Estimation of uncertainty in an open-channel network mathematical model
Since no mathematical model can perfectly describe a concrete system, with each model should be associated an estimate of its deviation from the actual system. Here, a mathematical model is given for open-channel networks that expresses the dynamic relationship, in terms of transcendental transfer functions, between the changes in gate openings and the corresponding variations in stored water volume in every chanal reach. By series expansion around \(s=0\) a linear time-invariant state variable model is then derived, together with the corresponding rational transfer matrix. With this model, taken as the nominal one, is associated a measure of its maximum distance from the exact models, expressed by the maximum singular value of a suitable matrix, for a variety of flow conditions in the channel, chosen such that a set of representative operating conditions is defined. This distance can be used for the synthesis of a robust control system.
scientific article; zbMATH DE number 4149965