Formal Description of Digital Control System Operation and Its Use in Designing

Abstract

A model of the required external behavior of the designed digital system specified by the scheme of the digital block connection and software is introduced. It is proposed to use a family of time-invariant dynamical systems as such a model; the family is specified by a set of terminal variables, the range of values of these variables, and the set of admissible interactions between the digital system and external medium. It is assumed that the designed digital system must provide the performance of a finite alphabet of functions each of which is characterized by its subset of admissible interactions. Based on this, the structure of the set of admissible interactions of the digital system is analyzed. The project of a correctly designed digital system also defines a family of time-invariant dynamical systems as an external behavior. The problem of debugging projects for digital systems is stated as a problem of comparing two families of time-invariant dynamical systems: on the one hand, the family specified by the requirements of the technical design assignment and, on the other hand, the family determined by the scheme of block connection and text of the digital system’s software.