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Research Papers

Rigid-Flexible Coupling Dynamic Modeling and Vibration Control for a Three-Axis Stabilized Spacecraft

[+] Author and Article Information
Lun Liu

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: lliu@hit.edu.cn

Dengqing Cao

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: dqcao@hit.edu.cn

Jin Wei

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: weijinhit@163.com

Xiaojun Tan

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: tanxiaojun.hit@aliyun.com

Tianhu Yu

School of Astronautics,
Harbin Institute of Technology,
P. O. Box 137,
Harbin 150001, China
e-mail: yuthjianyang@yeah.net

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 7, 2016; final manuscript received February 21, 2017; published online May 30, 2017. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 139(4), 041006 (May 30, 2017) (14 pages) Paper No: VIB-16-1288; doi: 10.1115/1.4036213 History: Received June 07, 2016; Revised February 21, 2017

An approach is proposed to obtain the global analytical modes (GAMs) and establish discrete dynamic model with low degree-of-freedom for a three-axis attitude stabilized spacecraft installed with a pair of solar arrays. The flexible spacecraft is simplified as a hub–plate system which is a typical rigid-flexible coupling system. The governing equations of motion and the corresponding boundary conditions are derived by using the Hamiltonian principle. Describing the rigid motion and elastic vibration of all the system components with a uniform set of generalized coordinates, the system GAMs are solved from those dynamic equations and boundary conditions, which are used to discretize the equations of motion. For comparison, another discrete model is also derived using assumed mode method (AMM). Using ansys software, a finite element model is established to verify the GAM and AMM models. Subsequently, the system global modes are investigated using the GAM approach. Further, the performance of GAM model in dynamic analysis and cooperative control for attitude motion and solar panel vibration is assessed by comparing with AMM model. The discrete dynamic model based on GAMs has the capability to carry out spacecraft dynamic analysis in the same accuracy as a high-dimensional AMM model. The controller based on GAM model can suppress the oscillation of solar panels and make the control torque stable in much shorter time.

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Figures

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Fig. 1

Sketch of a three-axis stabilized spacecraft installed with a pair of solar arrays: (a) coordinate systems, (b) geometric relations (top view), and (c) deformation of the solar panel

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Fig. 2

Solar array model: (a) section view of solar array and the cell of honeycomb core and (b) equivalent isotropic model for the honeycomb sandwich panel

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Fig. 3

Finite element model of the flexible spacecraft in ansys

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Fig. 4

The first eight global mode shapes of the flexible spacecraft (L=9 m): (a) the first mode, S(1, 1); (b) the second mode, AS(1, 1); (c) the third mode, S(2, 1); (d) the fourth mode, AS(2, 1); (e) the fifth mode, AS(1, 2); (f) the sixth mode, S(1, 2); (g) the seventh mode, S(3, 1); and (h) the eighth mode, AS(3, 1). The rigid body motion of spacecraft is exaggerated.

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Fig. 5

The first, second, fifth, and sixth global mode shapes of the spacecraft obtained from GAM approach (L=9 m): (a) the first mode, S(1, 1); (b) the second mode, AS(1, 1); (c) the fifth mode, AS(1, 2); and (d) the sixth mode, S(1, 2)

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Fig. 6

Dynamic response excited by a torque pulse for a spacecraft installed with a pair of solar panels (L=9 m)

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Fig. 7

Block diagram of LQR controllers based on GAM2 and AMM2 models

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Fig. 8

Time response for the flexible spacecraft with GAM2 and AMM2 controllers (L=9 m): (a) attitude angle θy, (b) tip deflection of the solar panel w1(L, b) (plate 1), and (c) control torque τy

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