LPV water delivery canal control based on prescribed order models

Abstract

This article addresses the problem of designing an LPV controller for a water delivery canal based on reduced complexity linear models with a priori chosen order. For that sake, by applying a method based on the Laplace transform and the linearization of the Saint-Venant equations, a finite dimensional rational transfer function is obtained for each canal reach. An LPV gain-scheduling controller that relies on H∞ optimization is then designed for local upstream canal control. The scheduling variables are the inlet canal flow and the downstream-reach mean level. The uncertainty bound is computed on the basis of the high frequency error of the frequency response of the model used with respect to the one of the infinite-dimensional model by linearizing the Sain-Venant equations. This approach has the advantage of yielding an LPV controller that relies on a model with specified complexity and to relate model uncertainty to physical canal parameters, allowing operation over an extended envelop of water flow and level equilibria.