Performance comparison of proportional-integral-derivative (PID) and model predictive control (MPC) for urban water load management

Urban water SCADA (supervisory control and data acquisition) loops must track setpoints (SP) under actuator constraints while remaining robust to disturbances and model uncertainty. This study presents a reproducible benchmarking framework for fair comparison of constrained model predictive control (MPC) and conventional proportional-integral-derivative (PID) under identical sampled-data execution and saturation limits. The framework represents reduced-order SCADA-type single-loop regulation using a discrete-time single-input single-output (SISO) deviation model with a strict fairness protocol (T_s = 0.1 s, u ∈ [−1, 1], fixed tuning). Three scenarios are evaluated: nominal step tracking, constant input disturbance (d = −0.25), and plant model mismatch via increased damping. Performance is assessed using transient metrics, root mean square error (RMSE), integral absolute error (IAE), steady-state error, and saturation activity. Results show MPC achieves faster responses and lower error via brief saturation, while PID remains largely unsaturated but slower. Under disturbance, both exhibit steady-state offset; however, MPC reduces overall and final error, motivating offset-free MPC.