Setpoint Tracking and Disturbance Attenuation for Gas Pipeline Flow Subject to Uncertainties using Backstepping

TL;DR

This paper develops a backstepping control method for gas pipeline pressure regulation that effectively manages uncertainties and disturbances in outlet flow, ensuring stable operation despite variable consumer demands.

Contribution

It introduces an observer-based PDE backstepping controller for uncertain flow disturbances, extending existing methods to handle bounded uncertainties in gas pipeline systems.

Findings

Controller successfully regulates outlet pressure under uncertain flow conditions.

Numerical simulations confirm robustness and effectiveness of the proposed control scheme.

Method extends to bounded disturbance scenarios, maintaining pressure stability.

Abstract

In this paper, we consider the problem of regulating the outlet pressure of gas flowing through a pipeline subject to uncertain and variable outlet flow. Gas flow through a pipe is modeled using the coupled isothermal Euler equations, with the Darcy-Weisbach friction model used to account for the loss of gas flow momentum. The outlet flow variation is generated by a periodic linear dynamic system, which we use as a model of load fluctuations caused by varying consumer demands. We first linearize the nonlinear equations around the equilibrium point and obtain a 2-by-2 coupled hyperbolic partial differential equation (PDE) system expressed in canonical form. Using an observer-based PDE backstepping controller, we demonstrate that the inlet pressure can be manipulated to regulate the outlet pressure to a setpoint, thus compensating for fluctuations in the outlet flow. Furthermore, we extend the observer-based controller to the case when the outlet flow variation is uncertain within a bounded set. In this case, the controller is also capable of regulating the outlet pressure to a neighborhood of the setpoint by manipulating the inlet pressure, even in the presence of uncertain fluctuations in the outlet flow. We provide numerical simulations to demonstrate the performance of the controller.