2025 , Volume 30, № 5, p.95-107

The study addresses the development of a mathematical model of a two-level digital control system with interrupts which will allow for the correct design of software for hierarchical control systems. The study used methodology of probability theory, Markov process theory, and queuing theory. As a result of the study, a mathematical model of a two-level digital interrupt control system was developed, in which, along with the main circuits that provide feedback on the state of actuators at the functional-logical level and the state of the control object as a whole, there are connections at the upper hierarchical level that provide control of the object through interruption. The structure of the model is presented as a Petri net that describes the “competition” between the generator and the interrupt handler. Expressions are obtained for calculating estimates of the probabilistic and time characteristics of the “competition” outcome. It is noted that, in general, statistical estimates depend on the history of the process of decreasing and increasing the current interrupt level. It is shown that for a Poisson interruption flow with an exponential distribution law of their processing time, the primary structural-parametric model can be represented by a model of a queuing system with a queue formed by interrupt levels. We calculate the dependence for the estimate of the increase in the computational complexity of the control program due to servicing interrupt requests. The proposed approach to constructing a model of the functioning of a two-level hierarchical control system with interrupts ensures the correct solution of a wide range of applied control problems with physical separation of controllers into hierarchical levels and implementation of control of the state of actuators of drives based on vector control with response to abnormal situations according to the principle of interrupting the control program with a return to the background mode.