Discreteness in Time and Evaluation of the Effectiveness of Automatic Control Systems: Examples of the Effect of Discreteness on Mathematical Patterns

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 seem-ingly 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 correct) that are the causes of these paradoxes.