Euler-Lagrange approach for modeling water pipelines with leaks

Resumen: This paper presents the modeling of water pipelines with leaks using the socalled Euler-Lagrange approach. The modeling is carried out taking into account the typical assumptions of the rigid water column theory, which considers that the fluid flowing in a pipeline is incompressible and that the wall of a pipeline is rigid. Some numerical results are presented to show the numerical behavior of a leaky pipeline model resulting from the use of the Euler-Lagrange approach. The numerical simulations were carried out taking into account the characteristics of a test apparatus located at Instituto Tecnológico de Tuxtla Gutiérrez.

¿Cómo citar?

Abner David Jiménez, Lizeth Torres & Francisco Ronay López-Estrada. Euler-Lagrange approach for modeling water pipelines with leaks. Memorias del Congreso Nacional de Control Automático, pp. 1-7, 2020.

Palabras clave

Pipeline Modeling, leak detection, Euler-Lagrange approach

• Abarca-Jiménez, G.S., Reyes-Barranca, M.A., MendozaAcevedo, S., Munguía-Cervantes, J.E., and Alemán Arce, M.A. (2016). Electromechanical modeling and simulation by the euler–lagrange method of a mems inertial sensor using a fgmos as a transducer. Microsystem Technologies, 22(4), 767–775.
• Adamkowski, A. and Lewandowski, M. (2006). Experimental examination of unsteady friction models for transient pipe flow simulation. Journal of Fluids Engineering, 128(6), 1351–1363.
• Avila-Becerril, S., Loría, A., and Panteley, E. (2016). A separation principle for underactuated lossless lagrangian systems. IEEE Transactions on Automatic Control, 62(10), 5318–5323.
• Baleanu, D., Sajjadi, S.S., Jajarmi, A., and Asad, J.H. (2019). New features of the fractional euler-lagrange equations for a physical system within non-singular derivative operator. In The European Physical Journal Plus, volume 134. Springer.
• Cheng, C. and Chen, T. (2016). Robust control of euler-lagrange mechanical systems with decentralized adaptive scheme. In 2016 International Automatic Control Conference (CACS), 227–231.
• Enríquez-Zárate, J., Abundis-Fong, H.F., Velázquez, R., and Gutiérrez, S. (2019). Passive vibration control in a civil structure: Experimental results. Measurement and Control, 52(7-8), 938–946.
• Hernández, J.R.B., de los Santos Ruiz, I., Estrada, F.R.L., Ortiz, F.L.T., and Puig, V. (2017). Diseño y modelado dinámico de una planta piloto para detección de fugas hidráulicas. In Congreso Nacional de Control Automático 2017, 2–7. AMCA, Monterrey, Nuevo León, México.
• Hernández, J.R.B., Estrada, F.R.L., Besaςon, G., Palomo, G.V., Ortiz, F.L.T., and Hernández, H.R. (2018). Modeling and simulation of hydraulic network for leak diagnosis. In Mathematical and Computational applications, Optimization in Control Applications, 234–244. MDPI, Basel, Switzerland.
• Ibrahim, A.G. and Elmandouh, A.A. (2020). Euler–lagrange equations for variational problems involving the riesz–hilfer fractional derivative. Journal of Taibah University for Science, 14(1), 678–696.
• Jeltsema, D. and Scherpen, J.M. (2009). Multidomain modeling of nonlinear networks and systems. IEEE Control Systems Magazine, 29(4), 28–59.
• Maré, J.C. (2016). Aerospace Actuators 1: Needs, Reliability and Hydraulic Power Solutions. Wiley-ISTE.
• Nault, J. and Karney, B. (2016). Improved rigid water column formulation for simulating slow transients and controlled operations. Journal of Hydraulic Engineering, 142(9), 04016025.
• Ortega, R., Perez, J.A.L., Nicklasson, P.J., and SiraRamirez, H.J. (2013). Passivity-based control of EulerLagrange systems: mechanical, electrical and electromechanical applications. Springer Science & Business Media.
• Pérez, R., Puig, V., Pascual, J., Quevedo, J., Landeros, E., and Peralta, A. (2011). Methodology for leakage isolation using pressure sensitivity analysis in water distribution networks. Control Engineering Practice, 19(10), 1157–1167.
• Rojas, M., Becerril, S.A., and Torres, L. (2019). An energy-based approach for modeling water distribution networks with faults. In Congreso Nacional de Control Automático 2019, 501–506. AMCA, Puebla, Puebla, México.
• Rossman, L.A. (2000). EPANET 2 USER MANUAL. Water Supply and Water Resources Division, National Risk Management Research Laboratory & Office of Research and Develoment, U.S. Environmental Protection Agency, Cincinnati, Ohio.
• Santos-Ruiz, I., López-Estrada, F.R., Puig, V., and Valencia-Palomo, G. (2020). Simultaneous optimal estimation of roughness and minor loss coefficients in a pipeline. Mathematical and Computational Applications, 25, 56.
• Scola, I.R., Besançon, G., and Georges, D. (2018). Optimizing Kalman optimal observer for state affine systems by input selection. Automatica, 93, 224–230.
• Soldevila, A., Blesa, J., Tornil-Sin, S., Duviella, E., Fernandez-Canti, R.M., and Puig, V. (2016). Leak localization in water distribution networks using a mixed model-based/data-driven approach. Control Engineering Practice, 55, 162–173.
• Su, J., Bak, J.H., and Hyun, J. (2019). Optimal trajectory generation for quadrotor with suspended load under swing angle constraint. In 2019 IEEE 15th International Conference on Control and Automation (ICCA), 549–554.
• Tchon, K. (2021). Endogenous configuration space approach in robotics research. In Automatic Control, Robotics, and Information Processing. Springer.
• Todini, E. and Pilati, S. (1988). A gradient algorithm for the analysis of pipe networks. In Computer applications in water supply, volume 1 systems analysis and simulation, 1–20.
• Torres, L. and Besançon, G. (2019). Port-hamiltonian models for flow of incompressible fluids in rigid pipelines with faults. In 58th IEEE Conference on Decision and Control. IEEE, Nice, France.
• Verde, C. and Torres, L. (2017). Modeling and Monitoring of Pipelines and Networks: Advanced Tools for Automatic Monitoring and Supervision of Pipelines, volume 7. Springer.
• Wellstead, P.E. (2000). Introduction to Physical System Modelling. Control Systems Principles.