Optimal choice of time-scaling factor for linear system approximations using Laguerre models

Author

Wang, L. ; Cluett, W.R.

Author_Institution

Dept. of Chem. Eng., Toronto Univ., Ont., Canada

Volume

39

Issue

7

fYear

1994

fDate

7/1/1994 12:00:00 AM

Firstpage

1463

Lastpage

1467

Abstract

Clowes (1965) illustrated how to select the optimal time-scaling factor for approximations of rational transfer functions using a series expansion of Laguerre functions. The present paper extends this result to approximations for general, L₂ stable, linear systems. As a direct application of this extended result, we are able to obtain approximations for irrational transfer functions which minimize the frequency domain error in the L₂ sense. Also, we give empirical solutions for the optimal time-scaling factor for approximations of first order plus delay systems which can then be applied to a larger class of overdamped systems

Keywords

frequency-domain analysis; linear systems; optimisation; parameter estimation; poles and zeros; step response; stochastic processes; transfer functions; L₂ stable linear systems; Laguerre models; first order plus delay systems; frequency domain error; irrational transfer functions; linear system approximations; linear time invariant system; optimal time scaling factor; overdamped systems; pole location; rational transfer functions; step response; time constant ratio; Delay effects; Delay estimation; Delay systems; Feedback loop; Frequency domain analysis; Linear approximation; Linear systems; Mathematical model; Transfer functions; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.299635

Filename

299635