Research On Nonlinear Fractional Active Suspension Control Of Linear Motor Based On Differential Geometry

In the actual driving process,the vehicle is often affected by the vibration and impact caused by uneven road surface,which seriously damages the smoothness and stability of the vehicle.Although the deformation of the tire can effectively absorb the impact force from the ground,most of the impact force mainly depends on the suspension device between the tire and the vehicle body to buffer,and the suspension device attenuates the vibration caused by the uneven road surface,so as to ensure that the vehicle can move forward smoothly.The active control of suspension vibration is studied by establishing a more accurate vehicle suspension model with fractional differential terms than the integer order model.The main research contents are as follows:First of all,because the damping elements in most types of suspension systems,including hydro pneumatic suspension,air suspension and magnetorheological suspension,have viscoelastic characteristics,traditional integral order suspension model can not accurately describe this kind of suspension model.Based on the characteristics that the evolution of fractional calculus is related to the past history,it is more accurate to describe the constitutive relationship of damping materials with memory characteristics by using differential equations with fractional differential terms.This paper improves the suspension model composed of linear stiffness and linear damping,increases the nonlinear stiffness and fractional damping,and proposes a nonlinear fractional suspension system dynamics model which can more simply and accurately reflect the viscoelastic suspension characteristics,so as to more succinctly and effectively describe the dynamic performance of the vehicle suspension system.Secondly,because the fractional order PI~?D~?control increases the differential order and the integral order,it has a more flexible adjustment structure.Based on the fractional order PI~?D~?control method,the active control of the nonlinear fractional order suspension system is studied.Three fractional order PI~?D~?controllers are designed by using genetic algorithm to control the acceleration of the car body,the dynamic deflection of the suspension and the dynamic displacement of the tire simultaneously,and compared with the integral order PID controller.Then Matlab/Simulink is used to compare and simulate the three kinds of suspension systems.The results show that:under the random road excitation and the pulse road excitation,both kinds of active control can improve the dynamic performance of the vehicle suspension to a certain extent,but the fractional PI~?D~?control is better.Then,the fractional order PI~?D~?controller is designed for the linear system based on the differential geometry method.At the same time,the active control force of the original system is obtained by using the nonlinear state feedback,and compared with the integral order PID controller.The above linear suspension system is only based on a single state variable for the system output to carry out local precise linearization,ignoring other state variables in the nonlinear fractional order active suspension system.Therefore,after analyzing and comparing the results of precise linearization of various state variables,a more concise state feedback control law is concluded,and then linear quadratic regulator(LQR)is designed for active control,and compared with only integer order PID control.Using Matlab/Simulink to compare and simulate the above active suspension system,the results show that the active control based on feedback linearization can effectively improve the dynamic performance of the nonlinear fractional order suspension system,but because the simplified feedback control law can reduce the complexity of the suspension system,so as to ensure that LQR control can effectively improve the driving performance of the vehicle.Finally,the linear motor type active suspension is used to replace the traditional motor type active suspension with the rotating motor and ball screw as the conversion mechanism.A dual loop control system is designed for linear motor active suspension.LQR active control based on feedback linearization is used in the outer loop and current decoupling control based on fractional order internal model is used in the inner loop.The simulation test of active suspension with linear motor is carried out with Matlab/Simulink.The results show that the current decoupling control based on fractional internal model can follow the control force of the active suspension well,which verifies the rationality of the nonlinear fractional active suspension model of active suspension with linear motor and the effectiveness of the active control and the control strategy of active suspension with linear motor.