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Procedia Engineering00 (2014) 000–000
www.elsevier.com/locate/procedia
“APISAT2014”, 2014 Asia-Pacific International Symposium on Aerospace Technology,
APISAT2014
Anti Measure Noise Research of Morphing Wing UAV
Su Haoqin, Bao Xiaoxiang*, Shi Hongwei, Liu Kai, Song Jing
The 11th Department of China Academy of Aerospace Aerodynamic, Beijing 100074, China
Abstract
The morphing UAV (Unmanned Aerial Vehicle) is a tendency for the future of UAV. When UAV changes construct of wings,
measure noise disturbance probably meet, then UAV bears larger change of aerodynamic force and moment, it’s for morphing
UAV to find a robust to fit this condition. This paper brings out LQG controller, which can solve measure noise problems and
control 6 freedom affine nonlinear equations. Simulation of morphing process is realized with LQG controller, which validate the
stability and robust of LQG robust controller.
© 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
Keywords: morphing wing UAV; LQG robust controller; gust; nonlinear model
1.Introduce
The morphing wing UAV (Unmanned Aerial Vehicle) can satisfy multitask requirements, and is a tendency for
the future of UAV. When morphing wing extending or shrinking, aerodynamics and moments verify largely, so a
kind of robust controller are needed to satisfy the transitional process[1~8]. This paper brings out the LQG controller
which can solve above problems.
2.Longitudinal model
In this paper, only longitudinal model of morphing UAV is considered. In formula (1), affine nonlinear express is
showed.
* Corresponding author. Tel.: +86-13581559863;.
E-mail address:yuhongyan09@163.com
1877-7058 © 2014 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of Chinese Society of Aeronautics and Astronautics (CSAA).
2
Su Haoqin, Bao Xiaoxiang, Shi Hongwei, Liu Kai, Song Jing / Procedia Engineering00 (2014) 000–000
x  f ( x )  B  u
(1)
Within (1), x  v  z h   is the vector about speed, attack angle, pitch rate, height and pitch angle. Input
vector u  z P is elevator and thrust force. f (x ) is the nonlinear express about state parameters, B matrix is the
control vector.
Linear equation can be got at trim point, in this way nonlinear express f (x ) can be linearized as formula (2).
V   AVV
  
   AV
 z    A zV
  
h   AhV
   0
AV
A
A z
Ah
0
0
A z
A z z
0
1
AV  V   BVz
A     Bz
   
A z    z    B zz
   
Ah  h   0
0     0
AVh
Ah
A z h
0
0
BVP 
BP 
 z 
B z P    
 P
0 
0 
(2)
Within (5), A,B matrix can be got from linearization method.
Aerodynamic force and moment in (1) can be expressed as formula (3)
X Y   Q  S  cx cy 
(3)
Mz  Q  S  Ba  mz
There are two sets of aerodynamic coefficients in morphing UAV formulas, one is low speed states, another is
high speed states. When aerodynamic parameters of morphing process is wanted to be got, above two sets of
aerodynamic coefficients are needed. Linear interpolation is divided into two types, one type is for time
interpolation, such as wing length L, wing area S, and mean aerodynamic chord Ba; another is for speed
interpolation, such as aerodynamic force and moment Cx, Cy, Cz, Mx , My , Mz . Formulas (4) and (5)
high
f (u )  ulow

low
high
uhigh
 ulow
t morphingtimedifference
(t  t morphingtime )
(4)
high
f (u)  ulow

low
high
uhigh
 ulow
Vmorphingspeeddifference
(V  Vmorphingspeed )
(5)
high
In formula (4), ulow denotes one state should be chosen from high speed state or low speed state.
tmorphingtimedifference is set as morphing time span. For example, when we calculate wing length in morphing state
from low speed state to high speed state, (4) can be expressed as (5)
L  Llwo 
Lhigh  Llow
t morphingtimedifference
(t  t morphingtime )
(6)
Parameters in formula (5) is the same as (4), but time should be replaced as speed。
Under measure noise condition, output of linearization equation (2) can be expressed as formula (7), which y is
output vector, C is state output matrix, and  is the white noise GAUSS process, and satisfy mean energy is larger
zeros[9~10].
y  Cx  


E  T    0
(7)
3.LQG controller design
Due to noise existing in systems (2), system states should be estimated with controller designing. Kalman filters is
Su Haoqin, Bao Xiaoxiang, Shi Hongwei, Liu Kai, Song Jing / Procedia Engineering 00 (2014) 000–000
3
used to finish above task, and LQ controller is designed to realize feedback regulation K, this method is called LQG
method, which is showed in figure 1.
Fig.1 LQG controller frame
Kalman filter is designed to find state estimated signal xˆ (t ) to minimize the covariance matrix
T
E x(t )  xˆ (t ) x(t )  xˆ (t )  , then xˆ ( t ) is used to replace the origin states.
Estimated states in figure 1 can be expressed as (8)
~
(8)
x  A~
x  Bu  K f  y  C~
x  Du 
So LQG regulation with observation can be expressed as (9)


 A  K f C  BK c  K f DK c
L
Kc

Kf 
0 
(9)
Fig.1 show the kalman filter construction. At last, controller signal can be got in (10)
u* (t )   K c  ~
x (t )
(10)
4.Simulation
Signal 1
(s-a)
H command
s(s+b)
x' = Ax+Bu
y = Cx+Du
LQG controller
morphing UAV
dz,P
h
Add1
measure noise
Add
Fig.2 linear simulation of morphing UAV with LQG controller
Nonlinear simulation of morphing UAV with LQG controller is showed in fig.2. Plant in figure is expressed in
formula (2), and only height value is outputted to join the feedback control, but measure noise may be met which
need to be supposed as white noise. Combined with measure noise, height is feedback to follow its command hc,
and error between them must be controlled by LQG, LQG outputs two values: thrust force and elevator, then closed
control is finished. Measure noise is set to be white noise which is zero mean and variance 1e  6 .
Linear simulation of the longitudinal model of morphing UAV run with LQG controller, the initial condition
include flight height 1000 m and flight speed 66 m/s. the following description is control strategy about morphing
UAV.
Wing shrinking time happen within 50s and 200s, and thrust force keep 150N before 50s. At the time of 50s,
thrust force increase to 300N linearly without control, and speed accelerate from 0.2Ma to 0.4Ma. At the time of
100s, wing shrinking time use 10s.
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Su Haoqin, Bao Xiaoxiang, Shi Hongwei, Liu Kai, Song Jing / Procedia Engineering00 (2014) 000–000
Wing extending time happen within 200s and 400s, and thrust force keep 300N before 200s. At the time of 250s,
thrust force decrease to 150N linearly without control, and speed decelerate from 0.4Ma to 0.2Ma. At the time of
250s, wing extending time use 10s.
Fig.3 height VS time
Fig.4 attack angle VS time
Fig.5 pitch angle VS time
Su Haoqin, Bao Xiaoxiang, Shi Hongwei, Liu Kai, Song Jing / Procedia Engineering 00 (2014) 000–000
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Fig.6 pitch rate VS time
Fig.7 speed VS time
Fig.8 elevator VS time
Figure 3~8 is the simulation process, and control policy is used to realized wing morphing process. All above
figure prove that morphing UAV can satisfy control requirement under complex condition such as noise joint. LQG
controller can only use height feedback to realize the whole state estimation, and finish the whole state feedback,
also, white noise can be filtered, and satisfy the control requirement.
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Su Haoqin, Bao Xiaoxiang, Shi Hongwei, Liu Kai, Song Jing / Procedia Engineering00 (2014) 000–000
5.Conclusion
LQG controller can inhibit measure noise and is realized in engineer easily, so LQG is used to control morphing
UAV, and simulation shows that LQG controller can control complex process of wing morphing, and only less
signal can be feedback to realized the whole flight parameters estimated.
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