Design and robustness analysis of decentralized constant volume-control for open-channels

Abstract

In this paper we consider a mathematical model for open-channels that expresses the dynamic relationships, in terms of transcendental functions, between the gate opening sections and the corresponding stored water volume variations in the different canal reaches with respect to an initial reference configuration of uniform flow. Series expansion around s=0 gives a state variable linear and time invariant model as well as the corresponding rational transfer matrix. The two transfer function matrices are related by a relationship that defines uncertainty in the output-multiplicative form. A proportional decentralized constant volume control is obtained by determining the state feedback gain matrix, with diagonal structure, that minimizes the H 2 norm of a suitable transfer matrix. The same procedure can be applied to an augmented system for designing a proportional integral decentralized control. In this way it is possible to obtain a null steady state error. Since the fundamental property which must be retained for all possible perturbations of the plant is stability of the feedback system, in this paper we have studied whether the proposed feedback designs are robust when output-multiplicative perturbations occur due to the low-frequency approximations and to the variations with respect to the reference configuration of uniform flow.