Multimodelling Steps for Free-Surface Hydraulic System Control
The chapter presents multimodelling steps of free-surface hydraulic system for the design of control strategies. This method makes it possible to represent, simply and accurately, the non-linear hydraulic system dynamics with large operating conditions. T
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ract. The chapter presents multimodelling steps of free-surface hydraulic system for the design of control strategies. This method makes it possible to represent, simply and accurately, the non-linear hydraulic system dynamics with large operating conditions. The multimodelling steps are performed in order to lead to the determination of a finite number of models. The models are selected online by the minimization of a quadratic criterion. It is an interesting alternative to the use of Saint Venant partial differential equations because it allows the design, the tuning and the validation of control strategies.The evaluation of the proposed method is carried out by simulation within the framework of a canal with trapezoidal profile showing its effectiveness. Keywords. Multimodelling, operating modes, online selection, hydrographic network.
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Introduction
Hydrographic networks are systems geographically distributed conveying water quantities gravitationally. They are composed of open-surface hydraulic systems (canals, rivers, etc.) which are used to satisfy the demands related to human activities (ecological discharge, agricultural and industrial needs, drinkable water, etc.). According to the recognized importance of water resource, the efficient management of these systems is essential today. It requires the proposal, the design and the tuning of control strategies through simulation, before their implementation on real systems. The free-surface hydraulic system dynamics is characterized by nonlinearities and important transfer delays. Although the Saint Venant Partial Differential Equations (PDE) accurately represent hydraulic system dynamics [2] [10], their resolution involves numerical approaches according to discretization schemes which are rather complex to implement, especially for designing and tuning a control strategy. The PDE simplification and linearization around an operating point lead to simplify models of the hydraulic system dynamics [7]. In the literature, most authors have proposed control strategies based on the PDE linearization [9]. However, the accuracy of these models is only acceptable on restricted interval around the operating point, and their use on large operating conditions requires robust controller design, as proposed in [8].
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The representation of the nonlinear systems with variable transfer delays involves the identification problem of a model with variable parameters or multiple models. In the literature, multimodelling approaches for the predictive control are described in [13] and in [12]. These methods are based on switching technics amongst several simple models. In the case of nonlinear systems with variable transfer delays, an algorithm for the estimation of the models most representative of the system dynamics is proposed in [14]. In these approaches, the number of models and their operating range are known a priori. The nonparametric modelling of the nonlinear system dynamics can also be carried out by Gaussian approaches [5]. The identification a
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