A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System.

Saddam Gharab,Vicente Feliu-Batlle,Raul Rivas-Perez

doi:10.3390/e21030309

Saddam Gharab, Vicente Feliu-Batlle + Show 1 more

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https://doi.org/10.3390/e21030309

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Abstract

This article addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model has been developed by taking into account the measurement errors caused by the different parts of our experimental setup: (a) the nonlinearity associated to the input signal, which is caused by the movements of the upstream gate, is avoided by using a nonlinear equivalent upstream gate model, (b) the nonlinearity associated to the output signal, caused by the sensor’s resolution, is avoided by using a quantization model in the identification process, and (c) the nonlinear behaviour of the canal, which is related to the working flow regime, is taken into account considering two completely different models in function of the operating regime: the free and the submerged flows. The proposed technique of identification is based on the time-domain data. An input pseudo-random binary signal (PRBS) is designed depending on the parameters of an initially estimated linear model that was obtained by using a fundamental technique of identification. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes. An accurate model has been obtained, which is composed of two submodels: a first order plus time delay submodel that accurately describes the dynamics of the free flow and a fractional-order plus time delay submodel that properly describes the dynamics of the submerged flow.

Highlights

Improving the management of the scarce available water resources is a most important research area because of the strong dependence of the mankind on fresh water [1]
This paper has addressed the modelization of the nonlinear dynamics of a laboratory hydraulic canal installed in the University of Castilla-La Mancha
Improving the precision of its dynamic model allows for a best design of the automatic control system of the canal, which is in charge of delivering the desired water flow at its downstream end

Summary

Introduction

Improving the management of the scarce available water resources is a most important research area because of the strong dependence of the mankind on fresh water [1]. Some updated statistics show that irrigated agriculture represents the largest consumer of fresh water that consumes a total percentage of 70% of all the available fresh water [2,3]. In those systems, water is transported and distributed through long distances by using irrigation main canals, which have huge water losses. Several researches have focused on improving the management and efficiency of hydraulic canals by means of introducing electronics and automation in these civil infraestructures. The establishment of dynamic models of the process to be controlled is of utmost importance in the design of automation systems, modelization of the dynamics of main irrigation canals has a lower level of development than modelization of other hydraulic infraestructures like dams, piping, hydroelectric plants and drinking

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