# 1. Basic concepts and definitions of the theory of identification

The development of computer technology has led to the creation of a huge number of complex devices, consisting not only of the technical facilities for various purposes, but also complex systems management, reliable and high-quality operation that allows you to implement the required processes in a variety of operating conditions.

However, when using such devices often occurs following a number of tasks.

1). Diagnostics - over the lifetime of the object is subjected to negative influences, including aging, so some of the characteristics of the object may be different from the nominal, which can lead to faulty operation and possibly cause damage to the device. However, by comparing the current signal with the reference of the object it is possible to determine the change in operating parameters and take appropriate action.

2). The optimum setting parameters - in most cases the device can operate in several modes, allowing to provide optimum performance and efficiency characteristics for the specific operation. Get a set of optimal values of the parameters of the object is possible by comparing the current process with the desired object.

3). Forecasting processes - on a known set of input and output signals of the object and the proposed structural diagram of the object is possible to determine the parameters of the model of the object, followed by a simulation that will allow not only to predict the process object through the required time, but also get a reaction system with other external influences on the object.

Develop models of the objects on the basis of observation and study of their properties allows

**the identification theory**.**Under Identity in the broad sense**refers to the determination of the structure and the parameters of the dynamic objects from the observed data: the impact of the input and output values. In this case, the object under study is a "black box", the structure and the parameters within which are completely unknown and must be determined.

**Under Identity in the narrow sense**it refers to the problem of determining the parameters of the elements in the known structure of a mathematical model of the object. In this case, the object under study is a "gray box" whose parameters are to be determined.

**Generalized solution to the problem of identification**can be reduced to the class definition of the object and the choice for a configurable model, and to determine the optimal quality criteria and the identification algorithm.

Creating models according to the results of experiments includes components such as a data set of candidate models and a criterion of quality, showing the degree of conformity of the selected model observations.

However, not always possible to build a model that would fully meet all the running processes of the real object.

**The main reasons for the imperfection of the models is**the wrong choice of quality criterion, the inferiority of candidate models, insufficient amount of raw data and error to find the optimal model using numerical methods of identification.Depending on the method of registration of the experimental data

**identification techniques**fall into three groups.In most cases, the object of study is disconnected from the system and its input is fed the control signal a desired shape (step and pulse timing signals, arbitrary time signals, harmonic signals, incidental exposure to the settings). This method of the experiment is called an a

**ctive identity**, which is widely used in the creation of new technologies to existing industrial facilities in the initial development of the mathematical model and to explore new phenomena.If the object of study can not be disconnected from the system, or you want to test it in the normal mode of operation, applies a

**passive identification**.Furthermore, there is

**mixed identification**when the object is not displayed in the normal mode of operation, but the control signals to its other effects are added, enabling the identification of the object without deteriorating the quality of the primary process controller.In general, the

**methods of identification are classified**on the basis of:1. Type of the object:

- Linear and nonlinear;

- Continuous and discrete;

- A one-dimensional and multi-dimensional;

- Steady and unsteady;

- Lumped and distributed parameters.

2. Identification of the structure of the object or model parameters.

3. Presentation of the experimental data in the time or frequency domain.

4. Identification of the real-time or post-processing mode.

5. The method of the experiment on the site.

6. The criterion of identification and estimation method.

7. Using a priori information.

In most cases, identification is carried out for

**linear dynamic systems in the time domain**of dependence of the output signal of the input received during the observation. In addition, identification of linear dynamic objects corresponding mathematical models in the form of the transfer function or differential equations convenient to use**frequency methods**that complement the developed methods of analysis and synthesis of systems in the frequency domain.