基于P-CS模型与数字孪生的星载天线反射器形面鲁棒性控制方法

doi:10.7527/S1000-6893.2023.28343

Abstract

Abstract:

The surface precision of the space-borne antenna reflector is the main influence factor of its electromagnetic performance. The active shape control methodology is an effective way to guarantee the surface precision of space-borne antenna reflectors in orbit. Considering the uncertain material properties of the space-borne antenna reflectors in orbit， a robust shape control method is proposed based on Probability-Convex Set （P-CS） model and digital twin in this paper. The uncertain material properties are quantified in a uniform model （P-CS model）. The P-CS model can be updated based on the Bayesian theory and driven by displacement monitoring data. According to the P-CS model， a voltage layout optimization model is proposed to achieve the optimal robustness of the surface precision under uncertainties. To solve such voltage layout optimization problem with multiple local optimal solutions and large scale of discrete variables， the voltage layout is described by a bounded field with space correlation based on the continuous representation and dimensionality reduction method， and then the design space is discretized and sequential sub-optimization problems are formed. The optimal solution can be achieved by solving sub-optimization problems one by one. The proposed method is used to solve an active shape control problem for a regular hexagon space-borne antenna reflector. Two cases with the constraints of applying one kind of voltage and four kinds of voltage are analyzed to demonstrate the validity and applicability of the proposed method.

Key words: space-borne antenna reflector, active shape control, robustness, structural layout optimization design, digital twin

CLC Number:

V214.4

Jiaqi HE, Weida WU, Yangjun LUO. A robust shape control method for space-borne antenna reflectors based on P-CS uncertainty quantification model and digital twin[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 328343.

Figures/Tables 20

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Table 1

Data samples S^P1 in period of t0,t1 for Case 1

序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$
1	29.41	6	29.68	11	29.52	16	30.45	21	30.07	26	28.82
2	30.53	7	28.71	12	29.53	17	29.40	22	28.92	27	29.63
3	28.80	8	28.78	13	29.16	18	30.37	23	29.67	28	29.25
4	28.87	9	30.06	14	29.13	19	30.48	24	29.35	29	30.45
5	29.66	10	29.35	15	30.51	20	28.95	25	29.29	30	29.52

Table 1

Table 2

Data samples S^P2 in period of t1,t2 for Case 1

序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$
1	17.63	6	16.20	11	16.32	16	16.28	21	17.31	26	17.52
2	17.81	7	16.56	12	17.94	17	16.84	22	16.07	27	17.49
3	16.25	8	17.09	13	17.91	18	17.83	23	17.70	28	16.78
4	17.83	9	17.92	14	16.97	19	17.58	24	17.87	29	17.31
5	17.27	10	17.93	15	17.60	20	17.92	25	17.36	30	16.34

Table 2

Table 3

Coefficients of P-CS model at various moments for Case 1

时刻	$P r 1$	$P r 2$	$P r 3$	$θ 1 / r a d$	$θ 2 / r a d$
$t 0$	1.732	1.732	1.732	0	0
$t 1$	1.063	1.067	1.065	0.221	0.021
$t 2$	1.071	1.068	1.068	0.578	0.078
$t 3$	1.069	1.067	1.069	0.358	0.153
$t 4$	1.070	1.066	1.068	0.421	-0.088

Table 3

Fig.8

Fig.9

Fig.10

Table 4

Data samples S^P1 in period of t0,t1 for Case 2

序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$
1	29.41	6	29.68	11	29.52	16	30.45	21	30.07	26	28.82
2	30.53	7	28.71	12	29.53	17	29.40	22	28.92	27	29.63
3	28.80	8	28.78	13	29.16	18	30.37	23	29.67	28	29.25
4	28.87	9	30.06	14	29.13	19	30.48	24	29.35	29	30.45
5	29.66	10	29.35	15	30.51	20	28.95	25	29.29	30	29.52

Table 4

Table 5

Data samples S^P2 in period of t1,t2 for Case 2

序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$	序号	$U o u t m a x / μ m$
1	17.63	6	16.20	11	16.32	16	16.28	21	17.31	26	17.52
2	17.81	7	16.56	12	17.94	17	16.84	22	16.07	27	17.49
3	16.25	8	17.09	13	17.91	18	17.83	23	17.70	28	16.78
4	17.83	9	17.92	14	16.97	19	17.58	24	17.87	29	17.31
5	17.27	10	17.93	15	17.60	20	17.92	25	17.36	30	16.34

Table 5

Fig.11

Table 6

Coefficients of P-CS model at different moments for Case 2

时刻	$P r 1$	$P r 2$	$P r 3$	$θ 1 / r a d$	$θ 2 / r a d$
$t 0$	1.732	1.732	1.732	0	0
$t 1$	1.069	1.075	1.069	0.674	0.215
$t 2$	1.448	1.081	1.066	0.785	-0.555
$t 3$	1.444	1.077	1.066	0.458	-0.223
$t 4$	1.440	1.079	1.064	0.620	0.015

Table 6

Fig.12

Fig.13

Fig.14

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A robust shape control method for space-borne antenna reflectors based on P-CS uncertainty quantification model and digital twin

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