Mathematical model of a digital control system with background controllers of the Neuman type for complex multicirculated objects

Abstract

In the work, a mathematical model of digital control of multi-circuit objects is built, taking
into account the real characteristics of a digital controller as an element of a control system.
The problem is formulated that the methods of modeling digital control systems are known and
are widely used in engineering practice, however, in the overwhelming majority, they involve
the formation of models that do not take into account the presence of time intervals between
transactions in a Von Neumann type computer.
To solve the problem, a typical block diagram of complex multi-loop control systems with
digital controllers of the Von Neumann type has been developed, which takes into account the
random nature of the processed data and real time delays between transactions.
It is proposed, taking into account the randomness of the time interval between transactions
and the stochastic nature of switching to conjugate operators, to consider a semi-Markov process
as an adequate model of the algorithm for the functioning of digital control systems.
On the basis of semi-Markov processes, a method is proposed for estimating the parameters
of time intervals between transactions in cyclic control algorithms, which makes it possible to
evaluate the characteristics of the system at the design stage, and therefore is the key to the
rational design of digital control systems for multi-circuit objects with control algorithms of
almost any complexity. An example of mathematical modeling of a two-circuit system with
digital control is presented.