Discrete-time modeling and output regulation of gas pipeline networks. (February 2021) - Xie, Junyao; Dubljevic, Stevan
Abstract: In this work, a discrete-time output regulator design is proposed for a class of gas pipeline networks to meet various operating requirements in energy scheduling. Based on the isothermal Euler equations, linearized continuous-time gas pipeline network models with boundary actuation and sensing in the infinite-dimensional space are established, with consideration of Rankine–Hugoniot conditions at junction joints. Cayley–Tustin bilinear transformation is applied for model time discretization without any spatial approximation, by which the continuous-time model with unbounded operators is transformed into an infinite-dimensional discrete-time system with all bounded operators and essential continuous-time properties are invariant under this transformation. Based on the internal model principle, the discrete output regulator is constructed and its solvability conditions are provided. Considering the unavailability of the full state information, observer design methods for state estimation of exogenous and pipeline systems are proposed in order to construct an output feedback regulator. Additionally, a stability analysis of the considered pipeline system is provided. Finally, two simulation examples representing a single gas pipeline and a star-shaped pipeline network are given to demonstrate the applicability of the proposed method. Highlights: A discrete-time output regulator design method for pipeline networks is proposed. Linear discrete-time distributed pipeline models with bounded operators are obtained. The discrete-time output regulator equations are formulated and proved. A Lyapunov analysis is provided to assess the stability of the pipeline models.