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This is to certify that the
thesis entitled

FUZZY LOGIC FDR EMBEDDED SYSTEMS:
DESIGN OF A REFRIGERATOR CONTRDLILER

presented by

Weijiang Robert Yu

has been accepted towards fulfillment
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ma chlefi-atd

 

FUZZY LOGIC FOR EMBEDDED SYSTEMS:

DESIGN OF A REFRIGERATOR CONTROLLER

By

Weijiang Robert Yu

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE

Department of Electrical and Computer Engineering

1999

ABSTRACT

FUZZY LOGIC FOR EMBEDDED SYSTEMS:
DESIGN OF A REFRIGERATOR CONTROLLER
By

Weijiang Robert Yu

Fuzzy logic design has been popular in the engineering domain for decades. Its
application ranges from control to decision support technology. Fuzzy logic design
overpowers the more conventional design strategies because of the ease with which it can
represent linguistic terms and ill-defined problems. Moreover, it is very simple to
implement using low cost micro-controller in solving complex and non-linear problems.
In this thesis, the motivation and relevance for applying fuzzy logic to embedded systems
is examined. The history of fuzzy logic and the concepts Of the mathematical foundation
that fuzzy logic is built on - fuzzy set theory - is studied. Research has concentrated on
the most popular fuzzy logic design methods for embedded systems. Details in
constructing fuzzification interface, defuzzification interface, and rule evaluation block
are presented. The hardware/software implementation issues are studied. This thesis also
provides a demonstration of applying fuzzy logic design to a home appliance followed by

results analysis and recommendations.

DEDICATION

This work is dedicated to my parents.

ACKNOWLEDGMENTS

This thesis would not have been possible without the help and support Of ECE
faculty and staff. Special thanks go to Mr. Carlo Adinata and EE482 Home Appliances
Design Team, who provided valuable data for my project, and many thanks tO Mr. Peter
Leslie Semig, who helped me check the grammar and format of this thesis. My thank also
goes to Whirlpool Corporation, who supplied the refrigerator that used in this
investigation. In addition, my thanks go tO Dr. Diane T. Rover and Dr. Bruce Kim for
their critical review of my thesis and their valuable suggestions to help me improve the
quality of my thesis. Most importantly, special recognition and thank goes to Dr. P. D.
Fisher, whose encouragement, guidance and support were essential for me to finish this

thesis.

TABLE OF CONTENTS

LIST OF TABLES .............................................................................. vii
LIST OF FIGURES ............................................................................ viii
CHAPTER 1
INTRODUCTION ................................................................................ 1
1.1 Objectives ........................................................................................ 2
1.2 Outline ............................................................................................ 2
CHAPTER 2
FUZZY LOGIC .................................................................................... 4
2.1 A Brief History Of Fuzzy Logic ............................................................... 4
2.2 Fuzzy Sets ......................................................................................... 5
2.3 Linguistic Hedges ................................................................................ 7
2.4 Frame Of Cognition .............................................................................. 9
CHAPTER 3
CONSTUCTION OF A FUZZY CONTROLLER .................................... 11
3.1 From Expert Control to Fuzzy Controlll
3.2 Structure of a Fuzzy Controller ............................................................... 14
3.2.1 Fuzzification ........................................................................... 15
3.2.2 Rule based knowledge base (Rule Evaluation).......... . . .......19
3.2.3 Defuzzification ............................................................................ 22
3.3 Issues Of Stability and Verification ........................................................... 27
CHAPTER 4
DEMONSTRATION AND ANALYSIS ................................................. 28
4.1 Introduction ...................................................................................... 28
4.2 A BriefReview Ofthe Structure OfRefrigerator...........................................29
4.3 Problems with Refrigerator .................................................................... 32
4.4 Solutions tO the Problems ..................................................................... 34
4.5 Hardware and Software Development Tool .............................................. 36
4.5.1 Hardware platform ...................................................................... 36
4.5.2 Software development ................................................................. 38
4.6 FuzzyTech Software ........................................................................... 39
CHPATER 5
ANALYSIS AND RESULTS ............................................................... 41
5.1 Introduction .................................................................................... 41

5.2 Interactive Analysis .......................................................................... 41

5.3 Defrost Fuzzy Controller Result and Analysis ............................................ 43
5.4 Conclusions ...................................................................................... 46
CHAPTER 6
RECOMMENDATIONS FOR FUTURE WORK ..................................... 48
APPENDIX A
DESIGN OF FUZZY DEFROSTING SYSTEM ..................................... 49
A.1 Introduction ................................................................................... 49
A2 General Information ........................................................................ .49
A.3 Project Description ........................................................................... 49
A.4 System Structure ............................................................................. 50
A5 Linguistic Variables ......................................................................... 50
A.5.l Output variable “Defrost_PeriOd” .................................................. 53
A.5.2 Input variable “DoorOpen_Time” .................................................. 54
A.5.3 Input variable “Humidity” ........................................................... 54
A6 Interface ....................................................................................... 55
A.7 Rule Blocks ................................................................................... 56
A.7.l Rule block “RBI” ..................................................................... 57
APPENDIX B .................................................................................... 58
B.1 Introduction ................................................................................... 58
B.2 Fuzzy Technology Language for Fuzzy Defrosting System ........................... 58
APPENDIX C .................................................................................... 65
Cl Introduction ................................................................................... 65
C2 Code ........................................................................................... 65

vi

LIST OF TABLES

3.1 Comparison Of Defuzzification Algorithms [3] ................................... 26
A-l Project Statistics ........................................................................... 49
A-2 Linguistic Variables ..................................................................... 52
A-3 Properties Of Linguistic Input Variables ............................................ 52
A-4 Properties Of Linguistic Output Variables ......................................... 53
A-5 Definition Points of Membership Functions for "Defrost_PeriOd" ...... 53

A-6 Definition Points Of Membership Functions for ‘DoorOpen_Time”....54

A-7 Definition Points of Membership Functions for “Humidity”...............55

A-8 Input Interfaces .............................................................................. 55
A-9 Output Interfaces ........................................................................... 55
A-lO Rules Of Rule Block “RBI” ............................................................ 57

vii

LIST OF FIGURES

3.1 Structure Of a Fuzzy Controller ........................................................ 14
3.2 Illustration Of Fuzzy Logic Terminology ......................................... 16
3.3 Different Shapes Of Membership Functions ...................................... 17
3.4 Values Stored for Optimal Fuzzification ........................................... 18
3.5 Illustration of Best Compromise ..................................................... 23
3.6 COA Defiizzification ...................................................................... 24
3.7 Illustration Of Most Plausible .......................................................... 25
4.1 Basic Structure of Refrigerator [9] ...................................................... 30
4.2 Heat Transfer Illustration Of Refrigerator [9] ....................................... 31

4.3 Block Diagram of Fuzzy Controller for a Refrigerator.........................35

5.1 Transfer Plot Of Fuzzy Defrosting Controller ...................................... 45
5.2 Time Response of Fuzzy Defrosting Controller ................................. 45
5.3 3D Plot Of Fuzzy Defrosting Controller ............................................ 46
A-l Structure Of the Fuzzy Logic Defrosting System ............................... 50
A-2 Membership Function of ‘Temperature’ ........................................... 51

A-3 Membership Function of ‘Defrost_PeriOd’ ........................................ 53

A4 Membership Function Of ‘DoorOpen _Time’ .................................... 54
A-5 Membership Function Of ‘Humidity’ .............................................. 55

viii

Chapter 1

INTRODUCTION

Fuzzy logic has been enjoying remarkable popularity since 1965, when Dr. L. A.
Zadeh first proposed this concept [1]. Fuzzy logic theory Offers a conceptual framework
for the representation of linguistic terms such as “very”, “maybe”, or “pretty fast”. Fuzzy
logic design provides a solution to either Optimal control problems where the choice Of
Optimality criteria is a matter Of experience, or ill-defined control problems where criteria
is not quite clear to the Boolean logic based modern computers. Industry experts
predicted that fuzzy logic would play an important role in embedded systems and become
a multibillion—dollar business [2].

Typical application areas of embedded systems include home appliance, consumer
electronics, industry controller, vehicular technology, robotics, power systems and image

processing and pattern recognition.

This thesis aims tO understand the motivation for fuzzy logic, grasp the
comprehensive concepts of fuzzy logic theory, summarize the fuzzy logic design
methodology for embedded systems, demonstrate certain fuzzy control algorithms for an

embedded system used in a home appliance, and present the results of the design.

1.1 Objectives

The main goal Of this thesis is tO summarize and Show the fuzzy logic design
methodology for embedded systems, the most commonly used “fuzzy” algorithms for
designing fuzzy controllers and to demonstrate its application in home appliance. Toward
this end, some specific Objectives were involved and these are briefly described below.

The relevance of fuzzy logic design for embedded systems was to be studied. A
refrigerator was to be examined and a refi’igerator controller for defrosting system by
using fuzzy logic was to be designed. The user interface and energy saving issues Of the

refrigerator were to be examined and compared with the conventional design.

1.2 Outline

This thesis is organized into five chapters, beginning with this introductory chapter.
The chapter is followed by an overview of the history of fuzzy logic, the concepts Of
fuzzy set, and the important issues on fuzzy logic related concepts such as Frame Of
Cognition and linguistic hedges. The next chapter describes the relationship between

expert system and fuzzy system, examines the structure of a fuzzy controller and the most

popular algorithms used by embedded system design engineers. In the next chapter,
chapter 4, two problems that used to be solved by conventional solution in home
appliance industry are examined, and two design proposals using fuzzy logic technology
to improve the performance of the refrigerator are suggested. Software implementation Of
the fuzzy defrosting system is demonstrated. The last chapter deals with the analysis Of
the results of the fuzzy defrosting system. Recommendations on further Optimization of
the fuzzy defrosting system and software/hardware implementation Of the temperature

setting feature.

Chapter 2

FUZZY LOGIC

2.1 A Brief History of Fuzzy Logic [3]

The modern logic can trace its origins back to ancient Greek philosophy. Due to the
efforts Of those famous philosophers, particularly Aristotle, a theory of logic -- the SO-
called “ The Law Of Thought” was born [4]. One of the most famous, the “law of
Excluded Middle” states that any proposition can be either True or False only. However,
Heraclitus who stated that it is possible for things to be both “True” and “Not True”

challenged this law.

It was then Plato who indicated that there is a third state (neither True nor False).
Then it was Lukasiewicz who first systematically proposed the concept that could be the
alternative to the Aristotle’s two-value logic [5].

In the early 20th century, Lukasiewicz introduced a three-value logic. He assigned a
numeric value tO the third state that can be translated as “possible”. Later on he found out
four-value logic, five-value logic and then he proposed that it is possible to have infinite-
value logic.

It is then until recently that the notion Of an infmite-value logic was developed. In
1965, Dr. L. A. Zadeh from University Of California, at Berkeley published his work
about “Fuzzy Sets” which mathematically described the fuzzy set theory [1]. This theory
uses the membership function to map the elements Of set to the values between 0 and 1
instead Of using characteristic function that maps all the elements of the set tO the value 0

and 1. He also proposed Operations on how to calculate firzzy logic.

2.2 Fuzzy Sets

Before we get to the concept Of the fuzzy set, let us remind ourselves Of Boolean
Logic, which is a cornerstone of all mathematical tool used. Based on this two-value
logic, no matter how complicated an Object is, we will assign it to one Of two
complementary categories, such as good and bad, Odd and even. Sometimes it does make
sense. For example, we can always classify integer numbers as Odd or even.
Nevertheless, we are faced with Objects that are ill defined and do not have clearly
defined boundaries in engineering tasks. Consider the categories such as low pressure,

high temperature, small errors etc., which convey a useful meaning that is only Obvious

under a certain context. However, the line between the inclusion and exclusion of an
Object for such categories are not clear. Therefore the conventional two-value logic is not
well fit for this kind Of problems.

Here is an example Of how two-value logic can give rise to undesired phenomena:
One piece of wood log does not constitute a pile nor two nor three... On the other hand
we will agree that 1 million pieces Of log constitute a pile. What is the clear—cut line in
between? Can we say that 42,000 pieces Of log don’t constitute a pile but 42,001 would
constitute a pile? As we can see, two-value logic can not perfectly explain this dilemma.
The key point Of fuzzy sets is that it extends the concept Of a set by admitting different
grades Of belonging, or so called membership. By fuzzy set concept, this wood log
problem can be easily solved by allowing for all intermediate situations between
complete membership and complete non-membership. The higher the value of the
membership Of an Object M defined by fuzzy set A, the stronger the link of the object to
the category described by A. SO in the above problem we can define 42,000 pieces Of log
satisfies the category “pile” at a degree equal to 89%, while 100 pieces of log is
characterized by a grade Of membership as 2%.
Definition as stated by W. Pedrycz [6]:
A fuzzy set A defined on a universe of discourse X is characterized by membership
function
A: X —> [0,1]
Where the grade of membership A(x) describes the degree to which x satisfies the
class defined by A. A(x) = 1 denotes all the elements are completely belong to A

while A(x) =0 denotes all the elements that definitely do not belong to A.

All the properties and laws of crisp set hold except for the exclusion law. However, the

exclusive law is an exception:

These two relationships Simply indicate the under-lap or over-lap between a fuzzy set and
its complement. The logic Operations defined on a fiizzy set can be described point-wise
as:

0 AN D(x,y) : min(x,y)

o OR(x,y) : max(x,y)

o NEG(x) : 1- it

Where x and y are two grades Of membership.

2.3 Linguistic Hedges

Linguistic hedges [7] are special linguistic terms that modify other linguistic term.

The terms such as very, high, medium or extreme are examples Of linguistic hedges.

Linguistic hedges are not applicable to the classic Boolean logic. Terms such as very
adult, very horizontal, or very rectangle are meaningless.

Any linguistic hedge, H, can be interpreted as a unary function [7], h, on [0,1]. If h

(a) < a, for all a e[0,l], the operation that represents the linguistic term is called strong;

if h (a) > a, for all a e[0,l], then the Operation is called weak The special case that h (a)

= a is called identity. A strong Operation reduces the truth-value Of the associate

proposition. A weak Operation on the contrary, increases the truth-value Of the
proposition. An Operation H has to satisfy the following self-explanatory conditions
summarized in [7]:
o h(0) = 0 and h(1)= 1;
o h is continuous function;
0 if his strong, then h'1 is weak and vice versa;
A popular class of functions that satisfy these conditions is
Ha(a) = a“,

Where aeR+, R+ is a set Of positive real numbers and a 6 [0,1]. When on < l, h is weak;
when or > 1, h is strong. SO choosing different values of 0t will let us define and
distinguish the meaning Of a linguistic term in different context. This is very usefidl when
constructing a membership function for an ill-defined system where nature language that
can only be understood in certain context is used. Consider the following example:

P1: Humidity is high,

P2: Humidity is very high,

P3: Humidity is medium high,
we let the linguistic hedges very and medium be represented by the strong Operation h(a)
= a2 and the h(a) = am. SO if according to our fuzzy set “High”, 50% moisture is
considered to be “High” at the grade of 0.8. Then VERY HIGH (50%) = (0.8) 2 = 0.64
and MEDIUM HIGH (50%) = (0.8) V’ = 0.89, and TRUTH (P2) = 0.64, and TRUTH (P3)
= 0.89. We find here that the stronger the assertion is the less true it is, which agrees with

our intuition.

 

2.4 Frame of Cognition [8,9]

When human beings are trying to solve some complicated problems, they first try
to classify their knowledge in terms Of some general concept and then to find out the
essential relationship between these concepts. This kind Of Top-Down approach can help
us to figure out more detailed solutions from those general knowledge and relationships
that connect them. This effort will not help us to find the exact numbers or values we
need to achieve our goal, but rather help us to classify some Objects into more general
categories like sets (fuzzy sets). It is known that human being can only memorize and use
very limited numbers Of concepts at a time in solving complicated problem, however, the
structure Of these concepts is important for efficient memorizing, recalling and utilizing.

When linguistic labels are defined by fuzzy sets, they assign a certain property to
all the values on the universe discourse. This property is known tO be the grade of
belonging. When the whole universe discourse is defined by labels, some Of the regions
will then be defined as compatible to the highest extent with the labels. The linguistic
label assigned to a certain variable forms a frame of cognition of the variable.

Fuzzy sets {F1, F2,. . ..} form a frame Of cognition A if:

0 A covers the universe, i.e. all elements of the universe belong to at least one label
with nonzero degree Of membership.

0 For each individual element, the sum Of the degree Of belong must be one for all

labels that are applicable to this element.

In general, the concept Of a frame Of cognition is a very helpful concept in the
application Of fuzzy sets by contributing to an efficient formation Of membership
functions that are essential to fuzzy logic design. This concept Of the fuzzy set is well
known for its importance in narrowing the gap between the pure numerical techniques
and the pure symbolic methods. The numerical techniques mainly used today by
computer stress particularly in precision and lack Of the necessary generality. On the
other hand, human beings can successfully finish some tasks without even knowing all
the exact values Of the parameters that involves in their actions. Fuzzy sets come in
between like a bridge. Each Object in the fuzzy set is described by symbols or so—called
labels - e.g., small, medium, or large. Meanwhile, these labels are connected with the
numerical characteristics Of the system through certain semantics. And these numerical
characteristics are expressed in the form of membership functions that have numerical
grades assigned to them. AS we can see later in this thesis, the trade Off between the
representation generality and the precision can be efficiently satisfied by modifying the
parameters Of the symbols and the number of the symbol itself. The modification is
largely done to the membership function and rule evaluation without any big changes in

the design structure.

10

Chapter 3

CONSTRUCTION OF A FUZZY
CONTROLLER

3.1 From Expert Control to Fuzzy Control

Tasks like driving an automobile on a snow-covered roadway, adjusting the water
temperature when we are taking a shower, or packing a fragile non-standard-shaped
object — while common in our life — continuously create tough challenges to the
embedded controlled robot. Let’s first take a look at how we accomplish our tasks in our

everyday life. When a particular task has to be solved, we first will — with our goal in

11

mind -— examine the current situation we are in and try to get as much information as we
can. Based on the information we have, we try to recall the entire set Similar situations we
have been in and their solutions from our experience (our memory serves as a huge
knowledge base in our brain). Then with the help Of the feedback from the result Of our
control actions and our goals we quickly achieve the best or close enough result to our
goal within a few actions. Consider the example Of controlling the temperature in a
building. People in each individual room tend to have different temperature preferences.
Hence, human being Operators have to be replaced in these processes Of control by
computers or embedded micro-controllers. These controllers must mimic the decision-
making skills of the room occupants.

A comprehensive module has to be built to undertake all the control activities.
However, just as human beings can not describe an object if they have no prior
knowledge of it, the controller cannot be constructed to replace human beings when it
does not incorporate a complete control knowledge base. The traditional modules used
in engineering all have the following premises [6]:

o The system has to be known; if there are some uncertainties with the system, the
control result gotten by the human-replaced controller can not be Optimal.

- The known system has to be clearly and completed defined by mathematical models.

0 The goal of the control has to be specified in some direct system related variables in
the term of clearly defined formulas. These variables are also called performance
indices.
Unfortunately, when the complexity of the system increases, incorporating these

assumptions completely into the control model is not realistic. This is due to the fact that

12

 

some Of the systems are nonlinear or some factors Of the systems are non-stationary, such
as time variant systems. A more common problem today is not only the difficulty at
finding such a complete model, but also the dilemma that a more precise model usually
leads to more complicated multi-valued fimctions with more undetermined parameters to
be estimated. Even after we overcome all these troubles and finally find such models, we
can only keep them as nice theoretical solutions in the textbook. Given the current
technology, it is almost impossible to use embedded systems with limited on-board
resources to implement the complicated equations that need extensive calculation time
while still satisfying the requirement of real-time control.

Moreover, in a real world task, it is likely that we can’t specify the performance
index that is supposed to be minimized in a numerical manner; i.e., the degree to which
difi‘erent people feel comfortable about the room temperature is different. Sometimes, a
complete mathematical model can not even be used to achieve the desired performance
index. This usually happens when more than one goal needs to be accomplished within
the control actions and where these goals are contradictory. A good example for this is
the air conditioner. Some people want the room to be kept cool while they also want the
air conditioner to be energy efficient.

This will explain the situation in the human Operator controlled system (or so
called expert system) where Operators can complete the task very well but can not explain
too much on why and how they achieved the optimality in the way they handled the
control activities. The answer in general is the effective use of the symbolic computation,
which is good at interacting with ill-defined problems or linguistic hedges, as well as

numerical values. The expert system owes its success to engineering heuristics.

I3

Heuristics plays an important role in achieving the compromise Of partial criteria Of
contradictory requirements. It is well accepted that the fuzzy controller is one Of many
kinds Of expert systems, which has a computerized inference mechanism tO represent

vague human decision.

A

FeedBack

 

 

 

 

 

 

 

 

.__.. Fuzzification ..___. Inference Engine = Defuzzification

 

 

 

 

 

 

 

 

 

Figure 3.1: Structure of a Fuzzy Controller

3.2 Structure of A Fuzzy Controller

It is worth emphasizing that the purpose Of fuzzy control is to analyze and process
fuzzy information using a non-fuzzy reasoning scheme. Its fuzziness comes from the
nature of the ill-defined problem (e. g., problems that are not clearly defined, such as what
the control action of the air conditioner should be if the room temperature is high), the
vague representation of the goal (e.g., what constitute energy efficiency), and the way the
knowledge base is built on. All this natures determine the structure of a fuzzy controller.

A typical fuzzy controller has three parts, as shown in Figure 3.1:

14

o Fuzzification
o Rule-based knowledge base (Rule Evaluation or so called Inference Engine)

1» Defuzzification

3.2.1 Fuzzification

Fuzzification process — so called input interface - involves domain transformation.
Some technical terms, as Shown in Figure 3.2, in this process are:
Labels: names that are used to describe the membership function i.e. short fast.
Universe discourse: the range Of all the possible value that is applicable to the system.
Crisp inputs: distinct real time input values.
Fuzzy inputs: the degree, on a 0 to 1 scale, to which the crisp input agrees the
membership function.
Membership function: each membership function is a fuzzy set. Each membership
function is a function that maps eligible crisp input value to a fuzzy input that satisfy the
concept of the term Of the labels that describe the membership function.
Scope of each label: The range of crisp inputs that the membership function will map.

With all Of these concepts, the membership function is the key for the

fuzzification process. As we will see later in this chapter, the way rule-based knowledge
base is assembled determines that at least one label must be assigned to each membership
function. These labels are always linguistic variables or linguistic representations of
technical figures Often used by human beings. For example, the technical figure
“Temperature” can have a linguistic interpretation {hot, medium warm, normal, medium

cold, freezing}. From psychology research on human beings, it has been shown that

15

humans use their Short-term memory to process the technical figures and the short-term
memory can handle only up to seven terms at a time. As it is general accepted as a rule,
real world engineering always use symmetric labels that have their number as three, five,

or seven.

labels
very cold cold medium warm

 

Membership
Function
input /

0.45 —————— crisp input
:
I
I
l

0

ln—SCODG —>l 2'08?

universe discourse

 

 

 

 

ll

Figure 3.2: Illustration Of Fuzzy Logic Terminology
In all these concepts, the membership function is the most important in the
fuzzification process. Membership function is established to assign numerical values to
the linguistic variable. It is this membership function that makes the fuzzy controller a
powerful but, also, a flexible tool to cope with the linguistic variable in the process of
control while still precise enough for computer implementation. The membership

function is unlike the characteristic function used in Boolean logic, where labels fully

16

agrees the characteristic function on one side of the clear cut boundary and doesn’t agree
at all on the other side. Instead, the crisp inputs within the scope of the membership
function changes gradually from fully inapplicable to fully applicable.

Many different shapes of membership function have been proposed by firzzy logic
research. Only four are used at practice (see Figure 3.3): Z-type, A-type (lambda), l'I-type
(PI), and S-type. These types are all normalized and therefore. their maximum is always 1
and minimum is always 0. Other kind of membership functions are discarded by
engineers at practice either because they are too complicated to implement for embedded
system or because they can be replaced by Z-type or S-type functions. Sometimes people
use cubic spline shape fimction to get better performance. This spline membership
function is still based on the previous four types but connect the maximum and minimum
using spline lines instead of straight lines. The improved performance, however, is

achieved by increasing the complexity of the implementation of the membership

IL /\

function.

PI-Type Lambda-Type
Z-Type S-Type

Figure 3.3: Different Shapes of Membership Functions

17

During the process of fuzzification, the membership function will take a real time
input value and assign a unique grade value for each given label. After the fuzzification,
there will be a fuzzy input for each label corresponding to the current crisp input. It is
important to know that the smn of the fuzzy inputs for all labels is 1.

Usually the computation for the membership is the most time consuming part.
However, by using the standard membership function, an optimal fuzzification algorithm
exists [10]. In this algorithm, membership fimction is represented by two base points and
two slopes. As indicated in Figure 3.4 that is shown below, since A and B are always
equal to 0 and 1, respectively, the generated code will only store this two points. In

addition, the code stores the slopes of the two straight lines that across A and B.

Slope_A

 

h--—-—---------------

 

 

0
Areal Area 2 Area 3 1

Figure 3.4: Values Stored for Optimal Fuzzification
Therefore, the membership in the figure for three different areas are:
Area 1: zero.

Area 2: min { (crisp input — A)* slope_A, 1}

Area 3: max {1 — (crisp input — B)*slope_B, 0}
Since only comparison, subtraction and one-step multiplication is used, the speed of
this Optimal algorithm is five times faster than the four points representation of the PI-

type membership on a normal micro-controller with no multiplier/divider.

3.2.2 Rule-based knowledge base (Rule Evaluation)

After we get the fuzzy input we need, we will proceed to the second part Of the
“fuzzy” processing — Rule Evaluation. The knowledge base is made up of if-then
statements with linguistics variables. For example, a typical rule will look like “IF the
Temperature is Hot and the Humidity is Wet THEN the cooling time is Long”. The
concept Of rule evaluation is to determine what the control action should be based on the
linguistics rules made by experts given the fuzzy input value. The rules are written in
nature language, however, it is confined to a set of predefined linguistics terms and
observes a strict syntax. The syntax is in the form of:

IF antecedent_l And antecedent_2 And
THEN consequent_l And concequent_2
Where each antecedent is in the form of:
Crisp Input Variable is Label
For example, Temperature is Hot. Here Temperature is the name of the crisp input
and Label is Hot, which is one of a few labels that describe the input membership
function of Temperature.
The consequent takes a similar form:

Crisp Output Variable is Label

19

For example, Cooling Time is Long. Here Cooling Time is the name of the crisp
output and Long is one Of many Labels that describe the output membership function Of ,
Cooling Time.

The term “And” is fuzzy Operator that will be applied to get the minimum value
from all the antecedents. Actually, fuzzy rules presented originally allow other fuzzy
Operators such as fuzzy OR and NOT as we mentioned in previous chapter. However,
when rules are implemented, normalized rule representation is used. For rules like “IF A
OR B THEN C” will be rewritten as “IF A THEN C” and “IF B THEN C”. For rule like
“IF NOT A THEN B” we still take this rule as it is in the form of “IF C THEN B”. But
we know if the truth value of A is 0.7, then the truth value of C which is NOT A is 0.3.
Some of rules doesn’t depend on any input variables, such as “Cooling Time is Long”.
This type of rule is called assertion. This kind of rules is not very common in the control
tasks, but sometimes it happens. It has the same properties when we calculate the truth-
value of rules.

Knowledge base is a rule block, which includes all the assertions and normalized
rules. One advantage of fuzzy logic knowledge base is that it is all made up of linguistics
terms like natural language. So the expert doesn’t have to know anything about
computers to write the rules. And when the programmer tries to implement the
knowledge base, he doesn’t have to have any prior knowledge of the expert system to
implement the rule base in the way the expert wants as long as rules are written in the
required format.

During the rule evaluation, fuzzy inputs of each label, which are gotten from

fuzzification will be plugged into corresponding rules that have the same crisp input

20

variable and labels. Then the truth-value of each individual rule will be calculated using
the Min-Max technique. The truth-value of each rule will be used to determine the truth-
value of the “THEN” part consequent. The truth-value of each consequent is called fuzzy
output. In the Min-Max technique, the minimum truth-value Of all the antecedents of each
rule will be written down as the truth-value of the current rule. Then afier all the rules
have their truth-values, we find the truth-values of all consequent in every rule and for
each consequent the fuzzy output is the maximum value of the truth-values of this
consequent in all rules. For instance, if we got the fuzzy inputs of each labels {Hot,
Medium, Cold} describing the crisp input variable Temperature are {0.8, 0.2, 0} and the
fuzzy inputs of labels {Wet, Medium, Dry} that describe crisp input variable Humidity
are {0.6, 0.4, 0.}. And the rule block has four rules (for the sake of simplicity, we also

denote Truth (#) as the truth value of rule ii):

1. IF Temperature is Hot (0.8) and Humidity is Wet (0.6)

THEN Cooling Time is Long. Truth (1) = min (0.8,0.6) = 0.6
2. IF Temperature is Medium (0.2) and Humidity is Dry (0.0)
THEN Cooling Time is Short. Truth (2) = min (0.2,0.0) = 0.0
3. IF Temperature is Cold (0.0) and Humidity is Medium (0.4)
THEN Cooling Time is Short. Truth (3) = min (0.0,0.4) = 0.0
4. IF Temperature is Medium (0.2) and Humidity is Medium (0.4)

THEN Cooling Time is Long. Truth (4) = min (0.2,0.4) = 0.2

21

SO the fuzzy output for label “Long” that describes crisp output “Cooling Time” is
max (0.2,0.6) = 0.6, and the fuzzy output for label “Short” that describes crisp output “
Cooling Time” is max (0.0,0.0) = 0.0. So given the membership functions assigning to
each crisp variables and the current rules, the rules inference generates the fuzzy outputs
{0.6,0.4,0.0} for labels {Long, Medium, Short} describing crisp output “Cooling Time”.
It is pretty clear that a control action will be taken for a time length somewhere between
“Long” and “Medium” as we defined. But we only have a general idea of what the time
length should be. In order to get the exact value that computer or micro-controller can
understand we need to defuzzify the fuzzy outputs and find the crisp value Of the output
variable. In real world task, rules can have different weight. SO some rules may have

higher priority than others, some rules may never fire.

3.2.3 Defuzzification

The conversion from linguistics fuzzy output to a real non-fuzzy value is called
defuzzification. The output membership function uses exact the same types of
membership functions as input membership function does. In practice, Singleton
membership functions are also used for output membership function for simplicity. There
are different defuzzification methods given the meaning of the linguistics terms. In

general, there are two big categories as being called by C. V. Altrock: Best Compromise

and Most Plausible Result [10].

0 Best Compromise:

22

In the previous example, fuzzy output is {O.6,0.4,0.0}. Let’s assume that the typical

values Of each labels for output Cooling Time are:

Long 30 minutes
Medium 15 minutes
Short 0 min

Then for the best compromise result, as indicated in Figure 3.5, we calculate the
expectation of Cooling Time:
30 x 0.6 + 15 x 0.4 = 24 minutes

Defuzzification methods that are used for best compromise include:

0 15 24 30

Figure 3.5: Illustration Of Best Compromise

Center Of Area (COA) / Center Of Gravity (COG):

This method first truncates the values of each label, which are above the fuzzy
output of that label and then try to find the balance point of the membership functions or
so called center of area / center of gravity. This balance point indicates the best
compromise (see Figure 3.6).

COA/COG works fine with those whose membership functions have identical shape.

If two membership functions have different shapes (the areas of membership function are

23

different), then the one that has bigger area will have a greater impact on the output than
the one that has smaller area when both have the same degree of validity. But, as we
know, having larger area simply means there are more values fit in the category described

by the label than the one with smaller area.

A short medium long

0.6

0.4

 

 

Figure 3.6: COA Defuzzification
Another disadvantage Of COA/COG method is its large amount of computation
involved during the process. This is mainly because the effort spent on calculating
integration of the truncated membership functions. For this reason. some fuzzy logic
processors use what so called fast COA. We can have a pretty good estimation of the
result by taking a few sample points over the membership function and superimpose
these samples. Since the overlapped areas of membership functions are neglected during

the calculation, this approach can only be seen as an approximation of COA.

Center of Maximum (COM:

24

This is an even simpler version of COA. The example given at the beginning of this
section uses this method. This approach only takes the typical value of each membership
function rather than calculates the area under each membership function. Notice that if
the output membership function is singleton, then COA/COG is the same as COM. COM is

a very popular solution in real world engineering due to its high computation efficiency.

0 Most plausible result

Sometimes best compromise doesn’t apply to some problems. For instance, a robot
is controlled by an embedded micro-controller. The output labels are {steer left 30°, stay
straight, steer right 30°}, and the fuzzy output are {0.5, 0, 0.5} indicating there is an
obstacle right in front of the robot. Under this circumstance, the robot should turn to
either left or right, both will be fine. However, if we are using the best compromise
method, we will get the steering angle 0, as shown in Figure 3.7. This is Obviously

wrong.

0.5 0.5

-15 15
Figure 3.7: Illustration of Most Plausible

The approach solving this Situation is called Mean of Maximum. Instead of
finding the balance point, MOM finds the most valid term and takes the typical value of

that term as the result.

25

A very important property of defuzzification is continuity. If small change of
input doesn’t cause a sudden change on any variables at the output end, then we will say
the defuzzification method used is continuous. In a closed-loop control process, the last
thing we want to happen is the output jump abruptly responding to small changes of
inputs. This will cause the output oscillation and therefore system instability. The
COA/COG and COM are continuous methods because the result gotten from these
methods are the compromise of all the possibilities, therefore abrupt jump can never
happen. The MOM, however, can sometimes come up solutions that are completely
Opposite. SO in the real world, an integrator will be connected to the fuzzy controller to
keep the output continuous. The “best compromise” methods are used mostly in
quantitative problems such as control, whereas the most plausible methods are used
mainly in decision support. A comparison between all the methods mentioned above is

listed in Table 3.1 below.

 

 

 

 

 

 

 

COA, COG FAST COA COM MOM
Categories Best Best Best Most Plausible
Compromise Compromise Compromise Result
Membership NO good for MF No good for Good Good
Function shape with different MF with
shape different shape
Computation Very low OK High Very High
efficiency
Continuity Yes Yes Yes NO
Applications Quantitative Quantitative Quantitative Decision making

 

 

 

 

 

 

Table 3.1: Comparison of Defuzzification Algorithms [10]

26

3.1 Issues of Stability and Verification

The issue of stability has been argued since the fuzzy logic concepts are proposed
[1 1]. Whether or not fuzzy logic is a viable way to enhance the performance achieved by
conventional approach has been challenged by lots of critics. The focus is on whether
there is a mathematics proof of the stability. It is known that the stability theory of the
conventional control completely suffices the fuzzy systems [10]. Fuzzy systems that have
the properties of deterministic, time invariant and nonlinear are classified in control
theory as nonlinear multi-band controller. Therefore, all the stability analysis that
applicable to the conventional nonlinear multi-variant controllers are applicable to the
fuzzy controller. But since most fuzzy systems have very complex nonlinear characters, it
is almost impossible to find a stability proof. Normally, a conventional approach that has

the same complexity is also impossible to get a stability proof.

27

Chapter 4

DEMONSTRATION AND ANALYSIS

4.1 Introduction

In this chapter, an application of using fuzzy logic to improve the performance
and the energy consumption of a home refrigerator will be demonstrated. Problems will
be stated and a solution using fuzzy logic algorithm will be suggested and designed. The
use of fuzzyTech [12] software will be demonstrated and analysis and recommendations
will be given.

Home appliances have been a very important part of people’s life today. People
are dealing with them in their everyday life. Companies have tried their best to bring the
most easily to use but least energy-consumed appliance to the market to attract the

customers. Thanks to today’s technology, they can offer a lot more dreams features to the

28

customers than they could five years ago [13]. However, home appliances are not
industry machines. Their costs have to be as attractive as their performance and they have
to have a high-level friendly user interface to satisfy the “non-technical” users. Fuzzy
logic is an innovation technology that allows implementing complex and intelligence
functions into embedded system. It has the advantages of implement non-linear and
adaptive control using limited system resource such as an 8-bit micro-controller. In this
demonstration, we will first examine a typical home appliance --- refrigerator from the

point of view of energy saving and user interface.

4.2 A Brief Review of the Structure of Refrigerator [14]

A refrigeration system, as shown in Figure 4.1, consists of a compressor,
condenser, dryer, capillary tube, evaporator and refrigerant. The compressor pumps
evaporated Freon gas from the evaporator coil and then compress it. When the Freon
returns to a liquid state, it gains heat. The heat is then released outside the cabinet. Afier
passing the condenser, the refi'igerant enters the capillary tube. This is a small metering
device that only allows an exact amount of liquid refi‘igerant to flow through before
entering the large tubing of the evaporator. AS the refrigerant leaves the small capillary
tube, the sudden increase in tube Size of the evaporator causes a drop in pressure that
allows the fluid to evaporate and cool down. Now it gains heat and ready to be cycled
again. See Figure 4.2 for the heat transfer illustration of refrigerator.

As the cycle continues, everything inside the food compartment would eventually
freeze. TO control the temperature, a thermostat is used to monitor temperature at the

evaporator and control the power to the compressor. AS the temperature inside the

29

refrigerator rises, the thermostat turns on the compressor. The thermostat can be adjusted
to control the desired refrigerator temperature by a knob as the one we see in most of the

refrigerator.

EVAPORATOR FAN

‘5"‘\'A:Ih_‘|.l
Jane’s-163 5-

 

Figure 4.1: Basic Structure of a Refrigerator [14]
During this process, the refrigerator not only picks up heat from food, but also
gets moisture from warm air caused by door opening. The moisture then forms the frost

on the evaporator. As frost accumulates to a certain point, it reduces the evaporator's

30

effectiveness. In order to keep the system operating properly, the refrigerator needs

periodic defrosting.

HEAT TRANSFER IN A REFRIGEMTOR

 

 

 

Figure 4.2: Heat Transfer Illustration of Refrigerator [[4]

There are three types of defrosting systems in use today--manual, cycle and
automatic (no frost). In the manual system, freezer defrosts by turning off the power and
let the ice melt. In the cycle system, an electric heater is activated when the compressor is
off to melt ice if there is any (freezer section still has to be done manually if there is a
heavy buildup of ice). An automatic defrost system consists of a low watt heater, a

thermostat to turn on and off the heater, and a timer to control the defrost cycle. As frost

31

accumulates, the timer starts the defrost cycle. Then, the compressor will be turned Off
and the heater will be turned on. After the frost cycle is finished, the thermostat turns Off
the heater and the timer allows the water to drain to a defrosting pan before starting the

compressor.

4.3 Problems with Refrigerator

In today’s home appliance industry, one most important issue is energy saving
[15,16]. The refrigerator is the most common home appliance and is one of the biggest
users of electricity in most homes. Depending on its age and size, the refrigerator can
account for as much as one third of a non-electrically heated home’s electricity usage.
They account for nearly 20 percent of residential electricity [15]. The energy saving goal
is not to cut the power consumption to zero, but to eliminate all the possibilities of energy
wasting. A tremendous extra power will be needed when the frost starts to accumulate in
the freezer. The frost accumulation reduces the evaporator’s effectiveness, and the
refrigerator gets warm. As mentioned above, we have three types of defrost system. The
first two types of system are no way user-friendly and therefore are out of consideration.
The automatic system is the most popular one in the market because of its user-friendly
interface and the no-frost result. But after taking a closer look at its defrost control
mechanism we found most of the unnecessary energy waste are coming from the defrost
system.

In spring 1998, a characterization test of a home refiigerator was conducted by

one of the Design Teams of the computer system design course in the Department of

32

Electrical and Computer Engineering, Michigan State University. The result [17] has
shown that there will be a huge temperature jump whenever the defrosting cycle kicks in.
when the defrosting cycle starts, the compressor was turned off and the heater was turned
on. The refrigerator with automatic defrost system defrost twice a day with each cycle
lasts around one hour. Defrost cycle starts kicking in everyday at a fixed schedule. This is
mainly due to the fact that the designer Of the defrosting system can not predict the time
of the accumulation of frost. SO no matter if there is frost, the compressor will be turned
off and the heater will be on when defrost cycle starts to guarantee a no-frost. During the
defi'ost cycle, the temperature in the freeze will go up to 15°C from -1 8°C for about one
hour. This unwanted temperature rise is no good to the food. And since when the defrost
cycle is off, the compressor has to use extra power to cool the temperature down to its
normal, energy waste will occur. In another word, if the customer just went grocery
shopping not long before the defrosting cycle starts, then the refrigerator will get warmed
up for an hour when it most needs at the moment is cooing down. Moreover, in the case
that the door of the refrigerator has been keeping closed for a long time such as when the
customer is away on vacation, refrigerator will still defrost twice a day even there is little
frost.

Another common energy waste comes from the customers themselves. For most
refrigerators, there is a knob for temperature control. However, a lot of customers don’t
know what the right temperature range the refrigerator should stay in to keep the food
fresh and to have less energy wastes. Sometimes, when there is a big load increase, i.e.
after grocery shopping, people tend to turn down the temperature setting to get a large

cooling effect. Because of this and lacking of the knowledge on what is the right

33

temperature, people tend to turn the temperature lower than necessary, and most of the
time they forget to turn it back up when the right temperature is reached and the food is
over cooled. Before the temperature setting is corrected, the extra energy used for the

unnecessary cooling is wasted.

4.4 Solutions to the Problems

The solution for the defrosting system to avoid unnecessary energy consumption
is adaptive defrost control [16], which removes the frost only when it is necessary. We
have noticed that two main factors that can cause the curnulating of frost are humidity
and temperature. Temperature changes in the freezer is largely caused by the frequency
of door openings and the length that the door is Opened (It is shown by surveys that the
normal door open time is 30 to 90 seconds). SO we can say the defrost cycle is a fimction
Of the humidity and the door Open time. And it is not linear. In a traditional non-linear
implementation, either a complete but complicated mathematical model has to be
generated or a look up table has to be provided. As the precision requirement increases,
both methods become unrealistic for a real time control using low cost micro-controllers.
So a two inputs fuzzy controller will be designed to overcome these difficulties. The fully
documented fuzzy defrosting controller design is provided in Appendix A.

As for solving the temperature setting problem, we first look at the mechanism Of
the compressor. Since the control Of compressor is hysteresis control, which set the upper
and lower limits for the temperature. The compressor is on only when the upper limit is

exceeded and is turned Off when the lower limit is hit. Big hysteresis setting delayed the

34

compressor’s switching activities while narrow hysteresis setting increases the frequency
of the switching activities. When the compressor switches too frequent, a lot of energy
will be used. However, when there is a time we need to start the cooling right away or we
have some food that have to stay in a strict temperature range to stay fresh, we have to
change the hysteresis setting lower. As mentioned in the previous chapter, fuzzy logic has
its advantage of reconciling conflicting requirements. The design idea of this fuzzy
controller to improve the temperature setting performance is presented below. Its
hardware and software implementation need further work and will be recommended in

Chapter 6.

F eedBack Temperature

+
—1
SetTemperaturel ' E) I ll—

Compresso?

 

 

 

 

 

 

 

 

 

Fuzzy
controller

Humidity ,,

 

’-
Defrost Period

 

 

Door Open Time

 

Figure 4.3: Block Diagram Of Fuzzy Controller for a Refrigerator
The Temperature Setting fuzzy controller is to have three inputs: difference
between the set temperature and the temperature in the refrigerator (or so-called feedback
error), changes of the set temperature, and the set temperature that is differentiated by
time. The output of the fuzzy controller goes to control the hysteresis and the compressor.
When the feedback error is big, fuzzy controller will send signal to the compressor so that
the desired temperature will be reached faster, and at the same time set the hysteresis big,

so disturbances will not cause unnecessary on-Off switches during this time. The time

35

differentiated set temperature is used by the fuzzy controller to remember for the user to
turn the temperature back up when the desired temperature is reached. This input will be
zero after a given time if the user doesn’t modify the set temperature any more. The
number Of changes of the set temperature is used to understand if the user want to set the
temperature specifically in a certain range. If the user wants to set the temperature
precise, he tends to adjust the setting more than once. When this happens, the hysteresis
will be set relatively small so the activities of the compressor will be more sensitive to the
temperature changes. The completed design block diagram of the refrigerator fuzzy

controller is given in Figure 4.3.

4.5 Software and Hardware Development Tool

4.5.1 Hardware platform
The target platform for developing fuzzy logic ranges from normal low cost 8 bit
micro-controllers with limited on board RAM and ROM to 64-bit RISC processors. The

development of fuzzy logic processor has experienced three phases:

0 Analog Fuzzy Processor

The analog fuzzy processor is made up by fuzzy logic gate. A voltage signal ranging
from +5V to -5V serves as the membership degree from 0 to 1. This type of processor
has never made its way out of the lab, mostly due to its inflexibility in implementation.

Any changes of the rules or membership functions require the re-design of the hardware.

0 Digital Fuzzy Processor

36

A digital fuzzy processor is a conventional digital processor a fuzzy instruction set.
This type of process can only support fuzzy computation. Two processors were used. One
host micro-controller that handles all the peripherals and I/O, and pre-computation, while
the fuzzy processor working on the fuzzication, rule evaluation and defuzzification. Both
processors are connected either by a series communication port or a dual ported RAM.

The host micro-controller will get the crisp input and send to the fuzzy processor.
After the fuzzy processor finish computing, it will send the result back. Because Of the
overhead of communication, the speed advantage of fuzzy processor is compromised.
And Since this digital fuzzy processor usually uses up to three chips (if includes and dual
ported RAM), the cost is very expensive. In addition, programming for the
communications needs extra efforts and extra interrupts in order to synchronize both

processors.

0 Integrated fuzzy logic processor
In this phase, manufacturers made it possible to integrate both processors within one

Chip. This effort reduces the communication overhead remarkably. There are two
approaches: An earlier approach treated the fuzzy logic processor just as another cell or
memory. This approach requires an additional silicon area and a full functionality of
ALU (Arithmetic Logic Unit). The latest approach is to enhance the instruction set of the
conventional micro-controller. It keeps the micro-controller’s own ALU and adds some
additional functions to it. This approach reduces a great deal of areas that the earlier
approach requires and the code of the micro-controller is much more compact since all

the existing instructions and registers can be used by the fuzzy processing too. This fuzzy

37

processor can be also used as a general—purpose micro-controller. Some manufacturers
even add hardware supports to the fuzzification, rule evaluation and defuzzification to
Speed up the computation even more. Since no re-design is needed for the micro-
controller, this integrated fuzzy processor has great potentiality. Manufacturer such as
Motorola has already put its new series micro-controller (i.e. MC68HC12) with fuzzy

logic module to the market [18, 19, 20].

4.5.2 Software development

Good design software should Offer good combinations of design, simulation,
optimization, testing, verification and implementation. There are mainly three types of
software development methods. The first one is just using any program language and
codes the whole fuzzy system. The second one is to use a pre-compiler to translate the
text version of the Fuzzy Logic Description Language or FTL (Fuzzy Technology
Language) into a programming language, i.e. ANSI C. The first one usually need re-
program a large portion when changes of the fuzzy system are made while the second one
is hard to debug due to the text representation. The third and the most popular one is
called virtual design interface. The whole design is a matter of drag-and-point graphic
implementation. The FTL or any programming code can be generated for specific
hardware platform by the code generator using this kind of virtual design software too.

The graphic design software tool I will be introduced is fuzzyTech. The author will

demonstrate the fuzzy defrost system using this software.

38

4.6 FuzzyTech Software [12][21]

o Linguistic Variables Editor

The editor is used to define the linguistic variables and their membership functions.
Membership functions are always defined point-wise using definition points that can be
easily dragged and positioned by the mouse. There are two alternatives exist to connect
the definition points: L-shape and S-shape. For S-shape, the user can specify the
asymmetry factor in the range from 0 to 1. For standard membership functions, only the
positions of the maximum points are required. The software will automatically generate

all the definition points.

0 Interface Options

For input interfaces, three algorithms are supported. The first one, Fuzzy Input.
Fuzzy input indicates that all the values are inputted into firzzy control system as a vector
of the grade of membership belongings. The second one is compute membership
function. This is the most popular fuzzification method used in almost all the
applications. As mentioned earlier, the method only stores the definition points and slops
and computes the fuzzification at run time. For a few micro-controller, the “look up
membership function” is also supported. The computation of the fuzzification is
completed in the compile time and stores in a table in the code. This method causes big

code size, but is faster overall if the computation for the fuzzification is too complex to

do during run time.

39

For output interface, different defuzzification methods exist too. “Fuzzy Output”
outputs a vector of the membership degree of the results of inference. Then there are
COM, COA, and MOM. For more details, refer to chapter 3. Among those, COM is the
most Often used algorithm. There is also one method called BSUM, which represents
Bounded Sum. This method uses the bounded sum rather than the maximum operator to

aggregate the individual areas. SO no overlap area will be computed more than once.

0 Rule Editor

Two alternatives of generating rules exist. One is called the spreadsheet rule editor.
IF-THEN rule statements can be generated automatically. Users can configure the rule
block the way they want it to be created.

1. Alpha cut: delete all rules with the weight less than the alpha value inputted by user.

2. Set DOS: sets the weights of rules to a fixed value

3. Create full rule block: creates rules for each combination of terms. For each possible
combination of input variables, a rule for each output variable is generated.

4. Created partial rule block: creates rules for each combination of terms. However, it is
different from the “created full rule block” in that the user has to specify the output.
The rule that is not specified with output will be considered incomplete and will be
erased when the editor is closed.

The other rule editor is called matrix rule editor. This editor is preferred when
designing a complex system. The variable terms will be put into a matrix with the degree
of membership belongings indicated by the shade of gray. Non-firing rules will be

identical to the zero-weighted rules.

40

Chapter 5

ANALYSIS AND RECOMMENDATIONS

5.1 Introduction

In this chapter, the use of interactive debug of fuzzyTech to analyze the defrosting
fuzzy control design will be introduced. The result will be demonstrated and analyzed.

Further hardware implementation and software tuning will be recommended.
5.2 Interactive Analysis

In fuzzyTech, after the initial design of a fuzzy controller is done, we can debug
and test the design using fuzzyTech’s interactive debug tool. Interactive debug mode can
be turned on by going to the menu Debug-> Interactive. In the debug mode, any input can

be selected and its value can be changed within its universe discourse. This debugger can

41

be used as a real time data feeder. Designers can then Observe the output value and

evaluate the result.

There are also three analyzers that can be turned on when the system is in debug

mode.

0 Transfer Plot

The transfer plot (Figure 5.1) will let users analyze input /Output characteristics. When
the analyzer is Open, two inputs and one output can be selected and resolution can be set
over there too. Two input variables are plotted in the horizontal and vertical axes while
the value of the selected output variable is indicated as plot color. The color bar on the

lower part of the window shows the color-value relation.

0 3D Plot
3D Plot (Figure 5.3) shows the input/output characteristics Of the fuzzy system. It allows
a plane that is drawn in the control space. Two inputs will be drawn in the horizontal and

vertical axis while the value of the output will be indicated as the plot color in the control

space.

0 Time Plot

Time Plot (Figure 5.2) lets the user to see the time response characteristics of the fiizzy
system. User can add as many inputs or outputs as they want and feed the simulated
system real time data using the interactive debugger, a time response series will be

plotted in the Time Plot.

42

5.3 Defrost Fuzzy Controller Result and Analysis

The Defrost fuzzy controller will take two inputs from humidity sensor and door
open detecting sensor. When door Opening is detected, a timer will start timing the length
of the door Opening. If the length of time is not long enough to start a defrost cycle, then
the time will be accumulated until the defrost cycle kicks in. Then the timer will be reset
to zero. Since the fuzzy defrost system only defrosts when necessary, the length of the
defiosting cycle is reduced. This helps to solve the problem the automatic defrost system
has. The automatic defrost system has a fixed length of defrosting cyclel hour) no matter
how much frost is. Testing is done using fuzzyTech’s interactive analyzers. First from
the 3D transfer Space (Figure 5.3), we can see the fuzzy controller has a wider control
zone with emphasis on some regions. This is largely due to the non-linearity of the door
open activity and different humidity situations. With more information being considered,
a wiser decision could be made by using fuzzy controller. In the plot the deep color and
Shallow color represent extreme situations and these two regions do not account for the
main part of the control space. There are more areas representing the situation between
the two extreme points, which is reasonable, and therefore the consequent output action
will be necessary and waste no extra energy. Moreover, the output will correspond
differently to different input values. For each one of the infinite inputs on the universe
discourse, the output will have one and only one unique value for it. This is the biggest
achievement over using conventional controller or look-up table. It is almost impossible

for the conventional design to take all situations into consideration while still using the

43

low cost micro-controllers. The code size of the defrosting fuzzy controller is only less
than 6K.

In the time plot, real time data were fed through the interactive debugger. The
time plot is shown in Figure 5.2. The data fed are randomly picked within the universe
discourse of one input with the other unchanged. Output is Observed and plotted with
both inputs in the same plot. We noticed that the output -- length of defrost cycle acts to
the Opposite of the trend Of humidity and accumulated door open time. AS humidity
increases the period between two consecutive defrost cycles is shortened, when the
humidity decrease then the defrosting cycle is prolonged. When there are frequent door
opening activities, defrosting cycle is shorter than normal. And the defrosting cycle is
prolonged if there are fewer doors Opening activity. All these agree our intuitive.

The concept and structure Of the designed controller has shown its superior to the
original automatic defrost system. This adaptive defrost fuzzy controller has its flexibility
in dealing with the entire situation the refrigerator might have and not adding tOO much
overhead. And due to the prompt response of the controller to different situations, no pre-
fixed schedule and extra defrosting length are needed. Therefore, energy is saved.
However, the result is far from optimal. This is partially due to the facts that for each
different individual refrigerator, the temperature characteristic is different. Further
membership and rule tuning are required for each individual type of refrigerator. A
thorough characterization of the refrigerator’s temperature behavior will be needed.
According to the results of characterization, the universe discourse, label scope and the

shape of the membership might have to be modified base on the new information.

 

 

 

 

Q ~_.n__.3 c I

 

 

 

 

 

 

 

 

 

Figure 5.1: Transfer Plot Of Fuzzy Defrosting Controller

 

Period

 

 

Blot Items:

[I elm {l Period
DoorO pen__T ime
Humidity

 

 

Figure 5.2: Time Response of Fuzzy Defi'osting Controller

45

 

[leliclthF'e

new ii 1 , ;
murmur. ‘
“11““ i

it ’t 'I
“it.!|.‘.,|.1.l‘...

\
I
“‘6
\\ it“ \
Seek“
‘O

\\

\
\“
\“

”s
‘9‘

‘
\t“

\‘ ‘C
0““
\ \b
\“ \\
. \\\\\\§

- \\
0‘
‘0‘“

. I ‘
\“\\‘
SN“

\\ \\
1 \\§\\\\ \

l\
.
l

 

l
1.75

l
2.63

.194:
7 7.88 8.75 9.83

 

10.50 11.38 1225 13.13

14

 

0

0.88

5.4 Conclusions

over several chapters. The work in this thesis serves to help understand the practical use
of fuzzy logic in embedded system design. These topics included defining the structure of

the fuzzy controller, choosing of the fuzzification, rule evaluation and defuzzification

The fuzzy logic concepts and design methodologies were presented in this thesis

Figure 5.3: 3D Plot of Fuzzy Defrosting Controller

algorithms, and designing hardware/software and analysis.

From the analysis, the advantage of fuzzy logic design is evident. As it is shown

in Figure 5.3, fuzzy controller deals with more situations with less system resources. The

46

whole code for programming the fuzzy controller is less than 6K, which is small enough
to be Stored in the 32K on-board memory Of some embedded system controller, i.e.,
handyboard. Since for each combination Of the inputs there is an unique output that can
be easily found through the membership function, real time processing — the bottleneck in
conventional controller for computing a complicated model — will never going to be a
problem. The quickness and easiness to get an output for a fuzzy controller is almost like
a lookup table. But a lookup table can never hold a large amount of data without
requiring more memory, and be able to store infinite combinations of input states.

Moreover, fuzzy controller is better Off solving ill-defmed, non-linear problems
and helps to solve problems with conflicting goals. In this fuzzy defrosting controller
case, the two conflicting goals energy efficiency and no frost results are well resolved by
adopting the adaptive defrost mechanism. Combining the simple but optimal
mathematical model — i.e., membership function — and heuristic estimations - i.e., the
average door Open time is 30 to 90 seconds, no prefixed defrost schedule is needed.
Thereafter, the length of each defrost cycle will be greatly shortened. The energy save
from the improved fuzzy defrost system is expected to be 50% while the no frost result
can still be guaranteed.

At last, since fuzzy logic controllers rely on the values within the universe
discourse and label scope to represent the numerical characteristic of the problem,
membership function and rule tuning are required for the same system working in
different environments. However, this very reason makes the fuzzy logic design
methodology very attractive and provides designers with a flexible but powerful design

tool which is easier to be implemented and optimized.

47

Chapter 6

RECOMMENDATIONS FOR FUTURE WORK

The demonstration of using fuzzyTech software to design the defrost system were
provided in the previous chapter and a recommended fidzzy controller for setting
temperature for energy saving and user- friendly interface was proposed. The next step
would be to implement the defrost controller onto the refrigerator, modify and tune the
membership function and rule base of the fuzzy controller based on the characterization
of the refrigerator. In addition to this, a software implementation for the fuzzy controller
that automatically set the temperature is recommended. This would provide the
opportunity to further explore the concepts and methodologies of fuzzy design and the

necessary experience to develop the fuzzy controller.

48

Appendix A

DESIGN OF FUZZY DEFROSTING SYSTEM

A.1 Introduction

This is the fully documented design of adaptive defrosting system using fuzzy
logic. In this part, the general information of the design, the fuzzy defrosting system
structure and the definition of the linguistic variables for the fuzzy defrosting controller
are described. Details on input/output interface, definition Of rule block, and the methods

that are used for fuzzy logic computations are presented.

A.2 General Information

Author: Weijjiang Robert Yu
Created: 1 1/1 7/98
Print Date: 5/22/99

Edition

Edition Name: fuzzyTECH 5.01 MCU-HC11/12 Explorer
Neuro Modul: NeuroFuzzy add-on Module not installed

A.3 Project Description
First Edition.
Variables

V les
V ' les

e Blocks
es

 

F unctions

TableA-l: Project Statistics

49

A.4 System Structure

The system structure, as shown in Figure A-l, identifies the fuzzy logic inference
flow from the input variables to the output variables. The fuzzification in the input
interfaces translates analog inputs into fuzzy values. The fuzzy inference takes place in
rule blocks that contain the linguistic control rules. The outputs of these rule blocks are
linguistic variables. The defuzzification in the output interfaces translates them into

analog variables.

 

 

 

 

Defrost System

 

 

Pt er DoorOpen_Ti

 

MIN
Baggifin-T' Defrost_Perio——IDelrosl_Perio m

m—

 

 

 

 

 

E.Ti.-i’_ Humidity

 

 

 

 

Figure A-l: Structure of the Fuzzy Logic Defrosting System

Figure A-l shows the whole structure of this fuzzy system including input
interfaces, rule blocks and output interfaces. The connecting lines symbolize the data

flow.

A.5 Linguistic Variables

50

This appendix contains the definition of all linguistic variables and of all
membership functions. Linguistic variables are used to translate real values into linguistic
values. The possible values Of a linguistic variable are not numbers but so called
'linguistic terms'. For example:

To translate the real variable 'Temperature' into a linguistic variable three terms,
'COld', ‘Pleasant' and 'Warm' are defined. Depending on the current temperature level
each of these terms describes the 'temperature’ more or less well. Each term is defined by
a membership function (MBF). Each membership function defines for any value of the
input variable the associated degree of membership of the linguistic term. The
membership functions of all terms of one linguistic variable are normally displayed in
one graph. The following figure (Figure A-2) plots the membership functions of the three
terms for the example 'Temperature'.

A 'Temperature' of 66 °F is a member of the MBFs for the terms:
Cold to the degree of 0.8
Pleasant to the degree of 0.2

Warm to the degree of 0.0

 

 

 

 

 

000 65.0 700 750 00.0
' Farrenhel

Figure A-2: Membership Function of 'Temperature'

51

Linguistic variables have to be defined for all input, output and intermediate
variables. The membership functions are defined using a few definition points only. The
following table (Table A-2) lists all linguistic variables of the system, their types and

their term names.

ariable Name erm Names
Time Short, Short, Normal, Long, Extreme Long

, Normal, Wet
N

 

Table A-2: Linguistic Variables

The properties of all input variables are listed in Table A—3.

 

 

 

[Eput Variable 'Min 'Max ase Var. Unit lFuzzification
[DoorOpen_Time 0 900 Second Compute MBF
[Humidity 0 1 Percent Compute MBF

 

 

 

 

 

Table A-3: Properties of Linguistic Input Variables

The properties Of all output variables are listed in the following table (Table A-4).
The default value of a variable is used if no rule is firing for this variable. Different
methods can be used for the defuzzification, resulting either into the Most Plausible

Result or the Best Compromise.

The Best Compromise is produced by the methods:
0 COM (Center of Maximum)
0 COA (Center of Area)

0 COA BSUM, a version especially for efficient VLSI implementations

52

The Most Plausible Result is produced by the methods:

- MOM (Mean of Maximum)

MOM BSUM, a version especially for efficient VLSI implementations

 

[Output Variable lMin [Default ax lBase Var. Unit efuzzification

 

 

 

 

Eefrost_Period 0 - 14 Days OM

 

 

 

Table A-4: Properties of Linguistic Output Variables

A.5.1 Output variable "Defrost_Period"

 

 

 

 

0.0 . _ . . .. . , W . ._ ._ .. K
00 . . 4.0 (7.0 . , 1110 14.0

Figure A-3: Membership Function of "Defrost_Period"

The output membership fimction is defined as Shown in Figure A-3.

erm Name . Points (x, )

0, 0) (1, 1)
14,0)

0,0) (1,0) ( .1)
10,0) (14,0)

0.0) ( ,0) (1 1)
14,0)

 

Table A-S: Definition Points of Membership Function for "Defrost_Period"

53

A.5.2 Input variable "DoorOpen_Time"

 

 

 

 

 

 

 

 

 

 

 

Eritrernefihort Short Normal Long Extreme_Long
1‘0? /\ ~ ’/’\‘-. '-
08 ~ ‘
0.8
04
0.2‘ ,1
0.0 , 3 ~
, 0.0 250.0 450.0 6500 9001:
Figure A-4: Membership Function of "DoorOpen_Time"
[Term Name Shape/Par. [Definition Points (x, y)
I‘Extreme_Shorlinear (0, l) (200, 0) (900, 0)
hort linear (0, 0) (200, 1) (400, 0)
(900, 0)
ormal linear (0, 0) (200, O) (400, l)
(600, O) (900, 0)
ong linear (0, 0) (400, O) (600, l)
(900, 0)
Extreme_Lon linear (0, 0) (600, 0) (900, l)

 

 

 

Table A-6: Definition Points of Membership Functions for "DoorOpen_Time"
Overall time of open door between two consective defrost cycle is defined in

Table A-6 and the membership function is shown in Figure A-4.

A.5.3 Input variable "Humidity"

54

 

 

 

 

 

 

Figure A-5: Membership Function of "Humidity"

 

 

 

 

 

[Term Name Shape/Par. [Definition Points (x, y)

lDry linear (0, 1) (0.15, l) (0.5, 0)
(1, 0)

[Normal linear (0, 0) (0.15, 0) (0.5, 1)
(0.845, 0) (1, 0)

lWet linear (0, 0) (0.5, 0) (0.845, 1)
(1, 1)

 

 

 

 

Table A-7: Definition Points of Membership Functions for "Humidity"
The membership function of “Humidity” is shown in Figure A-5 and defined as

indicated in Table A-7.

A.6 Interfaces

 

 

 

[Input Variable lIo-Mapping uzzification
[DoorOpen_Time Compute MBF
[Humidity Compute MBF

 

 

 

Table A-8: Input Interfaces

 

[Output Variable o-Mapping 7Defuzzification

 

 

 

Eefrost_Period COM

 

Table A-9: Output Interfaces

55

The methods that will be used for firzzy logic computations for fuzzification and

defuzzification are shown in Table A-8 and Table A-9.

A.7 Rule Blocks

The rule blocks contain the control strategy Of a fuzzy logic system. Each rule
block confines all rules for the same context. A context is defined by the same input and
output variables Of the rules.

The rules' 'if part describes the situation, for which the rules are designed. The
'then’ part describes the response of the fuzzy system in this situation. The degree of
support (DOS) is used to weigh each rule according to its importance.

The processing of the rules starts with calculating the 'it‘ part. The operator type
of the rule block determines which method is used. The Operator types MIN-MAX, MIN-
AVG and GAMMA are available. The characteristic of each operator type is influenced

by an additional parameter. For example:

MIN-MAX, parameter value 0 = Minimum Operator (MIN)
MIN -MAX, parameter value 1 = Maximum Operator (MAX)
GAMMA, parameter value 0 = Product Operator (PROD)

The minimum Operator is a generalization of the Boolean 'and'; the maximum
operator is a generalization of the Boolean 'or'.

The fuzzy composition eventually combines the different rules to one conclusion.
If the BSUM method is used all firing rules are evaluated, if the MAX method is used

only the dominant rules are evaluated.

56

A.7.1 Rule block "RBI"

Parameter
Aggregation: MINMAX
Parameter: 0.00
Result Aggregation: MAX
Number of Inputs: 2
Number of Outputs: 1
Number of Rules: 15

Table A-10 defines all the rules for fuzzy defrosting controller.

IF
Time
Short .00
.56
.20
.81
.59
.48

.90
.82
.75
.17

. 1
.52
et .30

 

Table A-10: Rules of Rule Block "RBI"

57

Appendix B

FUZZY TECHNOLOGY LANGUAGE FOR
FUZZY DEF ROSTING SYSTEM

B.1 Introduction

Appendix B is the design of the fuzzy defrosting system written in text format. As
we mentioned earlier, this is also a kind of software code that can be used to implement
the fuzzy controller. The difference between this fuzzy technology language and the other
popular programming languages is that the fuzzy technology language has to be
precompiled using either compilers for C or for assembly language to generate real C

codes or assembly codes before use.

B.2 Fuzzy Technology Language for Fuzzy Defrosting System

PROJECT {
NAME = DEFROST_SYSTEM.FTL;
TITLE =DEFROST_SYSTEM;
AUTHOR = Weijjiang Robert Yu;
DATEFORMAT = M.D.YY;
LASTCHANGE = 11.18.98;
CREATED = 11.17.98;
SHELL = EXPL12;
COMMENT {

First Edition} /* COMMENT */

SHELLOPTIONS {

ONLINE_REFRESHTIME = 55;
ONLINE_TIMEOUTCOUNT = 1100;
ONLINE_PORT = SERIAL;
ONLINE_CODE = OFF;
COMMENTS = ON;
TRACE_BUFFER = (ON, PAR(100));

58

FTL_BUFFER = (OFF, PAR(1));
PASSWORD = OFF;
PUBLIC_IO = ON;
FAST_CMBF = OFF;
FAST_COA = OFF;
F ILE_CODE = OFF;
BTYPE = 8_BIT;
} /* SHELLOPTIONS */
MODEL {
VARIABLE_SECTION {
LVAR {
NAME = Defrost_Period;
BASEVAR = Days;
LVRANGE = MIN(0.000000), MAX( 14.000000),
MINDEF(0), MAXDEF(255),
DEF AULT_OUTPUT(0.500000);
RESOLUTION = XGRID(0.100000), YGRID( 1 .000000),
SHOWGRID (ON), SNAPTOGRID(ON);
COMMENT {
The time between two consecutive defrost cycles} /"‘ COMMENT */
COLOR = RED (0), GREEN (0), BLUE (255);
TERM {
TERMNAME = Short;
POINTS = (0.000000, 0.000000),
(1.000000, 1.000000),
(5.000000, 0.000000),
(14.000000, 0.000000);
SHAPE = LINEAR;
COLOR = RED (0), GREEN (0), BLUE (255);

TERM {

TERMNAME = Normal;

POINTS = (0.000000, 0.000000),
(1.000000, 0.000000),
(5.000000, 1.000000),
(10.000000, 0.000000),
(14.000000, 0.000000);

SHAPE = LINEAR;

COLOR = RED (128), GREEN (0), BLUE (0);

TERM {
TERMNAME = Long;
POINTS = (0.000000, 0.000000),
(5.000000, 0.000000),
(10.000000, 1.000000),
(14.000000, 0.000000);

59

SHAPE = LINEAR;
COLOR = RED (0), GREEN (128), BLUE (128);

}/*LVAR*/

LVAR {

COMMENT {

NAME = DoorOpen_Time;

BASEVAR = Second;

LVRANGE = MIN(0.000000), MAX(900.000000),
MINDEF(0), MAXDEF(255),

DEF AULT_OUTPUT(0.500000);

RESOLUTION = XGRID(5.000000), YGRID(1.000000),
SHOWGRID (ON), SNAPTOGRID(ON);

Overall time of open door between two consective defrost cycle.) /* COMMENT */
COLOR = RED (0), GREEN (128), BLUE (0);

TERM {

TERM {

TERM {

TERM {

TERMN AME = Extreme_Short;

POINTS = (0.000000, 1.000000),
(200.000000, 0.000000),
(900.000000, 0.000000);

SHAPE = LINEAR;

COLOR = RED (255), GREEN (0), BLUE (0);

TERMNAME = Short;

POINTS = (0.000000, 0.000000),
(200000000, 1.000000),
(400.000000, 0.000000),
(900.000000, 0.000000);

SHAPE = LINEAR;

COLOR = RED (0), GREEN (128), BLUE (0);

TERMNAME = Normal;

POINTS = (0.000000, 0.000000),
(200.000000, 0.000000),
(400.000000, 1.000000),
(600.000000, 0.000000),

(900.000000, 0.000000);
SHAPE = LINEAR;
COLOR = RED (0), GREEN (128), BLUE (128);

TERMNAME = Long;
POINTS = (0.000000, 0.000000),
(400000000, 0.000000),

60

TERM {

}
} /* LVAR */
LVAR{

TERM {

TERM {

TERM {

(600.000000, 1.000000),
(900000000, 0.000000);

SHAPE = LINEAR;

COLOR = RED (128), GREEN (0), BLUE (0);

TERMNAME = Extreme_Long;

POINTS = (0.000000, 0.000000),
(600.000000, 0.000000),
(900.000000, 1.000000);

SHAPE = LINEAR;

COLOR = RED (0), GREEN (128), BLUE (128);

NAME = Humidity;

BASEVAR = Percent;

LVRANGE = MIN (0.000000), MAX( 1 .000000),
MINDEF(0), MAXDEF(255),
DEFAULT_OUTPUT(0.500000);

RESOLUTION = XGRID(0.005000), YGRID(1.000000),
SHOWGRID (ON), SNAPTOGRID(ON);

COLOR = RED (255), GREEN (0), BLUE (0);

TERMNAME = Dry;
POINTS = (0.000000, 1.000000),
(0.150000, 1.000000),
(0.500000, 0.000000),
(1.000000, 0.000000);
SHAPE = LINEAR;
COLOR = RED (255), GREEN (0), BLUE (0);

TERMNAME = Normal;
POINTS = (0.000000, 0.000000),
(0.150000, 0.000000),
(0.500000, 1.000000),
(0.845000, 0.000000),
(1.000000, 0.000000);
SHAPE = LINEAR;
COLOR = RED (0), GREEN (128), BLUE (0);

TERMNAME = Wet;
POINTS = (0.000000, 0.000000),
(0.500000, 0.000000),

61

(0.845000, 1.000000),
(1.000000, 1.000000);
SHAPE = LINEAR;
COLOR = RED (0), GREEN (0), BLUE (255);
I
} /* LVAR */
} /* VARIABLE_SECTION */

OBJECT _SECTION {

INTERFACE {
INPUT = (Humidity, CMBF);
POS = -213, -1;

}

INTERFACE {
INPUT = (DoorOpen_Time, CMBF);
POS = -219, -146;

INTERFACE {
OUTPUT = (Defiost_Period, COM);
POS = 109, -74;

RULEBLOCK {
NAME = RBI;
INPUT = DoorOpen_Time, Humidity;
OUTPUT = Defrost_Period;
AGGREGATION = (MIN_MAX, PAR (0000000));
RESULT_AGGR = MAX;
POS = -66, -102;
RULES {
IF DoorOpen_Time = Extreme_Short
AND Humidity = Dry
THEN Defi'ost_Period = Long WITH 0.000;
IF DoorOpen_Time = Extreme_Short
AND Humidity = Normal
THEN Defrost_Period = Long WITH 0.563;
IF DoorOpen_Time = Extreme_Short
AND Humidity = Wet
THEN Defrost_PeriOd = Normal WITH 0.195;
IF DoorOpen_Time = Short
AND Humidity = Dry
THEN Defrost_Period = Long WITH 0.813;
IF DoorOpen_Time = Short
AND Humidity = Normal
THEN Defrost_Period = Normal WITH 0.586;
IF DoorOpen_Time = Short

62

AND Humidity = Wet
THEN Defrost_PeriOd = Normal WITH 0.477;
IF DoorOpen_Time = Normal
AND Humidity = Dry
THEN Defrost_PeriOd = Normal WITH 0.352;
IF DoorOpen_Time = Normal
AND Humidity = Normal
THEN Defrost_Period = Normal WITH 0.898;
IF DoorOpen_Time = Normal
AND Humidity = Wet
THEN Defrost_PeriOd = Normal WITH 0.820;
IF DoorOpen_Time = Long
AND Humidity = Dry
THEN Defrost_PeriOd = Normal WITH 0.750;
IF DoorOpen_Time = Long
AND Humidity = Normal
THEN Defrost_Period = Normal WITH 0.172;
IF DoorOpen_Time = Long
AND Humidity = Wet
THEN Defrost_Period = Short WITH 0.859;
IF DoorOpen_Time = Extreme_Long
AND Humidity = Dry
THEN Defrost_PeriOd = Normal WITH 0.711;
IF DoorOpen_Time = Extreme_Long
AND Humidity = Normal
THEN Defrost_PeriOd = Short WITH 0.516;
IF DoorOpen_Time = Extreme_Long
AND Humidity = Wet
THEN Defrost_PeriOd = Short WITH 0.305;
} /* RULES */

REMARK {
TEXT = Defrost System;
POS = -86, -195;
FONTSPEC = -32, 700, 0, 0, 0, 18, 0;
F ONTNAME =Times New Roman;
COLOR = RED (0), GREEN (0), BLUE (128);
}
} /* OBJECT _SECTION */
} /* MODEL */
} /* PROJECT */

TERMINAL {
BAUDRATE = 19200;
DATABITS = 8;
PARITY = 0;

63

STOPBITS = 1;
PROTOCOL = NO;
CONNECTION = PORTI;
INPUTBUFFER = 256;
OUTPUTBUFFER = 256;

} /* TERMINAL */

ONLINE {
TIMESTAMP = 1998111821523500;

} /* ONLINE */

Appendix C

ASSEIVIBLY CODE FOR FUZZY DEFROSTING
CONTROLLER

C.1 Introduction

This appendix is documented with the assembly code generated for the fuzzy
defrosting controller for using Motorola’s MC68HC11/MC68HC12 micro-controller. The
code is ready to be downloaded to the micro- controller if the current design is not to be

changed. Any changes Of parameters to the design will need re-generation of the code.

C.2 Code

' ----- FuzzyTECH 5.01 MCU-HC11/12 Explorer --- Pre-assembler
---------- code generation date: Sat May 22 15:14:38 1999 -------

project: DEFROSI
MCU: 12

 

 

 

 

~19 VI. ‘0"

XDEF _defrosl
XDEF _initdefi'osl

; input/output interface Of controller ------------
XDEF _DoorOpen_Time_defrOSl ;00H .. FFH
XDEF _Humidity_defrosl ;00H .. FFH
XDEF _Defrost_Period_defrosl ;00H .. FFH

; external functions of fuzzy library .............
XREF flms
XREF com

; external variables of fuzzy library .............
XREF fuzptr
XREF _invalidflags
XREF itcnt
XREF tpptr
XREF crisp
XREF otcnt

 

 

 

 

switch .bss

65

; RAM i/O-vars
fuzvals: ;8 + 3 + 0
fvs:

_t_DoorOpen_Time_defrosl: ds.b 5
_t_Humidity_defrosl: ds.b 3
_t_Defrost_Period_defrosl: ds.b

crispio: '3

 

 

 

 

 

 

 

_DoorOpen_Time_defrOSI: ds.b l
_Humidity_defros1: ds.b 1
_Defrost_Period_defrosl: ds.b 1
switch .text
; standard term definition (x1, x2, x3, x4) ----------
tpts:

dc.b $00, $00, $00, $39

dc.b $00, $39, $39, $71

dc.b $39, $71, $71, $AA

dc.b $71, $AA, $AA, $FF

dc.b $AA, $FF, $FF, $FF

dc.b $00, $00, $26, $80

dc.b $26, $80, $80, $D7

dc.b $80, $D7, $FF, $FF
; xcom table (defuzzification)
xcom:

dc.b $12, $53, $86
; rule table(s)
_rt0:

dc.w fvs+$0, fvs+$5, $FFFE
dc.w fvs+$A, $FFFE
dc.w fvs+$0, fvs+$6, $FFFE
dc.w fvs+$A, $FFFE
dc.w fvs+$0, fvs+$7, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$1, fvs+$5, $FFFE
dc.w fvs+$A, $FFFE
dc.w fvs+$l, fvs+$6, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$1, fvs+$7, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$2, fvs+$5, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$2, fvs+$6, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$2, fvs+$7, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$3, fvs+$5, $FFFE
dc.w fvs+$9, $FF FE

66

dc.w fvs+$3, fvs+$6, $F FF E
dc.w fvs+$9, $FFFE
dc.w fvs+$3, fvs+$7, $FFFE
dc.w fvs+$8, $FFFE
dc.w fvs+$4, fvs+$5, $FFFE
dc.w fvs+$9, $FFFE
dc.w fvs+$4, fvs+$6, $FF FE
dc.w fvs+$8, $FFFE
dc.w fvs+$4, fvs+$7, $FFFE
dc.w fvs+$8, $FFFF

 

 

 

 

 

 

 

rtO:
dc.b $00, $8F, $31, $CF, $95, $79, $59, $E5, $Dl, $BF, $2B
dc.b $DB, $35, $83, $4D
_defrosl:
; fuzzification
ldy #fuzvals
ldd #tpts
std tpptr
ldab #$5
stab itcnt
ldab _DoorOpen_Time_defrosl
stab crisp
jsr flms
ldab #$3
stab itcnt
ldab _Humidity_defrosl
stab crisp
jsr flms
; inference init
; rule block 0
ldx #_rt0
ldy #rt0
ldaa #255
sec
sei ;patch
revw ;min aggregation, product composition
cli ;patch
; defuzzification

 

 

clr _invalidflags
ldy #fuzvals + $8

ldx #xcom + $0
ldab #$3

67

stab otcnt

jsr com
bcc out0valid
ldab #$09

out0valid: stab _Defrost_Period_defrosl

ldab _invalidflags

 

 

rts ;end Of fuzzy controller
; initdefrosl
_initdefrosl :

ldy #$3

ldaa #0
begin:

staa fuzvals + $7,y

dey

bne begin

rts

;data size knowledge base (bytes):
;RAM: 14 0000EH

;ROM: 140 0008CH
;TOTAL: 154 0009AH

9

end

68

BIBLIOGRAPHY

Bibliography

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