## 4 Results and Discussion
### Simulation of Control System
#### 4.1.2 Determination of Optimal PID Coefficient  
Based on the above initial PID coefficients, PID coefficients with a low overshoot, settling time, and steady-state error were determined through simulation. Table 2 shows response performances of the shuttle shifting and clutch actuators, according to the PID coefficients. To evaluate the determined PID coefficients, the response performances of the shuttle shifting actuator under the determined PID coefficients (K\({}_{\text{P}}\) = 6.50, K\({}_{\text{I}}\) = 5.70, and K\({}_{\text{D}}\) = 0.240) and arbitrary control coefficient pairs through the developed simulation program were compared, as shown in Figure 10a. In this case, the arbitrary  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Range shift**} & \multicolumn{4}{c}{2 nd} & \multicolumn{4}{c}{3 rd} \\ \hline \multicolumn{2}{c}{**Driving shift**} & 1 st & 2 nd & 3 rd & 4 th & 1 st & 2 nd & 3 rd & 4 th \\ \hline \multirow{3}{*}{**Rotational speed**} & **Forward** & 66 & 79 & 93 & 124 & 147 & 174 & 205 & 276 \\ \cline{2-10}  & **Reverse** & 55 & 65 & 76 & 102 & 121 & 143 & 168 & 225 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculated rotational speed of transmission by each gear ratio at engine-rated rotational speed.  
control coefficient pair indicates the optimum coefficient pair when the K\({}_{\rm P}\) is set to 6.30 (K\({}_{\rm P}\) = 6.30, K\({}_{\rm I}\) = 4.80, and K\({}_{\rm D}\) = 0.155) and the optimum coefficient pair when the K\({}_{\rm P}\) is set to 6.70 (K\({}_{\rm P}\) = 6.70, K\({}_{\rm I}\) = 6.05, and K\({}_{\rm D}\) = 0.330). In the case of the PID coefficients of K\({}_{\rm P}\) = 6.30, K\({}_{\rm I}\) = 4.80, and K\({}_{\rm D}\) = 0.155, the maximum overshoot, settling time, and steady-state error were 8.50%, 1.18 s, and 0%, respectively. In addition, in the case of the PID coefficients of K\({}_{\rm P}\) = 6.70, K\({}_{\rm I}\) = 6.05, and K\({}_{\rm D}\) = 0.330, the maximum overshoot, settling time, and steady-state error were 1.50%, 3.74 s, and 4.5%, respectively. Therefore, the PID coefficients (K\({}_{\rm P}\) = 6.50, K\({}_{\rm I}\) = 5.70, and K\({}_{\rm D}\) = 0.240) of the shuttle shifting actuator with a maximum overshoot of 3%, settling time of 0.440 s, and steady-state error of 0% were determined. To evaluate the determined PID coefficients, the response performances of the clutch actuator were compared, as shown in Figure 10b. In this case, the arbitrary control coefficient pair indicated the optimum coefficient pair when K\({}_{\rm P}\) was set to 1.25 (K\({}_{\rm P}\) = 1.25, K\({}_{\rm I}\) = 2.85, and K\({}_{\rm D}\) = 0.065) and the optimum coefficient pair when K\({}_{\rm P}\) is set to 1.65 (K\({}_{\rm P}\) = 1.65, K\({}_{\rm I}\) = 4.15, and K\({}_{\rm D}\) = 0.325). In the case of the PID coefficients of K\({}_{\rm P}\) = 1.25, K\({}_{\rm I}\) = 2.85, and K\({}_{\rm D}\) = 0.065, the settling time was 2.50 s. In addition, in the case of the PID coefficients of K\({}_{\rm P}\) = 1.65, K\({}_{\rm I}\) = 4.15, and K\({}_{\rm D}\) = 0.325, the settling time was 1.68 s. In both cases, the control performance was lower than the settling time of 1.06 s and, so, the best-performing PID coefficients were K\({}_{\rm P}\) = 1.45, K\({}_{\rm I}\) = 3.45, and K\({}_{\rm D}\) = 0.190. Therefore, as the determined PID coefficients not only satisfied the overdamping and underdamping control of the shuttle shifting and clutch actuators, respectively, but also had a small error with the target position, it was concluded that the determined PID coefficients were applicable to the automatic shift control of the clutch.