基于反馈线性化的插秧机路径跟踪模糊预测函数控制

    Fuzzy predictive function control for the path tracking of transplanters using feedback linearization

    • 摘要: 为了提高插秧机路径跟踪系统的控制精度和鲁棒性,该研究提出一种基于反馈线性化的模糊预测函数控制方法。在Frenet坐标系下建立插秧机运动学模型,并采用状态反馈方法对模型进行精确线性化处理,通过选取Morlet小波函数作为基函数,以及依据横向误差、横向误差变化率和参考路径曲率设计模糊规则在线调整性能指标函数中的加权系数,进而运用预测函数控制算法求解路径跟踪控制律。Matlab/Simulink仿真试验结果表明,当插秧机作业速度为0.5、1.0、1.5 m/s时,对于直线路径跟踪情况,模糊预测函数控制的横向误差均渐近趋于0,行驶轨迹皆无超调,上线距离分别为1.2、2.3和3.3 m;对于曲线路径跟踪情况,模糊预测函数控制的横向最大绝对误差分别为0.7、2.4和5.1 cm,横向标准差分别为0.4、1.5和2.8 cm。与常规模型预测控制相比,模糊预测函数控制在确保路径跟踪系统实时性的前提下,提高了系统的控制精度,改善了系统的动态性能,并且对作业速度与参考路径曲率变化具有更强的鲁棒性。水田实车试验结果表明,模糊预测函数控制能够使插秧机在不同作业速度下平稳有效地跟踪参考路径,并具有较高的控制精度和鲁棒性;当插秧机作业速度为0.5、1.0与1.5 m/s时,模糊预测函数控制的横向最大绝对误差分别为5.9、7.5和9.8 cm,直线路径横向标准差分别为1.4、1.7和2.7 cm,曲线路径横向标准差分别为2.5、3.6和5.5 cm,跟踪效果满足插秧机实际作业要求。该研究可为插秧机路径跟踪预测控制方法研究提供参考。

       

      Abstract: 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.

       

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