Title:
|
Self-bounded controlled invariant subspaces in measurable signal decoupling with stability: minimal-order feedforward solution (English) |
Author:
|
Zattoni, Elena |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
41 |
Issue:
|
1 |
Year:
|
2005 |
Pages:
|
[85]-96 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The structural properties of self-bounded controlled invariant subspaces are fundamental to the synthesis of a dynamic feedforward compensator achieving insensitivity of the controlled output to a disturbance input accessible for measurement, on the assumption that the system is stable or pre-stabilized by an inner feedback. The control system herein devised has several important features: i) minimum order of the feedforward compensator; ii) minimum number of unassignable dynamics internal to the feedforward compensator; iii) maximum number of dynamics, external to the feedforward compensator, arbitrarily assignable by a possible inner feedback. From the numerical point of view, the design method herein detailed does not involve any computation of eigenspaces, which may be critical for systems of high order. The procedure is first presented for left-invertible systems. Then, it is extended to non-left- invertible systems by means of a simple, original, squaring-down technique. (English) |
Keyword:
|
geometric approach |
Keyword:
|
linear systems |
Keyword:
|
self-bounded controlled invariant subspaces |
Keyword:
|
measurable signal decoupling |
Keyword:
|
non-left-invertible systems |
MSC:
|
93B27 |
MSC:
|
93B50 |
MSC:
|
93C05 |
MSC:
|
93C10 |
MSC:
|
93C35 |
MSC:
|
93C55 |
idZBL:
|
Zbl 1249.93071 |
idMR:
|
MR2131127 |
. |
Date available:
|
2009-09-24T20:07:09Z |
Last updated:
|
2015-03-23 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135641 |
. |
Reference:
|
[1] Basile G., Marro G.: Controlled and conditioned invariant subspaces in linear system theory.J. Optim. Theory Appl. 3 (1969), 5, 306–315 Zbl 0172.12501, MR 0246661, 10.1007/BF00931370 |
Reference:
|
[2] Basile G., Marro G.: Self-bounded controlled invariant subspaces: a straightforward approach to constrained controllability.J. Optim. Theory Appl. 38 (1982), 1, 71–81 Zbl 0471.93008, MR 0687139, 10.1007/BF00934323 |
Reference:
|
[3] Basile G., Marro G.: Controlled and Conditioned Invariants in Linear System Theory.Prentice Hall, Englewood Cliffs, NJ 1992 Zbl 0758.93002, MR 1149379 |
Reference:
|
[4] Basile G., Marro, G., Piazzi A.: A new solution to the disturbance localization problem with stability and its dual.In: Proc. ’84 Internat. AMSE Conference on Modelling and Simulation, Athens 1984, Vol. 1.2, pp. 19–27 |
Reference:
|
[5] Corradini M. L.: Self-bounded controlled invariants for singular systems.Kybernetika 30 (1994), 6, 639–644 Zbl 0832.93032, MR 1323666 |
Reference:
|
[6] Marro G., Prattichizzo, D., Zattoni E.: Convolution profiles for right-inversion of multivariable non-minimum phase discrete-time systems.Automatica 38 (2002), 10, 1695–1703 Zbl 1011.93022, MR 2134008, 10.1016/S0005-1098(02)00088-2 |
Reference:
|
[7] Piazzi A.: A new solution to the regulator problem with output stability.IEEE Trans. Automat. Control AC-31 (1986), 4, 341–342 10.1109/TAC.1986.1104260 |
Reference:
|
[8] Schumacher J. M.: On a conjecture of Basile and Marro.J. Optim. Theory Appl. 41 (1983), 2, 371–376 Zbl 0517.93009, MR 0720781 |
Reference:
|
[9] Wonham W. M.: Linear Multivariable Control: A Geometric Approach.Third edition. Springer–Verlag, New York 1985 Zbl 0609.93001, MR 0770574 |
Reference:
|
[10] Wonham W. M., Morse A. S.: Decoupling and pole assignment in linear multivariable systems: a geometric approach.SIAM J. Control 8 (1970), 1, 1–18 Zbl 0206.16404, MR 0270771, 10.1137/0308001 |
. |