Abstract
In this paper a two-input, two-output (TITO) fractional order mathematical model of a laboratory prototype of a hydraulic canal is proposed. This canal is made up of two pools that have a strong interaction between them. The inputs of the TITO model are the pump flow and the opening of an intermediate gate, and the two outputs are the water levels in the two pools. Based on the experiments developed in a laboratory prototype the parameters of the mathematical models have been identified. Then, considering the TITO model, a first control loop of the pump is closed to reproduce real-world conditions in which the water level of the first pool is not dependent on the opening of the upstream gate, thus leading to an equivalent single input, single output (SISO) system. The comparison of the resulting system with the classical first order systems typically utilized to model hydraulic canals shows that the proposed model has significantly lower error: about 50%, and, therefore, higher accuracy in capturing the canal dynamics. This model has also been utilized to optimize the design of the controller of the pump of the canal, thus achieving a faster response to step commands and thus minimizing the interaction between the two pools of the experimental platform.
Highlights
The scarcity of fresh water has become a progressively-growing problem worldwide [1].Water usage has grown by more than twice the rate of the world population increase during the last century, causing frequent conflicts between different users [2]
The dynamics of the TITO system is utilized to propose a systematic methodology to design a proportional integral (PI) controller for the pump that outperforms the proportional integral derivative (PID) utilized experimentally, which was designed by trial and error
These simulations show that the PI controller designed by considering a fractional-order model of the canal provides a wider bandwidth and, a faster response to step commands, than the PI designed from the integer-order model
Summary
The scarcity of fresh water has become a progressively-growing problem worldwide [1]. The degree of adequacy of the cited models for the design of high performance control systems is not that required due to the nonlinear and distributed behavior of the canal, as well as to model parameter uncertainties, e.g., [6] This means that there are still significant unsolved problems in this field. A TITO (two input/two output) fractional-order model of a canal with two pools is proposed, which has been derived based on a prototype laboratory hydraulic canal. This model is obtained by means of a direct system identification approach [41], which allows the immediate derivation of a continuous-time model using continuous-time model identification tools [42]. The dynamics of the TITO system is utilized to propose a systematic methodology to design a proportional integral (PI) controller for the pump that outperforms the PID utilized experimentally, which was designed by trial and error
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