Browse > Article
http://dx.doi.org/10.5391/JKIIS.2005.15.6.765

Improved Digital Redesign for Fuzzy Systems: Compensated Bilinear Transform Approach  

Kim, Do-Wan (Yonsei University)
Joo, Young-Hoon (Kunsan National University)
Park, Jin-Bae (Yonsei University)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.15, no.6, 2005 , pp. 765-770 More about this Journal
Abstract
This paper presents a new intelligent digital redesign (IDR) method via the compensated bilinear transformation to design the digital controller such that the digital fuzzy system is equivalent to the analog fuzzy system in the sense of the state-matching. This paper especially consider a multirate control scheme with a predictive feature, where the digital control input is held constant N times between the sampling points. More precisely, the multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the state measured at the sampling points, the delayed measurements. For this system, the IDR conditions incorporated with stabilizability in the format of the linear matrix inequalities (LMIs) are derived. The superiority of the proposed technique is convincingly visualized through a numerical example.
Keywords
Intelligent digital redesign (IDR); fuzzy control; digital control; fuzzy system; linear matrix inequalities (LMIs);
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. G. Voulgaris, M. A. Dahleh, and L. S. Valavani, 'H$\infty$ and H$\in$ optimal controllers for periodic and multirate systems,' Automatica, vol. 30, pp. 251-263, 1994   DOI   ScienceOn
2 Y. H. Joo, L. S. Shieh, and G. Chen, 'Hybrid state space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems,' IEEE Trans. Fuzzy Syst., vol. 7, no. 4, pp. 394-408, 1999   DOI   ScienceOn
3 W. Chang, J. B. Park, Y. H. Joo, and G. Chen, 'Design of sampled-data fuzzy-model-based control systems by using intelligent digital redesign,' IEEE Trans. Circ. Syst. I, vol. 49, no. 4, pp. 509-517, 2002   DOI   ScienceOn
4 W. Chang, J. B. Park, H. J. Lee, and Y. H. Joo, 'LMI approach to digital redesign of linear timeinvarint systems,' IEE Proc., Control Theory Appl., vol. 149, no. 4, pp. 297-302, 2002
5 H. J. Lee, J. B. Park, and Y. H. Joo, 'An efficient observer-based sampled-data control: Digital redesign approach,' IEEE Trans. Circuits Syst. I, vol. 50, no. 12, pp. 1595-1601, 2003   DOI
6 T. Chen and L. Qiu, 'H$ \infty $ design of general multirate sampled-data control systems,' Automatica, vol. 30, pp. 1139-1152, 1994   DOI   ScienceOn
7 B. A. Francis and T. T. Georgiou, 'Stability theory for linear time-invariant plants with periodic digital controllers,' IEEE Trans. Automat. Contr., vol. 33, no. 9, pp. 820-832, 1988   DOI   ScienceOn
8 L. Qiu and T. Chen, 'H2 -optimal design of multirate sampled-data systems,' IEEE Trans. Automat. Contr., vol. 39, pp. 2506-2511, 1994   DOI   ScienceOn
9 H. J. Lee, H. Kim, Y. H. Joo, W. Chang, and J. BPark, 'A new intelligent digital redesign for T–S fuzzy systems: global approach,' IEEE Trans. Fuzzy Syst., vol. 12, no. 2, pp. 274-284, 2004   DOI   ScienceOn
10 H. O. Wang, K. Tananka, and M. F. Griffin, 'An approach to fuzzy control of nonlinear systems: Stability and design issues,' IEEE Trans. Fuzzy Syst., vol. 4, no. 1, pp. 14-23, 1996   DOI   ScienceOn
11 P. G.Voulgaris and B. Bamieh, 'Optimal H$\infty$ and H$ \in$ control of hybrid multirate systems,' Syst. Contr. Lett., vol. 20, pp. 249-261, 1993   DOI   ScienceOn
12 K. Tananka, T. Kosaki, and H. O. Wang, 'Backing control problem of a mobile robot with multiple trailers: fuzzy modeling and LMI-based design,' IEEE Trans. Syst. Man, Cybern. C., vol. 28, no. 3, pp. 329-337, 1998   DOI   ScienceOn
13 L. S. Shieh, W. M. Wang, J. Bain, and J. W. Sunkel, 'Design of lifted dual-rate digital controllers for X-38 vehicle,' Jounal of Guidance, Contr. Dynamics, vol. 23, pp. 629-339, Jul., 2000   DOI   ScienceOn
14 H. Fujimoto, Y. Hori, and A. Kawamura, 'Perfect tracking control based on multirate feedforward control with generalized sampling periods,' IEEE Trans. Ind. Electron., vol. 48, no. 3, pp. 636-644, 2001   DOI   ScienceOn
15 W. Chang, J. B. Park, and Y. H. Joo, 'GA-based intelligent digital redesign of fuzzy-model-based controllers,' IEEE Trans. Fuzzy Syst., vol. 11, no. 1, pp. 35-44, 2003   DOI   ScienceOn
16 T. Chen and B. Francis, 'Optimal Sampled-Data Control Systems,' Springer, 1995
17 H. Bo and A. N. Michel,'Some qualitative properties of multirate digital control systems,' IEEE Trans. Automat. Contr., vol. 44, pp. 765-770, 1999   DOI   ScienceOn
18 P. Colaneri and G. De Nicolao, 'Multirate LQG control of continuous- time stochastic systems,' Automatica, vol. 31, pp. 591-596, 1995   DOI   ScienceOn