## 2 Materials and Methods
### Steering Control Module Design  
The structure of the steering controller (SC), which was provided by Jinan Keya Electron Co., Ltd. (Jinan, China), is listed in Figure 2. Its internal reluctance incremental encoder was used as the feedback component, the speed mode was selected for motor control, and the command was sent using the RS232 serial port. The electric steering wheel controlled the splined shaft, making the guide wheels continuously approach the expected rotation angle. The technical parameters of the motor are listed in Table 2.  
As shown in Figure 3, the angle sensor was installed on the left front wheel of the tractor to measure the front wheel rotation angle, and its value was returned to the SC to finish the control cycle. The DWQT V05-120-G from Beijing Tianhaike Technology Development Co., Ltd. (Beijing, China) was selected as the angle sensor. Its specific performance parameters are listed in Table 3.  
A principal block diagram of the SC is presented in Figure 4, where a double closed-loop PID control algorithm with a dead zone was designed to improve the anti-interference ability of the SC. The inner loop realizes the speed control of the motor, and the outer loop \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Rated Voltage (V) & 12 \\ Rated Torque (N-m) & 7 \\ Rated Speed (rpm) & 100 \\ Control Mode & RS232 \\ \hline \end{tabular}
\end{table} 
Table 2: Technical parameters of Koya motor. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Motor power (kw) & 81 \\ Length \(\times\) Width \(\times\) Height (mm \(\times\) mm \(\times\) mm) & 4436 \(\times\) 2250 \(\times\) 2765 \\ Ground clearance (mm) & 440 \\ Working speed (km/h) & 2.69–37.65 \\ Minimum turning radius (m) & 5.6 \\ Front wheel thread (mm) & 1760 \\ Rear wheel thread (mm) & 1820 \\ Motor power (kw) & 81 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of Dongfanghong 1104. Figure 2: Physical diagram of steering actuator installation. **(a)** Installation schematic: (I) steering wheel; (2) motor; (3) support bracket; (4) splined shaft. **(b)** Structural diagram. realizes the steering wheel angle control. The incremental PID speed control of the inner loop is written as follows:  
\[\Delta V=k_{p}(e_{V}(k)-e_{V}(k-1))+k_{i}e_{V}(k)+k_{d}(e_{V}(k)-2e_{V}(k-1)+e_{V} (k-2)) \tag{1}\]  
where \(k_{p}\), \(k_{i}\), and \(k_{d}\) denote the PID parameters (Table 4); \(e_{V}(k)\) is the speed deviation value at the current moment, and the motor speed is directly measured by the internal reluctance encoder; \(e_{V}(k-1)\) is the speed deviation at sampling moment \(k-1\); and \(e_{V}(k-2)\) is the speed deviation at sampling moment \(k-2\). The discrete PID angle control of the outer loop is formulated as follows:  
The dead zone of the outer loop angle control is 2.5\({}^{\circ}\). During the drive control process, if the difference between the expected angle and the actual angle is less than 2.5\({}^{\circ}\), the motor will not engage, and the PID controller is considered to have reached the target value. This method can effectively reduce the wear of the steering system caused by frequent motor control. To prevent the motor from being damaged by the over-saturation of the steering actuator, the steering wheel angle threshold was set to \(\pm\)20\({}^{\circ}\). Since the steering angle generally does not jump during the normal operation of the tractor, a sine wave signal was used to investigate the steering tracking characteristics of the electric steering wheel. As shown in Figure 5a, by designing a sine wave signal as the expected rotation angle and inputting it into the steering control system, the rotation angle amplitude was set within [\(-\)15\({}^{\circ}\), 15\({}^{\circ}\)], and the front wheel steering angle information was read in real-time through the RS232 serial port.