Characteristic model based adaptive controller design and analysis for a class of SISO systems

一类SISO系统基于特征模型的极点配置自适应控制设计与分析

Abstract

The design of an adaptive controller and stability analysis of the corresponding closed loop system are discussed for a class of SISO systems based on the characteristic model method. The obtained characteristic model is a second-order slow time-varying linear system with a compress mapping function for the system modeling error. The pole placement method is used to design the controller, and sufficient conditions for the stability of the closed loop system are obtained based on the robust control theory of slow time-varying systems with perturbations. The effectiveness of the proposed method is illustrated by two numerical examples.

摘要

创新点

本文针对一类仿射非线性连续SISO系统, 通过压缩映射思想构建一个简洁二阶的慢时变差分方程作为其对应原连续系统的特征模型。 同时, 充分考虑特征建模过程中离散截断误差和未建模误差对系统稳定性的影响, 给出了在上述误差满足稳定收敛的条件下基于特征模型的自适应控制设计能够保证原系统镇定的充分条件。 从而将针对原系统的复杂控制设计问题转化成特征模型基础上的极点配置自适应控制问题, 该方法具有较强的工程实现意义。 最后通过仿真给出了不同极点配置方法的性能比较, 验证了所提方法的有效性。

This is a preview of subscription content, access via your institution.

References

  1. 1

    Wu H X, Hu J, Xie Y C. Characteristic model-based intelligent adaptive control. Beijing: China Science and Technology Press, 2009

    Google Scholar 

  2. 2

    Wu H X, Hu J, Xie Y C. Characteristic model-based adaptive control method and applications. IEEE Trans Syst Man Cybern Part C-Appl Rev, 2007, 37: 213–221

    Article  Google Scholar 

  3. 3

    Wang Y. Stability analysis of characteristic model based all-coefficient adaptive control for a class of minimum-phase linear system. Proc Eng, 2012, 29: 2410–2420

    Article  Google Scholar 

  4. 4

    Gao S G, Dong H R, Ning B. Characteristic model-based all-coefficient adaptive control for automatic train control systems. Sci China Inf Sci, 2014, 57: 092201

    Google Scholar 

  5. 5

    Xie Y C, Hu J. The application of the intelligent adaptive control method based on characteristic model in rendezvous and docking. J Syst Sci Complexity, 2013, 33: 1017–1023

    MATH  Google Scholar 

  6. 6

    Zhang Z, Hu J. Stability analysis of a hypersonic vehicle controlled by the characteristic model based adaptive controller. Sci China Inf Sci, 2012, 55: 2243–2256

    MathSciNet  Article  MATH  Google Scholar 

  7. 7

    Gong Y L, Wu H X. Characteristic model-based adaptive attitude control for hypersonic vehicle. J Astronaut, 2009, 31: 2122–2128

    Google Scholar 

  8. 8

    Wang L J. Characteristic model-based attitude controller and adaptive filter design for the hypersonic vehicle. Aerosp Control Appl, 2011, 37: 14–20

    Google Scholar 

  9. 9

    Yu H X, Lei Y J. Characteristic-model-based attitude control for satellites with input saturation. Aerosp Control Appl, 2013, 39: 44–53

    Google Scholar 

  10. 10

    Luo X, Li J. Fuzzy dynamic characteristic model based attitude control of hypersonic vehicle in gliding phase. Sci China Inf Sci, 2011, 54: 448–459

    MathSciNet  Article  MATH  Google Scholar 

  11. 11

    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

    MathSciNet  Article  MATH  Google Scholar 

  12. 12

    Meng B, Wu H X. Proof of characteristic model of linear system. Sci China Ser-E: Tech Sci, 2007, 37: 1258–1277

    Google Scholar 

  13. 13

    Sun D Q, Wu H X. Characteristic model and control method of MIMO high-order linear systems. Aerosp Control, 2004, 22: 4–10

    Google Scholar 

  14. 14

    Meng B, Wu H X. On characteristic modeling of a class of flight vehicles’ attitude dynamics. Sci China Tech Sci, 2010, 53: 2074–2080

    Article  MATH  Google Scholar 

  15. 15

    Wang Y. Stability analysis of characteristic model-based adaptive method for a class of minimum-phase nonlinear system. Control Theory Appl, 2012, 29: 1097–1107

    Google Scholar 

  16. 16

    Li H, Sun Z Q, Min H B, et al. Fuzzy dynamic characteristic modeling and adaptive control of nonlinear systems and its application to hypersonic vehicles. Sci China Inf Sci, 2011, 54: 460–468

    MathSciNet  Article  MATH  Google Scholar 

  17. 17

    Li C Y, Guo L. A dynamical inequality for the output of uncertain nonlinear systems. Sci China Inf Sci, 2013, 56: 112–120

    MathSciNet  Google Scholar 

  18. 18

    Nešić D, Teel A R. A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Trans Automat Control, 2004, 49: 1103–1122

    MathSciNet  Article  Google Scholar 

  19. 19

    Wang Y. Analysis for some stability properties of all-coefficient adaptive controller. Aerosp Control Appl, 2012, 38: 10–16

    Google Scholar 

  20. 20

    Xie Y C, Wu H X. The robustness of the all-coefficient adaptive control method. Acta Automat Sin, 1997, 23: 151–159

    MathSciNet  MATH  Google Scholar 

  21. 21

    Meng B, Wu H X. Convergence and stability of the golden-section control. J Astronaut, 2009, 30: 2128–2132

    Google Scholar 

  22. 22

    Chen L, Shen S P. Stability analysis of golden section adaptive control system based on multivariable characteristic model. Tech Automat Appl, 2013, 32: 11–15

    Google Scholar 

  23. 23

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

    MathSciNet  MATH  Google Scholar 

  24. 24

    Yan Z, Wang J. Robust model predictive control of nonlinear systems with unmodeled dynamics and bounded uncertainties based on neural networks. IEEE Trans Neural Netw Learn Syst, 2014, 25: 457–469

    Article  Google Scholar 

  25. 25

    Aswani A, Gonzalez H, Sastry S S, et al. Provably safe and robust learning-based model predictive control. Automatica, 2013, 49: 1216–1226

    MathSciNet  Article  MATH  Google Scholar 

  26. 26

    Wang Z M. Sampled-data stabilization controller design of continuous-time nonlinear control systems: an approach based on their approximate discrete-time models (in Chinese). Dissertation for the Doctoral Degree. ShangHai: East China Normal University, 2003

    Google Scholar 

  27. 27

    Nešić D, Teel A R. Stabilization of sampled-data nonlinear systems via backstepping on their Euler approximate model. Automatica, 2006, 42: 1801–1808

    MathSciNet  Article  MATH  Google Scholar 

  28. 28

    Fidan B, Zhang Y, Ioannou P. Adaptive control of a class of slowly time varying systems with unmodeling uncertainties. IEEE Trans Automat Control, 2005, 50: 915–920

    MathSciNet  Article  Google Scholar 

  29. 29

    Wang Y Z, Feng G. On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems. Sci China Inf Sci, 2013, 56: 108202

    MathSciNet  Google Scholar 

  30. 30

    Kreisselmeier G. Adaptive control of a class of slowly time varying plant. Syst Control Lett, 1986, 8: 97–103

    Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yu Kang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, J., Kang, Y., Meng, B. et al. Characteristic model based adaptive controller design and analysis for a class of SISO systems. Sci. China Inf. Sci. 59, 052202 (2016). https://doi.org/10.1007/s11432-015-5310-1

Download citation

Keywords

  • characteristic model
  • modeling error
  • pole placement
  • perturbation analysis
  • sampling system

关键词

  • 特征模型
  • 未建模误差
  • 极点配置
  • 扰动分析
  • 采样系统