Periodic Solution Of A Class Of Vehicle Suspension System With Time Delay

The active suspension system of an automobile absorbs the energy generated by impact and vibration during driving through structures such as shock absorbers and shock absorbers,thereby ensuring the smooth and safe operation of the vehicle and playing a good cushioning role.In recent years,achieving effective control of vehicle motion by adjusting the factors that affect the motion of active suspension has become a major issue for our research.At the same time,scholars have also considered the impact of time delays caused by vehicle acceleration,deceleration,turning,and other processes,as well as different types of damping on driving.Many classical differential equation models and delay differential equation models have been established to analyze the existence conditions and stability of periodic solutions of differential equations.In this paper,we consider the approximate periodic solution of a class of1/4 automotive active suspension models with time delays.Using multi scale method to obtain approximate solutions of periodic solutions of delay differential equations.The amplitude equation of the delay differential equation is derived.Through the correspondence between the equilibrium solution of the amplitude equation and the approximate periodic solution of the original delay differential equation,the stability of the equilibrium solution of the amplitude equation is obtained,which is the stability of the approximate periodic solution of the original delay differential equation.This article is divided into three chapters.The first chapter is an introduction,which briefly introduces the physical background of automotive active suspension systems,as well as classic differential equation models and delay differential equation models.Chapter 2 introduces the relevant stability theories,multi-scale methods,and other preparatory knowledge required for this article.Chapter 3 is about using the multi-scale method to obtain the approximation and stability of periodic solutions of differential equations with newly added time delays.Firstly,an amplitude equation is derived using the multi-scale method,and the equilibrium solution of the amplitude equation corresponds to the approximate solution of the periodic solution of the original delay differential equation.That is,the stability of the equilibrium solution of the amplitude equation corresponds to the stability of the periodic approximate solution of the original delay equation.Secondly,the conditions for the existence of equilibrium solutions of the amplitude equation were discussed.Finally,stability theory was used to determine the conditions that satisfy the stability of the periodic solution approximation solution of the original timedelay system,and the optimal control range of each parameter under stable conditions was obtained.The results obtained demonstrate the effectiveness of the new model,as well as the consideration of the time delay term,which makes the control of actual vehicle suspension motion more accurate.