A New Approach to the Simplification of Water-Supply Network Models

Abstract The aim of the paper is to present a procedure by which a simplified linear dynamical model in the discrete or continuous form can be derived, starting from an originally complex physical model. The procedure is based on an algorithm for the identification of continuous multivariable systems from sampled data which is applied on the input-output data resulting from the simulation of the water-supply system on a digital computer. In the paper some mathematical methods are described, required for the realisation of the following procedure: 1. dynamical simulation of the water-supply system. 2. recording of system outputs (reservoir levels), inputs (pump controls) and disturbances (consumer demands) 3. identification of the “unknown” system concerned, based on a discrete linear multivariable canonical model, applying the least squares method on the recorded data 4. transformation of the discrete input-output model into the statespace model 5. transformation of the discrete model into the continuous one, using the concept of the matrix logarithm function Following the described procedure, the water-supply system of a small town near Ljubljana has been approximated by a linear tiDeinvariant multivariable model which is very suitable for further development of optimal control algorithms. Also a comparison between the output responses of the original nd simplified model is given.

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