Optimizing gear shifting quality with backstepping control for automatic transmission

Abstract: The Automatic Transmission is widely equipped in the heavy-duty trucks, while the driving comfort reduction during gear shift is the major drawbacks, and the optimization of gear shifting process is quite challenging due to the various objectives. With the development of modern control theory, it has been widely applied into gear shifting duration, such as PID control, genetic algorithm and dynamic programming et al. In this paper, a backstepping control strategy is proposed to enhance the gear shift quality, which will transform the multi-objective optimization to a single target tracking as well. According to the gear shifting dynamic model, gear shifting can be divided into four phases, lower gear phase, torque phase, inertial phase and higher gear phase. The clutch output torques during engagement and disengagement are derived considering the motion states of the off-going and on-coming clutches. The trajectory target is defined on the basis of the rotatory input and output speed of the transmission. Since the torque is hard to be measured accurately and the transmission output speed does not has obvious change during the torque phase of gear shifting, we will adjust the current of pressure reducing valves in the inertial phase. By analyzing the motion states of off-going clutch and on-coming clutch, the mathematical model of output torque for clutches has been built in this paper. The backstepping method and state stability theory (ISS) are utilized in the sliding mode controller to control the synchronization torques by tuning the valves current. The shifting quality is assessed in terms of the shift time, jerk and sliding friction work which are considered into the objective function in sliding control problem. All of them are fitted as three-order polynomial functions, and the controller parameters are evaluated according to the system parameters and the margin of errors. Based on the reference trajectory, the speed of driven plate on-coming clutch decreases as a third order polynomial during inertial phase which lasts about 0.4s. When the torque of turbine evaluates around 200 Nm, the k1 and k2 are equal 15 and 4 respectively to satisfy the steady error e1 less than 10 rad/s and ε1 is less than 280 rad/s2. The gear shifting model is established in AMEsim platform interfacing with the controller model in Simulink. At the 1.13 s, the gear shifting simulation becomes to the torque phase. At the same time, the oil pressure of off-going clutch Cd start to decrease until the pressure come to zero. While the oil pressure of on-coming clutch become to increase after 0.18 s, the pressure rise to the desired value slowly. The process is going to be the inertial phase from 1.43s. The results of co-simulation suggest that the controller tracked the objective rotate speed closely and the maximum jerk of vehicle was around 6 m/s3 and fulfills the standard of China (17.64 m/s3). The designed slider controller is shown to track the trajectory precisely, and the proposed backstepping method is therefore able to improve the transmission shifting quality. Additionally, the future work is to validate the real performance of this method.