Fractional-order mathematical model of an irrigation main canal pool

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.Additional key words: prototype hydraulic canal; system identification; parameter estimation; canals automation; management of water resources.

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

“…Previous papers on identifying the dynamics of this system [25,[27][28][29] reported linear models-of either integer or fractional order natures-that were fitted to responses of the canal to step commands. These models were identified around a specific operating point and badly reproduced the canal behaviour when the operating point diverged from that specific one.…”

“…However, the comparison was carried out between a relatively simple integer-order model and a quite complex fractional-order model, leaving the question of whether it would be possible to obtain more accurate results with fractional-order models of similar complexity as integer-order models open. This question was somehow solved later in [25], in which a simple fractional-order model whose differential equation is…”

“…We have used the hydraulic canal system installed in the laboratory of the Mechanics of Fluids of the University of Castilla La Mancha. In a first work, a fractional-order model with a time delay was characterized for the main pool of the canal in [25], by means of a direct system identification approach [26] that allows the immediate derivation of a continuous-time model using continuous-time model identification tools. Later, the two pools that constitute the canal were identified and a TITO (two input/two output) fractional-order model was obtained in [27] that took into account the coupling existing between the two pools.…”

Design of a PIα Controller for the Robust Control of the Steam Pressure in the Steam Drum of a Bagasse-Fired Boiler

“…During the past three decades, the subject of fractional calculus, i.e., the calculation of integrals and derivatives of any arbitrary real or complex order, has gained considerable popularity and importance, principally owing to its demonstrated applications in diverse and widespread fields of science and engineering [27], [28]. Fractional order operators have, therefore, also been applied with satisfactory results to model and control processes with complex dynamic behaviors [29]- [33].…”

On the Modelling and Control of a Laboratory Prototype of a Hydraulic Canal Based on a TITO Fractional-Order Model

“…In recent years, increasing attention has been paid to fractional-order calculus as a powerful tool with which to model and control a broad range of real industrial processes, e.g., [7,[25][26][27][28][29][30][31][32][33][34]. In particular, fractional order differential equations are more adequate than integer-order equations when modeling certain processes in which distributed dynamics are dominant, as occurs in electrochemical processes [35,36], thermal processes [37,38], or hydraulic processes [39,40].…”