两挡变速器换挡过程最优控制的伪谱法求解

Pseudo-spectral Method for Optimal Control of Two-Speed Transmission in Shift Process

随着新能源汽车的发展,采用多挡位变速器在保证车辆动力性的前提下,可以提高电机效率。为了减小换挡冲击,提升乘坐舒适性,需要对驱动电机和换挡电机进行协调控制。本文中以两挡变速器为研究对象,提出了一种基于Radau伪谱法的变速器换挡策略,选取冲击度和滑摩功作为两挡变速器换挡品质的评价函数,利用插值多项式对换挡过程中系统的状态变量和控制变量进行逼近,由插值多项式的导数值近似代替动力学方程中状态变量的微分值,将换挡过程的最优控制问题转换为非线性规划问题,并利用现有的非线性规划问题求解器进行求解。采用MATLAB软件对两挡变速器的换挡问题进行伪谱法求解,得到了两挡变速器换挡过程的最优控制轨迹,验证了伪谱法的有效性和优异性。

With the development of electric vehicles,multi-gear transmission can improve the efficiency of the motor under the premise of ensuring the power performance of the vehicle.In order to reduce the impact of shifting and improve ride comfort,coordinated control of the drive motor and the shift motor is required.In this paper,taking the two-speed transmission as the research object,a shift strategy based on Radau pseudo spectral method is proposed.The impact degree and sliding friction work are selected as the evaluation functions of the shifting quality of the two-speed transmission.The state variables and control variables of the system in the shifting process are approximated by interpolation polynomials,and the derivative value of interpolation polynomials is used to approximate the differential value of the state variables in the dynamic equations.The optimal control problem of shifting process is transformed into a nonlinear programming problem,which is solved by the existing nonlinear programming problem solver.Using MATLAB software to solve the shift problem of the two-speed transmission with pseudo spectral method,the optimal control trajectory of the two-speed transmission is obtained,which verifies the effectiveness and superiority of the pseudo spectral method.