Nonlinear Dynamics And Control Of Hydro-pneumatic Suspension Systems With Fractional Order Terms

With the growth and development of economy and technology,the market has become more and more interested in the performance of cars,and the suspension,which connects the chassis to the body and has a great impact on the performance of the car,is also attracting attention.The superior performance of the hydro-pneumatic suspension,which uses oil to transfer pressure and inert gas to provide elastic forces and damping through the valve ports,ensures good performance.However,as the system is highly nonlinear,the study of the non-linear dynamics of the hydro-pneumatic suspension system is particularly important if the stability of the system is to be ensured in the first place if good performance of the vehicle is to be ensured.This paper takes a multi-axle special vehicle’s anti-roll hydraulically interconnected suspension system as the research object,firstly introduces the classification of hydropneumatic suspension and its principle,and then derives the non-linear elastic force and non-linear damping force expressions for the 1/4-body four-degree-of-freedom suspension model and the 1/2-body seven-degree-of-freedom suspension model under the consideration of along-travel resistance.Since the oil and gas suspension system is a viscoelastic system,in order to describe the system more accurately,fractional order theory is introduced into the modelling and the fractional order defined by RL is used to model the fractional order elastic force and the fractional order damping force respectively.The effect of the initial pressure,initial volume,cylinder bore,piston outer diameter and throttle bore on the elastic force,inherent frequency and damping force of the suspension is investigated through simulink simulation.The effect of the fractional order on the elastic force and damping force of the suspension is also investigated.A comprehensive evaluation function of the suspension is designed by means of the optimal control idea,and the optimal order of the single-axle hydraulically interconnected suspension model and the semi-vehicle hydraulically interconnected suspension model are found by the value of the comprehensive evaluation function.Secondly,a random road input with sinusoidal superimposed white noise is established and the fractional linear dynamics of a single-bridge hydraulically interconnected suspension system with fractional order and a half-vehicle hydraulically interconnected suspension system with fractional order are analysed by means of MATLAB numerical simulations in this paper.The effects of the external excitation parameters,including excitation amplitude and frequency,and the internal parameters,such as initial pressure,initial volume and flow coefficient,on the non-linear dynamics of the system are investigated.Finally,control forces are applied based on the modelling of a single-axle hydraulically interconnected suspension.A sliding film variable structure controller with a double power convergence law is designed by means of sliding film control theory,and the active control forces are calculated.The control effect of the controller is also verified by comparing the non-linear dynamics chaotic part of the previous paper.