Investigation of linear models for control of water flow and temperature in a water supply system

In some cases, the object model is a set of parallel models of the same general appearance, but with different parameters. The most common model is a model in the form of a serial connection of a first- or second-order filter and a delay link. An example is the water supply system of a large residential building or a group of houses. From the most general considerations, we can expect that such an object can be approximately described by a simpler model, replacing the sum of identical-looking models with different parameters with a single model of this type with averaged parameters, however, finding many parameters simply in the form of an average is, apparently, an unreasonable approach. It seems more reasonable to find the parameters by the approximating model by numerical optimization, in which the integral from the module or from the square of the deviation of the output signal of such a model from the output signal of the exact model is minimized when the test signal is applied. For linear models, the most reasonable test signal is a single step effect. This article tests this hypothesis and provides the results of this test.