1

1 PID

1.1 PID

PID

(1) PID PID

PID 1

PID

PID 1 1,2

1. , 430070 E-mail: cwjxjjabc@163.com

2. , 430070 E-mail: liujiaoyu_2006@163.com

: PID PID

PID PIDPID

(RBFNN) BPBP RBF PID

BP PID RBF : PID ,RBF ,BP ,

Neural Network PID Controller Auto-tuning Design and Application

Xiong Jingjing1, Liu Jiaoyu1,2 1. The College of Automation, Wuhan University of Technology, Wuhan 430070

E-mail: cwjxjjabc@163.com

2. The College of Automation, Wuhan University of Technology, Wuhan 430070 E-mail: liujiaoyu_2006@163.com

Abstract: The simple PID controller can’t get the satisfied degree especially for the time-varying objects and non-linear systems the traditional PID controllers can do nothing for them .to non-linear systems the NN PID controller has a good controller effect in the non-line premature turning and optimizing. The NN PID controller can make both neural network and PID control into an organic whole which has the merit of any PID controller for its Simple construction and definite physical meaning of parameters and also has the self learning and adaptive functions of a neural network. Radial basis function neural network(RBFNN)is a kind of three-layer feed forward neural network with single hidden layer ,there is Great difference between it’s structure and learning algorithms with BP neural network ’s. so in the Paper

the NN PID is used to achieve PID parameters self adjustments on RBF NN identification. an improved single neural adaptive PID controller is presented and PID control based on BPNN is studied in detail. A new self-adaptive learning model of RBF neural net work as established successfully. Key Words: PID control, radial basis function neural network, BP neural network, Gradient-descent algorithms

1: PID

1370978-1-4673-5534-6/13/$31.00 c©2013 IEEE

2: PID

PID (2) PID

PID 2

1.2 PID

: (1) (2)

(3) (4)

2 PID

PIDPID PID PID

PID PID PIDPID Z N

(1) Z N

( ) 1s

pp

KeG s T sτ−

= + (1)

K

pT τ Z N PID 1

pk iT dT

;

1 Z N PID

o

c

TT

p

c

kk

i

c

TT

d

c

TT

PI 0.2 0.36 1.05 …

PID 0.16 0.27 0.4 0.22

(2) :

PID

3

PID:

PIDPID

PIDPID

PID

3 PID

PID PIDPID

PID

u(t) y

3:

2013 25th Chinese Control and Decision Conference (CCDC) 1371

3.1 PID

PIDe(k) e(k)

PIDxi e(k)+ e(k)

( ) ( ) ( ) ( )kxkwkkuku ii

i=

++=3

11

(2)

( ) ( ) ( )

=

=3

1/

iiii kwkwkw

(3) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( )kekxkukzkwkw

kekxkukzkwkwkekxkukzkwkw

D

P

I

Δ++−=Δ++−=

Δ++−=

333

222

111

111

ηηη

(4)

( ) ( ) ( ) ( ) ( )kekzkekeke =−−=Δ ,1

MATLAB

( ) ( ) ( )( ) ( )2632.0110.0

226.01368.0

−+−+−+−=

kukukykky

(5)

( ) ( )( )tkrin π4sinsgn5.0= 1msPID

Hebb DeltaHebb Hebb

4~ 7 :

PID yout

3.2 BP PID

BP PID

(1) BP MQ

( )0)2(ijw ( ) ( )02

liw

k=1

5: Delta

7:

4: Hebb

6: Hebb

8: BP PID

1372 2013 25th Chinese Control and Decision Conference (CCDC)

(2) rin(k) yout(k)error(k)=rin(k)-yout(k)

(3) NNNN PID kpki kd

(4) PID u(k) (5) ( )kwij

)2( ( ) ( )kwli2

PID (6) k=k+1 (1)

MATLAB

( ) ( ) ( )( ) ( )1

111

2 −+−+−= ku

kyoutkyoutka

kyout (6)

( )ka

( ) ( )keka 1.08.012.1 −−= =0.28 =0.04

[-0.5,0.5]

(1) rin(k)= 1.0 (2) rin(k)=sin ( )tπ2 S=1 S=2

9 13 : 9 BP

PID12 BP PID

310−

4 RBF PID

4.1 RBF

RBF

RBF RBF 3.5X=(x1,x2, ,xn)T RBF

H=[h1,h2, hj, ,hm]T ,hj

−= 22

expj

jj b

CXh

(7) j

Cj=[cj1,cj2, cji, cjn]T,

9:

10:

11:

12:

2013 25th Chinese Control and Decision Conference (CCDC) 1373

i=1 2 n B=[b1,b2, ,bm]T bj

j

W=[w1,w2, ,wj, ,wm]T

ym(k)=w1h1+w2h2+ wmhm]

( ) ( )( )2

21

kykyoutJ mI −= (8)

RBF

Lm c

b w:

L

d Ld

b2

=

M RBF K

RBF

RBFNN

( ) ( ) ( ) ( )( )( ) ( )( )21

1

−−−+

−+−=

kwkw

hkykyoutkwkw

jj

jmjj

αη

(9)

( ) ( )( ) 3

j

jjjmj b

CXhwkykyoutb

−−=Δ

(10) ( ) ( )

( ) ( )( )21

1

−−−+

Δ+−=

kbkb

bkbkb

jj

jjj

αη

(11)

( ) ( )( ) 2j

jijjmji b

cxwkykyoutc

−−=Δ

(12) ( ) ( )

( ) ( )( )21

1

−−−+

Δ+−=

kckc

ckckc

jiji

jijiji

αη

(13)

Jacobian ()

( )( )

( )( ) 2

1

1 j

jij

m

jj

m

b

xchw

kky

kuky −

=Δ∂

∂≈

Δ∂∂

= (14) x1= u(k)

4.2 RBF PID

RBF PID PID

( ) ( ) ( )kyoutkrinkerror −= (15) PID

( ) ( ) ( )( ) ( )( ) ( ) ( ) ( )21232

11

−+−−==

−−=

kerrorkerrorkerrorxckerrorxc

kerrorkerrorxc

(16)

( ) ( ) ( )( ) ( ) ( )( )

( ) ( ) ( )( ))2

12(

1

21

−+−−++

−−=Δ−Δ+−=

kerrorkerrorkerrorkkerrork

kerrorkerrorkkukukuku

di

p

(17)

( ) ( )1xcuykerror

ku

uy

yE

kEk

ppp

Δ∂∂=

∂Δ∂

Δ∂∂

∂∂−=

∂∂−=Δ

η

ηη (18)

( ) ( )2xcuykerror

ku

uy

yE

kEk

iii

Δ∂∂=

∂Δ∂

Δ∂∂

∂∂−=

∂∂−=Δ

η

ηη (19)

( ) ( )3xcuykerror

ku

uy

yE

kEk

ddd

Δ∂∂=

∂Δ∂

Δ∂∂

∂∂−=

∂∂−=Δ

η

ηη (20)

14: RBF PID

1374 2013 25th Chinese Control and Decision Conference (CCDC)

uy

Δ∂∂

Jacobian

MATLAB

( ) ( ) ( )( )211

111.0−+

−+−−=kyout

kukyoutkyout

21) ( ) ( )( )ttrin π2sinsgn0.1=

RBF u(k),yout(k),yout(k-1) M=1 RBF

PID 15 16 M=2PID 17

4.3

15 17 RNF

BPRBF BP

RBF BP

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, , 2003. [2] PDI

2001.5 22(5):23-25. [3] PI [J].

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[12] PID .1999 No.2:19-21

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[15] Krotolica R, Ozguner U, Chen H, etal.Stability of linear feedback system with random communication delays[J].Internationl Journal of Control, 1994, 59(4)925-953

[16] A1esLeonardi, HorstBiehof An efficient construction of RBF networks.[J] Neural networks1998.963-973MDL.hased.11(8) .

15:

16:

17:

2013 25th Chinese Control and Decision Conference (CCDC) 1375