Model Predictive Control for Water Level Control in the Case of Spills
Publication: Journal of Irrigation and Drainage Engineering
Volume 143, Issue 3
Abstract
Model predictive control (MPC) is one of the most popular control techniques that has been widely used in many fields of water resources management, such as canal control for drainage, irrigation, and navigation. MPC uses an internal mathematical model to describe system dynamics over a given prediction horizon and then minimizes a hard-constrained optimization problem based on actual objectives. Due to the use of hard constraints, the optimization problem may occasionally be infeasible. A compromise is sometimes made to look for a feasible solution by softening the hard constraints, which means that the limit on water levels or flows is allowed to be violated to a certain extent. For example, water in a canal may go above the top of a dike during a high-discharge event, resulting in a spill. This amount of spilling water leaves the water system and does not flow back, which therefore should be deducted in the mathematical model of the water system. To deal with this spill, past studies often utilized a hybrid model and an integer optimization. However, the system in the hybrid model is usually nonlinear and nonsmooth, especially when it transits from one discrete state to another. In this paper, an alternative way is proposed to link the spill with the softened constraint, still maintaining the linearity of the water system. Results show that the proposed way to tackle the spilling water is easy to implement and the water level is more accurately regulated around the setpoint in a canal control problem.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The initial idea of the paper came from a discussion with Dr.ir. Peter-Jules van Overloop a few days before he passed way. The authors appreciate all his deep kindness and contributions for the canal control society. The authors also would like to thank the anonymous reviewers for their careful reading and insightful comments.
References
Camacho, E., and Bordons, C. (1999). Model predictive control, Springer, Sevilla, Spain.
Ficchì, A., et al. (2016). “Optimal operation of the multireservoir system in the seine river basin using deterministic and ensemble forecasts.” J. Water Resour. Plann. Manage., 05015005.
Guru, P. (2009). “Soft constraints for robust MPC of uncertain systems.” IFAC Proc., 7(11), 225–230.
Hashemy, S. M., Monem, M. J., Maestre, J. M., and van Overloop, P.-J. (2013). “Application of an in-line storage strategy to improve the operational performance of main irrigation canals using model predictive control.” J. Irrig. Drain. Eng., 635–644.
Horvath, K., Petreczky, M., Rajaoarisoa, L., Duviella, E., and Chuquet, K. (2014). “MPC control of water level in a navigation canal—The Cuinchy-Fontinettes case study.” 2014 European Control Conf. (ECC), IEEE, Strasbourg, France, 1337–1342.
Joseph-Duran, B., Jung, M. N., Ocampo-Martinez, C., Sager, S., and Cembrano, G. (2014a). “Minimization of sewage network overflow.” Water Resour. Manage., 28(1), 41–63.
Joseph-Duran, B., Ocampo-Martinez, C., and Cembrano, G. (2014b). “Hybrid modeling and receding horizon control of sewer networks.” Water Resour. Res., 50(11), 8497–8514.
Maciejowski, J. (2002). Predictive control: With constraints, 1st Ed., Prentice Hall, Upper Saddle River, NJ.
Maestre, J. M., Raso, L., van Overloop, P.-J., and de Schutter, B. (2013). “Distributed tree-based model predictive control on a drainage water system.” J. Hydroinf., 15(2), 335.
Ocampo-Martinez, C., and Puig, V. (2010). “Piece-wise linear functions-based model predictive control of large-scale sewage systems.” IET Control Theory Appl., 4(9), 1581–1593.
Puig, V., et al. (2009). “Predictive optimal control of sewer networks using CORAL tool: Application to Riera Blanca catchment in Barcelona.” Water Sci. Technol., 60(4), 869.
Raso, L., Schwanenberg, D., van de Giesen, N. C., and van Overloop, P.-J. (2014). “Short-term optimal operation of water systems using ensemble forecasts.” Adv. Water Resour., 71, 200–208.
Sadowska, A., van Overloop, P.-J., Burt, C., and de Schutter, B. (2014). “Hierarchical operation of water level controllers: Formal analysis and application on a large scale irrigation canal.” Water Resour. Manage., 28(14), 4999–5019.
Sills, G. L., Vroman, N. D., Wahl, R. E., and Schwanz, N. T. (2008). “Overview of New Orleans levee failures: Lessons learned and their impact on national levee design and assessment.” J. Geotech. Geoenviron. Eng., 556–565.
SOBEK 2.13 [Computer software]. Deltares, Delft, Netherlands.
Stelling, G. S., and Duinmeijer, S. P. A. (2003). “A staggered conservative scheme for every Froude number in rapidly varied shallow water flows.” Int. J. Numer. Methods Fluids, 43(12), 1329–1354.
Tian, X. (2015). “Model predictive control for operational water management: A case study of the Dutch water system.” Ph.D. thesis, Delft Univ. of Technology, Delft, Netherlands.
Tian, X., van Overloop, P.-J., Negenborn, R. R., and van de Giesen, N. C. (2015). “Operational flood control of a low-lying delta system using large time step model predictive control.” Adv. Water Resour., 75, 1–13.
van Overloop, P.-J. (2006). “Model predictive control on open water systems.” Ph.D. thesis, Delft Univ. of Technology, Delft, Netherlands.
van Overloop, P.-J., Clemmens, A. J., Strand, R. J., Wagemaker, R. M. J., and Bautista, E. (2010). “Real-time implementation of model predictive control on Maricopa-Stanfield irrigation and drainage district’s WM canal.” J. Irrig. Drain. Eng., 747–756.
van Overloop, P.-J., Weijs, S., and Dijkstra, S. (2008). “Multiple model predictive control on a drainage canal system.” Control Eng. Pract., 16(5), 531–540.
Xu, M., van Overloop, P.-J., and van de Giesen, N. C. (2013). “Model reduction in model predictive control of combined water quantity and quality in open channels.” Environ. Modell. Software, 42, 72–87.
Zafra-Cabeza, A., Maestre, J. M., Ridao, M. A., Camacho, E. F., and Sánchez, L. (2011). “A hierarchical distributed model predictive control approach to irrigation canals: A risk mitigation perspective.” J. Process Control, 21(5), 787–799.
Information & Authors
Information
Published In
Journal of Irrigation and Drainage Engineering
Volume 143 • Issue 3 • March 2017
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 2, 2015
Accepted: Aug 24, 2016
Published online: Oct 3, 2016
Published in print: Mar 1, 2017
Discussion open until: Mar 3, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.