TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol.12, No.4, April 201
4, pp. 2628 ~ 2
6
3
5
DOI: http://dx.doi.org/10.11591/telkomni
ka.v12i4.4754
2628
Re
cei
v
ed Se
ptem
ber 7, 2013; Re
vi
sed
Octob
e
r 13, 2
013; Accepte
d
No
vem
ber
3, 2013
Pitch Channel Control of Airship with Adaptive Sliding
Mode
Xinli Zhang*, Yunan Hu, Baoliang G
e
ng
Dep
a
rtment of control e
ngi
ne
erin
g, Naval A
e
ron
autica
l
An
d Astronaut
ic
al
Universit
y
, Ya
nti, 2640
01
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: 3934
55
3@q
q
.
com
A
b
st
r
a
ct
Based on
the non
lin
ear mod
e
l
of airsh
i
p pit
c
h
ch
a
n
n
e
l,
a
kind of
sli
d
in
g mo
de
c
ontro
l meth
od is
desi
gne
d w
i
tho
u
t any
pri
o
r i
n
formatio
n
a
b
o
u
t airsh
i
p
par
a
m
eters. T
he
ad
a
p
tive tur
n
in
g l
a
w
is ad
opte
d
t
o
solve
the
unk
n
o
w
n
infor
m
atio
n of
airsh
i
p
in
mo
de
l.
So t
he
w
hole
infor
m
at
ion
for co
ntrol
l
e
r ca
n us
ed
ar
e
only t
he
meas
ure
m
e
n
t of p
i
th a
ngl
e a
n
d
its
an
gle
spe
ed.
Detail
ed
si
mu
l
a
tion
are
do
ne
for tw
o situati
o
n
s
such as airs
hip
flying w
i
th big
trust and small
trust Nu
meric
a
l si
mul
a
tio
n
re
sults show
s that the airshi
p ca
n
fly smooth
a
n
d
safe. Esp
e
ci
al
ly, the c
ontro
ll
er ca
n us
e
the sam
e
g
r
ou
p of p
a
r
ame
t
e
r
s
du
ri
ng
al
l
ki
nd
s
o
f
abov
e flyin
g
co
nditi
ons. So it show
s that the
propos
ed
meth
o
d
is reaso
n
a
b
le
and effective.
Ke
y
w
ords
: air
s
hip, pitch ch
a
nne
l, ada
ptive, slidi
ng
mo
de
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
Comin
g
into
21th
centu
r
y, the value
o
f
Nea
r-Sp
a
ce
ha
s a
r
ou
se
d pe
ople'
s
attention
greatly,
and Nea
r-Sp
a
ce Vehicle
s
a
r
e very
con
c
e
r
n
ed by pe
ople
,
and then th
e airship
with
many
ex
celle
nce
s
be
com
e
s pop
ular
rese
arch su
bj
ect in
inte
rn
ational [1
-8].
Among
the
key
techn
o
logie
s
applie
d in de
velopment of
the airs
hip
,
the design
of Auto-co
n
trol system is th
e
most im
po
rta
n
t one
, a
nd t
he d
e
velopm
ent of th
e ai
rship
will
be
a
chall
enge
mi
ssi
on
be
cau
s
e of
its
es
pec
i
al complexity [9-17].
Previou
s
work in
pa
pe
r [1
-3] di
scu
s
sed
the
m
odel
o
f
airship
an
d
its PID cont
rol. It is
easy to make
a concl
u
si
on
that PID control is
still the most useful method until
now. It has m
any
advantag
es such as
it
i
s
very
simpl
e
and
effe
ct
ive and trustful.
But in this
pape
r, a
kin
d
of
adaptive
slidi
ng mo
de m
e
thod i
s
u
s
e
d
i
n
the d
e
si
gn
of co
ntrolle
r f
o
r ai
rship’
s pi
tch
chan
nel.
With
the sim
u
latio
n
analy
s
is
we found th
at it is also
very
effective. It almost h
a
s th
e
sam
e
swiftn
ess
and
robu
stne
ss
ch
aracte
rs a
s
the PID cont
rol met
hod. And it i
s
worth to
p
o
int out that
the
adaptive
strat
egy is u
s
ed t
o
solve t
he
u
n
ce
rtaintie
s o
f
the mod
e
l of
ai
rship,
so
it
is different fro
m
PID co
ntrol
method. So i
t
is also a
effective
metho
d
for the
ana
lysis a
nd
con
t
roller
de
sign
of
compl
e
x flying obje
c
t. Esp
e
cially, this m
e
thod i
s
mo
re
conve
n
ient t
han PID m
e
thod to
cop
e
with
high orde
r sy
stem and u
n
certaintie
s and
nonline
a
ritie
s
.
2. Model Des
c
ription
Based
on th
e previo
us
work, th
e pitch
cha
nnel m
o
del of airshi
p
can
be d
e
scribed
as
follows
:
()
()
M
xf
x
g
x
u
(1)
And
]
[
z
x
q
w
u
x
,
M
sat
i
sf
ie
s:
11
1
3
22
31
3
3
1
1
1
1
aa
a
aa
M
(2)
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Pitch Cha
nne
l Control of Ai
rshi
p with Ad
aptive Slidin
g
Mode (Xinli
Zhang
)
2629
The definition
of
ij
a
see the d
e
finition of
M
in previou
s
work.
Cho
o
se the expect value
of all states
,,
,
,
,
uw
q
x
z
are
,,
,
,
,
dd
d
d
d
d
uw
q
x
z
,Define
the error vari
able
d
ex
x
，
ex
，
then it hold:
()
(
)
M
ef
x
g
x
u
(3)
Use the inverse matrix of
M
:
11
()
()
eM
f
x
M
g
x
u
(4)
To make it co
nvenient for readin
g
, some
function
s ca
n be written a
s
follows:
6
5
4
3
2
1
)
(
f
f
f
f
f
f
x
f
，
0
0
0
0
0
1
0
0
0
0
)
(
2
1
k
k
x
g
，
T
u
u
u
2
1
(5)
Whe
r
e:
cos
sin
sin
cos
sin
)]
sin(
)
sin(
)
2
sin(
)
2
sin(
)
2
/
cos(
[
)
(
)]
sin(
)
sin(
)
2
sin(
)
2
sin(
)
2
/
cos(
[
)
(
)
2
/
sin(
)
2
sin(
cos
[
)
(
3
2
1
3
2
1
2
11
2
2
1
33
6
5
4
3
2
1
w
u
w
u
q
W
a
C
C
C
Q
rv
wq
ma
C
C
C
Q
q
ma
qu
m
m
C
C
Q
wq
m
m
f
f
f
f
f
f
z
M
M
M
z
z
z
z
z
X
X
Define:
6
5
4
3
33
1
31
2
22
3
13
1
11
6
5
4
3
2
1
1
)
(
f
f
f
f
a
f
a
f
a
f
a
f
a
f
f
f
f
f
f
x
f
M
a
a
a
a
a
a
(6)
And,
0
0
0
)
(
1
2
1
1
2
u
k
u
k
u
u
x
g
(7)
Then the
syst
em can b
e
written as follows:
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2628 – 2
635
2630
0
0
0
1
2
33
2
31
1
1
22
1
2
13
2
11
6
5
4
3
2
1
u
k
a
u
a
u
k
a
u
k
a
u
a
f
f
f
f
f
f
z
x
q
w
u
a
a
a
a
a
a
(8)
3. Adaptiv
e
Sliding Mod
e
Control of
Attitude
Assu
me the
velocity of airshi
p is a
co
nstan
t, it means that the
power of airship is a
con
s
tant, a
n
d
the
control o
b
jective i
s
to
desi
gn
a
cont
rolle
r
su
ch th
at the pit
c
h
a
ngle
ca
n tra
c
e a
con
s
tant,
without lo
st g
e
nerality, a
s
su
me the
pitch
angl
e i
s
3
.
57
/
2
d
, define the
sli
d
ing
mode a
s
:
q
c
s
d
)
(
1
1
(9)
And solve the
derivatives o
f
1
s
:
1
2
33
2
31
3
33
1
31
1
1
1
u
k
a
u
a
f
a
f
a
q
c
q
q
c
s
(10)
Con
s
id
er
th
e sep
a
ratio
n
d
e
s
ign metho
d
and
u
s
e
1
u
to control th
e hei
ght of ai
rship
and
use
2
u
to contro
l the flying distance of airsh
i
p, then assu
me
1
u
is a co
nstant and de
si
gn.
2
4
3
2
1
1
1
0
1
ˆ
ˆ
ˆ
ˆ
u
k
k
q
k
s
k
s
k
u
(11)
Then,
)
ˆ
ˆ
ˆ
ˆ
(
2
4
3
2
1
1
2
33
2
31
3
33
1
31
1
1
u
k
k
q
k
s
k
k
a
u
a
f
a
f
a
q
c
s
(12
)
And arrang
e it as:
1
1
2
33
0
2
33
1
2
4
2
33
31
3
2
33
3
33
1
31
2
2
33
1
1
1
1
)
ˆ
(
)
ˆ
(
)
ˆ
(
)
ˆ
(
s
k
k
a
k
k
a
a
u
k
k
a
a
k
k
a
f
a
f
a
q
k
k
a
c
s
a
s
(13)
Define:
2
2
2
33
1
~
ˆ
k
k
k
a
c
(14)
Then,
2
2
33
2
ˆ
~
k
k
a
k
(15)
Also define:
3
2
33
3
33
1
31
3
ˆ
~
k
k
a
f
a
f
a
k
(16)
Whe
r
e,
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Pitch Cha
nne
l Control of Ai
rshi
p with Ad
aptive Slidin
g
Mode (Xinli
Zhang
)
2631
)
(
3
33
1
31
3
f
a
f
a
k
a
(17)
And define:
4
2
33
31
4
ˆ
~
k
k
a
a
k
(18)
Also define:
1
2
33
0
2
33
1
1
ˆ
~
k
k
a
k
k
a
a
k
(19)
And arrang
e the slidi
ng mo
de as:
1
1
2
4
3
2
1
1
1
~
~
~
~
s
k
u
k
k
q
k
s
a
s
(20)
De
sign the tu
rning la
w of a
daptive para
m
eter,
1
1
1
1
ˆ
s
s
k
(21)
Also de
sign t
he turnin
g la
w of adaptive
param
eter e
s
timation.
1
2
4
4
ˆ
s
u
k
(22)
And desi
gn th
e estimation
value as:
q
s
k
1
2
2
ˆ
(23)
At last, desig
n turning la
w
for
3
ˆ
k
.
1
3
3
ˆ
s
k
(24)
Cho
o
se the whole Lyap
uno
v function as:
4
1
2
2
33
2
1
)
~
(
2
1
2
1
i
i
i
a
k
k
a
s
V
(25)
And solve its
derivatives a
s
:
a
a
k
k
k
a
s
a
V
3
3
2
33
3
2
1
1
~
1
(26)
Whe
r
e:
3
2
33
3
33
1
31
3
ˆ
~
k
k
a
f
a
f
a
k
(27)
Then the
system can
be
stable with th
e
assumptio
n
that the control paramete
r
1
a
is big
enou
gh. So consi
der give
n
interval
d
x
aro
und state
x
, s
i
nc
e
a
k
3
is bound
e
d
, then ther
e
exists a
1
a
big
enou
gh th
at
make
s the
d
e
rivatives of
Lyapun
ov fun
c
tion i
s
sm
all
than
zero.
It
also me
an
s that the syste
m
can be
sta
b
le.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2628 – 2
635
2632
4. Numerical Simulation
No
w the num
erical simul
a
tion is don
e to sho
w
the rig
h
tness of abo
ve design. To
make
the velocity to be a con
s
tan
t, design a ve
locity cont
roll
er first. To m
a
ke it simpl
e
and al
so with
out
infect the real
control effe
ct, we can a
s
sume the
po
wer of airship to be a con
s
ta
nt, so we de
sign
5000
2
u
, now the
ve
locity of
airship i
s
about
s
m
/
20
. And if
we
cho
o
se
10000
2
u
, the
velocity of airship
can b
e
s
m
/
30
a
r
oun
d. The si
mulation resu
lt is as follows.
Figure 1. Forward Velo
city
Figure 2. Forward Velo
city
Base o
n
the
assumptio
n
that the forwa
r
d
spee
d of
air can b
e
a
stable
co
nst
ant, the
tracin
g
co
ntro
ller
of a
given
pitch
a
ngle
o
f
airshi
p
can
be d
e
si
gne
d
as foll
ows. T
he
cont
rol
effect
of given
pitch
angl
e
3
.
57
/
2
d
and
3
.
57
/
10
d
is
given a
s
foll
o
w
figu
re
s,
wh
ere
the
co
ntrol
para
m
eters
is d
e
sig
ned
as follows:
1
1
c
，
3
.
0
0
k
,
001
.
0
1
,
005
.
0
2
,
002
.
0
3
,
3
.
57
/
2
d
.
So the con
c
l
u
sio
n
ca
n be
made acco
rding
to the above cu
rves.
The airshi
p can climb
from 0 m to 1700m in 2
0
00 s with a g
i
ven pitch an
gle 2 deg
ree.
And the curve of actuato
r
is
smooth a
nd the pitch a
ngl
e only has
o
n
e
overshoot
without chatters.
Con
s
id
erin
g increa
sing the
powe
r
and th
e forwa
r
d
sp
e
ed to verify the effectivene
ss of the pitch
angle controll
er,
cho
o
se
10000
2
u
, assume the ini
t
ial height is 1
,
and the expected pit
c
h
angle i
s
20 d
egre
e
, the co
ntrol pa
ramet
e
r is
keep the
same a
s
abo
ve, the simulation re
sult is
s
h
ow
as
b
e
l
ow
fig
u
r
es
.
Figure 3.
Fo
rward Velo
city
Figure 4.
Vert
ic
al Veloc
i
ty
0
100
200
300
400
500
600
700
800
900
1000
0
5
10
15
20
25
t/
s
m/
s
0
100
200
300
400
500
600
700
800
900
1000
0
5
10
15
20
25
30
35
t/
s
m/
s
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
5
10
15
20
25
t/
s
水平
行速度
飞
（）
m/s
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-0.
2
5
-0.
2
-0.
1
5
-0.
1
-0.
0
5
0
t/
s
垂向
行速度
飞
（）
m/s
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Pitch Cha
nne
l Control of Ai
rshi
p with Ad
aptive Slidin
g
Mode (Xinli
Zhang
)
2633
Figure 5.
Angle Veloc
i
ty
Figure 6.
Pitch Angle
Figure 7.
Flying Di
stan
ce
Figure 8.
Hei
ght
Figure 9.
Act
uator Angl
e
Figure 10.
Fo
rwa
r
d Velo
cit
y
Figure 11.
Vertic
al Veloc
i
ty
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-4
-3
-2
-1
0
1
2
3
4
5
6
x 1
0
-4
t/
s
角速度（
）
r
ad/
s
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-1
-0.
5
0
0.
5
1
1.
5
2
2.
5
3
3.
5
t/
s
姿角
态
（）
deg
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
0.
5
1
1.
5
2
2.
5
3
3.
5
4
x 1
0
4
t/
s
水平
行距离
飞
（）
m
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
200
400
600
800
1000
1200
1400
1600
1800
t/
s
行高
度
飞
（）
m
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
1.
4
t/
s
舵偏角
（
）
deg
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
5
10
15
20
25
30
35
t/
s
水平
行速度
飞
（）
m/
s
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-1.
4
-1.
2
-1
-0.
8
-0.
6
-0.
4
-0.
2
0
t/
s
垂向
行速度
飞
（）
m/
s
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 4, April 2014: 2628 – 2
635
2634
Figure 12.
An
gle Velocity
Figure 13.
Pitch Angle
Figure 14.
Fly
i
ng Di
stan
ce
Figure 15. He
ight
Figure 16. Actuator Angle
We can find that the forwa
r
d sp
eed of
a
i
rshi
p is still stable and it is about
s
m
/
27
, and
the airshi
p
ca
n also fly wit
h
a
smo
o
th resp
on
se
with
a big
pitch a
ngle, whe
r
e t
he max
actu
a
t
or
angle
is sma
ll than
11
de
gree.
Also
th
e cli
m
bi
ng
speed
is in
cre
a
se
d a
n
d
th
e it
can
rea
c
h
2100
0m heig
h
t in 2000
s.
5. Conclusi
on
Con
s
id
erin
g the above t
w
o
situation
s
th
at flying ship
flies with bi
g
trust an
d sm
all trust,
all the control
l
er paramete
r
s ca
n be ke
e
p
the same
without any turning. And all flying pro
c
e
s
ses
are
ve
ry smo
o
th
an
d safe, so
th
e whole
control
effe
c
t
is
s
a
tis
f
ac
tory
. It tes
t
ifies
t
hat the method
prop
osed in this pa
per i
s
e
ffective for airship pit
c
h cha
nnel control.
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-1
0
1
2
3
4
5
x 1
0
-3
t/
s
角速度（
）
r
ad/
s
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-5
0
5
10
15
20
25
30
35
t/
s
姿角
态
（）
deg
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
1
2
3
4
5
6
x 1
0
4
t/
s
水平
行距离
飞
（）
m
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
0.
5
1
1.
5
2
2.
5
x 1
0
4
t/
s
行高
度
飞
（）
m
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
2
4
6
8
10
12
t/
s
舵偏角（
）
deg
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Pitch Cha
nne
l Control of Ai
rshi
p with Ad
aptive Slidin
g
Mode (Xinli
Zhang
)
2635
What i
s
wo
rth
y
pointing out
is that the w
hole controlle
r only u
s
ed th
e pitch a
ngle
and its
spe
ed
withou
t any other
speci
a
l inform
ation ab
out
the airshi
p st
ructure o
r
pa
rameters. So
it
mean
s that th
e adaptive m
e
thod is
effective to c
ope t
he un
kno
w
n f
unctio
n
s in th
e whol
e airsh
i
p
model
s. And
the
cont
roll
er
paramete
r
s a
r
e
not
ne
ce
ssary to
chang
e d
u
rin
g
differe
nt flying
con
d
ition. It
mean
s that the pro
p
o
s
e
adaptive
slidi
ng mode
con
t
rol method i
s
rea
s
o
nabl
e
for
airship contro
l.
Referen
ces
[1]
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u
ckerman.
Inertia
F
a
ctors
of Ell
i
ps
oids
for Use
in
Airs
h
i
p D
e
si
gn.
N
a
c
a
Re
ports
. 2
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; 14(
3): 45-
50.
[2]
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a, SS Buen
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i
nd
Spee
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y
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danc
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2002; 2
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16-1
24.
[3]
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o
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us o
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a
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eal-T
ime Si
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bird
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lin
g an
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e
chno
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onf
erenc
e an
d Exhibit, Ke
yston
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.
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Y.
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he Stratosph
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he 2nd
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c
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y
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o
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o
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e
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e
rod
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ma
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e
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i
qu
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o
stats
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d A
i
rshi
ps
. AIAA
Lighter-
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y
ste
m
s Confere
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2
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heory of
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opic T
u
rbul
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e
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one
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eep
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i
g
h
-Al
t
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a
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”
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a
tio
n
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ontro
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d Exhib
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[12]
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t. Modeli
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ar-Spac
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l
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g
e
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l
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o
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etric
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l
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