Robust Gain Scheduling Based on Fuzzy Logic Control and LMI Methods

퍼지논리제어와 LMI기법을 이용한 강인 게인 스케줄링

  • Chi, Hyo-Seon (Dept. of Mechanical Engineering, Korea Advanced Institute of Science and Technology) ;
  • Koo, Kuen-Mo (Dept. of Mechanical Engineering, Korea Advanced Institute of Science and Technology) ;
  • Lee, Hungu ;
  • Tahk, Min-Jea (Dept. of Mechanical Engineering, Korea Advanced Institute of Science and Technology) ;
  • Hong, Sung-Kyung
  • 지효선 (한국과학기술원 기계공학과) ;
  • 구근모 (한국과학기술원 기계공학과) ;
  • 이훈구 ((주)쎄트렉아이) ;
  • 탁민제 (한국과학기술원 기계공학과) ;
  • 홍성경 (세종대학교 항공우주공학과)
  • Published : 2001.01.01

Abstract

This paper proposes a practical gain-scheduling control law considering robust stability and performance of Linear Parameter Varying(LPV) systems in the presence of nonlinearities and uncertainties. The proposed method introduces LMI-based pole placement synthesis and also associates with a recently developed fuzzy control system based on Takagei-Sugenos fuzzy model. The sufficient conditions for robust controller design of linearized local dynamics and robust stabilization of fuzzy control systems are reduced to a finite set of Linear Matrix inequalities(LMIs) and solved by using co-evolutionary algorithms. The proposed method is applied to the longitudinal acceleration control of high performance aircraft with linear and nonlinear simulations.

References

  1. J. F. Shamma and M. Athans, 'Guaranteed properties of gain scheduled control for linear parameter-varying plants,' Automatica, vol. 27, pp. 559-564, 1991 https://doi.org/10.1016/0005-1098(91)90116-J
  2. J. F. Shamma and M. Athans, 'Analysis of gain scheduled control of nonlinear plants,' IEEE Transactions on Automatic Control, vol. 35, no. 8, 1970 https://doi.org/10.1109/9.58498
  3. J. C. Doyle, K. Glover, P. Khargonekar, and B. Francis, 'State space solutions to standard $H_2$ and $H_{\infty}$ control problems,' IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831-848. 1989 https://doi.org/10.1109/9.29425
  4. P. Apkarian and P. Gahinet, 'A convex characterization of gain-scheduled H∞ controllers,' IEEE Transactions on Automatic Control, vol. 40, no. 5, pp. 853-864, 1995 https://doi.org/10.1109/9.384219
  5. M. Chilali and P. Gahinet, '$H_{infty}$ design with pole placement constraints: An LMI approach,' IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 358-367, 1996 https://doi.org/10.1109/9.486637
  6. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Transactions on Systems Man Cybernet, vol. 15, pp. 116-132, 1985
  7. K. Tanaka, T. Ikeda, and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control:Quadratic stability, $H_{\infty}$ control theory, and linear matrix inequalityes,' IEEE Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 1-13, 1996 https://doi.org/10.1109/91.481840
  8. M. J. Tahk and B. C. Sun, 'Co-evolutionary augmented lagrangian methods for constrained optimization', IEEE Transactions on Evolutionary Computation https://doi.org/10.1109/4235.850652
  9. B. L. Stevens and F. L. Lewis, 'Aircraft control and Simulation', Wiley Interscience, 1992
  10. G. F. Franklin and J. D. Powell, 'Feedback control of dynamic systems,Feedback control of dynamic systems', Addison Wesley, 1994
  11. T. Back, 'Evolutionary algorithm in theory and practice,Evolutionary algorithm in theory and practice', Oxford University Press, 1966
  12. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, 'The LMI control toolbox,' Proceedings of the 33rd Conference on Desicion and Control, pp. 2038-2041, 1994 https://doi.org/10.1109/CDC.1994.411440
  13. A. M. Kuethe and C. Y. Chow, 'Foundation of aerodynamics', John wiley & Sons, pp. 518, 1986