Synthesis and implementation of non-integer integrators using RLC devices

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.

[1]  Xavier Moreau,et al.  Generalised approach on fractional response of fractal networks , 2002 .

[2]  Xavier Moreau,et al.  The CRONE Suspension: Management of the Dilemma Comfort-Road Holding , 2004 .

[3]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[4]  Olivier Cois,et al.  Systèmes linéaires non entiers et identification par modèle non entier : application en thermique , 2002 .

[5]  Xavier Moreau,et al.  Modelling of Hydractive CRONE Suspension as a Hybrid System , 2003, ADHS.

[6]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[7]  A. Oustaloup,et al.  Taking into Account of Non-Linearities in the CRONE approach: Application to Vibration Isolation , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[8]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[9]  T. Poinot,et al.  Identification of Fractional Systems Using an Output-Error Technique , 2004 .

[10]  D.S.G. Pollock,et al.  Realisations of finite-sample frequency-selective filters , 2009 .

[11]  Xavier Moreau,et al.  ACTIVE ROLL CONTROL DEVICE FOR VEHICLES EQUIPPED WITH HYDROPNEUMATIC SUSPENSIONS , 2006 .

[12]  Xavier Moreau,et al.  The CRONE Suspension: Modelling and Stability Analysis , 2003 .

[13]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[14]  A. Oustaloup,et al.  Fractional Differentiation in Passive Vibration Control , 2002 .

[15]  Xavier Moreau,et al.  Limited-Bandwidth Fractional Differentiator: Synthesis and Application in Vibration Isolation , 2007 .

[16]  A. Oustaloup,et al.  First generation CRONE control , 1993, Proceedings of IEEE Systems Man and Cybernetics Conference - SMC.

[17]  A. Oustaloup,et al.  Modeling and identification of a non integer order system , 1999, 1999 European Control Conference (ECC).

[18]  Jun Lin,et al.  Modélisation et identification des systèmes d'ordre non entier , 2001 .