Geodesic
Mathematical model of a digital control system with background controllers of the Neuman type for complex multicirculated objects
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 129-141

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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.
Keywords: semi-Markov process, wandering time, digital control system, controller, digital control system control algorithm, transaction. 
@article{CHEB_2020_21_3_a11,
     author = {E. V. Larkin and A. N. Privalov and T. A. Akimenko and I. N. Larioshkin},
     title = {Mathematical model of a digital control system with background controllers of the {Neuman} type for complex multicirculated objects},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {129--141},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a11/}
}
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E. V. Larkin; A. N. Privalov; T. A. Akimenko; I. N. Larioshkin. Mathematical model of a digital control system with background controllers of the Neuman type for complex multicirculated objects. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 129-141. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a11/