TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 13, No. 2, Februa
ry 20
15, pp. 287 ~ 291
DOI: 10.115
9
1
/telkomni
ka.
v
13i2.695
8
287
Re
cei
v
ed
No
vem
ber 3, 20
14; Re
vised
De
cem
ber 1
9
,
2014; Accep
t
ed Jan
uary 2
,
2015
Study on Adaptive PID Control Algorithm Based on
RBF Ne
ural Network
Qi Xuemei
，
Zhang Jingd
ong
Schoo
l of T
r
an
sportatio
n
an
d Automob
ile E
n
gin
eeri
ng, Pan
z
hih
ua Un
ivers
i
t
y
,
Panzh
i
hu
a, 61
700
0, Chi
n
a
A
b
st
r
a
ct
Aim at the l
i
m
it
ation of tr
ad
itio
nal PID contr
o
l
l
er has certa
i
n
li
m
i
tation, the traditi
ona
lPID control i
s
often difficu
lt to obtai
n satisfac
tory
control p
e
r
f
orma
nce, a
nd
the RBF
neur
al
netw
o
rkis diffi
cult to meet th
e
requirem
ent of
real-tim
e contr
o
l system
.To overcom
e
i
t, an adaptive PID
control
strat
e
gy based
on (RBF)
neur
al n
e
tw
ork ispro
pose
d
i
n
this pa
per. T
he res
u
ltss
h
o
w
that the pro
pose
d
co
nt
roll
er is pr
actical
an
d
effective, bec
ause of th
e adaptability, st
rong robustness
and s
a
tisfact
o
ry
controlperf
o
rmanc
e.It is also
revea
l
ed fro
m
simu
lati
on re
sults that the prop
osed c
ont
rol al
gorith
m
i
s
valid for DC
motor a
nd a
l
s
o
provi
des the th
eoretic
al an
d e
x
peri
m
e
n
tal b
a
s
is
.
Ke
y
w
ords
:
ad
aptive PID cont
roller, RBF
ne
u
r
al netw
o
rk, DC motor
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
PID controll
e
r
s are the most co
mmo
n indust
r
ial pro
c
e
ss
cont
rolle
r, its structure is
simple, g
ood
robu
stne
ss
and hi
gh reli
ability, and the PID
controller i
s
wi
del
y used i
ndu
strial
pro
c
e
ss cont
rol
[1]
.
Howev
e
r, the co
nve
n
tional PID controlle
r ha
s
a ce
rtain limiting, esp
e
ci
ally
the controlle
d object cont
ains a no
nlin
ear an
d
time-varying cha
r
acteri
stics,the
traditionalPID
control i
s
often difficult to
obtain
satisf
actory
co
ntro
l perfo
rma
n
ce [2]. Since
the pa
ramete
rs
empiri
cal fo
rmula of PID cont
rolle
r i
s
pro
p
o
s
ed
b
y
the Ziegle
r
and
Nieh
ols,
and th
e m
any
method
s have
be
en used for
the
pa
ram
e
ter setting
o
f
the PID
co
n
t
roller.
With t
he d
e
velopm
ent
of intelligent
control theo
ry, the intelligent cont
ro
l te
chn
o
logy wa
s intro
d
u
c
ed
in PID cont
ro
l b
y
many sch
o
lars, an
d p
r
ovid
ed n
e
w
meth
od me
an
s fo
r the PID
co
ntroltechnol
ogy
.In recent yea
r
s,
the artifici
al
neural n
e
two
r
k
ha
s b
een
used in
co
mplex proce
s
s control,
a
nd ha
s
attra
c
ted
wide
sp
rea
d
attention [3, 4]. Becau
s
e the neu
ral
netwo
rk
ha
s ada
ptive learni
ng, pa
rallel
processi
ng
and the
strong ability of f
ault tole
rance.The neural
network adaptivePID contro
l
scheme
which is lo
cally a
pproxim
ated
by the
RBFn
etworki
s
a
d
o
p
ted in
this p
aper,
and
in
orde
r
to improve th
e system a
ccura
cy
, robu
st
ness an
d ada
ptiveness [5].
2. RBF func
tion
The Ra
dial
Basis F
u
n
c
tion (RB
F
) is a neur
al n
e
twork which
was p
u
t forward by
J.Moodya
nd
C.Da
rken in
the late 198
0
s
, it is
a thre
e layer feed
forwa
r
d n
e
twork
with
singl
e
hidde
n layer (Figure 1), is
a kind
of loca
l approx
imation of the neu
ral net
work. T
he RBFi
s a ki
n
d
of three layer forward net
work. The m
appin
g
whi
c
h
is from the input to the output is nonli
near,
and the
map
p
ing
whi
c
h i
s
from hid
den l
a
yer
spa
c
e to
the output
space is li
nea
r [6]. It simulates
the neu
ral
ne
twork
stru
cture for the
pa
rtial adj
u
s
tmen
t of the hum
an b
r
ain
and
each receivin
g
domain. RBF
is a kind of
local app
rox
i
mation
network, which h
a
s be
en
proved that the any
pre
c
isi
on
app
roximate
s an
y continu
o
u
s
functio
n
. Th
i
s
kind
of net
work
ch
ara
c
t
e
risti
c
s is tha
t
it
onlyha
s
a fe
w output of
con
n
e
c
tion p
o
we
r influe
nc
e aim at local input spa
c
e, so that lo
cal
approximatio
n netwo
rk h
a
s the adv
a
n
tage
s of fasterle
arning
spe
ed [7]. Therefo
r
e, the
RBF
netwo
rk
can
signifi
cantly a
c
celerate the lear
ni
ng spee
d and avoid l
o
cal mini
mu
m probl
em, which
is suita
b
le for the real-time
control.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 287 – 291
288
Figure 1. Three layer feed
forwa
r
d n
e
twork
with sin
g
l
e
hidde
n laye
r
In the stru
cture of RBF
netwo
rk,
12
[,
,
]
T
n
X
xx
x
is the input vector of netwo
rk.
Assu
ming th
e radi
al ba
sis vecto
r
s
o
f
the RBF netwo
rk i
s
12
[,
,
]
T
n
H
hh
h
. Wher
e
j
h
isga
ussia
n
ba
sis fun
c
tion:
2
2
e
xp(
)
,
1
,
2
,
.
2
j
j
j
XC
hj
m
b
(1)
The j netwo
rk nod
e of ce
nter vecto
r
is
,1
2
,
,
[,
,
]
T
ij
j
j
i
j
n
j
Cc
c
c
c
. As
s
u
ming
the
basi
s
width v
e
ctor of net
work is
12
[,
,
]
T
m
B
bb
b
,
j
b
is the b
a
si
s wi
dth pa
ramete
r of n
o
de, and
is greater th
an ze
ro. The
weight vect
or of network is
12
[,
,
]
m
Ww
w
w
.The out
put of the
netwo
rk i
s
given as:
11
2
2
()
mm
m
yk
w
h
w
h
w
h
w
h
(2)
Assu
ming the
ideal output i
s
()
yk
, the performance index
function i
s
:
2
1
()
(
(
)
(
)
)
2
m
Ek
y
k
y
k
(3)
Based o
n
the
gradie
n
t descent metho
d
, the iterat
ive algorithm of ou
tput powe
r
, node center a
n
d
base width p
a
ram
e
tera
re:
()
(
1
)
(
()
()
)
(
(
1
)
(
2
)
)
jj
m
j
j
j
wk
wk
y
k
y
k
h
w
k
w
k
(4)
2
3
((
)
(
)
)
j
jm
j
j
j
XC
by
k
y
k
w
h
b
(5)
(
)
(1
)
(
(1
)
(
2
)
)
jj
j
j
j
bk
bk
b
b
k
b
k
(6)
,
2
((
)
(
)
)
j
ji
ji
m
j
j
x
c
cy
k
y
k
w
b
(7)
(
)
(1
)
(
(1
)
(
2
)
)
i
j
ij
ij
ij
ij
ck
ck
c
c
k
c
k
(8)
Whe
r
e
is learning rate,
is m
o
mentum fa
ctor.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Study on Ada
p
tive PID Co
ntrol Algorith
m
Based on RBF Ne
ural
Network (Qi
Xuem
ei)
289
Ja
cobi
an mat
r
ix algorithm i
s
as follo
ws:
11
2
1
()
()
()
()
m
j
m
jj
j
j
cx
yk
yk
wh
uk
uk
b
(10
)
Whe
r
e
1
()
x
uk
.
3. Design of
Adap
tiv
e
PID Con
t
roller
Bas
e
d on th
e BRF
Neur
a
l
Net
w
o
r
k
There are m
any function
form of RBF
neur
al network, G
a
u
ss f
unctio
n
wa
s
sele
cted
inthis a
r
ticle
as the
hidd
en
layer no
de fu
nction
acco
rd
ing to its u
n
iq
ue adva
n
tage
s [8]. Base
d
on
the RBF n
e
u
r
al net
wo
rk, t
he ad
aptive
PID co
ntrol
system structu
r
e i
s
a
s
sho
w
n in
Figu
re
2.
Neu
r
al
netwo
rk
ada
ptive PID co
ntrolle
r adj
ust
s
the
con
n
e
c
tion
weig
hts of
n
eural
net
work NN
and the thre
e
paramet
ers of PID acco
rding to t
he square error o
f
the
given input and syst
em
outputa
s
the obje
c
tive function [9]. The PID cont
roll
er is appli
ed
to the control
l
ed obje
c
t, and
make
s the
system output
close to
the gi
ven input of system.
Figure 2. Adaptive PID Controlle
r
ba
sed
on the BRF neural network
The co
ntrol e
rro
r of PID co
ntrolle
ris give
n as follo
wing
:
()
()
()
error
k
rin
k
yout
k
(11
)
The thre
e inp
u
ts of PID is given followin
g
as:
(1)
(
)
(
1)
x
c
e
r
ror
k
error
k
(12
)
(2
)
(
)
x
c
e
rro
r
k
(13
)
(3
)
(
)
2
(
1
)
(
2)
x
c
e
r
r
o
rk
e
r
r
o
rk
e
r
r
o
rk
(14
)
Control algo
ri
thm is given as:
()
(
1
)
(
)
uk
uk
uk
(15
)
(
)
((
)(
1
)
)
(
)
((
)
2
(
1
)
(
2
)
)
pi
d
u
k
k
e
rro
r
k
er
ro
r
k
k
e
rro
r
k
k
e
rro
r
k
er
ro
r
k
erro
r
k
(16
)
Whe
r
e
,,
pi
d
kk
k
areth
e
prop
ortio
n
, integral a
nd di
fferential parameters
res
p
ec
tively.
The tuning in
dex of neural
netwo
rk i
s
sel
e
cted a
s
:
2
1
()
()
2
Ek
e
r
r
o
r
k
(17
)
The gradie
n
t desce
nt method is u
s
ed for adjustme
n
t of
,,
pi
d
kk
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 13, No. 2, Februa
ry 2015 : 287 – 291
290
()
(
1
)
p
pp
EE
y
u
y
k
e
rror
k
x
c
ky
u
k
u
(18
)
()
(
2
)
i
ii
EE
y
u
y
k
e
rror
k
x
c
ky
u
k
u
(19
)
()
(
3
)
d
dd
EE
y
u
y
k
e
rror
k
x
c
ky
u
k
u
(20
)
The
y
u
can be o
b
tained by th
e identificatio
n of neural n
e
t
work.
4. Simulation
In this
se
ctio
n, usi
ng th
e
PID
control
prin
cipl
e b
a
s
ed
on
RBF
neural n
e
two
r
km
akes
simulationfor DC motor i
n
MATLAB. Parameters
of the sy
ste
m
for
simula
tion are:KP=0.3,
KD=
0
.3, KI=
0
.1,the trans
fer func
tion of t
he DC motor
is
:
2
103
()
15
Gs
ss
(21
)
Whe
r
e the
sampling time
is 2m
s, the i
nput
si
gnal i
s
step
sign
al, netwo
rk
hidd
en layer
neuron
s num
ber is m = 6
.
The Figure 3 sho
w
s the
squ
a
re
wave
resp
on
se cu
rve without the
adaptive
setti
ng PID control st
rategy
b
a
se
d
on
RBF
neural net
work. Th
e Figure 4 sh
ows
the
squ
a
re
wave
re
spo
n
se curve
with the
adaptiv
e set
t
ing
PID con
t
rol
st
rategy based
o
n
RBF
neural n
e
two
r
k. T
he Fi
gure 5, Fig
u
re
6 and
Fi
gu
re
7 reflect th
e process of
PID pa
ram
e
ter
adju
s
tment. F
r
om th
e
simul
a
tion
curve
we can
se
e tha
t
the adj
uste
d
onlin
e PID
controlle
r
ba
se
d
on the
RBF
neural n
e
two
r
k
ha
s g
ood
control effe
ct, and the
co
ntrol effe
ct compa
r
ing
si
mple
PIDis greatly improved. T
h
is sho
w
s th
at aim at
the controlled o
b
ject which h
a
s no
nline
a
r
and
time-varying
para
m
eter, th
e algorith
m
h
a
s
tra
c
e abilit
y and anti-int
e
rferen
ce abil
i
ty.
Figure 3. The
step sig
nal without the ada
ptive
settingPID ba
sed o
n
RBF
NN
Figure 4. The
step sig
nal with the adapti
v
e
setting PID b
a
se
d on RBF
NN
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Study on Ada
p
tive PID Co
ntrol Algorith
m
Based on RBF Ne
ural
Network (Qi
Xuem
ei)
291
Figure 5. The
adaptive sett
ing cu
rve of ki
Figure 6. The
adaptive sett
ing cu
rve of kp
Figure 7. The
adaptive sett
ing cu
rve of kd
5. Conclusio
n
In this pa
per,
based on
RBF neural ne
twork
ad
aptive PID co
ntrol
strategyi
s
p
r
opo
sed
for the DC
motor. The
result
s sho
w
that the
pro
p
o
se
d controll
er is
pra
c
tical and effe
ctive,
becau
se of th
e adapta
b
ility, strong
rob
u
s
tne
ss
and
sa
tisfacto
ry co
ntrol pe
rform
ance. RBFNe
u
ral
netwo
rk
ada
p
t
ive PID controller a
c
hi
eve
d
goo
d co
ntro
l effec
t. It is
als
o
revealed from s
i
mulation
results that t
he p
r
op
osed
co
ntrol
algo
rithm i
s
vali
d for DC m
o
tor
and
al
so p
r
ovide
s
t
he
theoreti
c
al an
d experim
ent
al basi
s
, and
the cont
rolle
r is a kin
d
of practical engi
ne
ering.
Referen
ces
[1]
Li Li
xi
an
g, Peng Hai
p
e
ng, W
ang Xia
ngd
o
ng.
PID para
m
etertuni
ng b
a
sed o
n
cha
o
tic ant s
w
a
r
m
.
Chin
ese Jo
urn
a
l ofScie
ntific Instrument
. 20
0
6
; 27(9): 11
04-
110
6.
[2]
KH Ang, G C
hon
g, Y Li. PID Contro
l S
y
s
t
em Anal
ys
is, Desig
n
a
nd T
e
chn
o
lo
g
y
.
IEEE Trans. on
Contro
l SystemT
e
ch
no
logy
.
200
5; 13(4): 55
9-57
6.
[3]
Li Yu
yi
ng, W
e
n Qiao
ya
n, L
i
Li
xia
ng, P
eng
Haip
en
g, Z
hu
Hui. Improv
ed
c
haotic
ant s
w
arm al
gorithm
.
Chin
ese Jo
urn
a
l of Sc
ientific I
n
strument.
20
0
9
; 30(4): 73
3-7
37.
[4]
Z
H
I Hui-qi
an
g, YANG Z
eng-j
u
n, T
I
AN Lian
g. AComp
a
rative
Stud
y on BP
N
e
t
w
o
r
k a
nd RB
F
Net
w
o
r
k
i
n
F
unction Ap
pro
x
im
atio
n.
Bullet
i
n of Scienc
e a
ndT
ech
nol
ogy.
2005; 2
1
(2):19
3-19
6.
[5]
Xi
a H
o
n
g
. A fa
st identific
atio
n
alg
o
rithm for
bo
x-co
xtra
nsfo
rmation bas
ed radi
al basis
f
u
nction ne
ural
net
w
o
rk.
IEEE Transactions on Neur
al Networks
. 2006; 1
7
(
4
): 1064-
10
69
[6]
ZHAN Li, SUN
Peng, CHEN
W
en-ba
i. Contr
o
l of
S
w
in
gUp
and Stab
iliz
ati
on of an Invert
ed Pen
d
u
l
um
Sy
s
t
e
m
.
Co
mp
uter Simul
a
tion
. 2006; 23(
8): 289-2
9
2
[7]
CONG Shu
a
n
g
, Z
H
ANG D
o
ng-j
un, W
E
I H
eng-
hua.C
o
mp
arative
Stud
y
on T
h
ree
Co
ntrol M
e
thods
of
theSin
gle Inv
e
r
t
ed-Pen
d
u
l
um
S
y
stem.
Syste
m
sEn
g
i
neer
in
g
and Electro
n
ic
s
. 2001; 23(
11)
: 47
－
49
[8]
Z
hang J
i
n
gdo
n
g
, W
en Gua
ng,
W
e
i Yon
g
q
i
ao
, Yin Guofu. R
B
F
Neura
l
Net
w
o
r
k PID for Bi
latera
l Ser
v
o
Contro
lS
ystem
.
TEL
K
OMNIK
A
. 2013; 11(
9): 5200-
52
09
[9]
Liu J
i
nk
un. MA
T
L
AB Simulati
on
w
i
t
h
Adv
a
n
c
ed PID
C
ontr
o
l. Pu
blis
hin
g
Hous
e of El
ect
r
onics In
dustr
y,
Beiji
ng. 20
11.
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