A path tracking system is required to fully meet the change of operating speed in the agricultural machinery. In this study, a predictive control system was proposed using a preview kinematics model. The model of preview heading error was also established using the preview following theory. The output equation was combined with the conventional state equation of path tracking error. The state space model of path tracking error was then constructed for the preview kinematic after linearization and discretization. Then the path tracking control was designed using a model predictive control algorithm and input parameterized attenuation. The co-simulation platform was built for the path-tracking control of agricultural machinery using CarSim and Simulink software. The simulation results showed that the lateral errors of straight path tracking asymptotically approached zero for the preview model predictive controller. There was no overshoot of driving curves at different operating speeds. Once the operating speeds of agricultural machinery were 1, 3 and 5 m/s, respectively, the maximum absolute values of lateral error were 8.52, 10.42, and 10.82 cm in the circular path tracking for the preview model predictive controller, whereas, the standard values of lateral error were 3.96, 5.83 and 6.17 cm, respectively. Once the control horizon layers were 10, 30 and 60, the operation period of the preview model predictive controller was reduced by 7.5%, 43.0% and 48.5%, respectively, compared with the conventional. The preview model predictive controller was used to dynamically adjust the preview distance and prediction horizon, according to the operating speed and path curvature, respectively. The dynamic performance of the path tracking system was effectively improved with the control accuracy. There was more balanced path tracking at different operating speeds, indicating the simpler parameter setting. The decay factor was also introduced to parameterize the control input. The amount of online optimization was greatly reduced to improve the real-time performance of path-tracking control. The field test platform of automatic driving was built to install the satellite antenna, satellite receiver, angle sensor, proportional reversing valve, controller, and vehicle touch screen on the agricultural machinery. In straight path tracking, the average maximum absolute values of lateral error were 3.50 and 5.32 cm, the average absolute values of lateral error were 1.46 and 1.93 cm, and the average standard values of lateral error were 1.71 and 2.38 cm, respectively, when the operating speeds of agricultural machinery were 1 and 5 m/s, respectively. In circular path tracking, the average maximum absolute values of lateral error were 9.62 and 15.34 cm, the average absolute values of lateral error were 5.17 and 7.86 cm, and the average standard values of lateral error were 4.82 and 8.39 cm, respectively, when the operating speeds of agricultural machinery were 1 and 5 m/s, respectively. The field test results showed that the preview model predictive controller shared a strong adaptability to the change of operating speed within the operating speed range of 0.5 to 5 m/s. Agricultural machinery quickly and stably tracked the reference path with high control accuracy. The average maximum absolute values and the average standard values of lateral error were less than 5.5 and 2.5 cm, respectively, for the straight path tracking, while less than 15.5 and 8.5 cm, respectively, for the circular path tracking. The preview model predictive controller can fully meet the actual control requirements of agricultural machinery, especially suitable for complex environments or high-speed conditions.

In order to improve the control accuracy and robustness of path tracking system for the transplanter, a fuzzy predictive function control method was proposed using feedback linearization in this study. The kinematic model of transplanter was established using Frenet coordinate system. The state feedback method was applied to the nonlinear transplanter system to make the closed loop system become linear system. The Morlet wavelet function was selected as the basis function in predictive function control. The control law of path tracking system for transplanter was designed by the predictive function control algorithm. The weighting coefficient of lateral error in the performance index function for the predictive function control was adjusted online by designing fuzzy rules according to the lateral error and the reference path curvature. The weighting coefficient of change rate of lateral error in the performance index function for the predictive function control was adjusted dynamically by designing fuzzy rules according to the lateral error and the change rate of lateral error. The simulation platform was built for path tracking control of transplanter using Matlab/Simulink software. The simulation results of the fuzzy predictive function control showed that the lateral errors of straight path tracking asymptotically approached zero, and there was no overshoot of actual driving curves at different operating speeds for the straight path tracking. In the straight path tracking, the in-line distance of the fuzzy predictive function control was 1.2, 2.3 and 3.3 m, and the in-line distance of the conventional model predictive control was 2.6, 2.3 and 4.6 m, respectively, when the operating speeds of transplanter were 0.5, 1.0 and 1.5 m/s, respectively. In the case of curve path tracking for the fuzzy predictive function control, the maximum absolute values of lateral error were 0.7, 2.4 and 5.1 cm, and the standard values of lateral error were 0.4, 1.5 and 2.8 cm, respectively, when the operating speeds of transplanter were 0.5, 1.0 and 1.5 m/s, respectively. In the case of curve path tracking for the conventional model predictive control, the maximum absolute values of lateral error were 4.3, 5.5 and 7.8 cm, and the standard values of lateral error were 3.1, 3.5 and 5.0 cm, respectively, when the operating speeds of transplanter were 0.5, 1.0 and 1.5 m/s, respectively. The average operation cycle of the fuzzy predictive function control algorithm was 0.012 s, which was 0.004 s less than that of the conventional model predictive control algorithm. Compared with the conventional model predictive control, the dynamic performance, control accuracy and robustness of path tracking system for transplanter were improved on the premise of ensuring the real-time performance by the fuzzy predictive function control. The automatic driving control system of transplanter was built to install the satellite antenna, satellite receiver, angle sensor, electric steering wheel, controller and vehicle-mounted touch screen on the transplanter. The field experiment was carried out with the automatic driving control system of transplanter. The field test results showed that the fuzzy predictive function control had the strong robustness to the changes of operating speed and reference path curvature. The transplanter tracked the reference path smoothly and effectively. The maximum absolute value of lateral error occurred near the intersection of the straight path and the curve path. Once the operating speeds of transplanter were 0.5, 1.0 and 1.5 m/s, the maximum absolute values of lateral error were 5.9, 7.5 and 9.8 cm, the standard values of lateral error for the straight path were 1.4, 1.7 and 2.7 cm, and the standard values of lateral error for the curve path were 2.5, 3.6 and 5.5 cm, respectively. The fuzzy predictive function control can fully meet the actual control requirements of transplanter, and provided a reference for the research on predictive control method of path tracking for transplanter.