## 1 Introduction
In [22; 23; 24], the dynamic programming algorithm was used to analyze and formulate the optimal brake pressure, engine speed trajectory and control logic of MT process to minimize vehicle jerks. However, these methods cannot be applied to actual vehicle control. In [25; 26], the motor torque change rate was limited using dynamic equations of planetary gear to reduce vehicle jerks. [PERSON] [27] used feedforward control for one motor and compensation control for the other based on the engine torque estimation to improve driving comfort. [PERSON] [28] designed an active damping-control system at the wheels to suppress system oscillation. [PERSON] [29] designed a motor torque compensation control method and established a vibration path control to change the dynamic characteristics of the engine during starting and stopping. [PERSON] [30] divided the MT process into four operational stages and adopted the fuzzy gain scheduling proportion integration differentiation (PID) controller to reduce fluctuations of the powertrain system. To some extent, although the above methods can reduce vehicle jerks and vibrations, they also ignore the influence of the limitations of battery-motor characteristics on vehicle jerks under different engine starting conditions. The above research during engine start-up for a hybrid powertrain system mainly focuses on the engine torque estimation, the limitation of the motor torque change rate, the compensation control based on the active damping and dynamic programming algorithm and so on. However, these methods do not fully consider the influence of factors such as ERT, the elastic characteristics of the transmission system, the battery power limitations or the maximum motor torque. In fact, these factors will diminish the effectiveness of the control system to reduce vehicle jerks under different engine starting conditions. To solve this problem, this paper proposes a dynamic torque coordinated control method during engine starting conditions (DTCC-ESC). In comparison with previous research, the main contributions of this paper include the following three aspects: (1) In the MT process during engine starting, an engine segment active control method before and after engine ignition is proposed to minimize the impact of ERT on system jerks and vibrations; (2) During starting, the engine demand-angular acceleration is optimized to modify the feedforward control of the engine starting process before ignition; and (3) Based on the zero-pole distribution method and the estimation algorithms of the system torque and speed, an active-damping feedback compensation control for system resonance (ADFC-SR) is modified to restrain the vibrations of the transmission system. By this method, the torque of the engine output shaft fluctuations can be reduced; meanwhile the torque of the two motors to compensate or offset driveline fluctuations can be optimally distributed, so that the compensation torque from MG1 and MG2 will not exceed the limit of its own maximum torque. Therefore, vehicle jerks in some engine-starting conditions can be effectively reduced. The rest of this article is organized as follows: In Section 2, the model of a compound power-split power transmission system is established, and this model has been verified by some experiments. In Section 3, the dynamic analysis during the engine starting process is carried out by using the equivalent lever method, and the problem to be solved in this paper is further described by using a flow chart. To address this problem, the DTCC-ESC method is proposed in Section 4. Then, in Section 5, the three control methods are simulated and compared under different engine-starting conditions. Finally, the simulation conclusions of the proposed control method are provided in Section 6.