Geodesic
Derivation of effective transfer function models by input, output variables selection
Kybernetika, Tome 38 (2002) no. 6, pp. 657-683 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Transfer function models used for early stages of design are large dimension models containing all possible physical inputs, outputs. Such models may be badly conditioned and possibly degenerate. The problem considered here is the selection of maximal cardinality subsets of the physical input, output sets, such as the resulting model is nondegenerate and satisfies additional properties such as controllability and observability and avoids the existence of high order infinite zeros. This problem is part of the early design task of selecting well-conditioned progenitor models on which successive design has to be carried out. The conditions for different type of degeneracy are investigated and this leads to necessary and sufficient conditions required to guarantee nondegeneracy. The sufficient conditions for nondegeneracy also lead to models with no infinite zeros. Furthermore, additional conditions are derived which guarantee controllability and observability of the resulting model. The results are then used to develop a selection procedure for natural subsets of inputs and outputs, which guarantee transfer function and input, output nondegeneracy, as well as controllability and observability of the resulting system. A parameterisation of solutions that satisfy the above requirements is given.
Transfer function models used for early stages of design are large dimension models containing all possible physical inputs, outputs. Such models may be badly conditioned and possibly degenerate. The problem considered here is the selection of maximal cardinality subsets of the physical input, output sets, such as the resulting model is nondegenerate and satisfies additional properties such as controllability and observability and avoids the existence of high order infinite zeros. This problem is part of the early design task of selecting well-conditioned progenitor models on which successive design has to be carried out. The conditions for different type of degeneracy are investigated and this leads to necessary and sufficient conditions required to guarantee nondegeneracy. The sufficient conditions for nondegeneracy also lead to models with no infinite zeros. Furthermore, additional conditions are derived which guarantee controllability and observability of the resulting model. The results are then used to develop a selection procedure for natural subsets of inputs and outputs, which guarantee transfer function and input, output nondegeneracy, as well as controllability and observability of the resulting system. A parameterisation of solutions that satisfy the above requirements is given.
Classification : 93B05, 93B07, 93B20, 93B40, 93B51, 93C05, 93C80
Keywords: input set; output set; controllability; observability 
@article{KYB_2002_38_6_a0,
     author = {Karcanias, Nicos and Vafiadis, Konstantinos G.},
     title = {Derivation of effective transfer function models by input, output variables selection},
     journal = {Kybernetika},
     pages = {657--683},
     year = {2002},
     volume = {38},
     number = {6},
     mrnumber = {1954391},
     zbl = {1265.93103},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2002_38_6_a0/}
}
TY  - JOUR
AU  - Karcanias, Nicos
AU  - Vafiadis, Konstantinos G.
TI  - Derivation of effective transfer function models by input, output variables selection
JO  - Kybernetika
PY  - 2002
SP  - 657
EP  - 683
VL  - 38
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2002_38_6_a0/
LA  - en
ID  - KYB_2002_38_6_a0
ER  - 
%0 Journal Article
%A Karcanias, Nicos
%A Vafiadis, Konstantinos G.
%T Derivation of effective transfer function models by input, output variables selection
%J Kybernetika
%D 2002
%P 657-683
%V 38
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2002_38_6_a0/
%G en
%F KYB_2002_38_6_a0
Karcanias, Nicos; Vafiadis, Konstantinos G. Derivation of effective transfer function models by input, output variables selection. Kybernetika, Tome 38 (2002) no. 6, pp. 657-683. http://geodesic.mathdoc.fr/item/KYB_2002_38_6_a0/

[2] Forney G. D.: Minimal bases of rational vector spaces with applications to multivariable systems. SIAM J. Control 13 (1975), 493–520 | DOI | MR

[3] Gantmacher G.: Theory of Matrices. Volume 2. Chelsea, New York 1959 | Zbl

[4] Georgiou A., Floudas C. A.: Structural analysis and synthesis of feasible control systems: Theory and applications. Chem. Eng. J. 67 (1989), 600–618

[5] Govind R., Powers G. J.: Control systems synthesis strategies. AIChE J. 28 (1982), 60–73 | DOI

[6] Kailath T.: Linear Systems. Prentice Hall, Englewood Cliffs, N.J. 1980 | MR | Zbl

[7] Karcanias N.: Global process instrumentation: Issues and problems of a system and control theory framework. Measurement 14 (1994), 103–113 | DOI

[8] Karcanias N.: Control problems in global process instrumentation: A structural approach. In: Proc. ESCAPE-6, Comput. Chem. Eng. 20 (1996), 1101–1106

[9] Karcanias N., Giannakopoulos C.: Necessary and sufficient conditions for zero assignment by constant squaring down. Linear Algebra Appl. 122–124 (1989), 415–446 | MR | Zbl

[10] Karcanias N., Hayton G. E.: State-space and transfer function invariant infinite zeros: A unified approach. In: Proc. 1981 Joint Automatic Control Conference, Univ. of Virginia, Charlottesville 1981, Paper TA–4C

[11] Karcanias N., Kalogeropoulos G.: On the Segre, Weyr characteristics of right (left) regular pencils. Internat. J. Control 44 (1986), 991–1015 | DOI | MR

[12] Karcanias N., Kouvaritakis B.: The output zeroing problem and its relationship to the invariant zero structure. Internat. J. Control 30 (1979), 395–415 | DOI | MR | Zbl

[13] Marcus M., Minc H.: A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon, Boston 1964 | MR | Zbl

[14] Mitrouli M., Karcanias N.: Computation of the GCD of polynomials using Gaussian transformations and shifting. Internat. J. Control 58 (1993), 211–228 | DOI | MR | Zbl

[15] Morari M.: Effect of design on the controllability of chemical plants. In: Proc. IFAC Workshop on Interaction between Process Design and Process Control, Imperial College 1992, pp. 3–16

[16] Morari M., Stephanopoulos G.: Studies in the synthesis of control structures for chemical processes: Part II: Structural aspects and the synthesis of alternative feasible control schemes. AIChE J. 26 (1980), 232–246 | DOI | MR

[17] Rijnsdorp J. E.: Integrated Process Control and Automation. Elsevier, Amsterdam 1991

[18] Rosenbrock H. H.: State–Space and Multivariable Theory. Nelson, London 1970 | MR | Zbl

[19] Skogestad S., Postlethwaite I.: Multivariable Feedback Control. Wiley, Chichester 1996 | Zbl

[20] Vardulakis A. I. G., Karcanias N.: Relation between strict equivalence invariants and structure at infinity of matrix pencils. IEEE Trans. Automat. Control AC–28 (1983), 99, 514–516 | DOI | MR

[21] Warren M. E., Eckberg A. E.: On the dimensions of controllability subspaces: A characterisation via polynomial matrices and Kronecker invariants. SIAM J. Control Optim. 13 (1975), 434–445 | DOI | MR