Pilot-Opening-Scheduled Gray-Box PWA Identification and Event-Triggered Predictive Control for PWM-Driven Electro-Hydraulic Proportional Valves

Predictive control of pulse-width modulation (PWM)-driven electro-hydraulic proportional valves is challenging because PWM commands affect main-spool motion through pilot-spool dynamics and control-chamber pressure build-up. This study develops a compact pilot-opening-scheduled piecewise affine (PWA) predictor that distinguishes command-level PWM hysteresis from the internal pilot-opening modes. A guarded model-selection procedure, termed PhysGuard, compares a warm-start predictor with a bounded-refinement candidate on a short-horizon rollout record that is excluded from fitting and refinement. Under reset-horizon validation, the retained predictor yields displacement root-mean-square errors (RMSEs) of 0.382 mm and 0.596 mm at 80 ms and 120 ms, respectively. The retained predictor is then embedded in a solver-free kinematic dead-zone-crossing-scheduled event-triggered model predictive control (K-DCS-ET-MPC) law. At each complete-search event, the controller evaluates a finite set of pilot-spool references; an inner servo then converts the selected reference into PWM. Over the full 20 s Simulink benchmark, K-DCS-ET-MPC executes 1025 complete finite-set searches, compared with 5001 for time-triggered model predictive control (TT-MPC), giving a 79.5% reduction in search count. Over the common 5–10 s comparison interval, it achieves the lowest mean absolute error (MAE) and RMSE among nine simulated controllers (0.0371 mm and 0.0569 mm). In the same interval, it executes 373 complete searches, compared with 1251 for full-rate kinematic dead-zone-crossing-scheduled model predictive control (K-DCS-MPC), reducing the search count by 70.18%. Linear finite-set model predictive control produces the smallest maximum absolute error. In a nominal bench test with a sinusoidal reference of 5.5 mm amplitude, the MAE and RMSE averaged over three complete cycles are 0.2358 mm and 0.2781 mm, respectively. The robustness results are simulation-based, and complete-search timing is obtained from host-side replay.