Chromosome Representation - Multiobjective Optimization Methodology: A Jumping Gene Approach - page 232

y d , ∆ y are negative y d , ∆ y are positive

1

0.5

y d , ∆ y

-R 0 R

(a)

Output negative Output

zero

Output positive

1

-R R

0

Output signal Δ u D ( nT )

(b)

Figure D.2
(a). Input. membership. function. and. (b). output. membership. function. for. the. D. component..
(From. Tang,. K.. S.,. Man,. K.. F.,. Chen,. G.,. Kwong,. S.,. An. optimal. fuzzy. PID. controller,. IEEE
TransactionsonIndustrialElectronics ,.48(4),.757-765,.2001.)

D (

)

where.the.regions.are.speciied.as.in . Figure.D.3a .. Similarly,. u nT ∆ .can.be.

computed.as

R Ky nT K y nT
R y nT
R Ky nT

[ ( ) − ∆ ( )]

d d

in Ω , Ω , Ω , Ω

1 2 5 6

2(2 | ( )|)

−

d

[ ( ) − K y nT ∆ ( )]

d d

in Ω , Ω , Ω , Ω

3 4 7 8

2(2 R K − | ( ∆ y nT )|)

d

1
2 [

− K y nT ∆ ( ) + R ] in Ω , Ω

d 9 10

1
2 [

y nT ( ) − R ] in Ω , Ω

( ) ∆ u nT =

d 11 12

D

. (D.3)

1
2 [

− K y nT ∆ ( ) − R ] in Ω , Ω

d 13 14

1
2 [

y nT ( ) + R ] in Ω , Ω

d 15 16

0 in Ω , Ω

17 19

− R

R

in
in

Ω
Ω

18

20

.

where.the.regions.are.speciied.as.in. Figure.D.3b .