A Method for Assessing the Stability of Digital Automatic Control Systems (ACS) with Discrete Elements. Hypothesis and Simulation Results

Vladimir Kodkin, Alexander Baldenkov and Alexander Anikin
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Vladimir Kodkin: Power engineering Faculty, South Ural State University, 454080 Chelyabinsk, Russia
Alexander Baldenkov: Power engineering Faculty, South Ural State University, 454080 Chelyabinsk, Russia
Alexander Anikin: Power engineering Faculty, South Ural State University, 454080 Chelyabinsk, Russia

Energies, 2021, vol. 14, issue 20, 1-15

Abstract: The article presents a new approach to the analysis of the stability of automatic systems with discrete links. In almost all modern automatic control systems (ACS), there are links that break signals in time. These are power controlled switches—transistors or thyristors operating in a pulsed mode and digital links in regulators. Time discretization significantly affects the stability of processes in the automatic control system. The theoretical analysis of such systems is rather complicated and requires a significant change in engineering approaches to analysis. With the improvement of digital controllers and a significant increase in their performance, this problem has practically been forgotten. However, its mathematical “content” has not changed since the 1980s when discreteness began to play a major role in hindering the transition to digital automatic control systems. In this paper, we propose a new approach that consists of interpreting the sampling operation by a link with the proposed frequency characteristic, which determines the suppression of input high-frequency signals. This link greatly simplifies engineering calculations and demonstrates the new capabilities of sampling systems. These possibilities include the rational distribution of digitalization resources—the number of bits and the sampling interval between the regulator channels, depending on the frequency range of the efficiency of these channels. We verify and confirm our theoretical statements through simulations and show how this approach makes it possible to formulate new principles of construction of seemingly well-known controllers—PID (Proportional Integral Differential) controllers and variable structure systems (VSS).

Keywords: discreteness; frequency response; automatic control system; PID controller; variable structure system with sliding processes (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
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