The synthesis of mathematical models of systems is carried out based on data obtained in the identification process. In cases where it is possible to influence input signals in a specific and deliberate way, identification is done by means of an active experiment. In many cases this is the only practical method, returning correct results in a finite time For this purpose, an experiment plan is set up so that later on, the simplest and most effective methods of model synthesis offered by the approximation theory or the mathematical statistics, can be used. In principle, the experiment plan depends on using the optimum predetermined input signals with respect to the objective function of the model, and on a measurement of strictly defined parameters of the output signals of the system under investigation. In effect, a set of data is attained which represents the model being sought, approximated by means of a selected algorithm. The model is most often denoted by means of differential equations, state equations or transfer functions. Models presented by means of algebraic polynomials, are also important. Special attention should be given to the synthesis of the models based on the Lagrange and Chebyshev polynomials or those making use of the least square method. The possibility of transforming models expressed by means of algebraic polynomials into models in the form of transfer functions seems to be particularly attractive.
KeywordsTransfer Function Power Series Impulse Response Kalman Filter Chebyshev Polynomial
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