输入量化下航天器位姿一体化预设时间控制

doi:10.7527/S1000-6893.2023.28558

Abstract

Abstract:

In the close-space missions such as spacecraft on-orbit repair and maintenance， it is often demanded for the spacecraft， which performs the task， to track the target spacecraft’s position and attitude simultaneously within a specific time window and limited communication bandwidth. To solve the attitude-orbit coupling control problem involved， an integrated predefined-time control strategy is proposed. Firstly， an error dynamic model of position and attitude integration for relative motion spacecraft is established in the framework of Lie group SE（3）. Then， the input quantization mechanism is introduced to reduce the communication frequency from the control system to the actuators. Subsequently， based on the derived practical predefined-time stable lemma， together with the back-stepping method， a nonsingular predefined-time pose tracking controller is designed. To improve the robust property of the system， a novel adaptive updating strategy to estimate and compensate for the system’s lump disturbance， and the quantizer parameters are exploited to reject the quantization error. This strategy could guarantee the predefined-time stability for the system， in the case of independent on the initial states， input quantization and the unknown disturbance， in addition， the upper bound of system’s convergence time is appointed by a control parameter in advance. Next， based on Lyapunov stability theory， the stability of the closed-loop system is proved. Finally， the simulation results verify the effectiveness of the proposed strategy.

Key words: on-orbit maintenance, integrated pose control, Lie group SE(3), input quantization, predefined-time control

CLC Number:

V448.2

Hongzhu ZHANG, Dong YE, Zhaowei SUN. Predefined-time integrated pose control for spacecraft under input quantization[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(22): 328558-328558.

Figures/Tables 15

Table 1

Parameters of controller and quantizer

参数	取值
$T, α, ϑ, d ¯$	$120 s, 0.4, 1.2, 0.001$
$ε 11, ε 12, ε 13$	$0.005, 0.005, 0.005$
$ε 14, ε 15, ε 16$	$0.005, 0.005, 0.005$
$K 1$	$d i a g (3,3, 3,0.6,0.6,0.6)$
$K 2$	$0.1 ⋅ d i a g (15,15,15,3, 3,3)$
$K 3$	$1.5 ⋅ d i a g (5,5, 5,1, 1,1)$
$Λ$	$d i a g (5,5, 5,3, 3,3)$
$ζ$	$[1.45,1.45,1.45,10.2,10.2,10.2]$
$ε 2$	$0.01 ⋅ [4,4, 4,5, 5,5]$
$u 1, s, u 2, s, u 3, s$ /（N·m）	$2.52, 2.52, 2.52$
$u 4, s, u 5, s, u 6, s$ /N	$15, 15, 15$
$σ 1, σ 2, σ 3$ /（N·m）	$1.42, 1.42, 1.42$
$σ 4, σ 5, σ 6$ /N	$10, 10, 10$
$u 1, m i n, u 2, m i n, u 3, m i n$ /（N·m）	$0.000 6, 0.000 6, 0.000 6$
$u 4, m i n, u 5, m i n, u 6, m i n$ /N	$0.000 5, 0.000 5, 0.000 5$
$δ 1, δ 2, δ 3$	$0.35, 0.35, 0.35$
$δ 4, δ 5, δ 6$	$0.33, 0.33, 0.33$

Table 1

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Table 2

Parameters of finite-time sliding mode controller

参数	取值
$α, β, ε, λ$	$2 / 3, 2 / 3, 0.025, 0.01$
$K 1$	$d i a g (2,2, 2,2, 2,2)$
$K 2$	$d i a g (3,3, 3,5, 5,5)$
$κ 1$	$0.1 ⋅ d i a g (2,2, 2,3, 3,3)$
$κ 2$	$0.01 ⋅ d i a g (3,3, 3,5, 5,5)$
$κ 3$	$0.01 ⋅ d i a g (8,8, 8,6, 6,6)$
$κ 4$	$0.01 ⋅ d i a g (6,6, 6,4, 4,4)$
$k$	$0.01 ⋅ d i a g (6,6, 6,6, 6,6)$
$ϑ 1$	$0.01 ⋅ d i a g (2.5,2.5,2.5,8, 18,8)$
$ϑ 2$	$0.01 ⋅ d i a g (3,3, 3,6, 5,6)$

Table 2

Table 3

Performance comparison between back-stepping predefined time controller and finite-time sliding mode controller

控制性能	状态变量	控制方法	初态1	初态2	初态3	初态4
收敛范围	姿态误差 $θ i / 10 - 3 °$	BsPdTC	3.72	3.88	3.71	4.08
	姿态误差 $θ i / 10 - 3 °$	FTSMC	4.77	5.24	3.83	4.82
	位置误差 $β i / 10 - 5 m$	BsPdTC	3.28	3.07	3.33	3.02
	位置误差 $β i / 10 - 5 m$	FTSMC	5.58	4.70	5.90	4.63
	角速度误差 $ω i / 10 - 3 ° ⋅ s - 1$	BsPdTC	1.60	1.48	1.58	1.63
	角速度误差 $ω i / 10 - 3 ° ⋅ s - 1$	FTSMC	16.1	16.7	16.3	16.8
	速度误差 $υ i / 10 - 6 m ⋅ s - 1$	BsPdTC	10.2	8.77	9.06	8.63
	速度误差 $υ i / 10 - 6 m ⋅ s - 1$	FTSMC	88.7	90.3	78.8	55.0
收敛时间	角速度和姿态 $T ω i$ ， $T θ i / s$	BsPdTC	76.2，75.8	79.1，78.5	79.5，79.5	84.1，85.5
	角速度和姿态 $T ω i$ ， $T θ i / s$	FTSMC	76.5，76.1	89.8，87.0	84.7，85.0	85.1，85.0
	速度和和位置 $T υ i$ ， $T β i / s$	BsPdTC	90.0，90.5	92.6，93.5	93.0，95.2	96.5，96.8
	速度和和位置 $T υ i$ ， $T β i / s$	FTSMC	89.6，89.7	116.1，115.6	116.5，115.8	127.6，126.8

Table 3

Fig.12

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Predefined-time integrated pose control for spacecraft under input quantization

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