##
**Analytical approximation of open-channel flow for controller design.**
*(English)*
Zbl 1147.76558

Summary: The integrator delay (ID) model is a popular and simple way to model a canal for control purposes. In this paper, particular attention is given to accurately model the delay and the integrator gain in any flow configuration. Based on a previous work by the authors allowing to have a very accurate frequency domain representation of Saint-Venant equations, the paper proposes a new approximate model: the integrator delay zero (IDZ) model has an integrator and a delay in low frequencies, and models the high frequencies by a constant gain and a delay. Analytical formulas are derived to compute the model parameters for a canal pool possibly in backwater conditions. The IDZ model is compared with an accurate model on two example canals for different flow conditions. The comparisons done in the frequency domain and in the time domain show the accuracy of the model.

### MSC:

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

### Keywords:

Open-channel flow; Hydraulic model; Analytical model; Laplace transform; Saint-Venant equations
PDFBibTeX
XMLCite

\textit{X. Litrico} and \textit{V. Fromion}, Appl. Math. Modelling 28, No. 7, 677--695 (2004; Zbl 1147.76558)

Full Text:
DOI

### References:

[1] | M. Shand, Automatic Downstream Control Systems for Irrigation Canals, Ph.D. Thesis, University of California, Berkeley, 1971; M. Shand, Automatic Downstream Control Systems for Irrigation Canals, Ph.D. Thesis, University of California, Berkeley, 1971 |

[2] | Corriga, G.; Salembeni, D.; Sanna, S.; Usai, G., A control method for speeding up response of hydroelectric stations power canals, Appl. Math. Modell., 12, 627-633 (1988) · Zbl 0661.93049 |

[3] | Ermolin, Y., Study of open-channel dynamics as controlled process, J. Hydraul. Eng., 118, 1, 59-71 (1992) |

[4] | Hancu, S.; Dan, P., Wave-motion stability in canals with automatic controllers, J. Hydraul. Eng., 118, 12, 1621-1638 (1992) |

[5] | Corriga, G.; Fanni, A.; Sanna, S.; Usai, G., A constant-volume control method for open channel operation, Int. J. Modell. Simulat., 2, 2, 108-112 (1982) |

[6] | J. Baume, J. Sau, P.-O. Malaterre, Modeling of irrigation channel dynamics for controller design, in: Conf. on Systems, Man and Cybernetics, SMC’98, San Diego, CA, 1998, pp. 3856-3861; J. Baume, J. Sau, P.-O. Malaterre, Modeling of irrigation channel dynamics for controller design, in: Conf. on Systems, Man and Cybernetics, SMC’98, San Diego, CA, 1998, pp. 3856-3861 |

[7] | Seatzu, C., Design and robustness analysis of decentralized constant volume-control for open-channels, Appl. Math. Modell., 23, 6, 479-500 (1999) · Zbl 0979.93515 |

[8] | O. Balogun, Design of Real-Time Feedback Control for Canal Systems Using Linear Quadratic Regulator Theory, Ph.D. Thesis, Department of Mechanical Engineering, University of California at Davis, 1985, 230 p; O. Balogun, Design of Real-Time Feedback Control for Canal Systems Using Linear Quadratic Regulator Theory, Ph.D. Thesis, Department of Mechanical Engineering, University of California at Davis, 1985, 230 p |

[9] | P.-O. Malaterre, Modélisation, Analyse et Commande Optimale LQR d’un Canal d’Irrigation, Ph.D. Thesis, ISBN 2-85362-368-8, Etude EEE no. 14, LAAS, CNRS, ENGREF, Cemagref (in French), 1994; P.-O. Malaterre, Modélisation, Analyse et Commande Optimale LQR d’un Canal d’Irrigation, Ph.D. Thesis, ISBN 2-85362-368-8, Etude EEE no. 14, LAAS, CNRS, ENGREF, Cemagref (in French), 1994 |

[10] | Schuurmans, J.; Bosgra, O.; Brouwer, R., Open-channel flow model approximation for controller design, Appl. Math. Modell., 19, 525-530 (1995) · Zbl 0835.76011 |

[11] | Aström, K., Limitations on control system performance, Eur. J. Control, 6, 1-19 (2000) |

[12] | X. Litrico, V. Fromion, Infinite dimensional modelling of open-channel hydraulic systems for control purposes, in: 41st Conf. on Decision and Control, Las Vegas, 2002, pp. 1681-1686; X. Litrico, V. Fromion, Infinite dimensional modelling of open-channel hydraulic systems for control purposes, in: 41st Conf. on Decision and Control, Las Vegas, 2002, pp. 1681-1686 |

[13] | Chow, V., Open-channel Hydraulics (1988), McGraw-Hill Book Company: McGraw-Hill Book Company New York, 680 p |

[14] | Litrico, X.; Georges, D., Robust continuous-time and discrete-time flow control of a dam-river system (I): Modelling, Appl. Math. Modell., 23, 11, 809-827 (1999) · Zbl 0949.93007 |

[15] | Freudenberg, J.; Looze, D., A sensitivity tradeoff for plants with time delay, IEEE Trans. Automat. Control, 32, 2, 99-104 (1987) · Zbl 0616.93024 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.