Synthesis and implementation of non-integer integrators using RLC devices

Abstract

The aim of this article is to introduce a new method used to implement non-integer operators, which is based on R, L and C electrical devices. Several configurations of RLC devices are emphasised. Our results show that only specific arrangements of RLC devices may lead to non-integer behaviour. We present a new synthesis method which is used to determine the electrical devices value based on high level parameters. We investigate a particular case of identical RLC cells which is widely used in automotive suspension controllers' implementation. Our results are applied to the implementation of the Citroen active suspension developed earlier by the Laps department (Moreau, Altet and Oustaloup 2004, ‘The CRONE Suspension: Management of Comfort-Road Holding Dilemma’, Journal of Nonlinear Dynamics, 38, 467–484) in collaboration with the PSA Company.