Robust Backstepping Design of Nonlinear Systems Using Adaptation Strategy for Uncertaninties

불확실성 적응기법을 이용한 비선형 시스템의 강인 백스테핑 설계

  • Kim, Dong-Heon (Dept. of Electronic Engineering Hanyang University) ;
  • Kim, Eung-Seok (Dept. of Electrical Engineering, Halla University) ;
  • Yang, Hae-Won (Dept. of Electronic computer Engineering, Hanyang University)
  • 김동헌 (한양대학교 전기공학과) ;
  • 김응석 (한라대학교 전기공학부) ;
  • 양해원 (한양대학교 전자 컴퓨터 공학부)
  • Published : 2001.07.01

Abstract

In this paper, we design a robust adaptive controller for a nonlinear system with uncertainties to be rejected via disturbance adaptation law. The nonlinear system considered has unknown nonlinear functions being influenced by external disturbance. The upper bound of unknown nonlinear functions at each time is estimated by using a disturbance adaptation law. The estimated nonlinear functions are used to design a stabilizing function a control input. Tuning function is used to estimates unknown system parameter without overparametrization. A set-point regulation error converges to a residual set close to zero asymptotically. The effectiveness of the proposed controller is investigated by computer simulation.

References

  1. I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, 'Systematic design of adaptive controllers for feedback linearizable systems,' IEEE Trans. on Automatic Control, vol. 36, pp. 1241-1253, 1991 https://doi.org/10.1109/9.100933
  2. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, 'Adaptive nonlinear control without over-parametrization,' Systems & Control Letters, vol. 19, pp. 177-185, 1992 https://doi.org/10.1016/0167-6911(92)90111-5
  3. M. Krstic, I. Kanellakopoulos and P. V. Kokotovic, 'Nonlinear adaptive control design,' Jon Wiley & Sons, 1995
  4. P. A. Ioannou and J, Sun, 'Robust adaptive control,' Prentice Hall, 1996
  5. H. K. Khalil, 'Nonlinear systems,' Prentice Hall, 1996
  6. 김민수, 현근호, 양해원, '백스테핑 기법을 이용한 적응 비선형 제어기 설계에 관한 연구,' 대한 전기학회 하계학술대회 논문집, pp. 588-591, 1999
  7. R. A. Freeman and P. V. Kokotovic, 'Backstepping design of robust controllers for a class of nonlinear systems,' Proceedings of the IFAC Nonlinear Control Systems Design Symposium, pp. 307-312, 1992
  8. W. Lin and T. Shen, 'Robust passivity and feedback design for minimum-phase nonlinear systems with structural uncertainty,' Automatica, vol. 35, pp. 35-47, 1999 https://doi.org/10.1016/S0005-1098(98)00120-4
  9. R. A. Freeman and P. V. Kokotovic, 'Design of 'Softer' robust nonlinear control laws,' Automatica, vol. 29, no. 6, pp. 1425-1437, 1993 https://doi.org/10.1016/0005-1098(93)90007-G
  10. F. Ikhouane and M. Krstic, 'Robustness of the tuning functions adaptive back stepping design for linear systems,' IEEE Trans. on Automatic Control, vol. 43, pp. 431-437, 1998 https://doi.org/10.1109/9.661616
  11. Z. P. Jiang and L. Praly, 'Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties,' Automatica, vol. 34, no. 7, .pp 825-840, 1998 https://doi.org/10.1016/S0005-1098(98)00018-1
  12. L. Praly, 'Almost exact modeling assumption in adaptive linear control,' Int. J. Contr., vol. 51, pp. 643-648, 1990 https://doi.org/10.1080/00207179008934090
  13. K. Itou, T. Shen, and K. Tamura, 'Robust control of minimum-phase nonlinear systems with disturbance attenuation,' Proc. 3rd Asian Control Conference, pp. 217-222, 2000
  14. Y. Zhang and P. A. Ioannou, 'Robustness of nonlinear control systems with respect to unmodeled dynamics,' IEEE Trans. on Automatic Control, vol. 44, no. 1, pp. 119-124, 1999 https://doi.org/10.1109/9.739093
  15. A. S. I. Zinober and P. Liu, 'Robust control of nonlinear uncertain via sliding mode with back stepping design,' UKACC Int. Conference on Control, 1996
  16. F. Gao, W. Q. Liu, V. Sreeram, and K. L. Teo, 'Robust control design of nonlinear adaptive control systems with unmodelled dynamics.' Proc. of the 36th Conf. on Decision & Control, pp. 2073-2078, 1997 https://doi.org/10.1109/CDC.1997.657072