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

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

Mixed $H_2/H_{$\infty}$ and $\mu$-synthesis Approach to the Coupled Three-Inertia Problem

혼합 $H_2/H_{$\infty}$과 $\mu$-설계이론을 이용한 3관성 문제의 해법

  • Published : 2001.11.01
Download PDF
⟨ Previous Next ⟩

Abstract

This study investigates the use of mixed $H_2/H_{$\infty}$ and $\mu$-synthesis to construct a robust controller for the benchmark problem. The model treated in the problem is a coupled three-inertial system that reflects the dynamics of mechanical vibrations. This kind of problem requires to be satisfied the robust performance (both in the time and frequency-domain specifications). We, first, adopt the mixed $H_2/H_{$\infty}$ theory to design a feedback controller K(s). Next, $\mu$-synthesis method is applied to the overall system to make use of structured parametric uncertainty. This process permits higher levels of controller authority and reduces the conservativeness of the controller. Finally, the feedforward controller is also used to improve the transient response of the output. We confirm that all design specifications except a complementary sensitivity condition can be achieved.

Keywords

References

  1. 原, 千田, 佐伯, 野波, '3慣性 べンチマ-ク問題 - 3慣性 系に對する位置制御 速度制御,' 計測と制御, 第34卷, 第5號, pp.403-409, 1995.
  2. 佐伯, 千田, 野波, 原, 'ロバスト制御のためのべンチマ-ク問題(II) - 位置制御體系の設計例,' 計測と制御, 第34卷 第6號, pp. 498-507, 1995.
  3. K. Zhou, J.C. Doyle and K. Glover, Robust Optimal Control, Prentice-Hall, 1996
  4. P. P. Khargonekar and M. Rotea, 'Mixed $H_2/H_{\infty}$ control: a convex optimization approach,' IEEE Trans. Automatic Control, vol. 36, no. 7, pp. 896-911, Feb., 1997 https://doi.org/10.1109/9.85062
  5. C. Scherer, D. Gahinet, and M. Chilali, 'Multiobjective output-feedback control via LMI optimization,' IEEE Trans. Automatic Control, vol. 42, no. 7, pp. 824-837, July, 1991 https://doi.org/10.1109/9.599969
  6. 松井, 堀, 'モ-タコントロ-ルの新しい技術,' 電氣學會 D部分誌, 113-D-10, pp. 1122-1137, 1993
  7. P. Gahinet, N. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Matheorks Inc., 1995
  8. T. Asai and S. Hara, 'Quadratic stabilization by the descript form representation with structured uncertainties,' 計測自動制御學會講演會, IS 2-3, pp. 925-928, 1992
  9. A. Packard and J. C. Doyle, 'The complex structured singular value,' Automatica, 29-1, pp. 71-109, 1993 https://doi.org/10.1016/0005-1098(93)90175-S
  10. T. Sugie and M. Vidyasagar, 'Further results on the robust tracking problem in two-degree-of-freedom control systems,' Systems & Control Letters, 13, no. 2, pp. 101-108, 1989 https://doi.org/10.1016/0167-6911(89)90026-1
  11. Y. W. Choe, H. K. Lee, 'Robust positioning control of a flexible arm using mixed $H_2/H_{\infty}$ control,' 3rd ASCC, pp. 268-273, July 4-7, 2000