Research On Solution Of Vehicle's Driving Stability Region Of Multi-DOF Based On Homotopy Method

The driving and steering condition of vehicle is one of the typical driving conditions.The driving torque and front wheel angle as the input correspond to driver's acceleration pedal and steering wheel respectively,which have an important impact on vehicle handling and stability.The driving stability region represents the combination of driving torque and front wheel angle,which can maintain stable driving state.Therefore,by solving the driving stability region can analyze the influence of driving torque and front wheel angle on vehicle handing stability and provide fundamental for vehicle handing stability integrated control.At the same time,the control structure of “feedforward and feedback” can be designed based on the driving stability region,which takes both driving torque and front wheel angle as control parameters.The control structure of “feedforward and feedback” can make full use of the advantage of small lag and timely action by feedforward.Moreover,it could keep the strength of overcoming kinds of interference and eliminating deviations by feedback.In essence,the driving stability region is determined by the bifurcation point in the space of driving torque and front wheel angle in the two-parameter coupling bifurcation of vehicle driving and steering.As a typical non-linear system,the bifurcation characteristics of vehicles are usually accompanied by the change of the equilibrium point.Therefore,the bifurcation point can be obtained by solving the equilibrium point,and then the driving stability region can be obtained.But the multi-DOF system of vehicle has strong nonlinearity and can not be solved by analytic method.The traditional numerical methods(such as Newton method)have strong sensitivity to initial values and can not solve the multi-peak system.The genetic algorithm and other optimization algorithms are facing the problems of slow convergence speed and easy to fall into the local optimal solution.By analyzing the characteristics of different degrees of freedom vehicle system in the whole phase space,it is found that there are similarities among different degrees of freedom vehicle systems,which have one stable equilibrium point and two unstable equilibrium points.Therefore,a method of solving the equilibrium point based on homotopy algorithm is proposed to solve the driving stability region.This paper mainly carries out the following research work:(1)The global phase space simulation of steering motion of different degrees of freedom vehicle system is carried out,and the similarity between different degrees of freedom vehicle systems is analyzed.A method of solving equilibrium point based on homotopy algorithm is proposed in combination with homotopy idea.Compared with the results of genetic algorithm,the results show that the solving of homotopy algorithm is more accurate and efficient.(2)The homotopy algorithm is used to calculate the values of the 2-DOF vehicle system equilibrium point varying with the front wheel angle,the 3-DOF vehicle system equilibrium point varying with the front wheel angle and the 5-DOF vehicle system equilibrium point varying with the front wheel angle and driving torque.On the one hand,the validity and generality of the homotopy algorithm are verified.On the other hand,the effects of different road conditions,front wheel angle and driving torque on the bifurcation characteristics of the equilibrium point are analyzed.(3)According to the definition of driving stability region and the result of solving the equilibrium point,the driving stability region can be obtained.The influence of driving torque and front wheel angle on vehicle handling stability can be seen intuitively,which has very important engineering application value.(4)Based on the obtained driving stability region,the driving stability region with or without the function of the vehicle stability controller is compared and analyzed.The driving stability region enlarged under the influence of the controller is obtained.The control effect of the controller in the whole driving region is quantitatively evaluated,which provides a theoretical basis for the development and evaluation of the vehicle handling stability control strategy.