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Research on the Strategy Method for the Final Translation Phase of Space Autonomous Rendezvous Li Nan 1 , Liu Zhenghua 2 , Li Huifeng 1 , and Zong Xiaoxiao 2 1) Department of Astronautics, Beihang University , Beijing, China ([email protected]) 2) Department of Automation science and electrical engineering, Beihang University, Beijing, China ([email protected]) Abstract—In this paper, a Multi-mode switching guidance control strategy is proposed for the final translation phase space autonomous rendezvous and docking precision-guided control problem. Firstly, dynamic model for spacecraft rendezvous is established and analyzed under the target coordinates. Secondly the final translation phase is divided into two parts, constant speed translation phase and inconstant speed translation phase. In the constant speed phase, PID controller is used for ensuring control precision. Considering the uncertainty and nonlinear characteristics of the system, a fuzzy controller is designed to realize the precise guidance for inconstant speed translation phase. The whole control process is based on the error threshold control method to reduce fuel consumption. The simulation results demonstrate the effectiveness of the proposed guidance control strategy. Finally, the method of converting the continuous control law into the relay-type control law is discussed. The relay-type control law is easier to realize in engineering application. Keywords—terminal, autonomous rendezvous, guidance method, orbit control 1 2 1 2 1) 2) PID 1 [1] [2] [3] [4] [5] [5] Richard min-max [6-7] Proceedings of the 10th World Congress on Intelligent Control and Automation July 6-8, 2012, Beijing, China 290 978-1-4673-1398-8/12/$31.00 ©2012 IEEE

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Page 1: [IEEE 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012) - Beijing, China (2012.07.6-2012.07.8)] Proceedings of the 10th World Congress on Intelligent Control

Research on the Strategy Method for the Final Translation Phase of Space Autonomous Rendezvous

Li Nan1, Liu Zhenghua2, Li Huifeng1, and Zong Xiaoxiao2 1) Department of Astronautics, Beihang University , Beijing, China ([email protected])

2) Department of Automation science and electrical engineering, Beihang University, Beijing, China ([email protected])

Abstract—In this paper, a Multi-mode switching guidance control strategy is proposed for the final translation phase space

autonomous rendezvous and docking precision-guided control problem. Firstly, dynamic model for spacecraft rendezvous is established and analyzed under the target coordinates. Secondly the final translation phase is divided into two parts, constant speed translation

phase and inconstant speed translation phase. In the constant speed phase, PID controller is used for ensuring control precision.

Considering the uncertainty and nonlinear characteristics of the system, a fuzzy controller is designed to realize the precise guidance for

inconstant speed translation phase. The whole control process is based on the error threshold control method to reduce fuel

consumption. The simulation results demonstrate the effectiveness of the proposed guidance control strategy. Finally, the method of

converting the continuous control law into the relay-type control law is discussed. The relay-type control law is easier to realize in

engineering application.

Keywords—terminal, autonomous rendezvous, guidance method, orbit control

1 2 1 2

1) 2)

PID

1

[1]

[2] [3]

[4]

[5] [5] Richardmin-max

[6-7]

Proceedings of the 10th World Congress on Intelligent Control and Automation July 6-8, 2012, Beijing, China

290 978-1-4673-1398-8/12/$31.00 ©2012 IEEE

Page 2: [IEEE 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012) - Beijing, China (2012.07.6-2012.07.8)] Proceedings of the 10th World Congress on Intelligent Control

[2]

[8]

2

ω

2

2

2

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y

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x y a

y x y a

z z a

ωω ω

ω

− =

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(1)

x y z

ω zxa ya za

Hill

(1) x y

x 2 yω y

2 xω

ρ βα

[ ]a a aρ β α=sa[ ]x y za a a=oa

cos cos sin cos sinsin cos cos sin sin

sin cos

x

y

z

a a a aa a a aa a a

ρ β α

ρ β α

ρ α

β α β β αβ α β β α

α α

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291

Page 3: [IEEE 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012) - Beijing, China (2012.07.6-2012.07.8)] Proceedings of the 10th World Congress on Intelligent Control

3.1

3

oa sa

3

, , , , ,T T T T T Tρ β α ρ β α,T Te ecρ ρρ ρ ρ ρ= − = −

, ( )T Te ecβ ββ β ρ β β= − = −, ( ) cosT Te ecα αα α ρ α α β= − = −

, ,e e eρ β α , ,ec ec ecρ β α cu

7

ij

: i j ijRule ij IF e u and ec u THEN u u= = = (3)

( ) ( )ij i jf u e u ec= ⋅ (4)

( )iu e ( )ju ec

,ij ij

i j

ijij

f uu

f= (5)

,

,

,

( ) /

( ) /

( ) /

ij ij iji j ijc

c ij ij iji j ij

cij ij ij

i j ij

f a fuu f a fu

f a f

ρρ

β β

αα

=

(6)

, ,ij ij ija a aρ β α

1

1

ec,a,e NB NM NS ZO PS PM PB

NB PB PB PM PM PS ZO ZO

NM PB PB PM PS PS ZO NS

NS PM PM PM PS ZO NS NS

ZO PM PM PS ZO NS NM NM

PS PS PS ZO NS NS NM NM

PM PS ZO NS NM NM NM NB

PB ZO ZO NM NM NM NB NB

3.2

( )tρ 0(0)ρ ρ=( ) 0Tρ = ( )=0tρ 0 0( )=t tρ ρ ρ+

PIDPID

P D Ic

c P D I

cP D I

K e K e dt K euu K e K e dt K eu K e K e dt K e

ρ ρ ρ ρ ρ ρρ

β β β β β β β

αα α α α α α

+ +

= + +

+ +

(7)

0IK ρ =

292

Page 4: [IEEE 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012) - Beijing, China (2012.07.6-2012.07.8)] Proceedings of the 10th World Congress on Intelligent Control

3.3

(2) 2 3

[8]

(1)

( )k

k

t T

ctt dt

+Δ=v u (8)

[ ]Tx y zv v v= Δ Δ Δv ( ) [ ]T

c cx cy czt u u u=u

(2)

, ,yx zcx cy cz

x y z

vv vt t ta a a

ΔΔ ΔΔ = Δ = Δ = (9)

xa ya za

(3) / 2kt T+ Δ

4 343km

0 0 0 0 0 0[ ] [100 10 20 1.2 0.6 0.2]T Tx y z x y z = − − −

m m/s -1=0.001136rad sω ⋅300s

10m 0.01m/sPID 0.01m/s Hill

4 5

4

5

0 50 100 150 200 250 300-20

0

20

40

60

80

100

• • (s)

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(m)

x

y

z

4

0 50 100 150 200 250 300-2.5

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-1

-0.5

0

0.5

1

• • (s)

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(m/s

)

vx

vy

vz

5

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PID

PID

[1] Tang, Guo-Jin, Luo, Ya-Zhong and Li, Hai-Yang, “Optimal

robust linearized impulsive rendezvous,” Aerospace Science

and Technology, vol. 11, no. 7-8, pp. 563-569,2007. [2] , , . .

293

Page 5: [IEEE 2012 10th World Congress on Intelligent Control and Automation (WCICA 2012) - Beijing, China (2012.07.6-2012.07.8)] Proceedings of the 10th World Congress on Intelligent Control

: , 2010.

[3] , , “ ,”

, no. 5, pp. 1-8,2004.

[4] , , , “

,” , no. 6, pp. 39-48,2010.

[5] Richard A and How J, “Performance Evaluation of Rendezvous

Using Model Predictive Control,” in AIAA GNC Conf. and

Exhi., vol. 5, Austin,Texas, August 2003, pp. 1-9. [6] , , “

,” , vol. 27, no. 3, pp. 416-421,2006.

[7] , , , “ ,” ,

vol. 24, no. 2, pp. 132-137,2003. [8] , “ ,”

, , 2006.

[9] . . : , 1995.

294