From infinite dimensional modelling to parametric reduced-order approximation: Application to open-channel flow for hydroelectricity

In this paper, it will be shown that open-channel hydraulic systems can be suitably represented for control purposes by using input delay linear parameter-varying (LPV) models. The physical equations on which this work is done are Saint-Venant equations applied to a non-rectangular cross section channel. These later are two coupled non-linear hyperbolic partial differential equations which are linearized and transformed into irrational transfer functions. An accurate model approximation procedure, denoted IPTFA (Irrational Proper Transfer Function Algorithm) is developed in order to obtain a rational transfer function plus input delays which is then parameterized by one single parameter: the initial steady-state discharge. Frequency domain responses of the irrational and reduced-order transfer functions are shown to match for a large range of discharge.