Stability Condition of Robust and Non-fragile $H^{\infty}$ Hovering Control with Real-time Tuning Available Fuzzy Compensator

  • Kim, Joon-Ki (Hitachi-LG Data Storage, Inc.) ;
  • Lim, Do-Hyung (School of Electrical Engineering and Computer Science, Kyungpook National University) ;
  • Kim, Won-Ki (School of Electrical Engineering and Computer Science, Kyungpook National University) ;
  • Kang, Soon-Ju (School of Electrical Engineering and Computer Science, Kyungpook National University) ;
  • Park, Hong-Bae (School of Electrical Engineering and Computer Science, Kyungpook National University)
  • Published : 2007.08.31

Abstract

In this paper, we describe the synthesis of robust and non-fragile $H^{\infty}$ state feedback controllers for linear systems with affine parameter uncertainties, as well as a static state feedback controller with poly topic uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile $H^{\infty}$ static state feedback controller with fuzzy compensator, and the region of controllers that satisfies non-fragility are presented. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a resulted polytopic region.

Keywords

References

  1. P. Dorato, C. T. Abdallah, and D. Famularo, 'On the design of non-fragile compensators via symbolic quantifier elimination,' Proc. of World Automation Congress in Anchorage, Alaska, pp. 9-14, 1998
  2. J. R. Corrado and W. M. Haddad, 'Static output feedback controllers for systems with parametric uncertainty and controller gain variation,' Proc. of Amer. Contr. Conf., San Diego, California, pp. 915-919, 1999
  3. P. Dorato, 'Non-fragile controller design: An overview,' Proc. of Amer. Contr. Conf., Philadelphia, Pennsylvania, pp. 2829-2831, 1998
  4. D. Famularo, C. T. Abdallah, A. Jadbabaie, P. Dorato, and W. M. Haddad, 'Robust non-fragile LQ controllers: The static state feedback case,' Proc. Amer. Contr. Conf., Philadelphia, Pennsylvania, pp. 1109-1113, 1998
  5. W. M. Haddad and J. R. Corrado, 'Robust resilient dynamic controller for systems with parametric uncertainty and controller gain variations,' Proc. of Amer. Contr. Conf., Philadelphia, Pennsylvania, pp. 2837-2841, 1998
  6. A. Jadbabie, C. T. Abdallah, D. Famularo, and P. Dorato, 'Robust, non-fragile and optimal controller via linear matrix inequalities,' Proc. of Amer. Contr. Conf., Philadelphia, Pennsylvania, pp. 2842-2846, 1998
  7. L. H. Keel and S. P. Bhattacharyya, 'Digital implementation of fragile controllers,' Proc. of Amer. Contr. Conf., Philadelphia, Pennsylvania, pp. 2852-2856, 1998
  8. L. H. Keel and S. P. Bhattacharyya, 'Robust, fragile, or optimal,' IEEE Trans. on Automatic Control, vol. 42, no. 8, pp. 1098-1105, 1997 https://doi.org/10.1109/9.618239
  9. J. H. Kim, S. K. Lee, and H. B. Park, 'Robust and non-fragile $H^{\infty}$ control of parameter uncertain time-varying delay systems,' SICE in Morioka, pp. 927-932, July 1999
  10. S. H. Cho, K. T. Kim, and H. B. Park, 'Robust and non-fragile $H^{\infty}$ controller design for affine parameter uncertain systems,' Proc. of Conf on Deci. and Contr., Sydney, Australia, pp. 3224-3229, 2000
  11. P. Apkarian and H. D. Tuan, 'Parameterized LMIs in control theory,' Proc. of IEEE Conf. Deci. and Contr., Florida, pp. 152-157, 1998
  12. H. D. Tuan and P. Apkarian, 'Relaxations of parameterized LMIs with control applications,' Int. J. of Robust Nonlinear Control, vol. 9, no. 2, pp. 59-84, 1999 https://doi.org/10.1002/(SICI)1099-1239(199902)9:2<59::AID-RNC392>3.0.CO;2-O
  13. M. Sugeno, I. Hirano, S. Nakamura, and S. Kotsu, 'Development of an intelligent unmanned helicopter,' Proc. of IEEE Int. Conf. Fuzzy Systems, vol. 5, pp. 207-219, 1994
  14. M. S. Kim, J. K. Kim, J. Y. Han, and H. B. Park, 'LQR based PID controller design for model helicopter in hover,' Proc. of the 3rd Int. Conf. on Computing, Communication and Control Technologies, pp. 155-160, 2005
  15. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994
  16. Raymond W. Prouty, Helicopter Performance, Stability and Control, Krieger Publishing Company, 1995