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Research Papers

Dynamic Modeling for a Flexible Spacecraft With Solar Arrays Composed of Honeycomb Panels and Its Proportional–Derivative Control With Input Shaper

[+] 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

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 22, 2015; final manuscript received February 26, 2016; published online May 25, 2016. Assoc. Editor: Ming Xin.

J. Dyn. Sys., Meas., Control 138(8), 081008 (May 25, 2016) (11 pages) Paper No: DS-15-1528; doi: 10.1115/1.4033020 History: Received October 22, 2015; Revised February 26, 2016

A high-precision dynamic model of a flexible spacecraft installed with solar arrays, which are composed of honeycomb panels, is established based on the nonconstrained modes of flexible appendages (solar arrays), and an effective cooperative controller is designed for attitude maneuver and vibration suppression by integrating the proportional–derivative (PD) control and input shaping (IS) technique. The governing motion equations of the system and the corresponding boundary conditions are derived by using Hamiltonian Principle. Solving the linearized form of those equations with associated boundaries, the nonconstrained modes of solar arrays are obtained for deriving the discretized dynamic model. Applying this discretized model and combining the IS technique with the PD controller, a hybrid control scheme is designed to achieve the attitude maneuver of the spacecraft and vibration suppression of its flexible solar arrays. The numerical results reveal that the nonconstrained modes of the system are significantly influenced by the spacecraft flexibility and honeycomb panel parameters. Meanwhile, the differences between the nonconstrained modes and the constrained ones are growing as the spacecraft flexibility increases. Compared with the pure PD controller, the one integrating the PD control and IS technique performs much better, because it is more effective for suppressing the oscillation of attitude angular velocity and the vibration of solar array during the attitude maneuver, and reducing the residual vibration after the maneuver process.

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Figures

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Fig. 1

Model of spacecraft with solar arrays: (a) sketch of spacecraft and (b) geometric relations

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Fig. 2

Solar array model: (a) sectional view of solar array and (b) schematic of honeycomb panel

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Fig. 3

Coordinates in the thickness direction for the honeycomb core and two face sheets

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Fig. 4

The first three mode shapes of a hub-beam system with tip masses obtained from different models (L=20 m): (a) and (b) non-normalized and normalized mode shapes

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Fig. 12

Time responses of the flexible spacecraft for using the PD + IS control (JR=1000 kg⋅m2)

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Fig. 11

Time responses of the flexible spacecraft for using the PD + IS control (JR=10 kg⋅m2)

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Fig. 10

Time responses of the flexible spacecraft for using the PD + IS control (JR=100 kg⋅m2)

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Fig. 9

The structure of PD control with IS

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Fig. 8

Time responses of the flexible spacecraft for using the pure PD control (JR=100 kg⋅m2)

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Fig. 7

The structure of pure PD control

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Fig. 6

The normalized mode shapes of the first four nonconstrained and constrained modes of solar arrays (JR=100 kg⋅m2, hc/h=0.7): (a)–(d), the first to the fourth mode shapes

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Fig. 5

Variation of the nonconstrained frequencies of the flexible spacecraft with respect to hc/h for various JR. Thedashed lines are frequencies of corresponding cantilever honeycomb panel (constrained frequencies). ×, JR=1 kg⋅m2; —○—, JR=10 kg⋅m2; , JR=102 kg⋅m2; , JR=103 kg⋅m2; , JR=104 kg⋅m2: (a)–(d), the first to the fourth frequencies.

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