Optimal pole shifting for continuous multivariable linear systems. (English) Zbl 0561.93026

Amin, M. H.

Int. J. Control 41, 701-707 (1985).

A method for shifting the real parts of the open-loop poles to any desired positions while preserving the imaginary parts is presented. The method is based on the mirror-image property which has been reported by B. P. Molinari [Automatica 13, 347-357 (1977; Zbl 0359.49001)]. In other words, Molinari’s results are extended and then a recursive approach is developed. In each step of this approach, it is required to solve a first-order or a second-order linear matrix Lyapunov equation for shifting one real pole or two complex conjugate poles respectively. The presented method yields a solutions which is optimal with respect to a quadratic performance index. The attractive feature of this method is that it enables solutions to complex problems to be easily found without solving any non-linear algebraic Riccati equation.

MSC:

93B55	Pole and zero placement problems
93C05	Linear systems in control theory
93C35	Multivariable systems, multidimensional control systems
93C99	Model systems in control theory

Keywords:

open-loop poles; mirror-image property; linear matrix Lyapunov equation; quadratic performance index

Citations:

Zbl 0359.49001

References:

[1]	ANDERSON B. D. O., Linear Optimal Control (1971) · Zbl 0321.49001
[2]	BAR-NESS Y., Int. J. Control 27 pp 421– (1978) · Zbl 0369.49001
[3]	GROUPE D., Int. J. Control 16 pp 881– (1972) · Zbl 0243.49019
[4]	LEHTOMAKI N. A., I.E.E.E.Trans. autom. Control 26 pp 75– (1981) · Zbl 0459.93024
[5]	MOLINARI B. P., Automatica 13 pp 347– (1977) · Zbl 0359.49001
[6]	SAFONOV M. G., IEEE. Trans, autom. Control 22 pp 173– (1977) · Zbl 0356.93016
[7]	SEBAKHY O. A., I.E.E.E. Trans, autom. Control 24 pp 355– (1979) · Zbl 0397.93017
[8]	SEZER M. E., I.E.E.E. Trans, autom. Control 26 pp 907– (1981) · Zbl 0544.93016
[9]	SOLHEIM O. A., Int. J. Control 15 pp 143– (1972) · Zbl 0225.49026
[10]	VITTAL RAO S., Proc. Instn elect. Engrs 122 pp 197– (1975)