Multivariable fractional-order model of a laboratory hydraulic canal with two pools

In this paper a fractional order model for an irrigation main canal is proposed. This system has two pools that present a strong interaction between them. Then a multivariable model with two inputs: the pump flow and the opening of an intermediate gate, and two outputs: the water levels in the two pools, is derived. The identification of the model parameters is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The accuracy of the proposed fractional order models is compared with the standard integer-order models of the canal. The parameters of the mathematical models have been identified by minimizing the Integral Square Error Index (ISE) existing between the time responses of the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of the integer-order and fractional-order models shows that the fractional-order model has significantly lower error: about 30%, and, therefore, higher accuracy in capturing the canal dynamics.