Effect of Hydropneumatic Components Nonlinearities on the CRONE Suspension

This paper presents a fractional system composed of a sprung mass and a suspension device with fractional impedance (fractance for short). More precisely, this fractance is a fractional integrator. Practical realizations of this fractional integrator based on hydropneumatic RC cells are presented in a limited frequency band. The main objective of this paper is to analyze the influence of the hydropneumatic RC cell nonlinearities, which constitute the hydropneumatic networks of the CRONE suspension, on the stability degree robustness when varying the sprung mass. First, the achievement of a nonlinear validation model is emphasized, and then, a linear synthesis model is presented. These two models are used in the second part of this paper to analyze the obtained performances and to show the influence of the nonlinearities. This analysis of performances is made first from a qualitative standpoint using the functional domain of each
$R_{i}$
and
$C_{i}$
element and then from the quantitative standpoint using the Volterra series. In fact, the difference between the response of the nonlinear model and the one of the first-order kernel (which represents the linear response of the system) allows the determination of the influence of the nonlinearities on the dynamic behavior for a particular signal input. The results obtained show that the RC cell nonlinearities composing the hydropneumatic networks of the CRONE suspension do not modify the stability degree robustness versus sprung mass variations, thus extending in a nonlinear context this robustness that is present in the linear context.