Title :
Havriliak-Negami function for thermal system identification
Author :
Sommacal, Laurent ; Melchior, Pierre ; Oustaloup, Alain
Author_Institution :
Dept. LAPS, IMS, Bordeaux
Abstract :
Fractional differentiation models have proven their usefulness in representing high dimensional systems with only few parameters. Generally, two elementary fractional functions are used in time-domain identification: Cole-Cole and Davidson-Cole functions. A third elementary function, called Havriliak-Negami, generalizes both previous ones and is particularly dedicated to dielectric systems. The use of this function is however not very popular in time-domain identification because it has no simple analytical impulse response. The only synthesis method of Havriliak-Negami elementary functions proposed in the literature is based on diffusive representation which sets restrictive conditions on fractional orders. A new synthesis method, with no such restrictions, is based on the splitting the Havriliak-Negami function into a Davidson-Cole function and a complementary one. Both functions are then synthesized in a limited frequency band using a recursive distribution of poles and zeros developed by [Ous95].
Keywords :
differentiation; identification; poles and zeros; Havriliak-Negami function; elementary fractional functions; fractional differentiation models; high dimensional systems; poles and zeros recursive distribution; thermal system identification; third elementary function; time-domain identification; Computational modeling; Dielectrics; Frequency synthesizers; Laplace equations; Machining; Poles and zeros; Signal synthesis; System identification; Time domain analysis; Turning;
Conference_Titel :
American Control Conference, 2008
Conference_Location :
Seattle, WA
Print_ISBN :
978-1-4244-2078-0
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2008.4586675