Title: Free and forced modes responses of fractional operators based on non-identical RLC cells

Authors: Roy Abi Zeid Daou, Clovis Francis, Xavier Moreau

Addresses: Department LAPS, Laboratoire IMS, University of Bordeaux I, 33405 Talence, Cedex, Bordeaux, France; Biomedical Technologies Department, Faculty of Public Health, Lebanese German University, Sahel Alma, Jounieh, P.O. Box 206, Lebanon. ' Faculty of Engineering I, Lebanese University, Al-Arz Street, Tripoli, Lebanon. ' Department LAPS, Laboratoire IMS, University of Bordeaux I, 33405 Talence, Cedex, Bordeaux, France

Abstract: In this article, we study the behaviour of the RLC cells for the four configurations that we presented earlier in Abi Zeid Daou et al. (2009a). An electric circuit is used in order to study the fractional behaviour and the robustness of these RLC operators and compare their responses to the behaviour of the fractance which is an ideal fractional operator (Moreau et al., 2003). This analysis is conducted for both natural and forced responses. In more details, the initial conditions of the capacitors and inductances are neglected in the first case and they are taken into consideration in the second one. The number of initial conditions is related to the number of RLC cells used. The robustness of all arrangements is analysed by varying the unsteady parameter value which is represented by an inductance in the electrical circuit. This inductance represents a different variable parameter in each field of application. For example, in the hydropneumatic domain, this inductance refers to the mass of the vehicle as the mass has the main influence on the dynamics and the robustness when designing the active suspension (Moreau et al., 2001). A conclusion will sum up the results for all four arrangements and a confirmation that the phase constancy and the robustness are present in both modes.

Keywords: state space representation; fractional controllers; dynamic behaviour; robustness; initial parameters influence; RLC cells; fractional operators; inductance; electrical circuits; phase constancy.

DOI: 10.1504/IJAIS.2010.034807

International Journal of Adaptive and Innovative Systems, 2010 Vol.1 No.3/4, pp.318 - 333

Available online: 23 Aug 2010

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