TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.5, May 2014, pp
. 3416 ~ 34
2
2
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i5.4914
3416
Re
cei
v
ed O
c
t
ober 2
4
, 201
3; Revi
se
d Decem
b
e
r
5, 2013; Accepte
d
De
cem
ber
24, 2013
Dynamic Characteristics for Leveling System o
f
Mobile
Elevatin
g Work Platforms
Xue-pe
ng Ca
o*
1,2
, Sheng-jie Jiao
1
, Lei
Cheng
2
, Jun Zhang
1
, Jin-ping Li
1
1
High
w
a
y
Mai
n
tenanc
e Equ
i
p
m
ent Natio
nal
Engi
neer
in
g La
borator
y, Ch
an
g’a
n
Univ
ersit
y
2
Construction
Machi
ner
y Co.,
Ltd. of XCM
G, Middl
e of Nan
e
r Hua
n
, Xi
’an,
Shann
xi
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: tiepen
g2
001
@ chd.ed
u.cn
A
b
st
r
a
ct
Focused on revealing variations
of dynam
ic char
acteristics of an auto-l
eveling system used in
mo
bil
e
el
evati
n
g w
o
rk platfor
m
s (MEW
P
) at large
hei
ght, a unifi
ed
mat
h
ematica
l
mod
e
l
co
mpos
ited o
f
a
series of sub-
m
o
dels was built for
the leveling system
s. A
n
effect on dy
namic char
acter
i
stics including
the
fast respons
e
and rel
a
tive
stability fro
m
varyin
g-par
a
m
eters w
a
s investigate
d
. Res
u
lts disp
laye
d
the
displ
a
ce
ment-a
ngl
e factor cha
ngi
ng w
i
th w
o
rk-cond
itions
te
nde
d to caus
e fluctuatio
ns
of the stabi
lity, w
h
il
e
enl
argi
ng the a
m
p
lifier g
a
in w
oul
d accel
e
rate
system
respo
n
se. Increasi
n
g
the area ratio
w
a
s conduciv
e
to
level
i
n
g
stabil
i
ty to be reinfor
c
ed, but lea
d
a diffe
rent res
pons
e spe
ed for forw
ard pro
c
ess or revers
e
level
i
n
g
, w
h
ich
w
a
s har
mful
to over
all
stab
il
ity. T
he
find
in
g
s
w
ould
provi
d
e esse
ntia
l the
o
ry gu
id
ance
for
the desi
gn a
n
d
man
u
facture
o
f
the leveli
ng s
ystem d
e
vices
of high a
l
titud
e
platfor
m
.
Ke
y
w
ords
:
autom
atic lev
e
ling system
, unified model,
varying-par
ameters anal
y
s
is, characteristics
variati
ons
Copy
right
©
2014 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
Having go
od
environme
n
t
al adaptabili
ties and hig
h
operating efficien
cie
s
, mobile
elevating work platform
s (MEWP)
with large
height a
nd big
workin
g spa
c
e
are
obtaine
d sp
e
c
ia
l
value by markets a
nd re
se
arche
r
s. The l
e
veling sy
ste
m
of platform is one of key
technolo
g
ie
s of
aerial
work
machi
n
e
r
ie
s, whi
c
h di
re
ctl
y
affects
the
perfo
rman
ce
s, su
ch a
s
saf
e
ty of operating
person
a
ls, o
peratin
g flexibility and ad
aptability to
environ
ment
[1-4]. The el
ectro
-
hyd
r
auli
c
controlled lev
e
ling sy
stem
with many strong poi
nt
s, such a
s
runnin
g
contin
uou
sl
y and smo
o
th
ly,
high control a
c
cura
cy and f
a
st re
spo
n
se spe
ed,
is ad
a
p
ted to a variety of MEWP
[5].
The typical compo
s
ition of
electro
-
hyd
r
aulic le
velin
g system is
sho
w
n in Figu
re 1, which
is a co
nsta
nt-value po
sitio
n
control syst
em. Prev
ious studie
s
focu
s on the mod
e
ling of ele
c
trical
and
hydra
u
lic syste
m
s with
out con
s
ide
r
i
ng im
pa
ct
s
of link me
ch
ani
sm
s for p
e
rfo
r
man
c
e
an
alysi
s
[6], while a unity model of entire hydro
m
ech
a
tro
n
ics system is propo
sed in thi
s
pap
er, and
we
analyze p
a
ra
meters-va
r
yin
g
imp
a
ct
s o
n
dynami
c
performan
ce
s
of leveling
sy
stem, which
wi
ll
provide a u
s
e
f
ul guidan
ce f
o
r actu
al leve
ling system d
e
sig
n
s.
2. Lev
e
ling
Mecha
n
ism and Modelin
g
2.1. Sy
stem
Composi
t
ion
and Lev
e
lin
g Mechanis
m
The leveling
system of M
E
WP is con
s
tituted of
elect
r
o-hydra
u
lic
prop
ortio
nal
valves 1,
balan
ce valv
es
2, asym
metric hydra
u
lic
cylinde
rs 4, four-lin
k tran
smi
ssi
o
n
me
cha
n
isms 5,
workin
g pl
atform
s 6, i
n
cli
nation
se
nso
r
s
7 a
nd
am
plifiers 8.sho
w
n
as Figu
re
1. The
level
i
ng
mech
ani
sm i
s
expressed
as: wh
en out
side inte
rf
ere
n
ce
s exe
r
ted
on the platform from b
o
o
ms
luffing and
bendi
ng
cause a
certain inclini
ng ang
le, the incli
nation
sensor feedbacks a
corre
s
p
ondin
g
an
gle
sig
n
a
l, whi
c
h
is
comp
ared
wi
th a
referent
input, a
nd
differential
si
gnal
magnified
by
amplifier dri
v
es the
pro
p
o
rtional
valve to p
r
odu
ce a
ce
rtain
displ
a
cement
. It
controls p
r
e
s
sure
oil into
the cylin
der
so th
at the
cylinder
ro
d h
a
s
a tele
sco
p
ic
amou
nt,
and
impels lin
kag
e
me
ch
anism
swingi
ng to
prod
uce a
di
spla
cem
ent o
u
tput op
po
site to th
e o
r
igi
nal
inclin
ation, which in
du
ce
s the platform to
resto
r
e a ho
rizontal
state.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Dynam
ic Ch
a
r
acte
ri
stics for Leveling S
y
stem
of Mobile Elevating
Wo
rk… (Xue
-peng
Cao
)
3417
Figure 1. Co
mpositio
ns of
Hydr
om
echa
tronics Leveli
ng System
2.2. Lev
e
ling Sy
stem Unified Modeling
Based o
n
the
leveling syst
em and auto
m
atic levelin
g comp
ositio
n as Figu
re
1 sho
w
n,
the leveling control blo
c
k diagram
is constructe
d a
s
Figu
re 2. In the next, e
a
ch
sub
-
mod
e
l is
built firstly, and then the uni
fi
ed modelin
g
will be integrated.
A
m
p
life
r
E
l
e
c
t
r
o
-
hydr
aul
i
c
Prop
or
t
i
o
n
a
l
V
a
l
v
e
C
y
l
i
nde
r
L
i
nka
ge
M
e
c
han
i
s
m
Wo
r
k
P
l
a
t
fo
rm
Ti
l
t
S
e
n
s
o
r
i
¦È
r
+
-
¦È
i
¦È
i
e
x
v
x
p
¦È
3
T
h
e
l
u
f
f
i
ng
and
B
e
ndi
ng o
f
B
o
o
m
s
Figure 2. Block
Diag
ram o
f
Auto-l
evelin
g Control System of MEWP
1
)
T
ilt s
e
ns
or
The tilt sensor wo
rks a
s
a prop
ortion
a
l
part, who
s
e
conversio
n
relation
shi
p
can be
expre
s
sed a
s
:
a
iK
(1)
Whe
r
e
i
,
,
a
K
resp
ectively deno
te feedba
ck
sign
al, tilt angle of platform, and pro
p
o
rtional
c
oeffic
i
ent.
2) Comparison amplifier
T
i
me
c
o
ns
ta
nt is
ver
y
sma
l
l (
t
τ
<1 m
s
), th
e am
plifier
can b
e
con
s
id
ered
a
s
a diff
eren
ce
with proportional fac
t
or [7].
()
ref
e
iK
i
i
(2)
Whe
r
e
e
K
is pro
portion
al fact
or of amplifier.
Combi
n
ing a
bove equ
atio
ns, the feed
back-
com
p
a
r
ed can be e
x
presse
d as
Lapla
c
e
function.
()
()
()
I
ae
Is
Ws
K
K
s
(3)
3) Elect
r
o-hydrauli
c
p
r
opo
rtional valve
From the
ref
e
ren
c
e [5], th
e relatio
n
ship
betwee
n
sp
ool-di
s
pl
ace
m
ent output
and inp
u
t
curre
n
t of the propo
rtion
a
l valve is conv
eyed as:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3416 – 34
22
3418
2
2
()
()
2
()
1
Vv
V
v
v
v
Xs
K
Ws
Is
s
s
(4)
Whe
r
e
v
,
v
are th
e hyd
r
auli
c
n
a
tural
freq
ue
ncy a
n
d
hydraulic dam
pin
g
ratio of
the
valve, and
v
K
is valve gain.
4) Asymmet
r
i
c
al hydrauli
c
cylinde
rs
cont
rolled by fou
r
-way valves
From literatu
r
es [8] an
d Figure 3, the tran
sfer fu
nction
com
p
rised of a
s
ymmetrical
hydrauli
c
cyli
nder a
nd fou
r
-way valve ca
n be den
oted
as:
2
22
32
22
2
2
2
2
1
1
(1
)
(
)
1
()
(
1
)
q
ce
t
VL
s
pe
c
e
p
p
pt
p
c
e
tt
t
c
e
t
c
e
ep
p
e
p
p
ep
p
K
KV
Xs
F
A
P
AT
K
AC
X
BV
B
K
m
V
m
K
KV
KK
ss
s
TA
C
A
C
T
A
C
A
C
TA
A
C
(5)
There i
s
no
elasti
c loa
d
;
mean
while
th
e viscou
s d
a
mping
co
efficient is ve
ry
small. So
output of pist
on displa
cem
ent and inp
u
t of spool movi
ng are give
n as:
2
2
()
/
()
2
()
(1
)
pq
p
h
h
V
h
h
Xs
K
A
Ws
Xs
s
ss
(6)
Whe
r
e
,
p
A
are
area ratio a
nd equivale
nt area,
12
=/
A
A
,
12
=(
)
/
2
p
AA
A
;
q
K
,
ce
K
are f
l
ow rat
e
gain an
d total flow rate
-p
ressu
r
e
coeffi
cient of the v
a
lve,
ce
c
t
p
KK
C
;
T
,
C
are
effective mo
dulu
s
varying
co
efficient
re
sulte
d
from
symm
e
t
ry cylin
d
e
rs and equival
e
nt
area
va
rying coeffici
ent
of
load flo
w
rat
e
,
2
2(
1
)
/
T
,
22
2(
1
)
/
(
1
)
C
;
e
,
t
V
are th
e effective b
u
lk mo
dulu
s
an
d
total volume
of the cylinder.
h
,
h
are hyd
r
aul
ic natu
r
al fre
quen
cy
an
d
hydrauli
c
d
a
m
ping
ratio,
2
=/
he
p
t
t
TA
C
m
V
，
//
2
hc
e
e
t
t
p
K
Tm
V
C
A
.
Figure 3. The
Schemati
c
Diagra
m
of
Asymmetri
c
al
Hydrauli
c
Cy
linders Controlled
by Four-way
Valves
Figure 4. The
Vector Chart
of Leveling
Mech
ani
sm
5
) Driving mechanism
s
Driving m
e
ch
anism
s
can
be expresse
d by tw
o cl
o
s
ed
polygon
s (Figu
r
e 4
)
, usin
g the
vector eq
uati
on and Eule
r'
s formul
a, wh
ich can be d
e
s
cribe
d
as:
11
0
0
11
0
0
cos
c
os
(
)
cos
sin
s
i
n
(
)
si
n
p
p
ll
L
x
ll
L
x
(7)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Dynam
ic Ch
a
r
acte
ri
stics for Leveling S
y
stem
of Mobile Elevating
Wo
rk… (Xue
-peng
Cao
)
3419
11
2
2
4
3
3
11
2
2
3
3
co
s
c
os
c
o
s
sin
s
in
sin
ll
l
l
ll
l
(8)
Whe
r
e
L
、
0
l
、
1
l
、
2
l
、
3
l
、
4
l
rep
r
e
s
ent length of
cylinde
r, ra
ck 0, p
endul
um rod 1, li
nk 2,
rocke
r
3, fixed hinge p
o
int
s
of the boo
m 4, respe
c
tively.
,
i
(
i
=
0
,1,
...,4) are angle between
each com
pon
ent and X-axi
s
po
sitive.
Solving abov
e equ
ation,
we
coul
d a
c
quire
expression
s am
ong
output di
spl
a
cem
ent,
rocke
r
di
spla
ceme
nt and i
nput straight-l
ine displa
cem
ent.
22
2
2
2
2
1
22
22
2
3
()
(
)
arcs
i
n
2t
a
n
bc
b
c
a
b
c
a
ab
AA
B
C
ar
c
BC
(9)
Whe
r
e
2
22
01
0
0
1
0
0
1
2c
o
s
,
2
s
i
n
,
p
al
l
b
l
l
c
L
X
l
l
,
13
1
3
1
1
4
2s
i
n
,
2
(
c
o
s
)
,
A
ll
B
l
l
l
22
2
21
4
1
4
1
2c
o
s
Cl
l
l
l
l
.
Since
0
relie
s on given lo
cation of hi
n
ge point
s an
d kee
p
s
a consta
nt. Therefore,
movement
regula
r
ities e
x
presse
d by
(9) bet
wee
n
3
and
p
x
are
indicated
a
s
a
co
mple
x
trigono
metri
c
relatio
n
ship.
In othe
r
wo
rds,
strong
nonlin
earitie
s are
di
splay
ed b
e
twe
en
the
output an
d the input. To
facilitate the
modelin
g
an
alysis, releva
nt para
m
eters are sub
s
tituted
into (9), an
d the both movi
ng relatio
n
shi
p
is sh
own Table 1.
Table 1. The
Moving Rel
a
tionship bet
we
en Cylind
e
r P
i
ston an
d Wo
rk Platform
Variable Value
Piston displacem
ent
p
x
/mm
0
66.6
128.2
197.5
280
372.
6
464.5
Platform displacement
3
/°
0
30
60 90 120
150
180
Usi
ng third
-
o
r
der polyn
omi
a
l fitting method to analyze
above data, we can obtai
n:
32
30
0
0
0
pp
p
ax
b
x
c
x
d
(10)
Whe
r
e
74
00
0
0
1
1
0
,
3
1
0
,
0
.
5
126
,
0
.
9
606
ab
c
d
.
Due to the value of
0
a
and
0
b
is far less than
0
c
, which illustrates t
he higher order part
s
are m
u
ch smaller
com
p
ared
with t
he first o
r
d
e
r for im
pa
ct on di
spla
ceme
nt tran
sfer
perfo
rman
ce,
so linea
r fitting method
ca
n be used.
3
lp
K
xm
(11)
Doin
g Lapla
c
e transf
o
rm,
a transmitting
functi
on for d
r
iving me
cha
n
ism
s
is give
n as:
3
()
()
()
ll
p
s
Ws
K
Xs
(12)
From (3), (4),
(6) and (12
)
,
the
unified
o
pen-l
oop t
r
an
sfer fun
c
tion
of leveling sy
stem i
s
built as:
3
22
22
()
()
22
()
(1
)
(
1
)
vh
vh
vh
s
K
Ws
ss
s
ss
s
(13)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3416 – 34
22
3420
Whe
r
e K is o
pen-l
oop g
a
in
,
/
ae
l
v
q
p
KK
K
K
K
K
A
The co
rrespo
nding
clo
s
ed
-loop tran
sfe
r
functio
n
ca
n b
e
written a
s
:
22
22
()
()
22
1(
)
(1
)
(
1
)
vh
vh
vh
Ws
K
Gs
Ws
ss
s
ss
K
(14)
3. D
y
namic
Char
acteristi
cs Analy
s
is
More
attentio
n is fo
cu
se
d t
o
investig
ate
par
a
m
eters
a
ffecting o
n
dy
namic characteristics
of leveling
system,
su
ch
a
s
fou
r-li
n
kag
e
me
ch
ani
sm
s,
a
s
ymmetri
c
al cylind
e
rs and amplifie
rs.
Based
on th
e
open
-lo
op transfe
r fun
c
tio
n
and
cl
as
si
c co
ntrol th
eory, these va
rying-p
a
ramete
rs
are analyzed as foll
ow.
The am
plifier gai
n
value depends
on sy
stem
stabilities,
other
para
m
eters a
r
e sh
own as
Table 2.
Table 2. Basi
c Para
meters of Leveling System
Components
Parameters
S
y
mbols
V
alues
Unit
Tilt sensor
Sensor coef.
a
K
-3
0.
8
1
0
[A/°]
A
mplifie
r
Prop.
coef.
e
K
283 -
Proportional
valve
Valve gain
v
K
4
51
0
[
m/
s
A
]
Natural fre
quenc
y
v
69 [rad/s]
Damping ratio
v
0.7 -
Flow rate g
a
in
q
K
2.4 [m
2
/s]
Fl
ow rate
-pres
s
u
re c
oef.
c
K
12
4.
0
1
0
[
5
m/
N
s
]
Four
-
w
a
y
valve
and c
y
linder
Total equivalent mass
m
t
800 [Kg]
Effective bulk mo
dulus
e
9
1.0
1
0
[Pa]
Big chamber are
a
A
1
3
5.0
1
0
[m
2
]
Small chamber area
A
2
3
2.
7
1
0
[m
2]
Internal leak-coef
.
C
ip
13
5.0
1
0
[
5
m/
N
s
]
External leak-co
e
f.
C
ep
0
[
5
m/
N
s
]
T
o
tal volume
V
t
3
2.
3
1
0
[m
3
]
Four
-link mechanism
Displacement-angle coeff.
l
K
2
3.9
1
0
[°/m]
1) The di
spl
a
ceme
nt-a
ngle
coefficie
n
t of four-lin
k me
chani
sm varie
s
Keeping th
e
gain
K
e
un
ch
ange
d an
d changi
ng the
displ
a
cement
-angl
e
coefficient
K
l
from 1
00 to
390, dyn
a
mic re
spo
n
se
cu
rves are
sh
o
w
n
as Figu
re
5. When
it b
e
com
e
s g
r
ea
ter,
system re
spo
n
se gets
fast
er,
but
ove
r
shoot is in
cre
a
s
ing.
Due
to
K
l
varies with
wo
rk
co
nditi
ons,
whe
n
empl
o
y
ing a con
s
tant amplifie
r gai
n,
whi
c
h ea
sily ca
use
s
dyn
a
mi
c pe
rforman
c
e
s
fluctuating. A
l
though
usin
g four-ba
r
lin
kag
e
s
co
uld
expand
angu
lar di
spla
cem
ent for leveli
ng
output, variation ran
g
e
s
of this coeffici
ent shoul
d b
e
con
s
trai
ne
d within pe
rmissi
ble area
to
ensure system
stability.
2)
The a
r
ea
ratio of asym
metric
cylinde
r varie
s
Keeping
big
cham
be
r a
r
e
a
A
1
un
ch
an
ged, the
are
a
ratio
coeffi
ci
ent
is taken
as
1,
1.85,3,
and
d
y
namic re
spo
n
se cu
rves a
r
e
sho
w
n
a
s
Figure 6. La
rger a
r
e
a
rati
o co
uld ind
u
c
e
smalle
r overshoot and bett
e
r stability.
Consi
deri
ng a
c
tual states, t
he large
r
inevitably leads to
a
thicker
cylin
der rod, whi
c
h can
stre
ngthen
rod
stability and
make the f
o
rce tran
smi
tting
smoothly, bu
t will brin
g
about the
ro
d with
q
u
ite
different sp
eed b
e
twe
e
n
outstret
c
h
and
retra
c
ting,
wh
ich
woul
d cre
a
te the platfo
rm havin
g a
distin
ct re
spo
n
se
sp
eed
at forwa
r
d l
e
veling
or reve
rse proce
s
s and n
o
t allow for overall sta
b
ili
ty of le
veling system. The
r
efore, sele
ct
ing
area
ratio
ne
eds to
con
s
id
er the
both i
m
pact
s
to
get
better
perfo
rmances un
de
r the
entire
work
p
r
oc
es
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Dynam
ic Ch
a
r
acte
ri
stics for Leveling S
y
stem
of Mobile Elevating
Wo
rk… (Xue
-peng
Cao
)
3421
3) Amplifier gain varies
Whe
n
the
ga
in
K
e
se
parately is 1
00,28
3 and
40
0, d
y
namic ch
ara
c
t
e
ri
st
ic
s cu
r
v
es
a
r
e
sho
w
n a
s
Fig
u
re 7. Th
e more am
plifier
gain in
cr
e
a
se
s, the faster l
e
veling sy
ste
m
respon
ds,
but
the oversho
o
t
gets la
rge
r
and a
r
ou
se
s
greate
r
o
s
c
ill
ation. At the expre
ssi
on of
open
-loo
p g
a
in
/
ae
l
v
q
p
K
KK
K
K
K
A
,sen
sor coeffi
cient
K
a
and valve coefficie
n
t
K
v
are not
cha
ngin
g
with
working
conditions, while flow gain coeffici
ent
K
q
and displa
cement-angl
e coeffici
ent
K
l
are varyin
g with
spo
o
l ope
nin
g
and o
u
tput
angula
r
di
sp
lacem
ent, re
spectively. In orde
r to mai
n
tain the con
t
rol
cha
r
a
c
teri
stics invaria
b
le, the gain
K
e
sho
u
ld vary synchro
nou
sl
y
with the both param
ete
r
s.
Considering t
he feasibility and e
ffectiv
eness of act
ual operat
ions,
sectional gain adjustm
ent
coul
d be ad
opted with
condition
s cha
nging, wh
ich
has adva
n
tage
s for better pe
rform
a
n
c
e
s
within varying-parameters
.
Figure 7. The
Curve
s
und
e
r
Differe
nt Amplifier Gai
n
s
4. Conclusio
n
A unified mo
del was
built
for the hyd
r
omec
hatroni
cs levelin
g sy
stem of ME
WP, and
sev
e
r
a
l v
a
riat
ions
of
dy
n
a
m
ic
cha
r
a
c
t
e
r
i
st
ic
s
wa
s
revealed
a
s
follo
ws,
whi
c
h
will
provid
e a
u
s
eful
guida
nce for actual levelin
g system d
e
si
gns.
(1) T
he di
spl
a
cem
ent-angl
e co
efficient
of f
our-lin
k m
e
ch
ani
sm be
come
s g
r
eate
r
, syste
m
respon
se
get
s faste
r
, but
overshoot
wo
uld be m
o
re
obviou
s
. For the leveling
system
with
a
con
s
tant amp
lifier gain, the
coefficie
n
t easily ca
us
es
dynamic p
e
rf
orma
nces flu
c
tuating, so this
cha
nge
sho
u
l
d
be co
nstrai
ned withi
n
pe
rmissibl
e ran
ges.
(2) An in
crem
ent of the are
a
ratio of asy
mmetric
cylin
der a
r
ea ratio
can indu
ce
smaller
overshoot an
d better sta
b
ility, but
overlarge valu
e
will make th
e platform h
a
ve a com
p
l
e
tel
y
different
re
sp
onse
spe
ed
at forward le
veling o
r
rev
e
rse p
r
o
c
e
ss, whi
c
h i
s
n
o
t co
ndu
cive
to
overall leveling stability.
Relative amplitude
Ti
me/s
Figure 6. The
Curve
s
und
e
r
Differe
nt Area
Ratio Coeffici
ents of Asym
metric
Cylind
e
r
Relative amplitude
Ti
me/s
Figure 5. The
Curve
s
und
e
r
Differe
nt
Displa
ceme
nt-angl
e Co
efficient
s of Four-links
Ti
me/s
Relative amplitude
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 5, May 2014: 3416 – 34
22
3422
(3) In
crea
sin
g
the am
plifier g
a
in m
a
ke
s sy
stem
re
spond fa
ste
r
, but incli
n
e
s
t
o
ca
use
system o
scill
ation. It is suitable to ado
pt a
section
a
l
gain adju
s
tment with co
ndition
s cha
n
g
ing
for paramete
r
-varying leveli
ng co
urse.
Ackn
o
w
l
e
dg
ements
The Spe
c
ial
Fund fo
r
Basic S
c
ie
ntific Re
se
arch of Ce
ntral
Colle
ges,
Cha
ng’an
University (Grant No.CHD2
011T
D01
7
，
CHD2
011Z
D016)
Referen
ces
[1]
Schima
neckf,
Merrifiel
d D.
A
e
rial
w
o
rk p
l
at
forms: safet
y
,
liab
ilit
y
& th
e
rental
cent
er.
Professio
nal
Safety
. 1998; 7
3
(1): 25-2
8
.
[2]
Smith A.
T
h
ing
s
looki
ng
up for aerial
w
o
rk platforms.
Diesel Progress
. 20
05
; 71(1): 12-14.
[3]
Xi
a Xiu-fe
ng. Devel
opm
ent o
f
China'
s aer
ial
platform vehic
l
e.
C
o
n
s
tru
c
tion
Me
ch
an
i
z
ation
. 2010; (9):
33-3
5
.
[4]
Cao
Xu
e-p
eng,
Chen
g Le
i, Ji
ao Sh
eng-
jie,
et al. T
e
chnica
l Status and tr
ends of Aer
i
al
w
o
rk pl
atform.
World Sci-Tec
h
R&D
. 201
2; 34(1
0
): 801-
80
4.
[5] Bora
Ery
ilmaz
，
Bruee
H. W
ilson. Unifi
ed m
ode
lin
g an
al
ysi
s
of a proporti
ona
l valve.
Jo
urna
l of the
Franklin Institut
e
. 2006: 4
8
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[6]
W
ang
xi
n, Son
g
Xia
o
-gu
a
n
g
, T
eng Ru-min,
et al. Simu
latio
n
an
d Res
earc
h
in A
e
ria
l
W
o
rk Platfor
m
Electro-h
y
d
r
au
l
i
c Prop
ortion
al
leve
lin
g s
y
ste
m
base
d
o
n
matlab.
Mac
h
i
ne too
l
a
nd hy
drau
lic
. 20
08;
36(4): 16
2-1
6
4
.
[7]
Z
hang
Li-p
in
g. Desig
n
ma
nua
l
of h
y
dra
u
lic
a
nd p
neum
atic
s
y
stem. Bei
j
i
n
g
:
Machin
er
y In
dustr
y
Pr
ess.
199
7: 453-
454.
[8]
Meng Z
h
eng-z
hen
g. Anal
ys
is
and
es
tabl
ish
m
ent of the transfer func
ti
on
for as
y
m
m
e
tri
c
h
y
dra
u
li
c
c
y
l
i
nd
ers co
ntrolle
d b
y
f
our-
w
a
y
valv
es.
Jou
r
nal
of Hefe
i U
n
iversity
(N
atu
r
al Sci
ences).
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:
23-2
7
.
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