1. Fuzzy Logic Control
What is Fuzzy Logic ?
Logic and Fuzzy Logic
Fuzzy sets
Fuzzy logic operators
Fuzzy logic controller

2. What is Fuzzy Logic ? General Control problem Fuzzy Logic Control
e.g. Temperature Controller
Set point = 25 Deg.C
Controller rule
If T>25.5 Deg.C then (turn heater off)
If T<24.5 Deg.C then (turn heater on)
Fuzzy Logic Control
If (too hot) then (turn heater off)
If (too cold) then (turn heater on)

3. Logic and Fuzzy Logic Logic - There are only two choices : 0 or 1,
yes or no, right or wrong, etc.
- and, or, nand, nor, not, xor
Fuzzy logic
- More choices between 0 and 1,
yes and no, young and old, etc.
e.g. a bit young, very young,
not young at all...
- fuzzy and, fuzzy or, fuzzy not

4. Fuzzy Sets Set of young people, A
- A=[0,20] : age from 0 to 20 years old.
- more than 20 years old = not young.
Fuzzy set of young people
years old = 100% young.
- 21 years old = 90% young.
- ....
- 25 years old= 60% young.
- 30 years old = 0% young

5. Fuzzy Sets (Example) Fuzzy set of young people - Young =1
- Not young=0
Young
Not Young 10 20 30 40 50 1

6. Operations in Fuzzy Sets
Fuzzy AND
- 1 AND 0 = 0
- 1 AND 0.6=0.6
AND 0.7=0.5
a AND b = min(a,b)
Fuzzy OR
- 1 OR 0 = 1
- 1 OR 0.6=1
OR 0.7=0.7
a OR b = max(a,b)
Fuzzy NOT
- NOT 1 = 0
- NOT 0.6=0.4
- NOT 0.1 =0.9
NOT a = 1 - a

7. Fuzzy Logic Controller
𝐺 𝐶 𝑠
𝐺 𝑃 𝑠
𝐻𝑠 + _
Input
Compensator
Plant
Output
R(s)
E(s)
C(s)
r(t)
e(t)
c(t)
Sensor
Input
Compensator
Plant
Output
R(s) +
E(s)
C(s)
Fuzzy Logic Controller
𝐺 𝑃 𝑠
r(t) _
e(t)
c(t)
Sensor
𝐻𝑠

8. Fuzzy Logic Controller
Fuzzifier
Fuzzy Operations based on Fuzzy rule sets
Defuzzifier
Fuzzifier
Combinations of AND, OR, NOT
Defuzzifier LP MP S MN LN

9. Fuzzification - Fuzzifier
Degree of membership : 0 ~ 1
Linguistic variables
LN : Large Negative very cold
MN : Medium Negative cold
S : Small just fine
MP : Medium Positive hot
LP : Large Positive very hot
Membership function
Triangular, bell, trapezoidal, haversine, Gaussian, exponential
Haversine : The function (1-cos(x))/2. It is written hav(x), and is equal to half the versine of x.

10. Membership Function - Triangular
Input (error)
membership
Degree of LN MN S MP LP
Set point
cold
hot

11. Membership Function - Triangular
Member of Speed : {Slow, Moderate, Fast}
Membership functions
0.5 1
Slow
Moderate
Fast
0.65
0.35 60 40 70
100
km/s
Speed=60 km/s
Degree of membership
slow=0.35, moderate=0.65, fast=0.00

12. Fuzzy Rule Sets If LN then (turn heater on)
If MN then (turn heater on)
If S then (do nothing)
If MP then (turn heater off)
If LP then (turn heater off)
If error LN then (turn heater on)
If error MN then (turn heater on)
If error S then (do nothing)
If error MP then (turn heater off)
If error LP then (turn heater off)

13. Combinations of AND, OR, NOT
Fuzzy Logic Controller (Example)
Temperature control
Fuzzy rule sets
Combinations of AND, OR, NOT
Fuzzifier LP MP S MN LN
Defuzzifier
error
slope
heater

14. Fuzzy Rule Sets If error LN then (heater LP)
If error MN AND slope LN then (heater LP)
If error MN AND slope MN then (heater MP)
If error MN AND slope S then (heater MP)
If error MN AND slope MP then (heater MP)
If error MN AND slope LP then (heater MP)
If error S AND slope LN then (heater LP)
If error S AND slope MN then (heater MP)
If error S AND slope S then (heater S)
If error S AND slope MP then (heater S)
If error S AND slope LP then (heater S)
If error MP then (heater S)
If error LP then (heater S)

15. Fuzzy Rule Sets & Rule Matrix
If error LN then (heater LP)
If error MN AND slope LN then (heater LP)
If error MN AND slope MN then (heater MP)
If error MN AND slope S then (heater MP)
If error MN AND slope MP then (heater MP)
If error MN AND slope LP then (heater MP)
If error S AND slope LN then (heater LP)
If error S AND slope MN then (heater MP)
If error S AND slope S then (heater S)
If error S AND slope MP then (heater S)
If error S AND slope LP then (heater S)
If error MP then (heater S)
If error LP then (heater S)

16. Fuzzy Inference
MAX-MIN (Mamdani Fuzzy Rules)
MAX-DOT or MAX-PRODUCT
AVERAGING
ROOT SUM SQUARE (RSS)
Takagi-Sugeno Fuzzy Rules

17. Defuzzification - Defuzzifier
Center of Area or Center of Mass
or Centroid of Area
Center of Gravity Method for Singletons
Bisector of Area
Mean of Maxima
Leftmost Maxima and Rightmost Maxima

18. Fuzzy Logic Controller Design (Example)
Water heating system
Boiler
TempSensor
LevelSensor 10
125 ํC
HeatKnob
Water inlet
Water outlet
Steam exhaust

19. Combinations of AND, OR, NOT
Fuzzy Logic Controller Design (Example)
1. Define inputs and outputs for Fuzzy Logic Controller
and Fuzzy Variables.
Fuzzy rule sets
Combinations of AND, OR, NOT
Fuzzifier XL L M S XS
Defuzzifier F
Level
[0,10]
Temp
[0, 125]
Heatknob

20. Fuzzy Logic Controller Design (Example)
2. Assign Membership Values to Fuzzy Variables.
0.5 1 XS S M L XL 10 20 30 40 50 60 70 80 90
100
110
120
Temp

21. Fuzzy Logic Controller Design (Example)
2. Assign Membership Values to Fuzzy Variables.
0.5 1 XS S M L XL 1 2 3 4 5 6 7 8 9 10
Level

22. Fuzzy Logic Controller Design (Example)
2. Assign Membership Values to Fuzzy Variables.
0.5 1 XS S F M L 1 2 3 4 5 6 7 8 9 10
HeatKnob

23. Fuzzy Logic Controller Design (Example)
3. Create a Rule Base and Decision Table.
IF Temp is Small and Level is Medium THEN set HeatKnob to Medium.
IF Temp is VerySmall and Level is Large THEN set HeatKnob to Large.

24. Fuzzy Logic Controller Design (Example)
4. Fuzzify inputs to FLC and Determine which Rules Fire.
Temp = 65 ˚ C and Level =6.5
Temp {M} = 0.45 and Temp {L} = 0.28
Level {M} =0.25 and Level {L} = 0.38

25. Fuzzy Logic Controller Design (Example)
5. Infer the Output Recommended by Each Rule.
Temp = 65 ˚ C and Level =6.5
Temp {M} = 0.45 and Temp {L} = 0.28
Level {M} =0.25 and Level {L} = 0.38

26. Fuzzy Logic Controller Design (Example)
5. Infer the Output Recommended by Each Rule.
0.5 1 XS S F M L 1 2 3 4 5 6 7 8 9 10
HeatKnob

27. Fuzzy Logic Controller Design (Example)
6. Defuzzify the Aggregated Fuzzy Set to form a Crisp Output.
0.5 1 XS S F M L 1 2 3 4 5 6 7 8 9 10
HeatKnob
4.66

28. Fuzzy Logic Controller Design (Example)
7. Implement the Designed Controller.
Implement as Hardware
Implement as Software

29. Fuzzy Logic Controller Design (Example)
Desgin
ABS Control
Crane Control
AC Room Temperature Control