Fig. 1.1 - Classification of kinds of modelling of systems

IDENTIFICATION OF MODELS OF SYSTEMS

The mathematical model received by means of theoretical researches of processes, proceeding in system, can be not to adequate real system. As a result of it the effect of management of system considerably decreases. ­ The direct estimation of parametres and system characteristics is not represented possible - напр to difficulty опред. характ. The concrete compressor during degradation - dismantling and ис. On спец. The stand. - it is carried out indirectly, through measured in result of experiment entrance and target signals of system. Besides, measurements of entrance and target signals ­ are carried out in the real conditions characterised by action of every possible noise and hindrances.

The specified circumstances have caused occurrence and development of one of the major directions of the theory of management and modelling ­ - identification of systems. As identification ­ we will understand further ­ process of construction of mathematical model of system on the basis of entrance in the course of its functioning entrance and target signals.

4.1. Definition, the basic concepts and features of problems of identification

The identification problem is formulated as follows: by results of supervision over entrance and target variables of system it is necessary to construct optimum somewhat (effective) mathematical model.

Generally system identification provides the decision ­ of following questions

Choice (specification) of a class and structure mathematical models of identified ­ system and language of the description of model;

Choice of a class and type of entrance influence;

Substantiation of criterion of affinity of system and model;

Choice of a method of identification and working out of the corresponding. To this method of numerical algorithms of an estimation of parametres of system;

Check of adequacy of the model received as a result of identification to real system.

Depending on volume of the aprioristic information on a class and system structures distinguish problems Structural identification and parametrical.

Structural identification - includesa choice of a class and structure of mathematical model - is made on the basis of the theoretical analysis of identified system with ­ use of the general laws of the processes proceeding in system or on the basis of the aprioristic information on similar ­ systems. Dares in the conditions of aprioristic uncertainty concerning system model. All терии on object can be used at моделированяи.

Parametrical идентификация.состоит in an estimation of parametres and system conditions at known structure and the set class of mathematical model.

Further the basic attention is given ­ a problem of the parametrical identification which general formulation is that.

For an estimation of conformity of model to real object the criterion of affinity of system and model is used To.

The parametres of model taught thus are an estimation of parametres of object.

At the decision of a problem of identification for equivalence definition between system and model the criterion of affinity (criterion of an error or function of losses), being some функционалом from an exit of object and an exit of model is used and identification process, thus, is reduced to the decision of the following extreme.

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