## Robust continuous-time and discrete-time flow control of a dam-river system. I: Modelling.(English)Zbl 0949.93007

Summary: A distributed parameter linear model is derived from simplified physical equations of one dimensional open channel hydraulics. This linear model relating downstream to upstream flow rates is then identified analytically to a second order transfer function with delay, that can be used for controller synthesis. Analytical formulas for exact sampling with zero and first order holds are also given for the discrete-time case. The modelling error made when considering linear models around different reference discharges in a given set can be evaluated with a bound on multiplicative and on additive uncertainties. These bounds are useful for controller robustness analysis and synthesis.

### MSC:

 93A30 Mathematical modelling of systems (MSC2010) 93C95 Application models in control theory
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### References:

 [1] Corriga, G.; Fanni, A.; Sanna, S.; Usai, G., A constant volume method for open-channel operations, International Journal of Modelling and Simulation, 2, 108-112 (1982) [2] Corriga, G.; Sanna, S.; Usai, G., Estimation of uncertainty in an open-channel network mathematical model, Applied Mathematical Modelling, 13, 651-657 (1989) · Zbl 0701.93003 [3] Papageorgiou, M.; Messmer, A., Continuous-time and discrete-time design of water flow and water level regulators, Automatica, 21, 649-661 (1985) · Zbl 0592.93003 [4] Ermolin, Y., Study of open-channel dynamics as controlled process, Journal of Hydraulic Engineering, 118, 59-71 (1992) [5] Schuurmans, J., Open-channel flow model approximation for controller design, Applied Mathematical Modelling, 19, 525-530 (1995) · Zbl 0835.76011 [6] P.O. Malaterre, Modelling, analysis and LQR optimal control of an irrigation canal (in French), LAAS-CNRS-ENGREF-Cemagref, 1994, p. 220; P.O. Malaterre, Modelling, analysis and LQR optimal control of an irrigation canal (in French), LAAS-CNRS-ENGREF-Cemagref, 1994, p. 220 [7] J.P. Baume, J. Sau, Study of irrigation canal dynamics for control purposes, in: International Workshop on the Regulation of Irrigation Canals: State of the Art of Research and Application, RIC’97 Marrakech, Maroc, 1997, pp. 3-12; J.P. Baume, J. Sau, Study of irrigation canal dynamics for control purposes, in: International Workshop on the Regulation of Irrigation Canals: State of the Art of Research and Application, RIC’97 Marrakech, Maroc, 1997, pp. 3-12 [8] V.T. Chow, Open-Channels Hydraulics, McGraw-Hill, New York, 1988, p. 680; V.T. Chow, Open-Channels Hydraulics, McGraw-Hill, New York, 1988, p. 680 [9] W.A. Miller, J.A. Cunge, in: K. Mahmood, V. Yevjevich (Eds.), Unsteady Flow in Open Channels, Water Resources Publications, Fort Collins, Colorado, 1975, pp. 183-257; W.A. Miller, J.A. Cunge, in: K. Mahmood, V. Yevjevich (Eds.), Unsteady Flow in Open Channels, Water Resources Publications, Fort Collins, Colorado, 1975, pp. 183-257 [10] J.L. Trouvat, Contribution to a better management of GAscony rivers, Taking into account variability of hydrograms transfer time in regulation algorithms (in French), ENGREF-Cemagref-CACG, 1991; J.L. Trouvat, Contribution to a better management of GAscony rivers, Taking into account variability of hydrograms transfer time in regulation algorithms (in French), ENGREF-Cemagref-CACG, 1991 [11] X. Litrico, D. Georges, Nonlinear identification of an irrigation system, in: Proceeding of the 36th IEEE Conference on Decision and Control, San Diego, USA, 1997, pp. 852-857; X. Litrico, D. Georges, Nonlinear identification of an irrigation system, in: Proceeding of the 36th IEEE Conference on Decision and Control, San Diego, USA, 1997, pp. 852-857 [12] P. Kosuth, Regulation of water transfer in canals. Modelling with transfer functions of a nonlinear sub-system: reach with gate, Modelling with neural network of a reach without gate (in French), Cemagref, LAAS-CNRS Toulouse, 1989, p. 121; P. Kosuth, Regulation of water transfer in canals. Modelling with transfer functions of a nonlinear sub-system: reach with gate, Modelling with neural network of a reach without gate (in French), Cemagref, LAAS-CNRS Toulouse, 1989, p. 121 [13] Moussa, Analytical solution for the diffusive wave flood routing problem with lateral inflow, Hydrological Processes 10 (1996) 1209-1227; Moussa, Analytical solution for the diffusive wave flood routing problem with lateral inflow, Hydrological Processes 10 (1996) 1209-1227 [14] J. Rey, Contribution to water transfer modelling and regulation for river-pond systems (in French), ENGREF-USTL-Cemagref, 1990, p. 80; J. Rey, Contribution to water transfer modelling and regulation for river-pond systems (in French), ENGREF-USTL-Cemagref, 1990, p. 80 [15] I.D. Landau, Identification et commande des systèmes, Hermès, 1993, p. 535; I.D. Landau, Identification et commande des systèmes, Hermès, 1993, p. 535 · Zbl 0864.93001 [16] Wittenmark, B., Sampling of a system with a time delay, IEEE Transactions on Automatic Control, 30, 507-510 (1985) · Zbl 0561.93041 [17] J. Sau, Retard fractionnaire, Personal communication, 1997, p. 5; J. Sau, Retard fractionnaire, Personal communication, 1997, p. 5 [18] Laughlin, D. L.; Rivera, D. E.; Morari, M., Smith predictor design for robust performance, International Journal of Control, 46, 477-504 (1987) · Zbl 0627.93024 [19] Zafiriou, E.; Morari, M., Design of robust digital controllers and sampling time selection for SISO systems, International Journal of Control, 44, 711-735 (1986) · Zbl 0602.93048 [20] K.J. Åström, B. Wittenmark, Computer-Controlled Systems, Theory and Design, Prentice-Hall, 1990, p. 544; K.J. Åström, B. Wittenmark, Computer-Controlled Systems, Theory and Design, Prentice-Hall, 1990, p. 544 [21] X. Litrico, Modelling of a dam-river system for robust continuous and discrete-time control, working paper, Cemagref-Montpellier, 1997, p. 17; X. Litrico, Modelling of a dam-river system for robust continuous and discrete-time control, working paper, Cemagref-Montpellier, 1997, p. 17
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