Partial Pole Assignment via Constant Gain Feedback in Two Classes of Frequency-domain Models

  • Wang, Guo-Sheng (Department of Control Engineering, Academy of Armored Force Engineering) ;
  • Yang, Guo-Zhen (Department of Control Engineering, Academy of Armored Force Engineering) ;
  • Duan, Guang-Ren (Center for Control Theory and Guidance Technology, Harbin Institute of Technology)
  • Published : 2007.04.30

Abstract

The design problem of partial pole assignment (PPA) in two classes of frequency-domain MIMO models by constant gain feedback is investigated in this paper. Its aim is to design a constant gain feedback which changes only a subset of the open-loop eigenvalues, while the rest of them are kept unchanged in the closed-loop system. A near general parametric expression for the feedback gain matrix in term of a set of design parameter vectors and the set of the closed-loop poles, and a simple parametric approach for solving the proposed problem are presented. The set of poles do not need to be previously prescribed, and can be set undetermined and treated together with the set of parametric vectors as degrees of design freedom provided by the approach. An illustrative example shows that the proposed parametric method is simple and effective.

Keywords

References

  1. M. H. Hsueh and H. A Sehitoglu, 'New eigenvalue placement method for linear dynamic systems,' Proc. of the 36th Conference on Decision and Control, San Diego, California USA, pp. 4286-4287, December 1997
  2. A. Eisinberg, G. Franze, and N. Salerno, 'The pole placement problem by output-gain feedback: An alternative formulation,' Proc. of the 37th Conference on Decision and Control, Tampa, Florida USA, pp. 1742-1744, December 1998
  3. L. John and K. Nicos, 'The pole placement map, its properties, and relationships to system invariants,' IEEE Trans. on Automatic Control, vol. 38, no. 8, pp. 1266-1270, 1993 https://doi.org/10.1109/9.233165
  4. K. Hitoshi and I. Akira, 'Pole assignment by state transition graph,' IEEE Trans. on Automatic Control, vol. 37, no. 8, pp. 1196-1201, 1992 https://doi.org/10.1109/9.151103
  5. A. Dirk and L. W. Jacques, 'Pole assignment for linear periodic systems by memoryless output feedback,' IEEE Trans. on Automatic Control, vol. 40, no. 4, pp. 735-739, 1995 https://doi.org/10.1109/9.376098
  6. G. R. Duan, 'Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control,' Int. J. Control, vol. 69, no. 5, pp. 663-694, 1998 https://doi.org/10.1080/002071798222622
  7. G. R. Duan, 'Eigenstructure assignment in descriptor linear systems via output feedback,' Int. J. Control, vol. 72, no. 4, 1999, pp. 345-364 https://doi.org/10.1080/002071799221154
  8. G. R. Duan and R. J. Patton, 'Eigenstructure assignment in descriptor systems via state feedback-A new complete parametric approach,' Int. J. Systems Science, vol. 29, no. 2, pp. 167-178, 1998 https://doi.org/10.1080/00207729808929509
  9. G. R. Duan, G. W. Irwin, and G. P. Liu, 'Disturbance attenuation in linear systems via dynamical compensators-A parametric eigen-structure assignment approach,' IEE Proceeding, Control Theory and Applications, vol. 146, no. 2, pp. 129-136, 2000 https://doi.org/10.1049/ip-cta:20000135
  10. G. S. Wang and G. R. Duan, 'State feedback eigenstructure assignment with minimum control effort,' Proc. of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China, vol. 1, pp. 35-38, June 2004
  11. G. R. Duan and G. S. Wang, 'P-D feedback eigenstructure assignment with minimum control effort in second-order dynamic systems,' Proc. of IEEE International Symposium of Computer Aid Control System Design, Taibei, China, pp. 344-349, September 2004
  12. G. S. Wang, B. Liang, and G. R. Duan, 'Reconfiguring second-order dynamic systems via state feedback eigenstructure assignment,' International Journal of Control, Automation, and Systems, vol. 3, no. 1, pp. 109-116, 2005
  13. G. S. Wang and G. R. Duan, 'Robust pole assignment via P-D feedback in a class of second-order dynamic systems,' Proc. of International Conference of Automation, Robots and Computer Vision, Kunming, China, pp. 1152-1156, 2004
  14. L. J. Chiang and H. D. Thorp, 'Partial eigenstructure assignment and its application to large-scale systems,' IEEE Trans. on Automatic Control, vol. 36, no. 3, pp. 340-347, 1991 https://doi.org/10.1109/9.73568
  15. W. W. Lin and J. N. Wang, 'Partial pole assignment for the vibrating system with aerodynamic effect,' Numerical Linear Algebra with Applications, vol. 11, pp. 41-59, 2004 https://doi.org/10.1002/nla.332
  16. S. Kenji, 'Partial pole placement by LQ regulators: An inverse problem approach,' IEEE Trans. on Automatic Control, vol. 43, no. 5, pp. 706-708, 1998 https://doi.org/10.1109/9.668841
  17. S. Atsushi, H. Ichijyo, and S. Kenji, 'Partial pole placement with specified stability margins,' Proc. of the 38th Conference on Decision and Control, Phoenix, Arizona USA, pp. 1389-390, December 1999
  18. G. R. Duan and G. S. Wang, 'Partial eigenstructure assignment for descriptor linear systems: A complete parametric approach,' Proc. of the Conference on Decision and Control, Hawaii, US, pp. 3402-3407, December 2003