ≥ µz(z) for all z ∈Z

µ
1

0 z
z*
67

(ii) Center of gravity method

• This procedure is the most prevalent and
physically appealing of all the defuzzification
methods.
• It is given by the algebraic expression
µ ( z ). z
Z

µz z* =
1 µ (z)Z

0
z
z* 68
(iii) Weight average method
• This method is only valid for symmetrical output
membership functions.
• The weight average method is formed by weighting
each membership function in the output by its
respective maximum membership value, z.
• It is given by the algebraic expression
µ ( z ).z
z

µ z* =
1
µ ( z)
z

0
z1 z2 z 69

(iv) Mean-max membership method

• This method is closely related to the first method,
except that the locations of the maximum
membership can be non-unique.
• This method is given by the expression a+b
z* =
µ 2
1

0 a z* b z
70
 2.3 Design procedure of the fuzzy logic
controller
• There is a general procedure that can be followed for designing a fuzzy
control system.

• Firstly, the designer have to identify the process input and output variables
that need to be considered. Thus, one must have a good knowledge on
the system to be controlled.

• Next, one should determine on the number of fuzzy partitions (or fuzzy
subsets) for the input and output linguistic variables.

• The number of fuzzy partitions of the input-output spaces should be large

enough to provide an adequate approximation and yet be small enough to
save memory space.

• This number has an essential effect on how fine a control can be obtained.

71

• In the third step, the designer has to choose the membership

functions for the input and output fuzzy variables.

• There are different types of membership functions available as

discussed in the previous module, however, the most common types
are triangular, trapezoidal and bell-shaped functions.

• After choosing the membership functions, the designer need to derive

the fuzzy control rules based on one of the four methods that have
been discussed.

• In many practical applications method (i) i.e. deriving from expert

experience and control engineering knowledge have been used.

• Next the inference engine need to be defined, but there is no

systematic methodology for realizing the design of an inference
engine. Most practitioners use empirical studies and results to provide
guidelines for their choices.
72
• Finally one have to choose the right choice of defuzzification method
for their particular application.

• Finally, once the fuzzy control system has been constructed, the
simulation of the system can be carried out.

• The performance of the system can be analyzed. If the results are not
as desired, changes are made either to the number of the fuzzy
partitions or the mapping of the membership functions and then the
system can be tested again.

• This trial-and-error approach will continue until satisfactory results are

obtained.

• Although this method is rather time-consuming and nontrivial, it has

been widely employed and has been used in many successful
industrial applications.

73

The design procedure of a fuzzy logic control system

Design Planning
-identify process input & output variables
-Identify Controllers inputs & outputs
- determine the number of fuzzy partitions
- choose types of membership functions
- derive fuzzy control rules-based
- define inference engine
- choose defuzzification method

Fuzzy Logic
Parameters Tuning Controller Operation
- mapping of membership
- Fuzzification
functions
- Fuzzy Inference
- fuzzy inference rules
- Defuzzification
- scaling factors

Simulation & Testing

No OK

Yes

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End
 2.4 Summary of Module 2
• As fuzzy logic has been successfully applied to many control
problems, more than any other areas of applications, in this module
we review some control system basics.

• In this module also we discussed some of the reasons behind the

success of fuzzy logic control systems.

• The basic components of a fuzzy logic controller has been

discussed which include techniques in fuzzification, knowledge
base, inference mechanism and defuzzification.

• The design procedure of the fuzzy logic controller is also discussed.

• Although we more specifically discussed fuzzy logic control, the
same techniques can be applied for the other areas as well such as
pattern recognition and diagnostic systems.

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