Investigation of multivariable automatic control systems for complex dynamic objects based on Petrov's paradigm

This paper considers some approaches to studying the properties of multivariable automatic control systems (MACSs), particularly their stability, based on different descriptive models. The theory presented below extends the previously known ideas of Academician B. N. Petrov, which are fundamental in the classical theory of automatic control. Petrov's theory is based on the structural and functional decomposition of MACSs into separate real subsystems and multidimensional connections between them, described by a new model, and the study of system properties using frequency methods. Therefore, this theory is related to the physical (engineering) approach to dynamical systems analysis. A method for describing MACSs by the individual characteristics of subsystems and the elements of multidimensional connections is suggested. Stability criteria for linear MACSs with identical subsystems and a stability criterion for the system's equilibrium are established. A technology for finding the parameters of periodic motions and assessing their stability for nonlinear MACSs is introduced. Some numerical examples with technical objects illustrate this technology for studying the properties of MACSs.