Reconfiguring Second-order Dynamic Systems via P-D Feedback Eigenstructure Assignment: A Parametric Method

  • Wang Guo-Sheng (Harbin Institute of Technology, Department of Control Engineering, Academy of Armored Force Engineering) ;
  • Liang Bing (Center for Control Theory and Guidance Technology, Harbin Institute of Technology) ;
  • Duan Guang-Ren (Center for Control Theory and Guidance Technology, Harbin Institute of Technology)
  • Published : 2005.03.01

Abstract

The design of reconfiguring a class of second-order dynamic systems via proportional plus derivative (P-D) feedback is considered. The aim is to resynthesize a P-D feedback controller such that the eigenvalues of the reconfigured closed-loop system can completely recover those of the original close-loop system, and make the corresponding eigenvectors of the former as close to those of the latter as possible. Based on a parametric result of P-D feedback eigenstructure assignment in second-order dynamic systems, parametric expressions for all the P-D feedback gains and all the closed-loop eigenvector matrices are established and a parametric algorithm for this reconfiguration design is proposed. The parametric algorithm offers all the degrees of design freedom, which can be further utilized to satisfy some additional performances in control system designs. This algorithm involves manipulations only on the original second-order system matrices, thus it is simple and convenient to use. An illustrative example and the simulation results show the simplicity and effect of the proposed parametric method.

Keywords

References

  1. D. P. Looze, J. L. Weiss, and N. M. Barrett, 'An automatic redesign approach for restructurable control systems,' IEEE Control System Magazine, vol. 5, no. 2, pp. 1621-1627, 1985
  2. Z. Gao and P. J. Artsaklis, 'Stability of the pseudo-inverse method for reconfigurable control systems,' Int. J. of Control, vol. 53, no. 2, pp. 520-528, 1991
  3. I. Takewaki, 'Inverse component-mode synthesis method for redesign of large structural systems,' Comput. Methods. Appl. Mech. Engrg, vol. 166, pp. 201-209, 1998 https://doi.org/10.1016/S0045-7825(98)00070-X
  4. P. C. Parks, 'Lyapunov redesign of model reference adaptive control systems,' IEEE Trans. on Automatic Control, vol. AC-11, no. 3, pp. 362-367, 1996
  5. W. Chang, J. B. Park, H. J. Lee, and Y. H. Joo, 'LMI approach to digital redesign of linear timeinvariant systems,' IEE Proc-Control Theory Appl, vol. 149, no. 4, pp. 297-302, 2002
  6. J. Jiang, 'Design of reconfigurable control systems,' Int. J. of Control, vol. 59, no. 2, pp. 395-401, 1994 https://doi.org/10.1080/00207179408923083
  7. Z. Ren, X. J. Tang, and J. Chen, 'Reconfigurable control system design by output feedback eigenstructure assignment,' Control Theory and Applications, vol. 19, no. 3, pp. 356-362, 2002
  8. G. R. Duan and G. P. Liu, 'Complete parametric approach for eigenstructure assignment in a class of second-order linear systems,' Automatica, vol. 38, no. 4, pp. 725-729, 2002 https://doi.org/10.1016/S0005-1098(01)00251-5
  9. G. R. Duan, G. S. Wang, and G. P. Liu, 'Eigenstructure assignment in a class of secondorder linear systems: A complete parametric approach,' Proc. of the 8th Annual Chinese Automation and Computer Society Conference, pp. 89-96, 2002
  10. 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, pp. 1152-1156, 2004