Multi-stage global trajectory optimization for the overlapping shift of a seamless two-speed transmission using Legendre pseudo-spectral method

Abstract

For a seamless two-speed transmission specially equipped in electric vehicles, the global trajectory optimization problem of the overlapping shift process with multiple stages and complex path/point constraints is investigated in this article. The overlapping shift principle and the dynamic models in each phase are also demonstrated in detail. The parameters to evaluate the shift quality are analyzed and then introduced into the objective function and constraints, respectively. The jerks in process and at the key moments have been distinguished and selected as the path and point constraints, respectively. Moreover, considering the joint characteristics of the torque phase and the inertia phase, the trajectory optimization problems in the above two phases are summarized as a multi-stage global trajectory optimization problem. Then, Legendre pseudo-spectral method is used to transfer the multi-stage global trajectory optimization problem into a nonlinear programming problem for numerical solutions. Finally, the effectiveness and feasibility of the multi-stage global trajectory optimization method have been verified through the comparison of the optimal shift trajectories under different conditions with that obtained by the piecewise trajectory optimization method.

Multi-Objective Optimal Gearshift Control for Multispeed Transmission Electric Vehicles

“…In addition, we set the torque variations of the motor, large sun gear, and carrier as control variables. Before obtaining the angular velocities of the small and large sun gears, the corresponding accelerations are required, as given by (9) and (10).…”

“…Tian et al [9] proposed a two-speed EV transmission and trajectory planning based on specific rules. Ye et al [10] applied minimization for EV gearshift trajectory planning for seamless two-speed transmission and proposed a coordinating controller to optimize the shift trajectories and improve the overlapping shift. Lu et al [11] designed a data-driven predictive gearshift controller to improve shifting and implemented the control on an FPGA platform to improve the execution efficiency.…”

Control strategy of automated manual transmission based on active synchronisation of driving motor in electric bus

“…where p suc is the shifting success probability, n is the tooth number of the sleeve spline, p 0 is the direct engagement probability of the mesh gear and the sleeve spline without contact, p 0 = nF=2p. Using equations (14) and 15, we can obtain the following u fstart is a random variable. Thus, Dv 3 is a variable whose value is determined by u fstart and Dv 0…”

Effect of clearance configuration on gear system dynamics

“…Therefore, multi-speed transmissions are being applied not only to traditional engine-driven vehicles, but also to electrical vehicles. [16][17][18][19] To shift between different gears, switch control engagement elements such as synchronizers or sleeves are essential for multi-speed transmissions. The synchronizer or sleeve can be arranged on either the input or the output shaft of the gear pair, with the engaging clearance accordingly being at the input or the output shaft.…”