Development of a mathematical apparatus for determining operator images of the desired quantized transition functions of finite duration

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.65477

Keywords:

quantized transition function, the Heaviside function, transition function of finite duration

Abstract

An important part of modern methods of synthesizing automatic control systems is selection of a characteristic polynomial that can provide the desired dynamics. However, standard polynomials allow only rough setting of the desired dynamic properties of a system.

A more convenient and clear alternative of imparting desired properties to the system in static and dynamic modes is to use not the standard characteristic polynomials but the desired transfer function that is not selected from a list of standard forms but is set solely on the basis of technological requirements and technical implementation capacity of a particular type of equipment.

The study suggests presenting the desired transition function of the automatic control system in a quantized form, i.e. as a set of operated coordinate values that change during a certain period that is relatively small in comparison with the duration of the transition process itself.

A possibility of using quantized transition functions is represented as the sum of time-shifted Heaviside functions for the synthesis of regulators in open-loop control systems. A method has been developed to determine analytically the operator images of the desired quantized transition functions of finite duration by relying only on the values of the signal levels in the quantization time and the value of the quantization period.

Author Biographies

Oleksiy Sheremet, Dniprodzerzhynsk State Technical University 2 Dniprobudivska str., Dniprodzerzhynsk, Ukraine, 51918

PhD, Associate Professor

Department of Electrical Engineering and Machinery

Oleksandr Sadovoy, Dniprodzerzhynsk State Technical University 2 Dniprobudivska str., Dniprodzerzhynsk, Ukraine, 51918

Doctor of Technical Sciences, Professor, Vice-Rector for Research

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Published

2016-04-22

How to Cite

Sheremet, O., & Sadovoy, O. (2016). Development of a mathematical apparatus for determining operator images of the desired quantized transition functions of finite duration. Eastern-European Journal of Enterprise Technologies, 2(2(80), 51–58. https://doi.org/10.15587/1729-4061.2016.65477

Issue

Vol. 2 No. 2(80) (2016): Information technology. Industry control systems

Section

Industry control systems

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Copyright (c) 2016 Oleksiy Sheremet, Oleksandr Sadovoy

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