Giới thiệu lý thuyết và ứng dụng của ogic mờ

FUZZY LOGIC
Menoufia University
Faculty of Electronic Engineering
4/2020

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References
08
07 Fuzzy on Simulink
05 Fuzzy at the Cmd line
06 PID – Fuzzy controller
Agenda
Introduction to Fuzzy
01
Fuzzification &
Defuzzification
02
Fuzzy application
03
04 FIS tool

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0
0.5
1
0 1 2 3 4 5 6 7 8 9 10
𝞵
(x)
x
Classical control
theory
1 0
On off
Yes No

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Classical set
theory
𝐴 = 0.1,0.3,0.5 & 𝐵 = {0.2,0.3,0.5,0.7}
𝒖𝒏𝒊𝒐𝒏 ∶ 𝐴 ∪ 𝐵 = {0.1,0.2,0.3,0.5,0.7}
𝒊𝒏𝒕𝒆𝒓𝒔𝒆𝒄𝒕𝒊𝒐𝒏 ∶ 𝐴 ∩ 𝐵 = {0.3,0.5}
𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 ∶ 𝐴 − 𝐵 = {0.1}
𝒄𝒐𝒎𝒑𝒍𝒆𝒎𝒆𝒏𝒕: ҧ
𝐴 = 0.9,0.7,0.5
𝒄𝒂𝒓𝒕𝒆𝒔𝒊𝒂𝒏 𝒑𝒓𝒐𝒅𝒖𝒄𝒕 ∶ 𝐴 × 𝐵
𝒅𝒆𝒎𝒐𝒓𝒈𝒆𝒏′
𝒔 𝒍𝒂𝒘 ∶ 𝐴 ∩ 𝐵 ′
= 𝐴′ ∪ 𝐵′
0.1
0.3
0.5
A
0.7
0.2
B

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Crisp set Vs Fuzzy set

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What Fuzzy Systems?
Confused
vague
blurred

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Fuzzy
he wrote that to handle biological systems "we need a radically
different kind of mathematics, the mathematics of fuzzy or cloudy
quantities which are not describable in terms of probability distributions"
1962
1965
Classical
control
Is a 160 m person is tall ?
True
Possibly True

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Types of membership function
𝝁 𝒙 =
𝟎 , 𝒙 ≤ 𝒂
𝒙 − 𝒂
𝒃 − 𝒂
, 𝒂 ≤ 𝒙 ≤ 𝒃
𝒄 − 𝒙
𝒄 − 𝒃
, 𝒃 ≤ 𝒙 ≤ 𝒄
𝟎 , 𝒙 ≥ 𝒄
Triangular
𝝁 𝒙 =
𝟎 , 𝒙 ≤ 𝒂
𝒙 − 𝒂
𝒃 − 𝒂
, 𝒂 ≤ 𝒙 ≤ 𝒃
𝟏 , 𝒃 ≤ 𝒙 ≤ 𝒄
𝒄 − 𝒙
𝒄 − 𝒃
, 𝒄 ≤ 𝒙 ≤ 𝒅
𝟎 , 𝒙 ≥ 𝒅
Trapezoidal
𝝁 𝒙 = 𝒆𝒙𝒑
− 𝒙 − 𝒄 𝟐
𝟐𝝈𝟐
Gaussian

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speed [m/s]
Human
knowledge-based
Rule-based
Fuzzy
IF AND
THEN
distance
speed
acceleration
small
speed is declining
maintain
IF distance perfect AND
speed is declining
THEN increase acceleration

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a self-parking car in 1983
Nissan has a patent saves
fuel
F U Z Z Y
App.
The fuzzy washing machines
were the first major consumer
products in Japan around
1990
the most advanced subway
system on earth in 1987

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Fuzzy Logic
Controller
Sensor
Fuzzification
Fuzzy
Inference
System
to be
controlled
Defuzzification
Membership
function of
input fuzzy set
Rule Base
Membership
function of
output fuzzy set
Feedback

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Defuzzification Methods
Centre of
largest area
Mean–max
membership
Maxima
(MOM)
Max-membership Centre
of sums
Centroid
method
Approx. Centroid
method

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Mean of Maxima (MOM) 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8
𝞵
Z
𝒁∗
=
𝒂 + 𝒃
𝟐 𝒁∗ =
𝟔 + 𝟕
𝟐
= 𝟔. 𝟓 𝒎

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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8
𝞵
Z
Centroid Method 2
also called center of area, center of gravity).
it is the most prevalent and physically appealing
of all the defuzzification methods
𝒁∗
=
𝟎. 𝟑 × (𝟏 + 𝟐 + 𝟑) + 𝟎. 𝟓 × (𝟒 + 𝟓) + 𝟏 × (𝟔 + 𝟕)
(𝟎. 𝟑 × 𝟑) + (𝟎. 𝟓 × 𝟐) + (𝟏 × 𝟐)
𝒁∗
= 𝟑. 𝟑𝟑 𝒎
𝒁∗ =
σ 𝝁(𝒁) 𝒁
σ 𝝁(𝒁)

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The approximate COA 3
𝒁∗ =
σ 𝝁(𝒁) 𝑪
σ 𝝁(𝒁)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8
𝞵
Z
𝒁∗
=
𝟎. 𝟑 × 𝟐. 𝟓 + 𝟎. 𝟓 × 𝟓 + (𝟏 × 𝟔. 𝟓)
𝟎. 𝟑 + 𝟎. 𝟓 + 𝟏
= 𝟓. 𝟒𝟏 𝒎

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Autonomous driving car
distance
speed
acceleration
13 m
-2.5 m/s
?
Knowledge
Rule base
Distance to next car [ m ]
v.small small perfect big v.big
Speed
Change
[ 𝒎𝟐
]
declining -ve small zero +ve small +ve big +ve big
constant -ve big -ve small zero +ve small +ve big
growing -ve big -ve big -ve small zero +ve small
speed [m/s]

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speed [m/s]
Knowledge
Rule base
Distance to next car [ m ]
v.small small perfect big v.big
Speed
Change
[ 𝒎𝟐
]
declining -ve small zero +ve small +ve big +ve big
constant -ve big -ve small zero +ve small +ve big
growing -ve big -ve big -ve small zero +ve small
0.4 0.25
0.4
0.6
0.6
0.75
0.75
0.25
0.25
0.4
0.25
0.6
Rule 1: IF distance is small AND speed is declining
THEN acceleration zero
Rule 2: IF distance is small AND speed is constant
THEN acceleration negative small
Rule 3: IF distance is perfect AND speed is declining
THEN acceleration positive small
Rule 4: IF distance is perfect AND speed is constant
THEN acceleration zero
max
Take
min

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Defuzzification using approximate COA

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Washing Machine
40
30
?
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
𝞵
(weight)
Weight (g)
v.Light light Heavy V.heavy
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
μ
(Dirtiness)
Dirtiness (%)
Almost Clean Dirty Soiled Filthy
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
μ
(detergent)
Detergent (%)
v.Light little Much V.Much Maximum
Knowledge
Rule base
Weight [ Kg ]
V.Light Light Heavy V.Heavy
Dirtiness
Almost
Clean
V.Little Little Much Much
Dirty Little Little Much V.Much
Soiled Much Much V.Much Maximum
Filthy V.Much Much V.Much Maximum
weight
dirtiness
amount of
detergent output

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heavy dirty Much
heavy soiled V.Much
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
μ
(Dirtiness)
Dirtiness (%)
Almost Clean Dirty Soiled Filthy
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
𝞵
(weight)
Weight (g)
v.Light light Heavy V.heavy
Light dirty little
Light soiled Much
0.4
0.4
0.4
0.8 0.8
0.6
0.6
0.2 0.2
0.2
0.6
0.2
Little 0.4
Much 0.6
V.Much 0.2
IF weight is light(0.4) AND dirtiness is dirty(0.8)
THEN detergent is little(0.4)
IF weight is light(0.4) AND dirtiness is soiled(0.2)
THEN detergent is Much(0.2)
IF weight is heavy(0.6) AND dirtiness is dirty(0.8)
THEN detergent is Much(0.6)
IF weight is heavy(0.6) AND dirtiness is soiled(0.2)
THEN detergent is V.Much(0.2)

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0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
μ
(detergent)
detergent
𝒁∗ =
𝟒𝟎 + 𝟔𝟎
𝟐
= 𝟓𝟎%
𝒁∗
=
𝒂 + 𝒃
𝟐
𝒁∗
=
𝟎. 𝟒 × 𝟐𝟓 + 𝟎. 𝟔 × 𝟓𝟎 + (𝟎. 𝟐 × 𝟕𝟓)
𝟎. 𝟒 + 𝟎. 𝟔 + 𝟎. 𝟐
𝒁∗ = 𝟒𝟓. 𝟖𝟑 %
𝒁∗ =
σ 𝝁(𝒁) 𝒁
σ 𝝁(𝒁)
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60 70 80 90 100
μ
(detergent)
Detergent (%)
approximate
COA
MOM
(Mean of Maxima )

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Service = 3
Food = 8
Rule 1 : IF Service is poor OR Food is rancid
THEN Tip is cheap
Rule 2 : IF Service is good THEN Tip is average
Rule 3 : IF Service is excellent OR Food is
delicious THEN Tip is generous
0.125
0.4
0
0
0.5
0.5
0.4
0.125

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Build Fuzzy
using
Fuzzy Logic Designer

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Build Fuzzy
at
the Command Line

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Generate new fuzzy
01
Add the first input (service)
02
Add its membership functions
03

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Add the rules to the FIS
05
Rule 1 : IF Service is poor OR Food is rancid
THEN Tip is cheap
Rule 2 : IF Service is good THEN Tip is average
Rule 3 : IF Service is excellent OR Food is
delicious THEN Tip is generous
1 - Index of membership function for first input
5 - Fuzzy operator (1 for AND, 2 for OR)
2 - Index of membership function for second input
3 - Index of membership function for output
4 - Rule weight

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PID Fuzzy
Controller
System

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𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤
𝐨𝐮𝐭𝐩𝐮𝐭: 𝐮 𝐤
𝐑𝐮𝐥𝐞: 𝐢𝐟 𝐞 𝐤 𝐢𝐬 … 𝐭𝐡𝐞𝐧 𝐮 𝐤 𝐢𝐬 …
P- like FLC
1

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𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤 , ∆ 𝒆(𝒌)
𝐨𝐮𝐭𝐩𝐮𝐭: ∆ 𝐮 𝐤
𝐑𝐮𝐥𝐞: 𝐢𝐟 𝐞 𝐤 𝐢𝐬 … 𝐚𝐧𝐝 ∆ 𝒆 𝒌 𝒊𝒔 … 𝐭𝐡𝐞𝐧 ∆𝐮 𝐤 𝐢𝐬 …
PI- like FLC
2

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𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤 , ∆ 𝒆 𝒌
𝐑𝐮𝐥𝐞: 𝐢𝐟 𝐞 𝐤 𝐢𝐬 … 𝐚𝐧𝐝 ∆ 𝒆 𝒌 𝒊𝒔 … 𝐭𝐡𝐞𝐧 𝐮 𝐤 𝐢𝐬 …
PD- like FLC
3

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𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤 , ∆ 𝒆 𝒌 , Σ 𝒆(𝒌)
𝐑𝐮𝐥𝐞: 𝐢𝐟 𝐞 𝐤 𝐢𝐬 … 𝐚𝐧𝐝 ∆ 𝒆 𝒌 𝒊𝒔 … 𝐚𝐧𝐝 Σ𝒆 𝒌 𝒊𝒔 … 𝐭𝐡𝐞𝐧 𝐮 𝐤 𝐢𝐬 …
PID- like FLC
3

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𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤
𝐨𝐮𝐭𝐩𝐮𝐭: ∆ 𝐮 𝐤
𝐈𝐧𝐩𝐮𝐭: 𝐞 𝐤 , ∆ 𝒆 𝒌 , Σ 𝒆(𝒌)

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Consider a system model is describe by:
𝒚 (𝒌) = 𝟎. 𝟔 × 𝒚 (𝒌 − 𝟏) + 𝒖(𝒌 − 𝟏)
PI-Like FLC is designed to regulate this system around a set point of R=2. Five fuzzy sets are used
to represent the linguistic variables NB, NS, Z, PS and PB for the controller both input and output
variables. Triangular membership functions are used to represent these fuzzy sets and defined on the
normalized domain [-1,1] as shown in Fig. 1. The suggested rule-base is depicted in table. If the
measured parameters are obtained as y(k-1)=1.5 and u(k-1)=0.5,find the controller output signal
taking into account the actual domain of the controller variables is [-2, 2].
Knowledge
Rule base
e(k)
NB NS Z PS PB
∆ 𝒆(𝒌)
NB NB NB NB NS Z
NS NB NB NS Z PS
Z NB NS Z PS PB
PS NS Z PS PB PB
PB Z PS PB PB PB

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42 of 24
𝒚 (𝒌) = 𝟎. 𝟔 × 𝒚 (𝒌 − 𝟏) + 𝒖(𝒌 − 𝟏)
𝒂𝒄𝒕𝒖𝒂𝒍 𝒅𝒐𝒎𝒂𝒊𝒏 ∈ −𝟐, 𝟐
𝒕𝒉𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍𝒍𝒆𝒓 𝒐𝒖𝒕𝒑𝒖𝒕 𝒔𝒊𝒈𝒏𝒂𝒍
find
𝒏𝒐𝒓𝒎𝒂𝒍𝒊𝒛𝒆𝒅 𝒅𝒐𝒎𝒂𝒊𝒏 ∈ [−𝟏, 𝟏]
𝑷𝑰 − 𝑳𝒊𝒌𝒆 𝑭𝑳𝑪
𝒚 𝒌 = 𝟎. 𝟔 × 𝒚 𝒌 − 𝟏 + 𝒖 𝒌 − 𝟏
= 𝟎. 𝟔 × 𝟏. 𝟓 + 𝟎. 𝟓 = 𝟏. 𝟒
𝒆(𝒌) = 𝑹(𝒌) − 𝒚(𝒌)
= 𝟐 − 𝟏. 𝟒 = 𝟎. 𝟔
𝜟𝒆 (𝒌) = 𝒆 (𝒌) − 𝒆 (𝒌 − 𝟏)
= 𝑹 𝒌 − 𝒚 𝒌 − 𝑹 𝒌 − 𝒚 𝒌 − 𝟏
= 𝒚 𝒌 − 𝟏 − 𝒚 𝒌
= 𝟏. 𝟓 − 𝟏. 𝟒 = 𝟎. 𝟏
𝑻𝒉𝒆 𝒂𝒄𝒕𝒖𝒂𝒍 𝒔𝒚𝒔𝒕𝒆𝒎 𝒐𝒖𝒕𝒑𝒖𝒕 𝒇𝒐𝒓 𝒕𝒉𝒆 𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝒗𝒂𝒍𝒖𝒆𝒔:
𝒚 𝒌 − 𝟏 = 𝟏. 𝟓
𝒖 𝒌 − 𝟏 = 𝟎. 𝟓

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43 of 24
𝒚 (𝒌) = 𝟎. 𝟔 × 𝒚 (𝒌 − 𝟏) + 𝒖(𝒌 − 𝟏)
𝒚 𝒌 = 𝟏. 𝟒
𝒂𝒄𝒕𝒖𝒂𝒍 𝒅𝒐𝒎𝒂𝒊𝒏 ∈ −𝟐, 𝟐
𝒕𝒉𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍𝒍𝒆𝒓 𝒐𝒖𝒕𝒑𝒖𝒕 𝒔𝒊𝒈𝒏𝒂𝒍
find
𝒆 𝒌 = 𝟎. 𝟔
𝒏𝒐𝒓𝒎𝒂𝒍𝒊𝒛𝒆𝒅 𝒅𝒐𝒎𝒂𝒊𝒏 ∈ [−𝟏, 𝟏]
𝑷𝑰 − 𝑳𝒊𝒌𝒆 𝑭𝑳𝑪
∆𝒆 𝒌 = 𝟎. 𝟏
𝑻𝒉𝒆 𝒏𝒐𝒓𝒎𝒂𝒍𝒊𝒛𝒆𝒅 𝒊𝒏𝒑𝒖𝒕 𝒗𝒂𝒍𝒖𝒆𝒔 𝒇𝒐𝒓 𝑭𝑳𝑪 𝒘𝒊𝒍𝒍 𝒃𝒆:
𝑮𝒆 =
𝟏
𝟐
= 𝟎. 𝟓 , 𝑮∆𝒆 =
𝟏
𝟐
= 𝟎. 𝟓 , 𝑮∆𝒖 =
𝟐
𝟏
= 𝟐
𝑻𝒐 𝒐𝒃𝒕𝒂𝒊𝒏 𝒔𝒄𝒂𝒍𝒊𝒏𝒈 𝒇𝒂𝒄𝒕𝒐𝒓𝒔:
𝒆𝒏 𝒌 = 𝑮𝒆 × 𝒆 𝒌
= 𝟎. 𝟓 × 𝟎. 𝟔 = 𝟎. 𝟑
∆𝒆𝒏(𝒌) = 𝑮∆𝒆 × ∆𝒆 𝒌
= 𝟎. 𝟓 × 𝟎. 𝟏 = 𝟎. 𝟎𝟓

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𝒇𝒖𝒛𝒛𝒊𝒇𝒊𝒄𝒂𝒕𝒊𝒐𝒏 ∶
𝝁𝒁_𝒆𝒏(𝒌) =
𝟏
𝟑
− 𝟎. 𝟑
𝟏
𝟑
− 𝟎
= 𝟎. 𝟏
𝝁𝑷𝑺_𝒆𝒏(𝒌) =
𝟎. 𝟑 − 𝟎
𝟏
𝟑
− 𝟎
= 𝟎. 𝟗
𝝁𝒁_∆𝒆𝒏(𝒌) =
𝟏
𝟑
− 𝟎. 𝟎𝟓
𝟏
𝟑
− 𝟎
= 𝟎. 𝟖𝟓
𝝁𝑷𝑺_𝒆𝒏(𝒌) =
𝟎. 𝟎𝟓 − 𝟎
𝟏
𝟑
− 𝟎
= 𝟎. 𝟏𝟓

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PS Z PS
PS PS PB
Z Z Z
Z PS PS
0.1
0.1
0.1
0.85 0.85
0.9
0.9
0.15 0.15
0.1
0.85
0.15
IF e (k) is Z (0.1) AND ∆𝒆(𝒌) is Z (0.85)
THEN ∆u(𝒌) is Z (0.1)
IF e (k) is Z (0.1) AND ∆𝒆(𝒌) is PS (0.15)
THEN ∆u(𝒌) is PS (0.1)
IF e (k) is PS (0.9) AND ∆𝒆(𝒌) is Z (0.85)
THEN ∆u(𝒌) is PS (0.85)
IF e (k) is PS (0.9) AND ∆𝒆(𝒌) is PS (0.15)
THEN ∆u(𝒌) is PB (0.15)
Knowledge
Rule base
e(k)
NB NS Z PS PB
∆ 𝒆(𝒌)
NB NB NB NB NS Z
NS NB NB NS Z PS
Z NB NS Z PS PB
PS NS Z PS PB PB
PB Z PS PB PB PB
Z 0.1
PS 0.85
PB 0.15

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∆𝒖𝒏 𝒌 =
𝟎. 𝟏 × 𝟎 + 𝟎. 𝟖𝟓 ×
𝟏
𝟑
+ (𝟎. 𝟏𝟓 ×
𝟐
𝟑
)
𝟎. 𝟏 + 𝟎. 𝟖𝟓 + 𝟎. 𝟏𝟓
∆𝒖𝒏 𝒌 = 𝟎. 𝟑𝟓
∆𝒖𝒏 𝒌 =
σ 𝝁(∆𝒖𝒏) 𝑪
σ 𝝁(∆𝒖𝒏)
approximate
COA
𝒅𝒆𝒇𝒖𝒛𝒛𝒊𝒇𝒊𝒄𝒂𝒕𝒊𝒐𝒏 ∶
∆𝒖 𝒌 = 𝑮∆𝒖 × ∆𝒖𝒏 𝒌
= 𝟐 × 𝟎. 𝟑𝟓 = 𝟎. 𝟕
𝒖 𝒌 = 𝒖 𝒌 − 𝟏 + ∆𝒖 𝒌
= 𝟎. 𝟓 + 𝟎. 𝟕 = 𝟏. 𝟐
𝑻𝒉𝒆 𝒂𝒄𝒕𝒖𝒂𝒍 𝒄𝒐𝒏𝒕𝒓𝒐𝒍 𝒐𝒖𝒕𝒑𝒖𝒕 𝜟𝒖 𝒌 𝒐𝒇 𝑭𝑳𝑪:
𝑻𝒉𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍 𝒔𝒊𝒈𝒏𝒂𝒍 𝒖 𝒌 𝒘𝒊𝒍𝒍 𝒃𝒆:

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Tank Level Control System
5 cm ?
0
0.25
0.5
0.75
1
1.25
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
𝞵
(Level)
Liquid level (cm)
low okay high
0
0.5
1
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
𝞵
(valve
control)
Valve control signal (%/s)
close fast no change open fast
Rule 1 : IF level is okay THEN valve is no change
Rule 2 : IF level is low THEN valve is open fast
Rule 3 : IF level is high THEN valve is close fast
Liquid level
Valve control
signal

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𝑻𝒂𝒏𝒌 𝑺𝒚𝒔𝒕𝒆𝒎
𝑺𝒊𝒎𝒖𝒍𝒂𝒕𝒊𝒐𝒏

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𝑺𝒖𝒃𝒔𝒚𝒔𝒕𝒆𝒎 𝑽𝒂𝒍𝒗𝒆
𝑺𝒖𝒃𝒔𝒚𝒔𝒕𝒆𝒎 𝑻𝒂𝒏𝒌
ሶ
ℎ =
1
𝐴
𝑞𝑖𝑛 −
𝑎
𝐴
2𝑔ℎ
𝑨 = 𝟎. 𝟒 𝒎𝟐
𝒂 = 𝟎. 𝟎𝟏𝟐 𝒎𝟐
𝒒𝒊,𝒎𝒂𝒙 = 𝟐𝟎 𝒍/𝒔
𝐴: 𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑎𝑛𝑘
𝑎: 𝑐𝑟𝑜𝑠𝑠 − 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑖𝑝𝑒

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𝒍𝒊𝒒𝒖𝒊𝒅 𝒍𝒆𝒗𝒆𝒍
𝒗𝒂𝒍𝒗𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍
𝒗𝒂𝒍𝒗𝒆 𝒐𝒑𝒆𝒏𝒊𝒏𝒈

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𝑻𝒂𝒏𝒌 𝑺𝒚𝒔𝒕𝒆𝒎 𝑺𝒊𝒎𝒖𝒍𝒂𝒕𝒊𝒐𝒏
With reference

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𝒍𝒊𝒒𝒖𝒊𝒅 𝒍𝒆𝒗𝒆𝒍
𝒗𝒂𝒍𝒗𝒆 𝒄𝒐𝒏𝒕𝒓𝒐𝒍
𝒗𝒂𝒍𝒗𝒆 𝒐𝒑𝒆𝒏𝒊𝒏𝒈

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With reference
Without reference

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References
[1] L.-X. Wang, A Course in Fuzzy Systems and Control. Prentice Hall PTR, 1997.
[2] S. N. Sivanandam, S. Sumathi, and S. N. Deepa, Introduction to Fuzzy Logic using MATLAB.
Springer, 2006.
[3] T. J. Ross, Fuzzy Logic with Engineering Applications, 2nd ed. Wiley, 2004.
[4] Essam Nabil, “Autonomous driving car,” March,2019, pp. 1–13.[presentation].
[5] Essam Nabil, “Fuzzy logic control system applications,” March,2019, pp. 1-30 .[presentation].
[6] Essam Nabil, “Tipping problem,” March,2019, pp. 1–18.[presentation].

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References
[7] “Build Fuzzy Systems Using Fuzzy Logic Designer - MATLAB & Simulink.” [Online]. Available:
https://www.mathworks.com/help/fuzzy/building-systems-with-fuzzy-logic-toolbox-
software.html. [Accessed: 22-Nov-2019].
[8] “Build Fuzzy Systems at the Command Line - MATLAB & Simulink.” [Online]. Available:
https://www.mathworks.com/help/fuzzy/working-from-the-command-line.html.
[Accessed: 22-Nov-2019]
[9] Essam Nabil, “Tank control system” March,2019, pp. 1–18.[presentation].
[10] Essam Nabil, “PID - Like Fuzzy Logic control” March,2019, pp. 1–39.[presentation].

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Thank You
Nourhan Selem Salm
FUZZY

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