TECHNICAL PAPERS
Oct 1, 1999

Control of Canal Flow by Adjoint Sensitivity Method

Publication: Journal of Irrigation and Drainage Engineering
Volume 125, Issue 5

Abstract

A new method for control of unsteady flow in open channels is presented. Control is achieved using an iterative approach, the Broyden, Fletcher, Goldfarb, and Shanno quasi-Newton method that utilizes an adjoint sensitivity method to efficiently compute gradient information. The adjoint equations are derived from the differential form of the full shallow-water equations in one dimension and the resulting sensitivies allow a wide class of flows to be controlled. In addition, the adjoint sensitivity method permits both scheduled and adaptive flow control to be achieved. Application of the method to scheduled flow control is presented.

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References

1.
ASCE. (1993). “Special issue: Canal system hydraulic modeling.”J. Irrig. and Drain. Engrg., ASCE, 119(4), 613–742.
2.
Bodley, W. E., and Wylie, E. B. (1978). “Control of transients in series channel with gates.”J. Hydr. Div., ASCE, 104(10), 1395–1407.
3.
Boris, J. P., and Book, D. L. (1973). “Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works.” J. Computational Phys., 11, 38–69.
4.
Chertok, D. L., and Lardner, R. W. (1996). “Variational data assimilation for a nonlinear hydraulic model.” Appl. Math. Modeling, 20, 675–682.
5.
Clemmens, A. J., Chair, ASCE Task Committee on Irrigation Canal System Hydraulic Modeling. (1993). “Unsteady-flow modeling of irrigation canals.”J. Irrig. and Drain Engrg., ASCE, 119(4), 615–630.
6.
Cooley, J. W., and Tukey, J. W. (1965). “An algorithm for the machine computation of complex Fourier series.” Mathematics of Computation, 19, 297.
7.
de Albuquerque, F. G., and Labadie, J. W. (1997). “Optimal nonlinear predictive control for canal operations.”J. Irrig. and Drain. Engrg., ASCE, 123(1), 45–54.
8.
Das, S. K., and Lardner, R. W. (1991). “On the estimation of parameters of hydraulic models by assimilation of periodic tidal data.” J. Geophys. Res., 96(C8), 15,187–15,196.
9.
Hall, M. C. G., and Cacuci, D. G. (1983). “Physical interpretation of adjoint functions for sensitivity analysis of atmospheric models.” J. Atmospheric Sci., 40, 2537–2546.
10.
Hall, M. C. G., Cacuci, D. G., and Schlesinger, M. E. (1982). “Sensitivity analysis of a radiative-convective model by the adjoint method.” J. Atmospheric Sci., 39, 2038–2050.
11.
Henderson, F. M. (1966). Open channel flow. Macmillan, New York.
12.
Hirsch, C. (1988). Numerical computation of internal and external flows. Vol. 2, Wiley, New York.
13.
Holly, F. M., and Merkley, G. P. (1993). “Unique problems in modeling irrigation canals.”J. Irrig. and Drain. Engrg., ASCE, 119(4), 656–662.
14.
Katopodes, N. D. (1984a). “A dissipative Galerkin scheme for open-channel flow.”J. Hydr. Engrg., ASCE, 110(4), 450–466.
15.
Katopodes, N. D. (1984b). “Two-dimensional surges and shocks in open channels.”J. Hydr. Engrg., ASCE, 110(6), 794–812.
16.
Katopodes, N. D., and Piasecki, M. (1996). “Site and size optimization of contaminant sources in surface water systems.”J. Envir. Engrg., ASCE, 122, 917–923.
17.
Lardner, R. W. (1993). “Optimal control of open boundary conditions for a numerical tidal model.” Comp. Methods in Appl. Mech. and Engrg., 102, 367–387.
18.
Lardner, R. W., Al-Rabeh, A. H., and Gunay, N. (1993). “Optimal estimation of parameters for a two-dimensional hydrodynamic model of the Arabian Gulf.” J. Geophys. Res., 98(C10), 18,229–18,224.
19.
Le Dimet, F.-X., and Talagrand, O. (1986). “Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects.” Tellus, 38A, 97–110.
20.
Marchuk, G. I. (1995). Adjoint equations and analysis of complex systems. Kluwer Academic, Boston.
21.
Panchang, V. G., and O'Brien, J. J. ( 1989). “On the determination of hydraulic model parameters using the adjoint state formulation.” Modeling marine systems. A. M. Davies, ed., Vol. 1, Boca Raton, Fla., 5–18,
22.
Piasecki, M., and Katopodes, N. D. (1997a). “Control of contaminant releases in rivers. I.: Adjoint sensitivity analysis.”J. Hydr. Engrg., ASCE, 123(6), 486–492.
23.
Piasecki, M., and Katopodes, N. D. (1997b). “Control of contaminant releases in rivers. II: Optimal design.”J. Hydr. Engrg., ASCE, 123(6), 493–503.
24.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (1992). Numerical recipes in FORTRAN. Cambridge University Press, New York.
25.
Reddy, J. M. (1990). “Local optimal control of irrigation canals.”J. Irrig. and Drain. Engrg., ASCE, 116(5), 616–631.
26.
Reddy, J. M., Dia, M., and Oussou, A. (1992). “Design of control algorithm for operation of irrigation canals.”J. Irrig. and Drain. Engrg., ASCE, 118(6), 852–867.
27.
Sanders, B. F. ( 1997). “Control of shallow-water flow using the adjoint sensitivity method,” Ph.D thesis, Dept. of Civ. and Envir. Engrg., University of Michigan, Ann Arbor, Mich.
28.
Sanders, B. F., and Katopodes, N. D. (1998). “Adaptive control of shallow-water waves.” Advances in Hydrosci. and Engrg., Vol. III, Proc., 3rd Int. Conf. on Hydrosci. and Engrg., K. P. Holz, W. Bechteler, S. S. Y. Wang, and M. Kawahara, eds., 261 (on CD-ROM).
29.
Sawadogo, S., Malaterre, P. O., and Kosuth, P. (1995). “Multivariable optimal control for on-demand operation of irrigation canals.” Int. J. Sys. Sci., 26(1), 161–178.
30.
Shanno, D. F., and Phua, K. H. (1980). “Remark on algorithm 500, a variable metric method for unconstrained minimization.” ACM Trans. Math. Software, 6, 618–622.
31.
Strelkoff, T. S., and Falvey, H. T (1993). “Numerical methods used to model unsteady canal flow.”J. Irrig. and Drain. Engrg., ASCE, 119(4), 637–655.
32.
Wylie, E. B. (1969). “Control of transient free-surface flow.”J. Hydr. Div., ASCE, 95(1), 347–361.
33.
Yeh, W. W.-G. (1986). “Review of parameter identification procedures in groundwater hydrology: The inverse problem.” Water Resour. Res., 22(2), 95–108.
34.
Zhao, D. H., Shen, H. W., Tabios, G. Q, III, Lai, J. S., and Tan, W. Y. (1994). “A finite volume two-dimensional unsteady flow model for river basins.”J. Hydr. Engrg., ASCE, 120(7), 863–883.
35.
Zou, J., and Holloway, G. (1995). “Improving steady-state fit of dynamics to data using adjoint equation for gradient preconditioning.” Monthly Weather Rev., 123, 199–211.

Information & Authors

Information

Published In

Go to Journal of Irrigation and Drainage Engineering
Journal of Irrigation and Drainage Engineering
Volume 125Issue 5October 1999
Pages: 287 - 297

History

Received: Apr 20, 1998
Published online: Oct 1, 1999
Published in print: Oct 1999

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Authors

Affiliations

Members, ASCE
Asst. Prof., Dept. of Civ. and Envir. Engrg., Univ. of California, Irvine, CA 92697.
Prof., Dept. of Civ. and Envir. Engrg., Univ. of Michigan, Ann Arbor, MI 48109.

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