*3.2. Control Accuracy Analysis of Control System*

In this study, the spreading accuracy of the control system was reflected by the flow error, flow control stability, and valve group response time under the condition of vehicle speed change. The open–shut processes of the solenoid valve were the main reasons for the fertilizer flow error. A degree of error was observed in the liquid supply of the self-priming jet pump, as well as the measurement of the flowmeter. Flowmeter error [22–24] was the main error. The potential main causes for the flow error are as follows: (i) the influence of sediment; (ii) the fluid contained many bubbles; (iii) the wave height being uneven during the flow of the liquid to be measured. In addition, the ultrasonic flowmeter was also possibly subject to external interference, such as the electromagnetic environment, which affects system accuracy.

In this control system, the flow error of the liquid manure mainly originated from the fluid. The absolute error of the fluid flow represents the difference between the reading value of the flowmeter and the actual flow, and the flow proportional error is the ratio of absolute error to actual flow.

Therefore, the flow error was calculated as follows (Equation (22)):

$$\begin{cases} \Delta\_0 = \left| V\_i - V\_j \right| \\ \Delta\_1 = \frac{\Delta\_0}{V\_i} \times 100\% \end{cases} \tag{22}$$

where Δ<sup>0</sup> (L/min) is the absolute error of the system flow, Δ<sup>1</sup> (%) is the relative error of the system flow, Vi (L/min) is the actual flow, and Vj (L/min) is the flow rate read by the flowmeter.

### *3.3. Experiment Results and Analysis*

#### 3.3.1. Control System Stability Experiment

The data measured by the ultrasonic flowmeter were transmitted to the upper computer through 4–20 mA current, while the actual liquid fertilizer flow of spraying and fertilization was measured using the test. We used the actual driving speed [25] of the traction liquid fertilizer spreader in the field. In the test, the vehicle speed was set to 1, 1.5, 2.0, and 2.5 m/s in the control system, and the flow relevant to every vehicle speed group was determined. Each flow group was measured 10 times, and the average value was taken after removing the highest and lowest values. Using a spraying amount of 300 L/hm2, the acknowledge fertilization quantities in the light of the above four different velocities were determined to be 10.8, 16.2, 21.6, and 27 L/min, according to Equation (1).

The system output flow was measured at four vehicle speeds. Six measurements were taken for each vehicle speed state. The duration of each measurement was 2 min. The mean value of the six measurements was considered with measurement flow of the velocity. Simultaneously, the absolute and proportional errors of every control system were noted. The experiment outcomes are listed in Table 2.

**Table 2.** Flow error of control system.


As shown in Table 2, the flow error of liquid manure controlled by classical PID was higher than that of BPNN—PID control and GA–BPNN–PID. The PID flow control average relative error was 5.50%. The maximum absolute error was 0.91 L/min. The average relative error of the flow controlled by fuzzy PID was 3.67%. The maximum absolute error was 0.83 L/min. The average relative error of the flow controlled by BPNN-PID was 3.37%. The maximum absolute error was 0.83 L/min. The average relative error of GA–BPNN-PID was 0.97%. The maximum absolute error was 0.29 L/min. The experiment outcomes demonstrated that the relative error of the GA-BPNN-PID on the system flow control was the smallest. In comparison with PID control, the relative error was reduced by 4.53 percentage points, and compared with BPNN–PID control, the relative error was reduced by 2.4 percentage points. The control system exhibited the highest stability.
