(740h) Meeting Energy Demands in Distributed Pipeline Systems

Distributed pipeline systems are increasingly built onshore and offshore for oil, gas and water transportation over the world, making cheaper, safer and better products available to local suppliers and consumers [1-2]. During the transportation, however, there are various and complex operational demands from large-diameter, long-distance pipelines to gathering and distribution pipeline systems, which is a challenging issue for pipeline condition regulation and integrity management. To address it, this work establishes a discrete-time infinite-dimensional pipeline system based on conservation laws of mass and momentum. In order to realize output regulation, a discrete Sylvester regulation equation is proposed and applied to different pipeline architectures, including single pipeline, Y-shaped pipelines, and star-shaped pipeline systems.

Based on conservation laws of mass and momentum in terms of flow rate and pressure, an infinite-dimensional transient hydraulic model is established for pipeline hydraulic dynamics modelling [2]. To account for realistic pipeline systems, different mechanical devices are considered in the pipeline systems, such as pump stations, valves and etc. Based on that, tangible pipeline systems are built by combining different pipeline arrangements and accessory devices. Considering the discrete nature and superiority, instead of using Euler discretization methods, the well-known Crank-Nicolson time discretization framework is utilized for continuous-time model discretization without spatial approximation or order reduction [3]. Thus, one can preserve fully spatial characteristics within distributed pipeline systems, leading to accurate fully spatial state observation and regulation.

In particular, a finite-dimensional continuous-time exo-system is used for reference and disturbance signals generation[4-5]. To link the continuous Sylvester regulation equations with the corresponding discrete counterpart, the Cayley transform is utilized for exo-system discretization [6]. Then, discrete regulation equations are constructed for discrete state feedback regulator design. Along this line, the multiple-input, multiple-output (MIMO) distributed pipeline systems are considered for output feedback regulator design based on state estimation. Finally, a set of simulations is given for output regulation of distributed pipeline systems to demonstrate the feasibility of the proposed technique.

References:

[1] Billmann, L., Isermann, R., 1987. Leak detection methods for pipelines. Automatica. 23 (3), 381-385.

[2] Xie, J., Xu X., and Dubljevic S., 2019. Long range pipeline leak detection and localization using discrete observer and support vector machine. AIChE Journal. DOI: https://doi.org/10.1002/aic.16532.

[3] Havu, V., Malinen, J., 2007. The Cayley transform as a time discretization scheme. Numerical Functional Analysis and Optimization 28 (7-8), 825-851.

[4] Francis B. A. and Wonham W. M., The internal model principle of control theory. Automatica. vol. 12, no. 5, pp. 457–465, 1976.

[5] Xu X. and Dubljevic S., 2016. Output regulation problem for a class of regular hyperbolic systems. International Journal of Control. vol. 89, no. 1, pp. 113–127.

[6] Xie J, Zhang L, and Dubljevic S, 2019. Discrete Output Feedback Regulator Design for Heterodirectional Hyperbolic Pipeline Systems. IEEE Transactions on Control Systems Technology, submitted.