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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Li, J. , and Yan, S. , 2014, “ Thermally Induced Vibration of Composite Solar Array With Honeycomb Panels in Low Earth Orbit,” Appl. Therm. Eng., 71(1), pp. 419–432. [CrossRef]
Hu, Q. , Shi, P. , and Gao, H. , 2007, “ Adaptive Variable Structure and Commanding Shaped Vibration Control of Flexible Spacecraft,” J. Guid. Control Dyn., 30(3), pp. 804–815. [CrossRef]
Bang, H. , Ha, C. K. , and Kim, J. H. , 2005, “ Flexible Spacecraft Attitude Maneuver by Application of Sliding Mode Control,” Acta Astronaut., 57(11), pp. 841–850. [CrossRef]
Sales, T. P. , Rade, D. A. , and De Souza, L. C. G. , 2013, “ Passive Vibration Control of Flexible Spacecraft Using Shunted Piezoelectric Transducers,” Aerosp. Sci. Technol., 29(1), pp. 403–412. [CrossRef]
Lee, K. W. , and Singh, S. N. , 2012, “ L1 Adaptive Control of Flexible Spacecraft Despite Disturbances,” Acta Astronaut., 80, pp. 24–35. [CrossRef]
Karray, F. , Grewal, A. , Glaum, M. , and Modi, V. , 1997, “ Stiffening Control of a Class of Nonlinear Affine Systems,” IEEE Trans. Aerosp. Electron. Syst., 33(2), pp. 473–484. [CrossRef]
Cai, G. P. , and Lim, C. W. , 2008, “ Dynamics Studies of a Flexible Hub–Beam System With Significant Damping Effect,” J. Sound Vib., 318(1), pp. 1–17. [CrossRef]
Zhang, J. , and Wang, T. , 2013, “ Coupled Attitude-Orbit Control of Flexible Solar Sail for Displaced Solar Orbit,” J. Spacecr. Rockets, 50(3), pp. 675–685. [CrossRef]
Hablani, H. B. , 1982, “ Constrained and Unconstrained Modes: Some Modeling Aspects of Flexible Spacecraft,” J. Guid. Control Dyn., 5(2), pp. 164–173. [CrossRef]
Jiang, J. P. , and Li, D. X. , 2011, “ Robust H-Infinity Vibration Control for Smart Solar Array Structure,” J. Vib. Control, 17(4), pp. 505–515. [CrossRef]
Jiang, J. P. , and Li, D. X. , 2010, “ Decentralized Guaranteed Cost Static Output Feedback Vibration Control for Piezoelectric Smart Structures,” Smart Mater. Struct., 19(1), p. 015018. [CrossRef]
Dietz, S. , Wallrapp, O. , and Wiedemann, S. , 2003, “ Nodal vs. Modal Representation in Flexible Multibody System Dynamics,” Multibody Dynamics, Jorge A. C. Ambrósio , ed., IDMEC/IST, Lisbon, Portugal.
Pan, K. Q. , and Liu, J. Y. , 2012, “ Investigation on the Choice of Boundary Conditions and Shape Functions for Flexible Multi-Body System,” Acta Mech. Sin., 28(1), pp. 180–189. [CrossRef]
Schwertassek, R. , Wallrapp, O. , and Shabana, A. A. , 1999, “ Flexible Multibody Simulation and Choice of Shape Functions,” Nonlinear Dyn., 20(4), pp. 361–380. [CrossRef]
Johnston, J. D. , and Thornton, E. A. , 1998, “ Thermally Induced Attitude Dynamics of a Spacecraft With a Flexible Appendage,” J. Guid. Control Dyn., 21(4), pp. 581–587. [CrossRef]
Hughes, P. C. , 1980, “ Modal Identities for Elastic Bodies, With Application to Vehicle Dynamics and Control,” ASME J. Appl. Mech., 47(1), pp. 177–184. [CrossRef]
Hughes, P. C. , 1974, “ Dynamics of Flexible Space Vehicles With Active Attitude Control,” Celestial Mech. Dyn. Astron., 9(1), pp. 21–39. [CrossRef]
Hablani, H. B. , 1990, “ Hinges-Free and Hinges-Locked Modes of a Deformable Multibody Space Station—A Continuum Analysis,” J. Guid. Control Dyn., 13(2), pp. 286–296. [CrossRef]
Hablani, H. B. , 1982, “ Modal Analysis of Gyroscopic Flexible Spacecraft: A Continuum Approach,” J. Guid. Control Dyn., 5(5), pp. 448–457. [CrossRef]
Hurty, W. C. , 1965, “ Dynamic Analysis of Structural Systems Using Component Modes,” AIAA J., 3(4), pp. 678–685. [CrossRef]
Craig, R. R. , and Bampton, M. C. C. , 1968, “ Coupling of Substructures for Dynamic Analyses,” AIAA J., 6(7), pp. 1313–1319. [CrossRef]
Liu, L. , and Cao, D. , 2016, “ Dynamic Modeling for a Flexible Spacecraft With Solar Arrays Composed of Honeycomb Panels and Its Proportional–Derivative Control With Input Shaper,” ASME J. Dyn. Syst. Meas. Control, 138(8), p. 081008. [CrossRef]
Vakil, M. , Fotouhi, R. , Nikiforuk, P. N. , and Heidari, F. , 2011, “ A Study of the Free Vibration of Flexible-Link Flexible-Joint Manipulators,” Proc. Inst. Mech. Eng. Part C, 225(6), pp. 1361–1371. [CrossRef]
Barbieri, E. , and OüZguüNer, U. , 1988, “ Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link,” ASME J. Dyn. Syst. Meas. Control, 110(4), pp. 416–421. [CrossRef]
Liu, L. , Cao, D. , and Tan, X. , 2016, “ Studies on Global Analytical Mode for a Three-Axis Attitude Stabilized Spacecraft by Using the Rayleigh-Ritz Method,” Arch. Appl. Mech., 86(12), pp. 1927–1946. [CrossRef]
Song, M. T. , Cao, D. Q. , and Zhu, W. D. , 2011, “ Dynamic Analysis of a Micro-Resonator Driven by Electrostatic Combs,” Commun. Nonlinear Sci. Numer. Simul., 16(8), pp. 3425–3442. [CrossRef]
Cao, D. Q. , Song, M. T. , Zhu, W. D. , Tucker, R. W. , and Wang, C. H. T. , 2012, “ Modeling and Analysis of the In-Plane Vibration of a Complex Cable-Stayed Bridge,” J. Sound Vib., 331(26), pp. 5685–5714. [CrossRef]
Paik, J. K. , Thayamballi, A. K. , and Kim, G. S. , 1999, “ The Strength Characteristics of Aluminum Honeycomb Sandwich Panels,” Thin-Walled Struct., 35(3), pp. 205–231. [CrossRef]
Lachiver, J. M. , 2012, “ Pléiades: Operational Programming First Results,” 12th International Conference on Space Operations (SpaceOps 2012), Stockholm, Sweden, June 11–15, pp. 1307–1316.
Hu, Z. , and Hong, J. , 1999, “ Modeling and Analysis of a Coupled Rigid-Flexible System,” Appl. Math. Mech., 20(10), pp. 1167–1174. [CrossRef]


Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

Finite element model of the flexible spacecraft in ansys

Grahic Jump Location
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.

Grahic Jump Location
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)

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

Block diagram of LQR controllers based on GAM2 and AMM2 models

Grahic Jump Location
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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