TELKOM
NIKA
, Vol. 11, No. 5, May 2013, pp. 2619 ~
2625
ISSN: 2302-4
046
2619
Re
cei
v
ed
Jan
uary 15, 201
3
;
Revi
sed Ma
rch 1
3
, 2013;
Acce
pted Ma
rch 2
3
, 2013
The Self-Adaptive Fuzzy PID Controller in Actuator
Simulated Loading System
Chua
nhui Zh
ang, Xiaodo
ng Song*
Beiji
ng Institute
of
T
e
chnolo
g
y
Room
224, Bui
l
d
in
g Qiushi, Be
ijin
g Institute of
T
e
c
hnol
og
y, N
o
. 5 Yard, Zhong
Guan C
un
South Street
Haid
ia
n District
,
Beijin
g, 010
6
891
52
42
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: zchnin
g
@1
2
6
.com
A
b
st
r
a
ct
This
paper
analy
z
es
the str
u
ct
ure pr
inciple
of th
e act
uat
or s
i
mulated
loading syst
em
wit
h
variabl
e
sti
ffn
ess, and
e
s
tab
l
i
s
he
s the simp
li
fie
d
mode
l
.
W
h
a
t
’
s
mor
e
,
it al
so
d
oes
a
r
e
se
arc
h
on
the ap
p
lic
ati
o
n
of
the se
lf-a
d
apt
i
v
e tun
i
n
g
of fu
zz
y
PI
D (Pro
p
o
rti
on Int
egr
ati
on D
i
ffer
ent
iat
i
on) i
n
act
uat
or
simul
a
t
ed l
o
a
d
i
n
g
system
wit
h
v
a
riable stiffnes
s. Be
c
aus
e t
h
e loading syst
em
is connect
ed wit
h
the st
eer
ing sy
stem
by
a
spri
n
g
ro
d, ther
e must b
e
stro
ng c
o
u
p
l
i
n
g
. B
e
si
de
s,
ther
e a
r
e al
so th
e p
a
r
a
metr
ic var
i
atio
ns acc
o
mpa
n
yi
n
g
w
i
th the
var
i
at
i
ons
of th
e stiffn
ess. B
a
se
d o
n
co
mp
e
n
sat
i
o
n
f
r
o
m
th
e fe
ed-f
o
rw
ard c
ontr
o
l
o
n
th
e d
i
stur
ba
n
c
e
brought by the
motion of st
eer
ing eng
ine, the system
perfor
manc
e can be
improved by using fu
zz
y
adaptive
adjust
ing PID c
ontr
o
l t
o
m
a
ke
up t
he changes of system
par
a
m
e
t
e
r caused by the changes
of the
stiffness.
By co
mbi
n
i
ng t
he fu
zz
y
co
ntro
l w
i
th trad
iti
o
n
a
l
PID co
nt
ro
l, fu
zz
y
a
d
apti
v
e
PID co
ntro
l is
ab
le to c
h
o
o
s
e
the
par
a
m
eters mo
re
pr
op
er
ly.
Key wo
rd
s
:
va
riabl
e stiffness loa
d
in
g, ada
pti
v
e control
l
er, fuzz
y
PID
Copy
right
©
2013 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
Steering load simulator is
a loading device whic
h is u
s
ed to provide external resistance
on the aircra
ft in
flight simulation when flying
[1].
Compare
d
wi
th early mechanical loadi
n
g
system which
provides sim
p
le linear roa
d
, electr
o-hydraulic loading
system supp
ly various ways
to load, but
electro-hydra
u
lic loading a
l
so has
man
y
shortcomin
gs [2]. For example, hydr
aulic
source volume, power
consum
ption and large
noise, low e
nergy efficiency, oil leakage,
malfunction,
besides, there is also redu
ndant force
because of its
structure
characteristics, which
seriou
sly influ
ence the loa
d
ing preci
s
ion and
system bandwidth. And now, th
e popular ele
c
tric
loading system is based on the mo
tor
servo system as the act
uators which
take use of the
constant torq
ue output of
the Torque M
o
tor to fini
sh the loading task. Compa
r
e
d
with the ele
c
tro
-
hydraulic system in workin
g band and actuator rang,
electric loadin
g
system has the
following
5
major advantages: 1) the small signal with a st
ronger
tacking ability and higher lo
ading resoluti
on
is pretty suita
b
le for work with small loa
d
; 2)
the system characteri
stics is stable
and influenced
little by
the environment; 3
)
the rotary motion of
the lo
ading system is suitable for torque loading;
4) the small v
o
lume is
con
v
enient for maintenanc
e; 5
)
low n
o
ise a
nd environme
ntal friendly [3].
Therefore, the electric loading system is
wi
dely used by the
researchers in the fie
l
d.
Both the
electro-hydraulic loading system
and electric loading system have the
problem
of redundant
force. Redun
dant force is
cause
d
by
the motion of the steering e
ngine, and it will
influence the precisio
n of the system. What’s mo
re, it
makes the sy
stem
frequen
cy width narrow
and destroys
the stability
[4
]. Therefore, how to dec
re
ase the redu
n
dant force is the key to desi
g
n
load simulator and improve the performance of the system
, and it is also the difficult point.
In
this
paper, under the control of the servo mechanism,
according to the calcula
t
ion of the H
o
st
computer, the system can
output
corre
sponding
stiffness an
d loa
d
the steering engine with the
variable stiffn
ess. In order to further improv
e the
system performance, on the basis of the
variable stiffness, the paper introduces
the fuzzy adaptive
PID control.
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2619 – 262
5
2620
2. Rese
arch
Metho
d
2.1. Structu
r
e Principle of Sy
stem
The loading system with
variable stiffn
ess is
co
nsisted of stiffn
e
ss se
rvo system and
torque servo system, and its basic st
ru
cture can be se
en in Figure1.
U(s
)
Figure 1. Basic struct
ure of loading system
After receivin
g the command of position
from th
e
processor, AC servo motor runs to the
appointed po
sition which
is correspo
n
d
ing to the
specified value of stiffne
ss of the elastic
material. And
the stiffness value of
the elasti
c material has been sta
ndardize
d before the system
running. According to the instruction of torque,
stiffness related
and torque sensor sig
nal, th
e
signal genera
t
ed by
the processor controls torque
motor, and the
n
, the steerin
g gear is loaded
with the help
of the coupl
ing shaft.
In
addition,
this
system can also be used as a const
ant
stiffness loading system for steer
ing gea
r. In this paper, the author does some research on t
he
torque servo system and analyzes
some
characteri
stics of it.
2.2. The Mod
e
l of Torque
Serv
o
Sy
stem
The torque servo system consists of torque mo
tor, ste
e
ring gear an
d the coupling part between
them, both
of
which are the
main factors
in build
ing the
model of
the
system. And
the simplified
model of the
system is shown in Figure 1.
1
Ls
R
1
J
sB
t
K
()
Us
()
e
Ts
()
s
()
l
Ts
()
I
s
e
K
Figure 2. Bloc
k of Transfer Function
In Figure 2,
you can see the block of tor
que motor transfer function, thus we can
get
mathematical model of
the
motor which is shown belo
w
.
t
2
et
KU
s
-
L
s
+
R
T
(
s
)
Ws
=
J
L
s
+
J
R+
B
L
s
+
(
B
R+
K
K
)
. (1)
Among them,
is the speed of motor, U is
input voltage of motor,
t
K
is
to
rque c
oeffic
i
ent
,
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TELKOM
NIKA
ISSN:
2302-4
046
The Self-Ada
ptive Fu
zzy P
I
D Cont
rolle
r in Ac
tuator Si
m
u
lated Load
ing … (Chua
nhui Zha
n
g
)
2621
e
K
is electrom
otive force coefficient of
counter
, L is armature in
ductance,
R is armature
resistan
ce, T
is output torq
ue of motor, J is
moment of inertia,
B is d
a
mping coefficient.
The balance equation of lo
ading motor and steering torque [5]:
()
d
d
TJ
K
dt
(2)
Combine Eq.1 and Eq.2, we can know the transfer function of
the system:
22
tm
m
e
t
d
32
mm
e
t
K
K
+
J
s
U
s
-
K
[
J
L
s
+
J
R+
B
L
s
+
(
B
R+
K
K
)
]
s
q
(
s
)
Ts
=
J
+
J
L
s
+
J
+
J
R
+
BL
s
+
BR
+
K
L
+
K
K
s
+
K
R
(3)
Among them,
d
is the angular displacem
ent of steering gear,
is an
gle of motor,
K is
the output stiffness of elastic material.
From the equation above,
we c
an see that the part w
i
th
d
(
s
)
is the disturbance caused
by the movement of the steering g
e
a
r. Howe
ver, the movement of steering gear can
be
measure
d
by other device, so we can
eliminate
this
kind of disturbance by usi
ng feed-forward
control [6]-[9], and the basic principle is shown in Figu
re 3.
Figure 3. Forward Feedba
ck
Among them,
can just offset the part
with
in syste
m
function, a
nd we
can get the final system tr
ansfer
function shown in Eq.4 below.
2
t
32
mm
e
t
KK
+
J
s
U
s
Ts
=
J
+
J
L
s
+
J
+
J
R
+B
L
s
+
B
R
+
K
L
+K
K
s
+K
R
(4)
2.3. Self-Ad
a
ptiv
e Tuning
of Fuzz
y
PID Con
t
roller
In self-adaptive fuzzy PID controller, error e
a
nd e
rro
r cha
nge e
c
sever as in
put
factors.
According
to the rules of fuzzy control, th
e contro
ller
can revise its
parameters of PID in time [10]
[11]. As a r
e
sult, it can meet requirements of
parameters of
PID in
different time,
thus
accompli
shin
g the self-adaptive cont
rol.
And the structure of the c
ontroller is shown in Figure 4.
In this pape
r,
the self-adapt
ive fuzzy PID
cont
roller i
s
a
pplied in the t
o
rque
servo
system,
so we should
consider the
function of the tw
o parameters and the relationship between them in
different time
. And the se
lf-adapt
ive fu
zzy control i
s
ba
sed o
n
the current
PID control.
By
calculating the curr
ent system error e a
nd e
rror
chan
ge ec, and then reaso
n
ing
with the fuzzy
rules, the controller get its
pr
oper param
eter in the
fuzzy matr
ix built before the ru
nning.
According
to the pra
c
tica
l experience,
the param
e
t
ers includin
g
、
、
, in
different cases of e and ec
should be adjust to
the principle below:
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02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2619 – 262
5
2622
a)
When
e is a
big value, in orde
r to
s
peed up
the
response
of
the system
and prevent
differential overflow cau
s
e
d
by the incre
a
se of e in th
e beginning,
should be
a b
i
gger one
while
should
be a
small value. At the same time, because
the sy
stem oversho
o
t might
increa
se be
cause
of the strong action
of the in
tegra
l
, we should l
i
mit the integral action
by
taking a smaller value of
;
b)
When e is a
medium value, in order to r
educe the ov
ershoot of t
he system to guarantee the
speed of
resp
onse,
should
be reduce
d
properly while the value of
and
should
b
e
moderate one
s;
c)
When e is a
small value, in order to re
duce steady-state error,
and
should
be of
bigger values. In
order to avoid the oscillation
of ou
tput in
the set
value and increa
se the anti-
jamming ability,
should be
a small one when |ec| is in
a bigger value.
PID
Controller
Fuzzy
Reaso
n
ing
G(s)
dt
de
e
d
y
p
k
i
k
d
k
Figure 4. Self-Adaptive Fuzzy PID Contr
o
ller
The input variable e and e
c
are
divided into se
ven fuzzy sub
s
ets, i
n
cluding Posi
tive Big
(PB), Positive Medium (PM), Po
sitive
Small (PS), Zero (Z),
Negative Small (NS), Negative
Medium (NM), Negative
Big (NB).
According to the rules above, we can get
fuzzy control
table below in Table1,2,3.
Table 1. Fuzzy Rules of
NB NM
NS
Z
PS
PM
PB
NB
NM
NS
Z
PS
PM
PB
PB
PB
PM
PM
PS
PS
Z
PB
PB
PM
PM
PS
Z
Z
PM
PM
PM
PS
Z
NS
NM
PM
PS
PS
Z
NS
NM
NM
PS
PS
Z
NS
NS
NM
NM
Z
Z
NS
NM
NM
NM
NB
Z
NS
NS
NM
NM
NB
NB
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The Self-Ada
ptive Fu
zzy P
I
D Cont
rolle
r in Ac
tuator Si
m
u
lated Load
ing … (Chua
nhui Zha
n
g
)
2623
Table 2. Fuzzy Rules of
NB NM
NS
Z
PS
PM
PB
NB
NM
NS
Z
PS
PM
PB
NB
NB
NB
NM
NM
Z
Z
NB
NB
NM
NM
NS
Z
Z
NM
NM
NS
NS
Z
PS
PS
NM
NS
NS
Z
PS
PS
PM
NS
NS
Z
PS
PS
PM
PM
Z
Z
PS
PM
PM
PB
PB
Z
Z
PS
PM
PB
PB
PB
Table 3. Fuzzy Rules of
NB NM
NS
Z
PS
PM
PB
NB
NM
NS
Z
PS
PM
PB
PS
PS
Z
Z
Z
PB
PB
NS
NS
NS
NS
Z
NS
PM
NB
NB
NM
NS
Z
PS
PM
NB
NM
NM
NS
Z
PS
PM
NB
NM
NS
NS
Z
PS
PS
NM
NS
NS
NS
Z
PS
PS
PS
Z
Z
Z
Z
PB
PB
A
ccording
t
o
t
he f
u
zzy
sub
s
et
{e,
ec},
w
e
can get PID param
eters correspo
nde
d
in the
tables. And c
o
mbine with the function b
e
low,
we can get the specific PID parameters.
p0
i0
p
p
i
d
i
d0
d
k=
k
+
k
k=
k
+
k
k=
k
+
k
Among them,
，
，
are the initial designed value which can be got with the
help of experience.
、
、
are PID parameters that you c
an get from
th
e tables.
3. Results a
nd Analy
s
is
In this paper, the basic p
a
rameters in
t
he simulation ca
n be
seen in Ta
ble
4. And
generalizatio
n performance standards a
r
e all unit matrix.
Table 4. The
basic param
e
t
ers
R/
Ω
L/mH
/V/rpm
J/Kg
/ Kg
/Nm/A
B/Nm/rpm
6.60 45.3
0.208
4.134*
9.92*
1.72 0
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ISSN: 23
02-4
046
TELKOM
NIKA
Vol. 11, No
. 5, May 2013 : 2619 – 262
5
2624
In order to ref
l
ect the advantages of
self-adaptiv
e fuzzy PID contro
ller, in the sim
u
lation, I
compare
the
output of fuzzy PID c
ontroller with comm
on PID contro
ller. In additio
n
, I also choo
se
a different inp
u
t signal, including step si
gnal and sine
signal, and different stiffne
ss values in the
experiments of simulation.
Experiment 1
:
with a fixed
stiffness value, we
explore the output
of different c
ontrollers
while the input signals are all step signals.
And the
result can be seen in Figure 5.
Figure 5. The output o
f
different controllers
while the input signals are all step signals
Results of Experiment 1: in Figure 5, we c
an
see th
at with a fixe
d stiffness, when the
step signal i
nputs, the overshoot
of the fuzzy PID controller
ha
s decrea
s
ed,
and the system
dynamic performance ha
s been improved.
Experiment 2: in the stiffn
ess value with
2 rad/s fre
quency variation, we expl
ore the
output of
the two controllers wi
th the same step signal. And the results of simulation can be se
en
in Figure 6.
Figure 6. The output o
f
the
two cont
rollers with the same step signal
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
The Self-Ada
ptive Fu
zzy P
I
D Cont
rolle
r in Ac
tuator Si
m
u
lated Load
ing … (Chua
nhui Zha
n
g
)
2625
Results of Experiment 2: in Figure 6, we
c
an see that when
stiff
ness cha
nges, fu
zzy PID
controller can
improve the
performance of the
system, but the impr
ovement is n
o
t obvious.
4. Conclusio
n
This pape
r st
udies the self
-adaptive fuzzy PID
contro
ller in the servo loading system of
variable stiffn
ess. As to the chara
c
terist
ics of va
riable stiffness, th
e feed-forward control help
s
to
eliminate the system interference
cau
s
e
d
by the movement of the
steering gea
r. And in the basis
of traditional PID, the author de
si
gned
fuzzy
control rules, introduci
n
g the self-ad
aptive fuzzy PID.
The re
sults o
f
simulation show that the
self-
adaptive fuzzy PID co
ntrolle
r impro
v
es the tracking
performance of the
loading system,
and it can also work in the c
ondition of
variable stiffness.
Referen
ces
[1]
Mingl
i F
u
, Go
ng
xi
a Z
h
a
ng.
Multich
ann
el s
t
eerin
g g
ear
motor serv
o l
oad
ing
d
e
vice
desi
g
n
a
n
d
realiz
atio
n of t
he me
asur
em
ent an
d co
ntro
l s
y
stem.
Mec
han
ical
an
d El
ectrical E
ngi
ne
erin
g
. 200
9;
38(1) (In Ch
ine
s
e).
[2] Yun;on
g
Ch
en
g.
Air defens
e miss
ile a
u
top
i
l
o
t desig
n
. Beij
i
ng: Aerosp
ace
press; 199
3. (In Chi
nese)
[3]
Xi
ao P
an. Vari
abl
e stiffness steerin
g lo
ad s
i
mula
ti
on s
y
ste
m
, Beijin
g Insti
t
ute of T
e
chnolog
y. 2
010
,
master degr
ee
pap
er. (In Chin
ese).
[4]
Ming W
a
ng. T
he res
earch
of
Electric l
oad
i
ng sim
u
lati
on.
Harbi
n
Ind
u
stri
al U
n
ivers
i
t
y
;
200
4, doctor
degr
ee p
aper.
(In Chin
ese).
[5]
Che
ngg
on
g Li
, Gongtao Jin
,
Z
ongxi
a
Jia
o
. El
ectric loa
d
simulator e
x
cess mom
e
n
t
generati
n
g
mecha
n
ism an
d suppr
essio
n
.
Journal of Be
ijin
g Univ
ersity
of Aeronautic
s and Astrona
utics
. 2006
,
32(2): 20
42
208
. (In Chinese).
[6]
Yunh
ua
Li. Lo
a
d
simul
a
tor re
d
und
ant mome
n
t
suppress
i
on
method.
Mac
h
i
ne too
l
an
d hy
drau
lic
. 19
99;
(2): 2722
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