Experimental Investigation of Upstream Water-Level Dynamics for a Standard Open-Channel Sluice Gate and a Simplified Model

Understanding how gate-opening variations affect the upstream water level is essential for quantitative water allocation and automation in irrigation canals. Using an indoor recirculating rectangular open-channel facility equipped with a standard flat sluice gate, we deployed five upstream water-level gauges (Points 1#D–5#H) and conducted step response tests and pseudo-random binary sequence (PRBS) tests under four representative operating conditions (Q ≈ 30–85 m3/h). For step tests, the upstream water-level dynamics were well approximated by a first-order plus dead-time (FOPDT) model. Under low flow (Condition A, Q ≈ 29.5 m3/h) with a 1.5 → 2.0 cm opening step, the identified parameters were K ≈ −15.4 mm/mm, L ≈ 4.5–5.7 s, and T ≈ 71 s, and the five points exhibited strong spatial consistency. Under higher flow (Condition B, Q ≈ 72.5 m3/h) with a 3.0 → 3.5 cm step, the gain magnitude decreased (K ≈ −10.6 mm/mm), the dead time increased moderately (L ≈ 8.0–10.3 s), and the time constant became smaller (T ≈ 41–43 s), indicating a faster response but weaker sensitivity to gate-opening changes. For PRBS tests, a discrete-time ARX (2,2,1) model was identified between gate opening and the upstream level deviation at Point 3#F. The identified ARX models achieved R2 of 0.992 (Condition C) and 0.946 (Condition D), with MAE and RMSE within 0.65–1.85 mm, and residual diagnostics supported the adequacy of the selected model structure. Finally, steady-state gains derived from dynamic identification were consistent with static water-level–flow–opening relations obtained from quasi-steady experiments, providing a physical basis for the models. The proposed simplified models offer a unified and engineering-friendly plant description for designing and comparing controllers such as PID, fuzzy control, and reinforcement learning-based approaches.