Delay-aware modeling and incremental-input MPC for active control of natural gas pipeline networks

Natural gas pipeline networks are increasingly required to respond to fast fluctuations in integrated energy systems. A major obstacle to real-time pressure control is the propagation delay of pressure waves, which is often neglected or absorbed into inertial dynamics in conventional control-oriented models. This study develops a delay-aware transfer-function model and reformulates it into an extended state-space representation by explicitly separating propagation delay from inertial response. Based on this model, and to constrain the rate of change of control actions and improve actuator smoothness under transient disturbances, an incremental-input delay-compensated model predictive controller (DC-MPC) is developed and compared with delay-ignored MPC (DI-MPC) and conventional operating strategies. Step-response validation against a high-fidelity transient gas-network simulator shows that the proposed model captures delayed pressure-wave propagation more accurately than the classical second-order transfer-function model, reducing the cumulative pressure-response deviation by 49.48%. In the simple pipeline case, DC-MPC achieves a mean absolute percentage deviation of 1.631% while reducing the total variation of compressor outlet pressure by 32.38% relative to DI-MPC, thereby suppressing overshoot and oscillatory control actions. In the 47-node natural gas network case, DC-MPC provides smoother control and lower tuning sensitivity, whereas DI-MPC achieves better tracking only at the expense of aggressive actuator movements and higher tuning sensitivity. These results demonstrate that explicitly accounting for propagation delay, together with incremental-input control design, improves prediction consistency, control smoothness, and the engineering feasibility of real-time pressure control in natural gas pipeline networks.