Staggered-phase flow control model for PWM high-frequency solenoid valves in orchard variable-rate spraying

A pulse width modulation (PWM) solenoid valve testing system capable of online adjustment of the phase difference was proposed to address the limited research on flow-control behavior of PWM driven solenoid valves under high-pressure (> 1 MPa), high-frequency (> 10 Hz) operating conditions in Chinese orchard variable-rate spray systems. This study designed and constructed an experimental platform that supports real-time adjustment of phase relationships among multiple valves and enables synchronized acquisition of upstream and downstream pressure and flow data with high temporal resolution for quantitative analysis. The platform facilitates controlled experiments under representative orchard spraying conditions which carried out three types of experiments: switching performance tests of domestic solenoid valves, suppression of staggered-phase pressure fluctuations, and flow characteristic measurements. The switching performance tests systematically evaluated eight domestic solenoid valves, which recorded the activation status of each valve at 0 MPa and 1.25 MPa under a 5-50 Hz frequency range and 10%-90% duty cycle. A comprehensive evaluation system was established based on five metrics: average activation rate at 0 and 1.25 MPa, activation rate difference, activatable frequency range, and stability. Comprehensive scores were calculated, Ultimately, the YCH31-12-2GSV solenoid valve emerged as the top performer (overall score: 0.997, stability score: 0.916), achieving an 86.1% high-pressure activation rate within the common operating frequency range of 5-20 Hz and demonstrating the highest robustness. The staggered-phase pressure fluctuation suppression test demonstrated that staggered-phase control reduced upstream pressure RMS (Root Mean Square) values by 21.19%, 6.19%, 16.85%, and 6.75%, respectively. Analysis of the pressure fluctuation spectrum upstream and downstream of the solenoid valve revealed particularly significant suppression of upstream pressure fundamental amplitude by staggered-phase control. The suppression rate peaks at 85.40% at 5 Hz, with rates of 79.90%, 82.79%, and 84.23% at 10, 15, and 20 Hz, respectively. Compared with synchronous (in-phase) driving, staggered-phase control significantly suppresses upstream pressure fluctuations. However, downstream (nozzle) pressure oscillations are not reduced, and their amplitudes are slightly higher than those under synchronous control. It can be significantly mitigated in engineering practice by improving the material of local piping networks or nozzle structures, such amplification effects. By stabilizing the upstream pressure and suppressing dominant harmonics, staggered-phase timing creates more consistent inlet conditions, which facilitates construction of more accurate flow-duty-cycle models and reduces flow irregularities at the nozzle caused by mainline oscillations. Flow characteristic testing established a phase-shift flow control model(R²>0.99) for orchard variable-spray PWM high-frequency solenoid valves operating within the 5-20 Hz frequency band. The optimal linear region was identified as 30%-80% duty cycle, where regression fitting yielded a relative flow error of approximately 3%. Test results indicate that within the linear zone, staggered-phase control significantly reduced traffic fluctuations and enhance stability. Furthermore, when the duty cycle exceeds 80%, the flow rate tends to stabilize, showing minimal increase with further rise in duty cycle, indicating a saturation trend beyond the linear operating range. The mean coefficient of variation (CV) for flow across all frequency bands decreased by 32.3%, 23.4%, 37.5%, and 62.9%, respectively. The reduction trend in CV aligns with the attenuation trend of the fundamental pressure fluctuation amplitude. These findings provide experimental data and technical references for selecting domestically produced high-frequency, high-voltage solenoid valves and optimizing flow regulation strategies in orchard PWM variable spray systems.