Linear Parameter Varying Modelling and Identification for Real-time Control of Open-flow Irrigation Canals

Irrigation canals are open-flow water hydraulic systems, whose objective is mainly to convey water from its source down to its final users. They are large distributed systems characterized by non-linearity and dynamic behavior that depends on the operating point. Moreover, in canals with multiple reaches dynamic behavior is highly affected by the coupling among them. The physical model for those systems leads to a distributed-parameter model whose description usually requires partial differential equations (PDEs). However, the solution and parameter estimation of those PDE equations can only be obtained numerically and imply quite time-consuming computations that make them not suitable for real-time control purposes. Alternatively, in this paper, it will be shown that open-flow canal systems can be suitably represented for control purposes by using linear parameter-varying (LPV) models. The advantage of this approach compared to the use of PDE equation is that allows simpler models which are suitable for control design and whose parameters can be easily identified from input-output data by means of classical identification techniques. In this paper, the well known control-oriented, model named integral delay zero (IDZ), that is able to represent the canal dynamics around a given operating point by means of a linear time-invariant (LTI) model is extended to multiple operating points by means of an LPV model. The derivation of this LPV model for single-reach open-flow canal systems as well as its extension to multiple-reach open-flow canals is proposed. In particular, the proposed methodology allows deriving the model structure and estimating model parameters using data by means of identification techniques. Thus, a gray-box control model is obtained whose validation is carried out using single-pool and two-pool test canals obtaining satisfactory results.