Skip to main content
SpringerLink
Log in

Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin’s minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. WALLRAPP, O. and WIEDEMANN, B. Dynamics of satellite with deployable rigid solar arrays. Multibody System Dynamics, 7(1), 101–125 (2002)

    Article  MATH  Google Scholar 

  2. KUANG, J., MEEHANB, P. A., LEUNG, A. Y. T., and TAN, S. Nonlinear dynamics of a satellite with deployable solar panel arrays. International Journal of Non-Linear Mechanics, 39(7), 1161–1173 (2004)

    Article  MATH  Google Scholar 

  3. KWAK, M. K., HEO, S., and KIM, H. B. Dynamics of satellite with deployable rigid solar arrays. Multibody System Dynamics, 20(3), 271–286 (2008)

    Article  MATH  Google Scholar 

  4. ZHANG, D. G. and ZHOU, S. F. Dynamic analysis of flexible-link flexible-joint robots. Applied Mathematics and Mechanics (English Edition), 27(5), 695–704 (2006) https://doi.org/10.1007/s10483-006-0516-1

    Article  MathSciNet  MATH  Google Scholar 

  5. ZHANG, D. G. Recursive Lagrangian dynamic modeling and simulation of mult-link spatial flexi-ble manipulator arms. Applied Mathematics and Mechanics (English Edition), 30(10), 1283–1294 (2009) https://doi.org/10.1007/s10483-009-1008-2

    Article  MathSciNet  Google Scholar 

  6. GE, X. S., CHEN, L. Q., and LIU, Y. Z. Optimal control of the deployment process of solar wings on spacecraft. Acta Astronautica, 60, 684–690 (2007)

    Article  Google Scholar 

  7. GE, X. S. and SUN, K. Optimal control of a spacecraft with deployable solar arrays using particle swarm optimization algorithm. Science China Technological Sciences, 54(5), 1107–1112 (2011)

    Article  MATH  Google Scholar 

  8. YAO, Q. J. and GE, X. S. Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy. Theoretical and Applied Mechanics Letters, 7(4), 258–263 (2017)

    Article  Google Scholar 

  9. GUO, Y. S. and CHEN, L. Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters. Applied Mathematics and Mechanics (English Edition), 29(9), 1131–1140 (2008) https://doi.org/10.1007/s10483-008-0903-z

    Article  MathSciNet  MATH  Google Scholar 

  10. DONG, Q. H. and CHEN, L. Impact dynamics analysis of free-floating space manipulator capturing satellite on orbit and robust adaptive compound control algorithm design for sup-pressing motion. Applied Mathematics and Mechanics (English Edition), 35(4), 413–422 (2014) https://doi.org/10.1007/s10483-014-1801-7

    Article  MathSciNet  MATH  Google Scholar 

  11. YU, X. Y. and CHEN, L. Modeling and observer-based augmented adaptive control of flexible-joint free-floating space manipulators. Acta Astronautica, 108, 146–155 (2015)

    Article  Google Scholar 

  12. YU, X. Y. and CHEN, L. Observer-based two-time scale robust control of free-flying flexible-joint space manipulators with external disturbances. Robotica, 35(11), 2201–2217 (2017)

    Article  MathSciNet  Google Scholar 

  13. JIANG, J. P. and LI, D. X. Robust H1 vibration control for smart solar array structures. Journal of Vibration and Control, 17(4), 505–515 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. JIANG, J. P. and LI, D. X. Decentralized robust vibration control of smart structures with parameter uncertainties. Journal of Intelligent Material Systems and Structures, 22(2), 137–147 (2011)

    Article  MathSciNet  Google Scholar 

  15. ZHANG, L. X., BAI, Z. F., ZHAO, Y., and CAO, X. B. Dynamic response of solar panel de-ployment on spacecraft system considering joint clearance. Acta Astronautica, 81(1), 174–185 (2012)

    Article  Google Scholar 

  16. LIU, L., CAO, D. Q., and TAN, X. J. Studies on global analytical mode for a three-axis attitude stabilized spacecraft by using the Rayleigh-Ritz method. Archive of Applied Mechanics, 86(12), 1927–1946 (2016)

    Article  Google Scholar 

  17. LIU, L. and CAO, D. Q. Dynamic modeling for a flexible spacecraft with solar arrays composed of honeycomb panels and its proportional-derivative control with input shaper. Journal of Dynamic Systems, Measurement, and Control, 138(8), 081008 (2016)

    Article  Google Scholar 

  18. LIU, L., CAO, D. Q., WEI, J., TAN, X. J., and YU, T. H. Rigid-flexible coupling dynamic modeling and vibration control for a three-axis stabilized spacecraft. Journal of Vibration and Acoustics, 139(4), 041006 (2017)

    Article  Google Scholar 

  19. LIU, L., CAO, D. Q., HUANG, H., SHAO, C. H., and XU, Y. Q. Thermal-structural analysis for an attitude maneuvering flexible spacecraft under solar radiation. International Journal of Mechanical Sciences, 126, 161–170 (2017)

    Article  Google Scholar 

  20. LI, H. Q., LIU, X. F., DUAN, L. C., and CAI, G. P. Deployment and control of spacecraft solar array considering joint stick-slip friction. Aerospace Science and Technology, 42, 342–352 (2015)

    Article  Google Scholar 

  21. LI, H. Q., LIU, X. F., GUO, S. J., and CAI, G. P. Deployment dynamics of large-scale flexible solar arrays. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics, 230(2), 147–158 (2015)

    Google Scholar 

  22. LI, H. Q., DUAN, L. C., LIU, X. F., and CAI, G. P. Deployment and control of flexible solar array system considering joint friction. Multibody System Dynamics, 39(3), 249–265 (2017)

    Article  MathSciNet  Google Scholar 

  23. LI, H. Q., DUAN, L. C., LIU, X. F., and CAI, G. P. Deployment and control of cable-driven flexible solar arrays. Aircraft Engineering and Aerospace Technology, 89(6), 835–844 (2017)

    Article  Google Scholar 

  24. GARG, D., PATTERSON, M., HAGER, W. W., RAO, A. V., BENSON, D. A., and HUNTING-TON, G. T. A unified framework for the numerical solution of optimal control problems using pseudospectral methods. Automatica, 46(11), 1843–1851 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. ROSS, I. M. and KARPENKO, M. A review of pseudospectral optimal control: from theory to flight. Annual Reviews in Control, 36(2), 182–197 (2012)

    Article  Google Scholar 

  26. HUANG, X., YAN, Y., ZHOU, Y., and Zhang, H. Pseudospectral method for optimal propellant-less rendezvous using geomagnetic Lorentz force. Applied Mathematics and Mechanics (English Edition), 36(5), 609–618 (2015) https://doi.org/10.1007/s10483-015-1936-7

    Article  MathSciNet  Google Scholar 

  27. GE, X. S., YI, Z. G., and CHEN, L. Q. Optimal control of attitude for coupled-rigid-body space-craft via Chebyshev-Gauss pseudospectral method. Applied Mathematics and Mechanics (English Edition), 38(9), 1257–1272 (2017) https://doi.org/10.1007/s10483-017-2236-8

    Article  MathSciNet  MATH  Google Scholar 

  28. FAHROO, F. and ROSS, I. M. Costate estimation by a Legendre pseudospectral method. Journal of Guidance, Control, and Dynamics, 24(2), 270–277 (2001)

    Article  Google Scholar 

  29. YAN, H., ROSS, I. M., and ALFRIEND, K. T. Pseudospectral feedback control for three-axis magnetic attitude stabilization in elliptic orbits. Journal of Guidance, Control, and Dynamics, 30(4), 1107–1115 (2007)

    Article  Google Scholar 

  30. TIAN, B. L. and ZONG, Q. Optimal guidance for reentry vehicles based on indirect Legendre pseudospectral method. Acta Astronautica, 68(7–8), 1176–1184 (2011)

    Article  Google Scholar 

  31. YANG, L., ZHOU, H., and CHEN, W. C. Application of linear Gauss pseudospectral method in model predictive control. Acta Astronautica, 96, 175–187 (2014)

    Article  Google Scholar 

  32. LIAO, Y. X., LI, H. F., and BAO, W. M. Indirect Radau pseudospectral method for the receding horizon control problem. Chinese Journal of Aeronautics, 29(1), 215–227 (2016)

    Article  Google Scholar 

  33. YAO, Q. J. and GE, X. S. Optimal reorientation of a free-floating space robot subject to initial state uncertainties. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 146 (2018)

    Article  Google Scholar 

  34. GILL, P. E., MURRAY, W., and SAUNDERS, M. A. SNOPT: an SQP algorithm for large-scale constrainted optimization. SIAM Review, 47(1), 99–131 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  35. BRYSON, A. E. and HO, Y. C. Applied Optimal Control: Optimization, Estimation, and Control, Hemisphere, New York (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Beijing Information Science and Technology University, Beijing, 100192, China

    Xinsheng Ge & Qijia Yao

  2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China

    Liqun Chen

Authors
  1. Xinsheng Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qijia Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liqun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinsheng Ge.

Additional information

Citation: GE, X. S., YAO, Q. J., and CHEN, L. Q. Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty. Applied Mathematics and Mechanics (English Edition), 39(10), 1437–1452 (2018) https://doi.org/10.1007/s10483-018-2378-8

Project supported by the National Natural Science Foundation of China (Nos. 11732005 and 11472058)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ge, X., Yao, Q. & Chen, L. Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty. Appl. Math. Mech.-Engl. Ed. 39, 1437–1452 (2018). https://doi.org/10.1007/s10483-018-2378-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-018-2378-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation