Skip to main content
SpringerLink
Log in

Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

The closed loop attitude stability of a hypersonic vehicle controlled by the characteristic model-based all-coefficient adaptive controller is studied in this paper, and an algorithm based on the computation of induced matrix 1-norm or ∞-norm is proposed. First of all, the Taylor series expansion is applied to discretize the inputoutput description of the attitude dynamics of the vehicle. The obtained difference equations have the same structure as characteristic model; thus the intervals which contain all possible values of certain characteristic model parameters are obtained. When the linear feedback controller is used in the feedback loop, with some conservation, the closed loop system is viewed as a class of interval time-varying systems defined by a number of free time-varying parameters. These free parameters take values from predefined intervals. The sufficient and necessary condition for the stability of this class of system is given. Finally, a sufficient condition for the stability of hypersonic vehicle attitude control loop is proposed and demonstration example is presented. The method proposed checks up the stability of the closed loop system by evaluating a finite number of matrix norms, and overcomes the difficulties brought by the time-varying nature of the characteristic model and parameter estimation.

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. Wu H X, Meng B. Review on the control of hypersonic flight vehicles. Adv Mech, 2009, 39: 756–765

    Google Scholar 

  2. Dydek Z T, Annaswamy A M. Adaptive control and the NASA X-15 program: a concise history, lessons learned, and a provably correct design. In: Proceedings of American Control Conference. Seattle, 2008. 2957–2962

  3. da Costa R R, Chu Q P, Mulder J A. Reentry flight controller design using nonlinear dynamic inversion. J Spacecraft Rockets, 2003, 40: 64–71

    Article  Google Scholar 

  4. Zhang Z, Hu J. Prediction based guidance algorithm for high-lift reentry vehicles. Sci China Inf Sci, 2011, 54: 498–510

    Article  MathSciNet  MATH  Google Scholar 

  5. Fujimori A, Terui F, Nikiforuk P N. Flight control design of an unmanned space vehicle using gain scheduling. J Guid Control Dynam, 2005, 28: 96–105

    Article  Google Scholar 

  6. Wallner E M, Well K H. Attitude control of a reentry vehicle with internal dynamics. J Guid Control Dynam, 2003, 26: 846–854

    Article  Google Scholar 

  7. Schumacher C, Khargonekar P P. Stability analysis of a missile control system with a dynamic inversion controller. J Guid Control Dynam, 1998, 21: 508–515

    Article  Google Scholar 

  8. Bennett D E. Space shuttle entry flight control overview. J Astronaut Sci, 1983, 31: 569–578

    Google Scholar 

  9. Li X D, Xian B, Diao C, et al. Output feedback control of hypersonic vehicles based on neural network and high gain observer. Sci China Inf Sci, 2011, 54: 429–447

    Article  MathSciNet  MATH  Google Scholar 

  10. Xu H J, Mirmirani M D, Ioannou P A. Adaptive sliding mode control design for a hypersonic flight vehicle. J Guid Control Dynam, 2004, 27: 829–838

    Article  Google Scholar 

  11. Mooij E. Numerical investigation of model reference adaptive control for hypersonic aircraft. J Guid Control Dynam, 2001, 24: 315–323

    Article  Google Scholar 

  12. Wu H X, Hu J, Xie Y C. Characteristic Model-Based Intelligent Adaptive Control. Beijing: China Science and Technology Press, 2009. 1

    Google Scholar 

  13. Meng B, Wu H X. The proof for characteristic model of linear time invariant systems. Sci China Ser E-Tech Sci, 2007, 37: 1258–1271

    Google Scholar 

  14. Qi C Z, Wu H X, Lü Z D. Study on the stability of multivariable all-coefficient adaptive control system. Contr Theor Appl, 2000, 17: 489–494

    MATH  Google Scholar 

  15. Yang J C, Hu J, Ni M L. Adaptive guidance law design based on characteristic model for reentry vehicles. Sci China Ser F-Inf Sci, 2008, 51: 2005–2021

    Article  MathSciNet  Google Scholar 

  16. Bauer P H, Premaratne K, Duran J. A necessary and sufficient condition for robust asymptotic stability of time-varying discrete systems. IEEE Trans Automat Contr, 1993, 38: 1427–1430

    Article  MathSciNet  MATH  Google Scholar 

  17. Ludyk G. Stability of Time-Variant Discrete-Time Systems. Braunschweig: Friedr Vieweg, 1985

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Beijing Institute of Control Engineering, Beijing, 100190, China

    Zhao Zhang & Jun Hu

  2. Science and Technology on Space Intelligent Control Laboratory, Beijing, 100190, China

    Zhao Zhang

Authors
  1. Zhao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao Zhang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, Z., Hu, J. Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller. Sci. China Inf. Sci. 55, 2243–2256 (2012). https://doi.org/10.1007/s11432-011-4455-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-011-4455-9

Keywords

Search

Navigation