The paper considers the types and classification of industrial PID controllers according to various types and groups. A group of linear controllers has been identified, which includes PID controllers, which are most widely used in various technical devices. Some well-known software systems that provide calculations for PID controllers are given. The transition from the mathematical notation of the trapezoidal expansion of the transfer function of the PID controller, used in the PID Tune option of the Matlab environment, to the equivalent transfer function, represented by the symbolic coefficients of the numerator and denominator polynomials, is shown. A theorem is proved that shows a one-to-one correspondence between the parameters P, I, D of the controller and the coefficients of the resulting transfer function. Flowcharts of algorithms for calculating transfer function coefficients (TF) from known values of controller parameters and calculating transfer function coefficients from known values of controller parameters are given. An illustrative example is considered.

Keywords: PID controller, transfer function, block diagram of the algorithm, Matlab environment

The paper proposes a method for calculating the interval values of the coefficients of the polynomials of the numerator and denominator of the transfer function. An algorithm is presented that describes the sequence of actions performed, which makes it possible to obtain interval coefficients for the study of both linear and nonlinear systems. An illustrative example is given, which shows the calculation of the interval values of transfer functions, both continuous and discrete systems based on the use of the Matlab system.

Keywords: control system uncertainties, robust stability, marine mobile objects, transfer function with interval coefficients

This article discusses the problem of network authentication of a client when a functional web-system consists of various services, each of which is represented by a separate site. Particular attention is paid to Single Sign On technology - a single entry point as a way to achieve centralized authentication. A comparison of tools that provide a single input is given, and a conclusion is made about the best of them. Based on the research, the author proposes the Gluu single entry point server as a server that satisfies all the requirements of the functional service system presented in the example, and also able to work within the framework of popular authentication protocols.

Keywords: functional service system, authentication, authentication protocol, single entry point, single entry point server, comparative analysis

Are represented the results of studies on the development of the high-temperature (oxidation-resistant) fibroarmirovannykh composites with the application of volcanic pumice. The application of basaltic fibers in the composites makes it possible to increase strength, high-temperature (oxidation-resistant) properties of composite and to decrease shrinkage strain. Are revealed optimum percentage reinforcements by the volume by the fibres of concrete matrix and the relationship of fiber length to the diameter with the application of a method of the mathematical planning of experiment. The mathematical models of the strength properties of the composite are obtained

Keywords: portland cement, volcanic pumice, basaltic fiber, high-temperature (oxidation-resistant) properties, limit, compression strength and bend of the composite