Fuzzy Logic Presentation Slides
These slides accompanied the presentation adapted for the first part of this book, Fuzzy logic implementation on embedded microcomputers. The quality of some slides reflects their origin as transparencies.
Byte Craft Limited |
35 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Linguistic |
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36 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Linguistic Variables
Degree of Membership
COOL WARM HOT 1 
0
0 |
37 |
75 |
112 |
150 |
Temperature
CRISP 
Temperature = 75
Given a crisp temperature of 75:
#Degree of Membership(COOL) = 0.0
#Degree of Membership(WARM) = 0.7
#Degree of Membership(HOT) = 0.23
Byte Craft Limited |
37 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Linguistic Variables
Degree of Membership
HOT 1 
0
0 |
37 |
75 |
112 |
150 |
Temperature
Linguistic Variable HOT
38 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Linguistic Variables
Degree of Membership
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90 |
HOT |
150 |
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75 |
112 |
150 |
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Temperature
Linguistic Variable HOT
LINGUISTIC Temperature TYPE unsigned int MIN 0 MAX 150
{
MEMBER HOT {73, 90, 150, 150}
}
Byte Craft Limited |
39 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy Operators
Degree of Membership
F_NOT operator
1 
F_NOT A |
A |
0
0 10 20 30 40 50 60 70 80 90 100
(Crisp)
Degree of Membership
F_OR operator
1
F_OR (A,B)
A B
0
0 10 20 30 40 50 60 70 80 90 100
(Crisp)
Degree of Membership
F_AND operator
1 |
F_AND (A,B) |
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A B |
0
0 10 20 30 40 50 60 70 80 90 100
(Crisp)
40 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Contoller
Set Point
Manipulated
Variable
Process
Process Error
Byte Craft Limited |
41 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Process
Proportional
Band
#Range of error to give full-scale proportional output
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Variable |
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5 volt band |
6 |
2 volt band |
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1 volt band |
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-2 |
-10 -5 -4 -3 -2 -1 0 1 2 3 4 5 10 |
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Process Error |
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42 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
DOM
Proportional
Band
1
Negative Zero Positive
0
Process Error
1
0
M Z P
Manipulated Variable
Byte Craft Limited |
43 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
1 
0
Process Error
1
0
M Z P
Rules:
#if pe is POSITIVE THEN mv IS M
#if pe is NEGATIVE THEN mv IS P
#if pe is ZERO THEN mv is Z
44 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller # Transfer Function
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-10 -5 -4 -3 -2 -1 0 1 2 3 4 5 10 |
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Process Error |
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Byte Craft Limited |
45 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
Performance
46 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
Performance
Byte Craft Limited |
47 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
1 
DOM Negative Zero Positive
0
Process Error
1
0
M Z P
48 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller # Transfer Function
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Variable |
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-10 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 |
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Process Error |
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Byte Craft Limited |
49 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller
1 
DOM Negative |
Positive |
0
Process Error
1
0
M Z P
Manipulated Variable
50 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller # Transfer Function
|
10 |
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Variable |
8 |
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6 |
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2 |
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Manipulated |
0 |
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-2 |
-10 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 |
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-4 |
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-6 |
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-8 |
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Process Error |
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-10 |
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Byte Craft Limited |
51 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Proportional
Controller |
# Computationally less intensive |
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DOM Negative |
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0
Process Error
1
0
M Z P
Manipulated Variable
52 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Bang Bang
Controller
Process
1
0
Setpoint
1
0
M P
Manipulated Variable
IF (process < setpoint)
THEN mv is P
ELSE mv is M
Byte Craft Limited |
53 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Bang Bang
Controller
# Transfer Function
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10 |
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Variable |
8 |
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Manipulated |
0 |
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-2 |
-10 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 |
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-4 |
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-6 |
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Process Error |
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-10 |
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54 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Bang Bang
Process
1 
0 NOTNORMAL
pe
1
0
M P
RULES:
IF pe IS NOTNORMAL THEN mv is P ELSE mv is M
Byte Craft Limited |
55 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Bang Bang # Transfer Function
|
10 |
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Variable |
8 |
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6 |
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4 |
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2 |
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Manipulated |
0 |
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-2 |
-10 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 10 |
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-4 |
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-6 |
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-8 |
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Process Error |
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-10 |
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56 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
PID
Controller
Set Point
Manipulated
Variable
Process
Process Error
Derivative
Integral
Byte Craft Limited |
57 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
PID
Controller
#Classical PID
#Manipulated variable is the sum of three terms:
mv = (pe × K1) + d pe × K2 + ($%pe × K3) d t
Fuzzy
PID
Controller
SP-
Error
#Break problem into separate control zones.
#Solve each part of the problem individually.
Process
Time
58 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy |
# Separate rules for |
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PID |
# |
Error term |
Controller |
# |
Derivative Term |
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Integral Term |
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Byte Craft Limited |
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Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy |
Irrigation |
Controller |
60 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Irrigation |
# Making the rules |
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Controller |
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Rotation
straight
1 
DOM acute |
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obtuse |
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0 |
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Byte Craft Limited |
61 |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Irrigation
Controller
#Each node has its own rules
IF angle IS straight THEN speed IS same
IF angle IS acute
THEN speed IS slowdown IF angle IS obtuse
THEN speed IS speedup
Fuzzy
Irrigation
Controller
#Differential Control
#speedup
#slowdown
#CONSEQUENCE functions may be non-linear
62 |
Byte Craft Limited |
Fuzzy Logic in Embedded Microcomputers and Control Systems
Fuzzy
Irrigation
Controller
#Normalized control values
#Degree of membership range is two degrees
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straight |
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DOM |
acute |
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obtuse |
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0 |
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The
Fuzzy
Advantage
#Normalized number system
#Natural smooth transition between different strategies
#Focus on problem solution, not problem analysis
#Works well on conventional embedded microprocessors
#Can easily be combined with conventional software
Byte Craft Limited |
63 |