## 3 Results and Discussion
### Simulation of Integrated Control Shift Control Strategy  
The jerk is obtained by adjusting the clutch engagement time to match the displacement ratio of the pump-motor hydraulic system under uncontrolled conditions (Figure 15), which is regarded as the most important indicator for evaluating the shifting stability of the tractor. It shows that the acceleration shock of the tractor is minimal at the maximum displacement of the pump-motor hydraulic system (\(H\) = (0,0,0)). Both early and late shifts at maximum displacement have great shock and poor stability. Especially when the gear shift is delayed, the reverse jerk of the tractor is large, so it is necessary to select the shift point at the maximum displacement of the pump-motor hydraulic system under no control conditions. The results under the different control strategies are shown in Figure 16. It shows that the fluctuation of jerk is different in various control strategies. The jerk is the minimum value of about 7.9 m/s\({}^{3}\) when \(H\) = (0,1,1), and during the delay control (\(H\) = (-1,1,1)), the fluctuation amplitude of the shift shock is the largest. Moreover, it is very obvious that the maximum value of jerk with control is smaller than that without control (Figure 15). For example, when the HMCVT is controlled at the transition point (\(H\) = (0,1,1)), its jerk is about 53.5% smaller than the jerk without control (\(H\) = (0,1,0)), which shows better transition smoothness. Therefore, the HMCVT system exhibits better shift smoothness in the shift control strategy. It is well known that if the shift time is too short, it requires a larger shift torque per unit time, so the resulting shift jerk is higher. The frequent shifting may cause excessive overlap in clutch and pump-motor fluid system matching; therefore, it may cause shifting instability. \begin{table}
\begin{tabular}{c c} \hline \hline
**Tractor Model** & **Parameter** \\ \hline Maximum speed & 50 km/h \\ Engine rated power & 200 hp/149.1 kw \\ Engine rated speed & 2100 r/min \\ Maximum mass & 10,500 kg \\ Driving wheel tire & 480/80R50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The basic parameters of tractor. Figure 15: The jerk in uncontrolled strategies (\(H\) = (x,1,0)). Therefore, a reasonable shifting time can reduce the jerk and improve the comfort of the tractor during shifting. In this study, a comprehensive control strategy (Equation (30)) is used to adjust the shift combination time, and the jerks with different control strategies are shown in Figure 17. There are \(H\) = (0,1,1), \(H\) = (0,1.5,1), \(H\) = (0,2,1), \(H\) = (0,2.5,1) four control optimization strategies, which show shifting at maximum displacement ratio. Figure 17 shows the variation of the extreme value of jerk for six different control strategies. The jerk degree of the optimized comprehensive control strategies is generally smaller than that of control strategies (\(H\) = (1,1,1), \(H\) = (-1,1,1)). When the clutch engagement is controlled, the tractor speed gradually becomes smooth as the response time of the control clutch increases. However, when the control time exceeds a certain limit, the speed change rate suddenly increases (\(H\) = (0,2.5,1)), which is represented by an increase in the magnitude of the shift shock. Although the pump-motor hydraulic system is always in working condition, the excessively long coupling time causes a power interruption between the two clutches, which results in drastic changes in tractor speed and a sharp drop in shifting quality. Therefore, this phenomenon should be avoided as much as possible in tractor operation and driving. It can be seen from Figure 17 that the jerk fluctuation is the smallest when the comprehensive control strategy is \(H\) = (0,2,1), which is about 6.05 m/s\({}^{3}\). Compared with the acceleration jerk when \(H\) = (0,1,1) with control, it is reduced by 23.4%, and compared with the acceleration jerk when \(H\) = (0,1,0) without control, it is reduced by 64.4%. Other jerks are shown in Table 2 under different control strategies.