Modeling and Simulation

*Control Theory in Engineering*

22 February 2019]

[18] Rpi Forum. Raspberry Pi View Topic—C vs Python for GPIO. 2017. Available from: https://www. raspberrypi.org/forums/viewtopic. php?f=33&t=22640 [Accessed:

**324**

**Chapter 15**

Patterns

**Abstract**

**1. Introduction**

**327**

*Vladimir Kodkin*

Discreteness in Time and

Examples of the Effect of

correct) that are the causes of these paradoxes.

of digital systems, pulse automatic control system

convenient, like working with mobile phones.

Evaluation of the Effectiveness

of Automatic Control Systems:

Discreteness on Mathematical

Discreteness is one of the fundamental categories in science, philosophy, mathematics, physics, and cybernetics. In the last 50 years, this concept and problem has occupied the minds of many practical engineers. There were situations in which discreteness began to play a major role, for example among the problems obstructing progress in automatic control systems and regarding the transition to digital systems. This chapter discusses the main approaches to the stability analysis of automatic control systems, proposed in fundamental works on the theory of automatic control (TAC). A proprietary approach is proposed, greatly simplifying engineering calculations, with almost no loss of analysis accuracy. It is shown, how this approach allows us to formulate new principles for the construction of seemingly well-known regulators—PID regulators and variable structure systems (VSS). In the last part of the chapter, it is proposed to analyze the famous paradoxes of science precisely from the point of view of the discreteness of the variables considered in these paradoxes. It is argued that it is discrete operations (not always

**Keywords:** automatic control systems, discreteness, accuracy and stability

Digital automatic control systems (ACS) have won everywhere. Their advantages

There are no problems with discreteness of output signals in terms of level and time for most ACS. The discreteness in time in fractions of milliseconds and in level

over analog are undeniable—these controllers implement control algorithms of

They are very reliable and stable. Most often, their setup is simple and

almost any complexity, completely inaccessible to analog ACS.
