Sliding Mode and PID Control for Pressure Regulation in Hydraulic Pipelines Under Leakage Disturbances

Abstract

A pipeline loses pressure to friction all the time, and to a leak some of the time. This study develops a nonlinear lumped-parameter model of a 1000 m hydraulic pipeline that accounts for momentum dynamics, Darcy–Weisbach friction, an orifice-type leakage disturbance, nonlinear valve pressure loss, and first-order actuator lag. The model is used to design and compare two pressure-regulation strategies: a PID controller with a causal derivative term and a sliding-mode controller based on an integral sliding surface formulated around a linearized equilibrium point. The controlled variable is the pressure immediately upstream of the regulating valve, with a desired value of 3 bar. Both controllers are evaluated against an uncontrolled fixed-valve baseline under an identical 350-second simulation scenario consisting of a startup period, a 100-second active-leak interval, and a post-leak recovery period. The results show that both controllers maintain the pressure close to its setpoint during the leakage event and reduce the mean absolute pressure error by more than 95% compared with the uncontrolled case. PID provides slightly faster recovery after the leak is removed, whereas the sliding-mode controller produces gentler valve motion and achieves comparable disturbance rejection. These findings demonstrate the potential of sliding-mode control for improving pressure regulation and robustness in hydraulic pipeline systems subject to leakage disturbances.