Research On Car Body Vibration-Suppression With Time-Delayed Control Containing Fractional Derivative

As people’s safety awareness and demanding for riding comfort have increasingly improved,combined with modern control technology and computer technology has improved and widely applied to vehicle engineering,which greatly promoted the development and design of the suspension system,many novel suspension systems are emerging with advanced control strategy.In recent years,the impact of the time delay on the vibration of dynamics system has attracted people’s attention and study.The successful application of fractional calculus theory in many fields brings new ideas to the research of vibration suppression of vehicle suspension.In this paper,the theory of fractional calculus and vibration suppression technology with time delay are jointly introduced to study vehicle suspension performance.Firstly,the relevant knowledge of fractional calculus theory is brief summarized,the digital implementation method of fractional differential operator is highlighted ready for simulation of fractional order systems.Secondly,1/4 vehicle suspension with delayed feedback control is established,the impact of time delay on the suspension system vibration is analyzed.The stability switch theory is used to stability analysis of the delayed dynamical systems.The damping objective function is established by Fourier transform in the frequency domain.Optimization analysis to objective function and selection of the optimal control parameters are accomplished using MATLAB software.The simulation results under different road excitation shows delayed feedback control suppresses vibration effectively.Finally,the fractional derivative and delayed feedback control are jointly added to the 1/4 vehicle suspension system.Stability switch method is used to analyse system stability,a weighted objective function is established in the frequency domain according to the vehicle ride comfort indicators and optimization analysis is done.Simulation results show that the fractional derivative and time delay applied to the suspension system can achieve good damping effect.Half-car model simulation results also indicate that the delayed control technology is based on fractional derivative can effectively improve suspension performance.Results in this paper suggest that the time delay control containing fractional derivative applied to the vehicle suspension system,can better reduce car body vibration and improve ride comfort of the vehicle.Contents of this paper provide a theoretical reference for active control of vehicle suspension.