Abstract
A new class of regional pole assignment problems for linear control systems is considered, in which each closed-loop system pole is placed in a desired separate region of the complex plane. A numerically stable method for regional pole assignment is proposed, in which the design freedom is parameterized directly by specific eigenvector (or principal vector) elements and pole location variables that can be chosen arbitrarily. Combined with an appropriate optimization procedure, the proposed method can be used to solve a wide range of optimization problems with pole location constraints, arising in the multi-input control systems design (H 2/H ∞ optimization with pole assignment, robust pole assignment, pole assignment with maximum stability radius, etc.).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Kautsky, J., Nichols, N.K., Van Dooren, P.: Robust pole assignment in linear state feedback. Int. J. Control 41, 1129–1155 (1985)
Byers, R., Nash, S.G.: Approaches to robust pole assignment. Int. J. Control 49, 97–117 (1989)
Liu, G.P., Patton, R.J.: Eigenstructure Assignment for Control System Design. John Wiley, Chichester (1998)
Magni, J.F.: Robust Modal Control with a Toolbox for Use with MATLAB. Kluwer Acad. Publ., Dordrecht (2002)
Kim, S.B., Furuta, K.: Regulator design with poles in a specified region. Int. J. Control 47, 143–160 (1988)
Kučera, V., Kraus, F.J.: Regional pole placement. Kybernetika 31, 541–546 (1995)
Chilali, M., Gahinet, P.: H ∞ design with pole placement constraints: an LMI approach. IEEE Trans. Autom. Control 41, 358–367 (1996)
Kučera, V., Kraus, F.J.: Robust regional pole placement: an affine approximation. Private communication (2003)
Petkov, P.H., Christov, N.D., Konstantinov, M.M.: Optimal synthesis of linear multi-input systems with prescribed spectrum. In: Proc. 25th Spring Conf. of UBM, Kazanlak, 6-9 April, pp. 141–149 (1996)
Petkov, P.H., Christov, N.D., Konstantinov, M.M.: Computational Methods for Linear Control Systems. Prentice-Hall, Englewood Cliffs (1991)
Petkov, P.H., Christov, N.D., Konstantinov, M.M.: Numerical analysis of the reduction of linear systems into orthogonal canonical form. Systems & Control Lett. 7, 361–364 (1986)
Higham, N.J.: Optimization by direct search in matrix computations. SIAM J. Matrix Anal. Appl. 14, 317–333 (1993)
Bartels, R.H., Stewart, G.W.: Algorithm 432: Solution of the matrix equation AX + XB = C. Comm. ACM 15, 820–826 (1972)
Khargonekar, P.P., Rotea, M.A.: Mixed H 2/H ∞ control: A convex optimization approach. IEEE Trans. Autom. Control 36, 824–837 (1991)
Pandey, P., et al.: A gradient method for computing the optimal H ∞ norm. IEEE Trans. Autom. Control 36, 887–890 (1991)
Sherer, C.: H ∞ -control by state feedback and fast algorithms for the computation of optimal H ∞ -norms. IEEE Trans. Autom. Control 35, 1090–1099 (1990)
Anderson, E., et al.: LAPACK Users’s Guide. SIAM, Philadelphia (1992)
Byers, R.: A bisection method for measuring the distance of a stable matrix to the unstable matrices. SIAM J. Sci. Stat. Comput. 9, 875–881 (1988)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Petkov, P.H., Christov, N.D., Konstantinov, M.M. (2007). Numerical Method for Regional Pole Assignment of Linear Control Systems. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_80
Download citation
DOI: https://doi.org/10.1007/978-3-540-70942-8_80
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
eBook Packages: Computer ScienceComputer Science (R0)