Abstract
Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power consumption. To this end, an optimal control strategy is proposed in this paper. In the water supply system model, the hydraulic resistance of the valve is estimated by the real data from a water supply system and it is considered to be a disturbance. The method which is used to solve the nonlinear optimal control problem is the interior point method. The method which is used in this paper can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users.
Similar content being viewed by others
References
Guidelines for water losses reduction—a focus on pressure management. Water Loss Reduction Homepage (2009). Available at http://www.waterloss-reduction.com/index.php?id=38
Ulanicki, B., Bounds, P., Race, J., Reynolds, L.: Open and closed loop pressure control for leakage reduction. Urban Water 2, 105–114 (2000)
Kingdom, B., Liemberger, R., Marin, P.: The challenge of reducing non-revenue water (NRW) in developing countries. Water Supply and Sanitation Sector Board Discussion Paper Series (2006)
Ormsbee, L.E.: The history of water distribution network analysis: the computer age. In: 8th Annual Water Distribution Systems Analysis Symposium (2006)
Cantoni, M., Weyer, E., Li, Y., Ooi, S., Mareels, I., Ryan, M.: Control of large-scale irrigation networks. Proc. IEEE 95, 75–91 (2007)
Polycarpou, M., Uber, J., Wang, Z., Shang, F., Brdys, M.: Feedback control of water quality. IEEE Control Syst. Mag. 22, 68–87 (2002)
Wang, Z., Polycarpou, M., Uber, J., Shang, F.: Adaptive control of water quality in water distribution networks. IEEE Trans. Control Syst. Technol. 14, 149–156 (2006)
Hu, Y., Koroleva, O., Krstic, M.: Nonlinear control of mine ventilation networks. Syst. Control Lett. 49, 239–254 (2003)
Koroleva, O., Krstic, M., Schmid-Schonbein, G.: Decentralized and adaptive control of nonlinear fluid flow networks. Int. J. Control 79, 1495–1504 (2006)
De Persis, C., Kallesøe, C.S.: Proportional and proportional-integral controllers for a nonlinear hydraulic network. In: Proc. 17th IFAC World Congress, vol. 17, pp. 319–324 (2008)
De Persis, C., Kallesøe, C.S.: Pressure regulation in nonlinear hydraulic networks by positive controls. In: Proc. 10th European Control Conference, vol. 19, pp. 1371–1383 (2009)
De Persis, C., Kallesøe, C.S.: Pressure regulation in nonlinear hydraulic networks by positive and quantized controls. IEEE Trans. Control Syst. Technol. 19, 1371–1383 (2011)
Chinchuluun, A., Pardalos, P.M., Enkhbat, R., Tseveendorj, I.: Optimization and Optimal Control: Theory and Applications. Springer, Berlin (2010)
Effati, S., Saberi, N.H., Jajarmi, A.: Hyperchaos control of the hyperchaotic Chen system by optimal control design. Nonlinear Dyn. 73(1–2), 499–508 (2013). doi:10.1007/s11071-013-0804-0
Gu, X.D., Zhu, W.Q., Xu, W.: Stochastic optimal control of quasi non-integrable Hamiltonian systems with stochastic maximum principle. Nonlinear Dyn. 70, 779–787 (2012)
Ming, Z., Hong, N., Rupeng, Z.: Stochastic optimal control of flexible aircraft taxiing at constant or variable velocity. Nonlinear Dyn. 62, 485–497 (2010)
Crespo, L.G., Sun, J.Q.: Stochastic optimal control of nonlinear systems via short-time Gaussian approximation and cell mapping. Nonlinear Dyn. 28, 323–342 (2002)
Jensen, T.N.: Plug and play control of hydraulic networks. Ph.D. Thesis (2012)
Tahavori, M., Jensen, T.N., Kallesøe, C.S., Leth, J., Wisniewski, R.: Toward model-based control of non-linear hydraulic networks. J. Vib. Control 19(14), 2145–2153 (2012). doi:10.1177/1077546312456582
Desoer, C.A., Khu, E.S.: Basic Circuit Theory. McGraw-Hill, New York (1969)
Gross, J.L., Yellow, J.: Handbook of Graph Theory. CRC Press, Boca Raton (2003)
Kallesøe, C.S.: Simulation of a district heating system with a new network structure. Technical Report, Grundfos Management A/S (2007)
Wyk, E.J.V., Falugi, P., Kerrigan, E.C.: Imperial college London optimal control software (ICLOCS) (2010)
Wächter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106, 25–57 (2006)
Rao, A.V.: A survey of numerical methods for optimal control. In: AAS/AIAA Astrodynamics Specialist Conference (2009)
Biegler, L.T., Zavala, V.M.: Large-scale nonlinear programming using IPOPT: an integrating framework for enterprise-wide dynamic optimization. Comput. Chem. Eng. 33, 575–582 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tahavori, M., Leth, J., Kallesøe, C. et al. Optimal control of nonlinear hydraulic networks in the presence of disturbance. Nonlinear Dyn 75, 539–548 (2014). https://doi.org/10.1007/s11071-013-1083-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-013-1083-5