×

zbMATH — the first resource for mathematics

Complete parametric approach for eigenstructure assignment in a class of second-order linear systems. (English) Zbl 1009.93036
This paper considers eigenstructure assignment via proportional-plus-derivative feedback control in a class of second-order linear systems in the form of \(\ddot q- A\dot q- Cq= Bu\). Under the controllability condition of the matrix pair \([A,B]\), simple complete parametric expressions for both the closed-loop eigenvector matrices and the feedback gain matrices are established in terms of the closed-loop eigenvalues and a group of parameter vectors. Both the closed-loop eigenvalues and the group of parameters can be properly chosen to produce a closed-loop system with some additional desired specifications. The main computations involved are the Smith form reductions of two polynomial matrices, or two sets of singular value decompositions when the closed-loop eigenvalues are known a priori. A third-order illustrative example is presented.

MSC:
93B55 Pole and zero placement problems
93B60 Eigenvalue problems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Balas, M.J., Trends in large space structure control theory: fondest hopes, wildest dreams, IEEE transactions on automatic control, 27, 522-535, (1982) · Zbl 0496.93007
[2] Bhaya, A.; Desoer, C., On the design of large flexible space structures (LFSS), IEEE transactions on automatic control, 30, 1118-1120, (1985) · Zbl 0574.93044
[3] Chu, E.K.; Datta, B.N., Numerically robust pole assignment for second-order systems, International journal control, 64, 4, 1113-1127, (1996) · Zbl 0850.93318
[4] Datta, B.N.; Rincon, F., Feedback stabilisation of a second-order system: A nonmodal approach, Linear algebra applications, 188-189, 135-161, (1993) · Zbl 0778.65047
[5] Diwekar, A.M.; Yedavalli, R.K., Stability of matrix second-order systems: new conditions and perspectives, IEEE transactions on automatic control, 44, 9, 1773-1776, (1999) · Zbl 0958.93081
[6] Duan, G.R., Solutions to matrix equation AV+BW=VF and their application to eigenstructure assignment in linear systems, IEEE transactions on automatic control, AC-38, 2, 276-280, (1993) · Zbl 0775.93098
[7] Duan, G. R., Thompson, S., & Liu, G. P. (1999). On solution to the matrix equation AV+EVJ=BW+G. Proceedings of 1999 IEEE Conference on Decision and Control pp. 2742-2743. Crowne Plaza Hotel, 100N. 1st Street, Phoenix, Arizona, USA, December 7-10, 1999.
[8] Juang, J.N.; Lim, K.B.; Junkins, J.L., Robust eigensystem assignment for flexible structures, Journal of guidance, control and dynamics, 12, 3, 381-387, (1989) · Zbl 0682.93023
[9] Kim, Y.; Kim, H.S.; Junkins, J.L., Eigenstructure assignment algorithm for mechanical second-order systems, Journal of guidance, control and dynamics, 22, 5, 729-731, (1999)
[10] Meirovitch, L.; Baruh, H.J.; Oz, H., A comparison of control techniques for large flexible systems, Journal of guidance, control and dynamics, 6, 302-310, (1983) · Zbl 0512.93012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.