×

Eigenstructure assignment for linear parameter-varying systems with applications. (English) Zbl 1217.93062

Summary: The aim of this paper is to show that a recently proposed technique for eigenstructure assignment of linear time-invariant systems can be extended to solve the corresponding eigenstructure assignment problem for linear parameter-varying systems, whose state-space matrices depend on a set of time-varying parameters that are bounded and available online. In particular, the design of eigenstructure assignment is performed without requiring any conditions on the closed-loop eigenvalues, and provides a simple, complete and analytical parametric approach as well as the most degrees of design freedom for the eigenstructure assignment problem of linear parameter-varying systems. A parameter-varying attitude control system of refueling spacecraft in-orbit is used to demonstrate the usefulness and practicality of the proposed approach.

MSC:

93B55 Pole and zero placement problems
65L09 Numerical solution of inverse problems involving ordinary differential equations
93B52 Feedback control
93B60 Eigenvalue problems
93C95 Application models in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Rugh, W. J.; Shamma, J. S., Research on gain scheduling, Automatica, 36, 10, 1401-1425 (2000) · Zbl 0976.93002
[2] Leith, D. J.; Leithead, W. E., Survey of gain-scheduling analysis and design, International Journal of Control, 73, 11, 1001-1025 (2000) · Zbl 1006.93534
[3] Shamma, J. S.; Athans, M., Analysis of gain scheduled control for nonlinear plants, IEEE Transactions on Automatic Control, 35, 8, 898-907 (1990) · Zbl 0723.93022
[4] Shamma, J. S.; Athans, M., Guaranteed properties of gain scheduled control for linear parameter-varying plants, Automatica, 27, 3, 559-564 (1991) · Zbl 0754.93022
[5] Abdullah, A.; Zribi, M., Model reference control of LPV systems, Journal of the Franklin Institute, 346, 9, 854-871 (2009) · Zbl 1298.93163
[6] Marcos, A.; Balas, G. J., Development of linear-parameter-varying models for aircraft, Journal of Guidance, Control, and Dynamics, 27, 2, 218-228 (2004)
[7] G.P. Liu, R.J. Patton, Eigenstructure assignment for control, an invited chapter in EOLSS Encyclopaedia, 2003.; G.P. Liu, R.J. Patton, Eigenstructure assignment for control, an invited chapter in EOLSS Encyclopaedia, 2003.
[8] Liu, G. P.; Patton, R. J., Eigenstructure Assignment for Control System Design (1998), Chichester, John Wiley & Sons · Zbl 0936.93024
[9] White, B. A., Eigenstructure assignment: a survey, IMechE, Systems and Control Engineering, 209, I1, 1-11 (1995)
[10] Lee, H. C.; Choi, J. W., Linear time-varying eigenstructure assignment with flight control application, IEEE Transactions on Aerospace and Electronic Systems, 40, 1, 145-157 (2004)
[11] J.J. Zhu, A necessary and sufficient stability criterion for linear time-varying systems, in: Proceedings of the 28th IEEE Southeastern Symposium on Systems Theory, Washington, USA, 1996, pp. 115-119.; J.J. Zhu, A necessary and sufficient stability criterion for linear time-varying systems, in: Proceedings of the 28th IEEE Southeastern Symposium on Systems Theory, Washington, USA, 1996, pp. 115-119.
[12] Tsakalis, K. S.; Ioannou, P. A., Linear Time-Varying Systems (1993), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ, pp. 124-147
[13] Duan, G. R.; Wu, G. Y.; Huang, W. H., Eigenstructure assignment for time-varying linear systems, Science in China (Series A, English edition), 34, 2, 246-256 (1991) · Zbl 0731.93046
[14] L. Bruyeere, A. Tsourdos, B.A. White, Polynomial eigenstructure assignment, application to missile autopilot, in: Proceedings of the 2005 IEEE Conference on Control Applications, Toronto, Canada, 2005, pp. 1355-1360.; L. Bruyeere, A. Tsourdos, B.A. White, Polynomial eigenstructure assignment, application to missile autopilot, in: Proceedings of the 2005 IEEE Conference on Control Applications, Toronto, Canada, 2005, pp. 1355-1360.
[15] White, B. A.; Bruyere, L.; Tsourdos, A., Mssile autopilot design using quasi-LPV polynomial eigenstructure assignment, IEEE Transactions on Aerospace and Electronic Systems, 43, 4, 1470-1483 (2007)
[16] F.Y. Ke, A. Tsourdos, B.A. White, LPV polynomial eigenstructure assignment for formation flying control around sun-earth \(L_2\); F.Y. Ke, A. Tsourdos, B.A. White, LPV polynomial eigenstructure assignment for formation flying control around sun-earth \(L_2\)
[17] Duan, G. R., Solution to matrix equation \(A V + B W = E V F\) and eigenstructure assignment for descriptor systems, Automatica, 28, 3, 639-643 (1992) · Zbl 0775.93083
[18] Duan, G. R., Solutions of the equation \(A V + B W = V F\) and their application to eigenstructure assignment in linear systems, IEEE Transaction on Automatic Control, 38, 2, 276-280 (1993)
[19] Duan, G. R., Eigenstructure assignment and response analysis in descriptor linear systems with state feedback control, International Journal of Control, 69, 5, 663-694 (1998) · Zbl 0949.93029
[20] Li, Z. Y.; Zhou, B.; Wang, Y.; Duan, G. R., Numerical solution to linear matrix equation by finite steps iteration, IET Control Theory & Applications, 4, 7, 1245-1253 (2010)
[21] Zhou, B.; Lam, J.; Duan, G. R., Gradient-based maximal convergence rate iterative method for solving linear matrix equations, International Journal of Computer Mathematics, 87, 3, 515-527 (2010) · Zbl 1188.65058
[22] Zhou, B.; Duan, G. R., An explicit solution to the matrix equation \(A X - X F = B Y\), Linear Algebra and its Applications, 402, 345-366 (2005)
[23] Zhou, B.; Duan, G. R., A new solution to the generalized Sylvester matrix equation \(A V - E V F = B W\), Systems & Control Letters, 55, 3, 193-198 (2006)
[24] Zhou, B.; Duan, G. R., On the generalized Sylvester mapping and matrix equations, Systems & Control Letters, 57, 3, 200-208 (2008) · Zbl 1129.93018
[25] Zhou, B.; Duan, G. R., On equivalence and explicit solutions of a class of matrix equations, Mathematical and Computer Modelling, 50, 9-10, 1409-1420 (2009) · Zbl 1185.15012
[26] Zhou, B.; Li, Z. Y.; Duan, G. R.; Wang, Y., Solutions to a family of matrix equations by using the Kronecker matrix polynomials, Applied Mathematics and Computation, 212, 2, 327-336 (2009) · Zbl 1181.15020
[27] Zhou, B.; Li, Z. Y.; Duan, G. R.; Wang, Y., Weighted least squares solutions to general coupled Sylvester matrix equations, Journal of Computational and Applied Mathematics, 224, 2, 759-776 (2009) · Zbl 1161.65034
[28] Zhou, B.; Lam, J.; Duan, G. R., On Smith-type iterative algorithms for the Stein matrix equation, Applied Mathematics Letters, 22, 7, 1038-1044 (2009) · Zbl 1179.15016
[29] Zhou, B.; Duan, G. R.; Li, Z. Y., Gradient based iterative algorithm for solving coupled matrix equations, Systems & Control Letters, 58, 5, 327-333 (2009) · Zbl 1159.93323
[30] D.J. Chato, Technologies for refueling spacecraft on-orbit, NASA TM-2000-210476, AIAA Paper 2000-5107, 2000.; D.J. Chato, Technologies for refueling spacecraft on-orbit, NASA TM-2000-210476, AIAA Paper 2000-5107, 2000.
[31] L. Zhang, The attitude dynamics and control of on-orbit refueling spacecraft, Master’s thesis, Harbin Institute of Technology, 2009.; L. Zhang, The attitude dynamics and control of on-orbit refueling spacecraft, Master’s thesis, Harbin Institute of Technology, 2009.
[32] Bara, G. I.; Daafouz, J.; Kratz, F.; Ragot, J., Parameter-dependent state observer design for affine LPV systems, International Journal of Control, 74, 16, 1601-1611 (2001) · Zbl 1101.93302
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.