Stochastic Optimal and Suboptimal Control of Irrigation Canals
Publication: Journal of Water Resources Planning and Management
Volume 125, Issue 6
Abstract
The Saint-Venant equations of open-channel flow were linearized using the Taylor series and a finite-difference approximation of the original nonlinear, partial differential equations. Using the linear optimal control theory, a proportional-plus-integral (PI) controller was developed for an irrigation canal with five pools. Since the order of the controller gain matrix was large, the Kalman filter was designed to estimate values for the state variables that were not measured. For this problem, there were a total of 45 state and five control variables. With two flow depth measurements per pool, values for the remaining 35 state variables were estimated using the Kalman filter. The simulated canal dynamics with the regional PI controllers along with the local Kalman filter were compared with the performance of the global control algorithms for achieving a constant-volume control and a constant-level control of an example irrigation canal. The performance of the regional constant-volume control algorithms was found to be as good as the performance of the global control algorithm, whereas the performance of the regional constant-level control algorithm was marginally acceptable.
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References
1.
Anderson, B. D. O., and Moore, J. B. ( 1990). Optimal control. Prentice Hall, Englewood Cliffs, N.J.
2.
Balogun, O., Hubbard, M., and DeVries, J. J. (1988). “Automatic control of canal flow using linear quadratic regulator theory.”J. Hydr. Engrg., ASCE, 114(1), 75–102.
3.
Begimov, I. ( 1981). “Analysis of automatic water-level control systems in irrigation canals.” Avtomatika i Telemekhanica, 9, 5–12 (in Russian).
4.
Begovitch, O., and Ortega, R. ( 1989). “Adaptive head control of a hydraulic open-channel model.” Automatica, 25, 103–107.
5.
Brammer, K., and Siffling, G. ( 1989). Kalman-Bucy filters. Artech House, Norwood, Mass.
6.
Burt, C. M. ( 1983). “Regulation of sloping canals by automatic downstream control,” PhD thesis, Utah State University, Logan, Utah.
7.
Buyalski, C. P., and Serfozo, E. A. ( 1979). “Electronic filter level offset (EL-FLO) plus reset equipment for automatic downstream control of canals.” Engrg. and Res. Ctr. Rep. #79-3, Bureau of Reclamation, United States Department of the Interior, Denver.
8.
Chevereau, G., and Schwartz-Benezeth, S. ( 1987). “BIVAL systems for downstream control.” Proc., ASCE Symp. on Plng., Operation, Rehabilitation, and Automation of Irrig. Water Delivery Sys., ASCE, New York, 155–163.
9.
Corriga, G., Sanna, S., and Usai, G. ( 1982). “Sub-optimal level control of open-channels.” Proc., Int. AMSE Conf., AMSE, Lyon, France, 67–72.
10.
Dora, T., and Varga, I. ( 1982). Design principles and dynamic problems of water distribution at the Kiskore irrigation projects.” ICID Bull., 31(2), 60–78.
11.
Garcia, A., Hubbard, M., and DeVries, J. J. ( 1992). “Open-channel transient flow control by discrete-time LQR methods.” Automatica, 28(2), 255–264.
12.
Haykin, S. ( 1996). Adaptive filter theory. Prentice Hall, Englewood Cliffs, N.J.
13.
Jacquot, R. G. ( 1995). Modern digital control systems. Marcel Dekker, New York.
14.
Kwakernaak, H., and Sivan, R. ( 1972). Linear optimal control systems. Wiley, New York.
15.
Laub, A. J. ( 1979). “A Schur method for solving algebraic Riccati equations.” IEEE Trans. Automatic Control, 24, 913–921.
16.
Le Moigne, G., Subramanian, A., Xie, M., and Giltner, S. ( 1994). “A guide to the formulation of water resources strategy.” World Bank Tech. Paper 263, The World Bank, Washington, D.C.
17.
Liu, F., Berlamont, J., and Feyen, J. (1995). “Downstream control of multireach canal systems.”J. Irrig. and Drain. Engrg., ASCE, 121(2), 179–190.
18.
Papageorgiou, M., and Messmer, A. ( 1985). “Continuous-time and discrete-time design of water flow and water level regulators.” Automatica, 21(6), 649–661.
19.
Reddy, J. M. ( 1990). “Evaluation of optimal constant-volume control for irrigation canals.” Int. J. Appl. Math. Modeling, 14, 450–458.
20.
Reddy, J. M. ( 1995). “Kalman filtering in the control of irrigation canals.” Int. J. Appl. Math. Modeling, 19(4), 201–209.
21.
Reddy, J. M. (1996). “Design of global control algorithm for irrigation canals.”J. Hydr. Engrg., ASCE, 122(9), 503–511.
22.
Reddy, J. M., Dia, A., and Oussou, A. (1992). “Design of control algorithm for operation of irrigation canals.”J. Irrig. and Drain. Engrg., ASCE, 118(6), 852–867.
23.
Rodellar, J., Gomez, M., and Bonet, L. (1993). “Control method for an on-demand operation of open-channel flow.”J. Irrig. and Drain. Engrg., ASCE, 119(2), 225–241.
24.
Stengel, R. F. ( 1986). Stochastic optimal control. Wiley, New York.
25.
Vaughn, D. R. ( 1970). “A nonrecursive algebraic solution for the discrete Riccati equation.” IEEE Trans. on Automatic Control, 15(5), 598–599.
26.
Zimbelman, D. D. ( 1981). “Computerized control of an open-channel water distribution system,” PhD thesis, Arizona State University, Tempe, Ariz.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 125 • Issue 6 • November 1999
Pages: 369 - 378
History
Received: Mar 14, 1996
Published online: Nov 1, 1999
Published in print: Nov 1999
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