Fuzzy Logic Controller

Fuzzy Logic Controller

Dr. Ir. Ari Santoso, DEA Email:[email protected]

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

1

Direct Control

End-user Controller

Ref

Deviations

Rule base

Actions

Outputs Process

Inference engine

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

2

Feedforward control and Gain Scheduling Disturbance

Fuzzy compensator

Deviation

u

Controller

Controller parameters Fuzzy gain schedule

Ref

Controller

Plant

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

Outputs

3

Fuzzy + PID Configurations Fuzzy

PID

Process

PID

(a)

Process

(b)

Fuzzy

Fuzzy

PID

Process

(c)

PID

Process

(d)

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

4

Elements Of A Fuzzy Controller Fuzzy controller

Preprocessing

Fuzzification

Rule base

Defuzzification

Postprocessing

Inference engine

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

5

Fuzzification Membership Function „

Gaussian µ (x) ⎡ 1 ⎛ x − x ⎞2 ⎤ µ A ( x) = exp ⎢− ⎜ ⎟ ⎥ ⎢⎣ 2 ⎝ σ ⎠ ⎥⎦

1

σ

„

Triangle

x µ (x) 1

( x − a) 2 µ A ( x) = 1 − b a b Laboratory of Control Engineering-Department of Electrical Engineering-ITS

6

Fuzzification Membership Function „

Trapezium

µ(x) =

0 (x-a) / (b-a) 1 1 – ((x-c) / (d-c)) 0

xd

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

7

Fuzzification Exp. Variable Linguistic „

Speed of Motor AC Š Low Speed

Š Medium Speed

( x − 500) 2 µ A ( x) = 1 − b

( x − 1000 ) 2 µ A ( x) = 1 − b

Š High Speed

µ A ( x) = 1 −

( x − 1500) 2 b

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

8

Fuzzification Exp. Variable Linguistic u A (X) Low

Medium

500

750

High

1000

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

9

Rule Based

∆e

Design of Rule Based e

c g b

consigne

k

f

d

h

j

e

l

i

a e

+

-

-

+

+

-

-

+ +

- -

∆e

-

-

+

+

-

-

+

+

-

- +

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

10

Rule Based Design of Rule Based ∆e \ e

GN

MN

PN

Zéro

PP

MP

GP

GN

GN

GN

GN

MN

PN

PN

Zéro

MN

GN

MN

MN

MN

PN

Zéro

PP

PN

GN

MN

PN

PN

Zéro

PP

MP

Zéro

GN

MN

PN

Zéro

PP

MP

GP

PP

MN

PN

Zéro

PP

PP

MP

GP

MP

PN

Zéro

PP

MP

MP

MP

GP

GP

Zéro

PP

PP

MP

GP

GP

GP

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

11

Defuzzification Maximum Of Mean (MOM) vo =

J v j

∑

j =1

J

v j = max vεV µ v ( v ) Vo J Vj µv(v) V

= nilai keluaran = jumlah harga maximum = nilai keluaran maksimum ke-j = derajat keanggotaan elemen pada fuzzy set v = semesta pembicaraan

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

12

Defuzzification Centre Of Area (COA) m

∑ vk µ v (vk )

vo = k =1

m

∑

k =1

vo m vk

µv(vk) V

µ v (vk )

= nilai keluaran = tingkat kuantisasi = elemen ke-k = derajat keanggotaan elemen pada fuzzy set v = semesta pembicaraan

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

13

Defuzzification Exemple Sangat Lambat Lambat

0

20 Sangat Dekat Agak Dekat

0

1

Cukup Cepat

Cepat Sekali 40 60 Kecepatan (km/jam)

80

Sedang Agak Jauh

Jauh Sekali 2 3 Jarak (m)

4

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

14

Rule Based Exemple Injak Penuh

Injak Sedang Injak Sedikit

Injak Agak Penuh Injak Sedikit Sekali 0

10

20 30 Posisi pedal rem (0)

40

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

15

Rule Based Exemple Aturan 1: Bila kecepatan mobil cepat sekali dan jaraknya sangat dekat maka pedal rem diinjak penuh Aturan 2: Bila kecepatan mobil cukup dan jaraknya agak dekat maka pedal rem diinjak sedang Aturan 3: Bila kecepatan mobil cukup dan jaraknya sangat dekat maka pedal rem diinjak agak penuh

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

16

Rule Based Exemple „

Rule 1

Cepat Sekali

0

20

40

Sangat Dekat

60

Kecepatan (km/jam)

80 0

1

2

3

40

Jarak (m)

10

20 30 40 Posisi pedal rem (0 )

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

17

Rule Based Exemple „

Rule 2 Cukup

0

20

40 60 Kecepatan (km/jam)

Agak Dekat

80 0

1

2

3 40 Jarak (m)

Injak Sedang

10

20 30 40 Posisi pedal rem (0 )

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

18

Rule Based Exemple „

Rule 3 Cukup

Sangat Dekat Injak Agak Penuh

0

20 60

40 80 Kecepatan (km/jam)

0

1 3

2 4 Jarak (m)

0

10 30

20 40 Posisi pedal rem (0)

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

19

Rule Based Exemple MOM : PPR = 200 CO A

0

10 40

10x0,2+20x0,4

MOM COA : PPR =

0,2+0,4 = 16,670

20

30

Posisi pedal rem (0)

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

20

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

21

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

22

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

23

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

24

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

25

Fuzzy + PID Configurations

Laboratory of Control Engineering-Department of Electrical Engineering-ITS

26