PHYSICAL AND MATHEMATICAL MODELING OF DYNAMICS OF HIGH-DIMENSIONAL NONLINEAR AUTOMATIC CONTROL SYSTEMS

The article is devoted to a comprehensive methodology for studying the dynamics of complex automatic control systems on the basis of a unified physical and mathematical approach. The authors show that classical analytical methods applicable to linear models of low orders cease to be effective in the transition to high-dimensional and, moreover, nonlinear control objects: computational requirements increase exponentially, and the obtained stability criteria turn out to be excessively conservative. To overcome these limitations, we propose a systematic use of large-scale modeling based on the principles of similarity theory. The paper consistently reveals the conditions of dynamic equivalence of the model and the original system, and substantiates the choice of scales that allow either to preserve the characteristic frequencies of processes, or, on the contrary, to compress or stretch the time scale to increase the experimental clarity. Special attention is paid to the role of electronic simulators, thanks to which multiple, repeatable reproduction of transients and fine-tuning of parameters in real time is possible. The methodological part is accompanied by an analysis of the historical evolution of the approach: from the first laboratory installations with mechanical analogy to modern digital benches integrating mathematical models, hardware-software interfaces and means of automatic parameter identification into a single environment. Integrated modeling not only significantly reduces the costs of debugging and testing of regulators, but also provides an opportunity for deep optimization of control structures and algorithms, especially in cases where direct calculation of parameters is impossible or economically inexpedient. As a result, an integral research platform is formed that combines the rigor of mathematical criteria, flexibility of engineering experimentation and high resource efficiency.