Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Multi-stage design procedure for modal controllers of multi-input defective systems

  • Chen, Yu Dong (Department of Mechanics, Jilin University, Nanling Campus Changchun)
  • Received : 2006.03.29
  • Accepted : 2007.06.07
  • Published : 2007.11.30
⟨ Previous Next ⟩

Abstract

The modal controller of single-input system cannot stabilize the defective system with positive real part of repeated eigenvalues, because some of the generalized modes are uncontrollable. In order to stabilize the uncontrollable modes with positive real part of eigenvalues, the multi-input system should be introduced. This paper presents a recursive procedure for designing the feedback controller of the multi-input system with defective repeated eigenvalues. For a nearly defective system, we first transform it into a defective one, and apply the same method to manage. The proposed methods are based on the modal coordinate equations, to avoid the tedious mathematic manipulation. As an application of the presented procedure, two numerical examples are given at end of the paper.

Keywords

Acknowledgement

Supported by : National Science Foundation of China

References

  1. Andry, A.N., Shapiro, E.Y. and Chung, J.C. (1983), 'Eigenvalue assignment for linear systems', IEEE T. Aero. Elec. Sys., 19(5), 711-729 https://doi.org/10.1109/TAES.1983.309373
  2. Chen, S.H., Tao, X. and Han, W.Z. (1992), 'Matrix perturbation for linear vibration defective systems', ACTA Mech. Sinica, 24(6), 747-755
  3. Chen, S.H. (1999), Matrix Perturbation Theory in Structural Dynamic Design (in Chinese), Science Press, Beijing
  4. Chen, Y.D., Chen, S.H. and Liu, Z.S. (2001), 'Modal optimal control procedure for near defective systems', J. Sound Vib., 245(1), 113-132 https://doi.org/10.1006/jsvi.2000.3481
  5. Chen, Y.D., Chen, S.H. and Liu, Z.S. (2001), 'Quantitative measurements of modal controllability and observability in vibration control of defective and nearly defective system', J. Sound Vib., 248(3), 413-426 https://doi.org/10.1006/jsvi.2000.3826
  6. Chen, Y.D. and Chen, S.H. (2003), 'Design procedure for modal controllers for defective and nearly defective systems', Struct. Eng. Mech., 15(5), 551-562 https://doi.org/10.12989/sem.2003.15.5.551
  7. Deif, A.S. (1982), Advanced Matrix Theory for Scientist and Engineers, Abacus House, England
  8. Dolgin, Y and Zeheb, E. (2005), 'Model reduction of uncertain systems retaining the uncertain structure', Syst. Control Lett., 54, 771-779 https://doi.org/10.1016/j.sysconle.2004.10.010
  9. Gantmacher, F.R. (2000), Theory of Matrices, Vol.1, AMS Chelsea Publishing, American Mathematical Society, Providence, Rhode Island
  10. Kimura, H. (1977), 'A further result on the problem of pole assignment by output feedback', IEEE T. Automat. Contr., 22(3), 458-463 https://doi.org/10.1109/TAC.1977.1101520
  11. Liu, Z.S., Wang, D.J., Hu, H.C. and Yu, M. (1994), 'Measure of modal controllability and observability in vibration control of flexible structures', J. Guid. Control Dynam., 17(6), 1377-1380 https://doi.org/10.2514/3.21363
  12. Maghami, P. and Gupta, S. (1997), 'Design of constant gains dissipative controllers for eigensystem assignment in passive systems', J. Guid. Control Dynam., 20(4), 648-657 https://doi.org/10.2514/2.4127
  13. Maghami, P.G. and Juang, J.-N. (1990), 'Efficient eigenvalue assignment for large space structures', J. Guid. Control Dynam., 13(6), 1033-1039 https://doi.org/10.2514/3.20576
  14. Meirovitch, L. (1990), Dynamics and Control, Wiley, New York
  15. Prattichizzo, D. and Bicchi, A. (1997), 'Consistent task specification for manipulation systems with general kinematics', J. Dyn. Syst. - T. ASME, 119(4), 760-767 https://doi.org/10.1115/1.2802388
  16. Prattichizzo, D. and Bicchi, A. (1998), 'Dynamic analysis of mobility and graspability of general manipulation systems', IEEE T. Robot., 14(2), 241-258 https://doi.org/10.1109/70.681243
  17. Shi, G.Q. and Zhu, D.C. (1989), 'Generalized modal theory for linear vibration defective systems (in Chinese)', ACTA Mech. Sinica, 21(2), 212-217
  18. Smagina, Y. and Brewer, I. (2002), 'Using interval arithmetic for robust state feedback design', Syst. Control. Lett., 46, 187-194 https://doi.org/10.1016/S0167-6911(02)00132-9
  19. Srinathkumar, S. (1978), 'Eigenvalue/eigenvector assignment using output feedback', IEEE T. Automat. Contr., 23(1), 79-81 https://doi.org/10.1109/TAC.1978.1101685
  20. Ugrinovskii, V.A. and Peterson, I.R. (2001), 'Robust stability and performance of stochastic uncertain systems on an infinite time interval', Syst. Control Lett., 44, 291-308 https://doi.org/10.1016/S0167-6911(01)00149-9
  21. Xu, T. and Chen, S.H. (1994), 'Perturbation sensitivity of generalized moes of defective systems', Comput. Struct., 52(2), 1377-1380

Cited by

  1. Feedback control design for intelligent structures with closely-spaced eigenvalues vol.52, pp.5, 2014, https://doi.org/10.12989/sem.2014.52.5.903
  2. Bifurcations of non-semi-simple eigenvalues and the zero-order approximations of responses at critical points of Hopf bifurcation in nonlinear systems vol.40, pp.3, 2007, https://doi.org/10.12989/sem.2011.40.3.335