Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Design Method of a Parallel Feedforward Compensator for Passivation of Linear Systems

선형 시스템 수동화를 위한 병렬 앞먹임 보상기 설계방법 연구

  • Published : 2004.07.01
Download PDF
⟨ Previous Next ⟩

Abstract

A passivity-based dynamic output feedback controller design is considered for a finite collection of non-square linear systems. Design of a single controller for a set of plants i.e. simultaneous stabilization is an important issue in the area of robust control design. We first determine a squaring gain matrix and an additional dynamics that is connected to the systems in a feedforward way, then a static passivating control law is designed. Consequently, the actual feedback controller will be the static control law combined with the feedforward dynamics. A necessary and sufficient condition for the existence of the parallel feedforward compensator is given by the static output feedback formulation. In contrast to the previous result [1], a technical condition for constructing the parallel feedforward compensator is removed by proposing a new type of the parallel compensator.

Keywords

References

  1. 손영익, '수동화 기법에 의한 비정방 선형 시스템의 강인 제어기 설계,' 제어·자동화·시스템공학회 논문지, 제8권, 제11호, pp. 907-915, 2002
  2. C. I. Bymes, A. Isidori, and J. C. Willems, 'Passivity, feedback equivalence, and the global stabilization of minimumphase nonlinear systems,' IEEE Trans. Automat. Contr., vol. 36, no. 11, pp. 1228-1240, 1991 https://doi.org/10.1109/9.100932
  3. H. K. Khalil, Nonlinear Systems, Prentice-Hall, 2nd Ed., 1996
  4. R. Sepulchre, M. Jankovic, P.V. Kokotovic, Constructive nonlinear Control, Springer-Verlag, 1997
  5. R. Ortega, A. Loria, P. J. Nicklasson, and H. Sira-Ramirez, Passivity-based Control of Euler-Lagrange Systems, Springer-Verlag, 1998
  6. H. Shim, J.H. Seo, A. R. Teel, 'Nonlinear observer design via passivation of error dynamics,' Automatica, vol. 39, pp. 885-892, 2003 https://doi.org/10.1016/S0005-1098(03)00023-2
  7. I. Bar-Kana, 'Parallel feedforward and simplified adaptive control,' Int. J. Adaptive Control and Signal Processing, vol. 1, no. 2, 95-109, 1987 https://doi.org/10.1002/acs.4480010202
  8. H. Kaufman, I. Bar-Kana, and K. Sobel, Direct Adaptive Control Algorithms, Springer-Verlag, 2nd Ed., 1998
  9. Z. Iwai and I. Mizumoto, 'Realization of simple adaptive control by using parallel feedforward compensator,' Int. J. Control, vol. 59, no. 6, pp. 1543-1565, 1994 https://doi.org/10.1080/00207179408923145
  10. A. G. Kelkar and S. M. Joshi, 'Robust control of non-passive systems via passification', In Proc. of American Control Conference, 1997 https://doi.org/10.1109/ACC.1997.611938
  11. M. Deng, Z. Iwai, and I. Mizumoto, 'Robust parallel compensator design for output feedback stabilization of plants with structured uncertainty,' Systems & Control Letters, vol. 36, pp. 193-198, 1999 https://doi.org/10.1016/S0167-6911(98)00091-7
  12. Y. I. Son, H. Shim, and J.H. Seo, 'Passification of nonlinear systems via dynamic output feedback', Journal of KIEE, pp. 23-28, 2000
  13. Y. Kawasaki, I. Mizumoto, R. Wakamiya, and Z. Iwai, 'Adaptive control of an inverted pendulum system,' In Proc. of Asia-Pacific Vibration Conference '93, Japan, vol. 3, pp. 1114-1119, 1993
  14. Y.-Y. Cao and Y.-X. Sun, 'Static output feedback simultaneous stabilization: ILMI approaach,' Int. J. Control, vol. 70, no. 5, pp. 803-814, 1998 https://doi.org/10.1080/002071798222145
  15. R. E. Benton, Jr. and D. Smith, 'A non-iterative LMI-based algorithm for robust static-output-feedback stabilization,' Int. J. Control, vol. 72, no. 14, pp. 1322-1330, 1999 https://doi.org/10.1080/002071799220290
  16. S. M. Joshi and A. G. Kelkar, 'Pasivity-based robust control of systems with redundant sensors and actuators,' Int. J. Control, vol. 74, no. 5, pp. 474-481, 2001 https://doi.org/10.1080/00207170010010588
  17. I. N. Kar, 'Design of static output feedback controller for uncertain systems,' Automatica, vol. 35, pp. 169-175, 1999 https://doi.org/10.1016/S0005-1098(98)00170-8
  18. Z. P. Jiang and D. J. Hill, 'Passivity and disturbance attenuation via output feedback for uncertain nonlineat systems,' IEEE Trans. Automat. Contr., vol. 43, no. 7, pp. 992-997, 1998 https://doi.org/10.1109/9.701109
  19. C. A. R. Crusius and A. Trofino, 'Sufficient LMI conditions for output feedback control problems,' IEEE Trans. Autonat. Contr., vol. 44, no. 5, pp. 1053-1057, 1999 https://doi.org/10.1109/9.763227
  20. Quanser Inc. Specialty - MAGLEV.pdf. Available at http://www.quanser.com
  21. J. C. Geromel, P. L. D. Peres, and S. R. Souza, 'Convex analysis of output feedback control problems: robust stability and performance,' IEEE Trans. Automat. Contr., vol. 41, no. 7, pp. 997-1003, 1996 https://doi.org/10.1109/9.508904
  22. B. D. O. Anderson and J. B. Moore, Optimal Control, Prentice-Hall, 1989