ON THE THEORY OF SYNTHESIS OF MINIMAL SCHEMES OF SYSTEMS CONTROL OF HYDRAULIC AND PNEUMATIC DRIVES

Abstract

Showed the strict compliance of the scientific direction "Synthesis of minimum control schemes of hydraulic and pneumatic drive systems" developed by the author with the point of view of general algebra, algebra of logic, graph theory and automata theory. The synthesis of the minimum graph of operations, which is a mathematical model of the control system, has been proved. The legitimacy of the methods of undivided decomposition of equations describing the scheme of the control system has been proved. The control system is considered as a cyclic Moore finite automaton. By a cyclic automaton (CA) we will understand the mathematical model of a device designed to control cyclic processes, which are a set of technological operations performed in a certain sequence. In this regard, the automaton at each clock necessarily passes into some new state, and for a finite number of cycles the target reaches any state, and its graph contains a contour, covering all states. In general, the CA may contain several circuits, so that each circuit is interpreted either as one of the possible sequences of technological operations due to the corresponding mode of operation, or as an independent and simultaneous execution of a number of sets of technological operations. A sequential decomposition of the CA is presented in order to represent it by the sequential operation of automata with one internal state. Such a consideration of the function of transitions will naturally lead to a decrease in the number of elements in the implementation of the CA. The study will be subjected to the CA, the graph of which consists of a single circuit, since the results obtained are easily generalized to multi-circuit CA. Obtaining a breakdown of the states of a cyclic automaton in the manner indicated above is performed directly according to any automaton description without any additional calculations, tables and other constructions.