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. 2025 Apr 15;25(8):2476.
doi: 10.3390/s25082476.

Structural Dynamics Analysis of a Large Aperture Space Telescope Based on the Linear State Space Method

Bin Ma  1   2   3 , Zongxuan Li  1   2   3 , Lin Li  4 , Yunfeng Li  1   2   3 , Youhan Peng  1   2   3 , Shuhui Ren  1   3 , Qingya Li  1   3 , Jiakun Xu  1   3
Affiliations

Structural Dynamics Analysis of a Large Aperture Space Telescope Based on the Linear State Space Method

Bin Ma et al. Sensors (Basel). .

Abstract

The linear state space model of an optical remote sensing camera with an aperture of φ572 mm was established using the structural dynamics and linear state space theory. Modal reduction was carried out using the balanced reduction method. Combined with the controllable and observability matrix, the model order was reduced. To obtain the frequency response curve between the excitation input point and the response output point, we performed a frequency response analysis with the reduced state space model. The initial frequency response curve was plotted and compared with the response curves of the DC gain method and the balanced reduction method. The accuracy and rationality of the simulation analysis were verified by dynamic tests. The balanced reduction method under state space representation provides a new method for studying the dynamics of lightweight opto-mechanical structures. It can characterize the inherent properties of the system by using the reduction model and has higher computational efficiency, which is helpful to analyze the frequency response characteristics of complex linear systems quickly and accurately.

Keywords: balance truncation; frequency response analysis; linear state space; structural dynamics.

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Conflict of interest statement

The authors declare no conflicts of interest.

Figures

Figure 1
Figure 1
Structural model of optical remote sensing camera with aperture of φ572 mm.
Figure 2
Figure 2
Block diagram of state space system.
Figure 3
Figure 3
Finite element modelling of optical remote sensing cameras.
Figure 4
Figure 4
Modal shapes of the first 6 modes.
Figure 4
Figure 4
Modal shapes of the first 6 modes.
Figure 5
Figure 5
Frequency response curve of the Finite Element Analysis.
Figure 6
Figure 6
DC value of each mode contribution versus mode number.
Figure 7
Figure 7
Sorted DC value of each mode versus number of modes included.
Figure 8
Figure 8
Comparison of the frequency response curves of all modes and DC gain reduced to 15th order modes.
Figure 9
Figure 9
Controllability/observability matrix of balanced system.
Figure 10
Figure 10
Controllability and observability matrix diagonal terms of balanced system.
Figure 11
Figure 11
Comparison of the frequency response curves of all modes and balanced reduced to 15th order modes.
Figure 12
Figure 12
Frequency response curves after all modes are compared with DC gain reduction and balanced reduction.
Figure 13
Figure 13
Frequency response curve comparison between finite element analysis (Patran) and state space methods.
Figure 14
Figure 14
Vibration test of optical camera.
Figure 15
Figure 15
Results of sine sweep test. (a) X-direction sine sweep test; Fx = 292.31 Hz. (b) Y-direction sine sweep test, Fy = 291.56 Hz. (c) Z-direction sine sweep test; Fz = 260.85 Hz.
Figure 15
Figure 15
Results of sine sweep test. (a) X-direction sine sweep test; Fx = 292.31 Hz. (b) Y-direction sine sweep test, Fy = 291.56 Hz. (c) Z-direction sine sweep test; Fz = 260.85 Hz.
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