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

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

DOI QR Code

Asymptotic Stabilization of Linear Systems with Time-Varying Input Disturbances Using Disturbance Observer Techniques and Min-Max Control Method

외란관측기법과 최대최소 제어방법을 이용한 시변 입력 외란을 갖는 선형 시스템의 점근 안정화

  • 송성호 (한림대학교 정보통신공학부) ;
  • 김백섭 (한림대학교 정보통신공학부)
  • Published : 2004.01.01
Download PDF
⟨ Previous Next ⟩

Abstract

This paper deals with asymptotic stabilization problems for linear systems with time-varying input disturbances. In order to eliminate the influence of a disturbance on the system, a disturbance observer is designed and the time-varying disturbance can be rejected using its estimated value. Since the disturbance observer is kind of low-pass filter, it has inevitably estimation errors. To eliminate the inflences on the performance due to these errors, the additional control is designed based on these estimation errors using a well-known min-max control method. It is shown that the asymptotic stability of the closed-loop system is guaranteed. In general, the min-max control method requires the switching of control inputs and the switching magnitude of the control input is determined by the disturbance estimation error bounds. As the error bounds can be made arbitrarily small by choosing the high gain for the disturbance observer, the control method suggested in this paper can reduce the chattering phenomena as small as possible. Therefore, it has superior performance to the existing ones.

Keywords

References

  1. M. T. White, M. Tomizuka and C. Smith, 'Improved track following in magnetic disk drives using a disturbance observer', IEEE/ASME Trans. Mechatronices, vol. 5, pp. 3-11, Mar. 2000 https://doi.org/10.1109/3516.828584
  2. B. K. Kom, H. T. Chol, W. K. Chung, and I. H. Suh, 'Analysis and design of robust motion controllers in the unified framework', Journal of Dynamic Systems, Measurement, and Control, vol. 124, pp. 313-321, 2002 https://doi.org/10.1115/1.1468995
  3. S. Komada, N. Machii, and T. Hori, 'Control of redundant manipulators considering order of disturbance observer', IEEE Trans. Ind. Electron, vol. 47, pp. 413-420, Apr. 2000 https://doi.org/10.1109/41.836357
  4. Y. J. Choi, W. K. Chung, and Y. Youm, 'Disturbance observer in $H{\infty}$ frameworks', IEEE IECON, pp. 1394-1400, 1996
  5. H. A. Zhu, G. S. Hong, C. L. Teo, and A. N. Poo, 'Internal model control with enhanced robustness', International Journal of Systems Science, vol. 26, no. 2, 277-293, February 1995 https://doi.org/10.1080/00207729508929036
  6. K. Ohnishi and K. Miyachi, 'Adaptive DC servo drive control taking force disturbance suppression into account', IEEE Transactions on Industry Application, vol. 24, no. 1 1998 https://doi.org/10.1109/28.87268
  7. C. H. Yim. J. H. Kang, S. H. Song, and D. I. Kim, 'New feedforward control of brushless DC motors using a novel disturbance suppressor', IEEE Industry Applications Society Annual Meeting, pp. 1910-1916, Oct. 1995 https://doi.org/10.1109/IAS.1995.530543
  8. S. Gutman, 'Uncertain dynamical systems-a lyapunov min-max approach', IEEE Trans. Automatic Control, vol. 24, no. 3, pp. 437-443, 1979 https://doi.org/10.1109/TAC.1979.1102073
  9. M. Corless, 'Guaranteed rates of exponential convergence for uncertain systems', Journal of Optimization Theory and Applications, vol. 64, no. 3, pp. 481-494, 1990 https://doi.org/10.1007/BF00939420
  10. B. R. Barmish, M. Corless and G. Leitmann, 'A new class of stabilizing controllers for uncertain dynamical systems', SIAM Journal of Contol, Optimization, vol. 21, no. 4, pp. 246-255, 1983 https://doi.org/10.1137/0321014
  11. C. T. Chen, Linear system theory and design, 3rd ed. Oxford, 1999
  12. V. M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall Inc., 1978