基于电动方向盘的拖拉机自动导航转向控制方法

为提高轮式拖拉机自动导航过程中转向控制的精度与稳定性，该研究以雷沃欧豹M704-2H拖拉机作为试验平台，采用电动方向盘作为转向执行机构，分析转向机械间隙对控制精度的影响，针对转向间隙特性设计转向控制算法。首先，为了获得准确的转向角，利用GNSS(global navigation satellite system)与二轮车模型快速标定虚拟轮转角，标定结果表明：虚拟轮转角的最大误差为1.3°，平均误差为0.11°。然后，对转向系统的机械间隙进行分析，设计一种带有间隙补偿的模糊PD(proportional derivative)转向控制算法，并在Simulink中验证算法的可行性。实车试验结果表明，该算法跟踪方波转角信号的响应时间为1.1 s，最大稳态误差为0.65°，平均稳态绝对误差为0.132°。跟踪正弦波转角信号的平均延时为0.5 s，最大误差为1.91°，平均绝对误差为1.09°。与无间隙补偿算法相比，有间隙补偿算法跟踪方波信号最大稳态误差减小了0.022°，平均稳态绝对误差减少了0.112°，角度误差在±0.2°内的时间提升了71%；跟踪正弦波信号最大误差减小了0.68°，平均绝对误差减小0.23°。田间直线导航转向控制试验结果表明，转角跟踪的绝对平均误差为0.61°，最大跟踪误差为2.82°，转向控制跟踪精度较高，稳定性好，满足导航作业需求。

Steering control system for a tractor using electric steering wheel

A steering control system is one of the key steps in the tractor''s automatic navigation. Many nonlinear factors (such as hydraulic dead zone, saturation zone, and mechanical backlash) can dominate the performance of steering control, even the accuracy and stability of tractor navigation. In this study, the Lovol Europa M704-2H tractor was taken as the test platform with the electric steering wheel instead of the onboard steering wheel as the actuator, where the angle sensor on the steering wheel axle of the tractor to measure the size of the wheel turning angle. The steering control system included the steering angle calibration and the steering control. The steering angle calibration aimed to obtain the limit angle and median AD value size of the tractor, and then the steering wheel angle size at any angle by linear fitting. The limit steering angle calibration was required for the tractor steering wheel close to the limit through a circle, the satellite positioning of the trajectory point, and the least squares, in order to obtain the minimum turning radius of the tractor. The two-wheel model of the tractor was then utilized to calculate the maximum steering angle. The median steering angle calibration was required for the tractor to drive a section of an approximate straight-line trajectory. The least squares method (LSM) was also used to identify the correction of the zero position for the accurate median AD value. The TZ-QX2A6/5T front wheel angle meter was selected to compare the front wheel angle with the sensor measurement. The results show that the maximum error of calibrated angle measurement was 1.3°, and the average error was 0.11°, fully meeting the demand of steering control. At the same time, the mechanical backlash of the steering system was firstly quantified, in terms of the angular size of steering wheel reversal across the free travel. The accurate size of mechanical backlash was obtained through experimental identification. Then, the fuzzy PD steering control with backlash compensation was designed at the same time. When the electric steering wheel was out of the free travel, the fuzzy PD control was adopted; when the electric steering wheel was in free travel, the steering control was compensated to add the backlash P control into the output of the fuzzy PD control. Simulation results in Simulink show that better performance was achieved in the tracking of the steering angle signals of square wave and sinusoidal wave, fully meeting the requirements. The fuzzy PD steering control with/without the backlash compensation was also used to compare the tracking performance of square wave and sinusoidal steering angle signals. The experimental results show that the response time of the square wave angle signal tracking without backlash compensation was 1.3 s, where the maximum and average steady-state errors were 0.672°, and 0.244°, respectively. The average delay time of the sine wave angle signal tracking without backlash compensation was 0.5 s, where the maximum and average errors were 2.59° and 1.32°, respectively. Compared to the algorithm without backlash compensation, the time of steering angle error within ±0.2° was improved by 71%, the maximum steady state error was reduced by 0.022°, and the average steady state absolute error was reduced by 0.112°. Once the backlash compensation was performed, the response time of the square wave angle signal tracking was 1.1 s, where the maximum and average steady-state errors were 0.65°, and 0.132°, respectively. The average delay time of the sine wave angle signal tracking was 0.5 s, the maximum and average errors were 1.91° and 1.09°, respectively. Compared to the algorithm without backlash compensation, the maximum error was reduced by 0.68°, and the average error was reduced by 0.23°. The experimental results show that the backlash compensation outstandingly improved the stability of steering control for the less control error. The linear navigation test on the leveled field showed that the maximum and absolute average errors of angle tracking were 2.82° and 0.61°, respectively, when the system was in a steady state. Therefore, better performance was achieved with the high accuracy of the steering control system.