## 3 Results and Discussion
### Plowing Cycle  
Plowing is the most common and heavy-duty tractor operation. The traction resistance and tractor speed were measured in the previous field plowing to accurately simulate actual working conditions. The plowing cycle is shown in Figure 7, where the tractor operates at an average speed of 7.76 km/h under an average draft force of 2963 N. This section mainly studied the effect of different k and PDR values on the efficiency performance of DICPS in a plowing cycle. The variation in the overall efficiency with changes in k and PDR is shown in Table 4. With increasing k, the overall efficiency showed a decreasing trend. A high k further increased the output torque of EM_S and decreased the enlarging function of EM_R. This made EM_S work in high-speed and low-torque regions or make EM_R work at high-torque and low-speed regions (where the motor's efficiency is low). As a result, these high k values reduced the overall efficiency. Therefore, only the case of \(k=1.6\) was subsequently analyzed. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **PDR = 0.2** & **PDR = 0.35** & **PDR = 0.5** & **PDR = 0.65** & **PDR = 0.8** \\ \hline \(k=1.6\) & 85.2 & 87.2 & 87.7 & 87.3 & 85.2 \\ \(k=3.6\) & 84.3 & 86 & 86.8 & 86.2 & 84.1 \\ \(k=5.6\) & 83.8 & 85.3 & 86.3 & 85.8 & 83.8 \\ \(k=7.6\) & 83.5 & 85 & 86.1 & 85.6 & 83.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Overview of parameter designs and their efficiency. Figure 7: Plowing cycle for an agricultural tractor. As shown in Table 4, the overall efficiency tended to increase and then decrease with increasing PDR, and the maximum value appeared at PDR = 0.5. It can be seen that the connection position of the two motors had little influence on overall efficiency; the efficiencies of PDR = 0.2 and PDR = 0.8 were almost the same. Therefore, only the simulation results with a PDR of 0.5-0.8 were analyzed in the present paper. Different PDR values were closely related to the working mode and the size of gear ratio \(i_{s}\) and \(i_{r}\) of the DICPS. A high PDR allowed a decrease in the sun gear ratio \(i_{s}\) and an increase in the ring gear ratio \(i_{r}\), resulting in an increase in the EM_S demand torque and a decrease in the EM_R demand torque, and changing the working mode of the DICPS. Figure 6 shows the working mode curves under different PDRs. The DICPS worked entirely in mode M2S when PDR was 0.5. When PDR = 0.65, the maximum torque of EM_S could not drive the DMET independently; the DICPS mainly worked in modes DMC and M1S. When PDR = 0.8, the DICPS worked entirely in mode DMC. It should be noted that for mode DMC, both motors were active at the same time, which means that both motors had power losses. Therefore, the longer the tractor was in mode DMC, the greater the power loss generated, and the lower the overall efficiency. As can be seen from Figure 8, when PDR was 0.8, the DICPS worked in mode DMC for the longest time, followed by PDR = 0.65. When PDR was equal to 0.5, it worked in mode DMC for the shortest time and had the highest efficiency, so overall efficiency first increased, and then decreased. However, the overall efficiency of SMPS under the plowing cycle was 77.9%. Even in the worst-case DICPS scenario (PDR = 0.8, \(k\) = 7.6), its efficiency was still higher than the SMPS. The motor speeds during the plowing cycle are shown in Figure 9. From the figure, it can be seen that the DICPS worked in the M2S mode at PDR = 0.5, which meant that the power demand of DMET could be met with the independent drive of EM_R while maintaining the highest overall efficiency. The DICPS worked in the DMC mode when PDR was 0.65 and 0.8, and, since the increase in PDR causes \(i_{r}\) to increase and \(i_{s}\) to decrease, the speeds of the two motors at PDR = 0.8 were greater than those at PDR = 0.65. The speed of the EM_T in the SMPS was lower than the EM_R in DICPS, because the total gear ratio of the SMPS was lower than that of the ring branch in the DICPS.