Abstract
In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE) performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
Highlights
Recent studies have shown that in many countries around the world an average of only 44% of the water conveyed by irrigation main canals reaches the crops for which it was intended, while the remaining percentage is lost during the water transportation process (Litrico & Fromion, 2009)
The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE) performance index existing between the models and the real-time experimental data obtained from the canal prototype
According to the responses obtained after carrying out the experiments developed, we have proposed three simple linear models with which to characterize the dynamic behavior of our hydraulic canal prototype
Summary
Recent studies have shown that in many countries around the world an average of only 44% of the water conveyed by irrigation main canals reaches the crops for which it was intended, while the remaining percentage is lost during the water transportation process (Litrico & Fromion, 2009). The design and implementation of effective water distribution control systems require mathematical models that accurately depict the dynamic behavior of irrigation main canal pools in realistic conditions (Litrico & Fromion, 2009). In the last few decades, increasing attention has been paid to fractional order calculus as a powerful tool with which to model and control real industrial processes (Bagley & Calico, 1991; Podlubny, 1999; Feliu-Batlle et al, 2005; Monje et al, 2010; Tavakoli-Kakhki et al, 2010) These controllers have been successfully applied during the control of water distribution in main irrigation canal pools (Calderon-Valdez et al, 2009; Feliu et al, 2009; Feliu-Batlle et al, 2011). This model is obtained by means of a direct system identification approach (Garnier & Young, 2004), which allows the immediate derivation of a continuous-time model using continuous-time model identification tools
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