Adaptive Backstepping Controller Design For Vehicle Nonlinear Suspension System

According to the development requirement of "Made in China 2025",the automobile field is rapidly developing.And people's requirements for vehicle comfort and safety are constantly increasing.The vehicle suspension system is one of the most important systems in vehicle chassis,which is used to support vehicle weight absorb and eliminate vlibration,and determine and affect ride comfort and haldling stability.The active suspension system is an adjustable system,which can adjust the vehicle system performance in real time according to different enviro?mental changes when driving?Thus,many scholars have coneducted extensive researcheson it.At the same timeIthe active suspension system is a typical nonlinear systemO In the related research,the nonlinearity of the component spring and damping should be fully considered.Besides,the parameters of thj vehicle suspension system will change in different environments and operating conditions.The changes of these paralmeters wi.l seriously affect the stability and robustness of trZhe active suspension system in the process of controller desigrn.Based on this)irn order to solve the above problems,the adaptive backstepping control method is developed,which can design the adaptive regulation law according to the change of external disturbance and control model,thus inliibiting the external disturbance to the system,as well as achieving precise control and effectively improving the system robustness.In this paper,different types of adaptive backstepping controllers are designed to improve the system perfoI;iance of the nonlinear suspension system under external disturbanceFThe nmain contributions of this study are described as follows:(1)The three road excitation model s are firstly established based on the collected road informiation derived from the experliment,and then the nonlinear passive suspension systeHm model is built.The output curves and the performance indexes for the vehicle nonlinear active suspension system are obtained in the simulation.(2)Two adaptive backstepping control methods for nonlinear active suspension system based on Lyapunov function are proposed.Firstly,considering the uncertainties of spring mass and moment of inertia,the dynamic model of 1/2 vehicle nonlinear active suspension is established,and a virtual control function is introduced to control the vertical and pitch motion of the vehicle;meanwhile,the adaptive control law is designed according to different Lyapunov functions to adjust the influence of the model uncertainties on the suspension system;finally,two active control forces are obtained.(3)The adjustable ideal reference trajectory curves are introduced,and the error tracking systems are established;an high-precision adaptive control law is designed,the state variables in active suspension system asymptotically track the predefined reference trajectories within a finite time;combined with Lyapunov stability theory,the global stability of suspension system is proved;simultaneously,the zero dynamic stability analysis on tire subsystem is conducted to ensure the boundness of the all safety performance indicators within the given limits.(4)Considering the influence of input time delay on the system,the nonlinear uncertain 1/4 vehicle active suspension model is established,and a novel adaptive backstepping controller based on Quadratic-Lyapunov function is des.igned.Meanwhile,according to linearization theory and vibration principle,a solution method of critical time delay is given,which can adjust to the differential input of the controller so that the corresponding controller critical delay can be solved.The controller critical delay can be calculated by the method for most closed-loop systems.