Improving the quality of control systems for energy equipment through enhanced mathematical modeling

Abstract

The article discusses the principles of mathematical modeling of a typical complex control
system with distributed parameters, namely an automated technological complex: a thermal power
station-power unit-unit (boiler, turbine generator, etc.). When modeling the control system for such
a complex, a simplified concept of a generalized control object was used, characterized only by a
small number of common main features - block composition and uniformity of the main power
equipment. It is determined that a compromise between simplicity and completeness of mathematical description of complex systems is achieved through a multi-level hierarchical
representation. Analysis has shown that the task of modeling distributed systems can be approached
in two formulations: the task of reflecting the distributed system and the task of reproducing the
state of the modeled system only at specific points in the technological space. Factors influencing
the limitations of mathematical modeling of complex systems are identified. These include the
complexity of methods, the specificity of the modeling object, and the need for large information
resources. It is shown that formalizing the laws of optimal control in the form of corresponding
algorithms, which represent the mathematical solution to the control problem, is currently one of the
most difficult and unresolved problems due to their large dimensionality and the absence of
universal mathematical solution methods. For challenging tasks of rational control, decomposition
of the main task, i.e., breaking it down into a series of simpler components, is an effective approach
to its solution. In decomposition, heuristic methods based on experience and intuition without
complete proof of the choice of proposed actions are widely used.