Synthesis Methodology of Control System under Optimal Resource Consumption

The article discusses the methodology for synthesizing optimal control based on the principle of minimizing energy costs for system control. A second-order control object was chosen as the system under study. A complete study of the system was carried out, a mathematical calculation was performed, and the optimal control was calculated. The obtained data was verified using simulation modeling. Algorithms of control systems that differ from optimal control and do not ensure the fulfillment of the selected optimality criterion have been studied. Various optimal controls were studied for various initial states of the system. Optimal control ensures the transition between the initial state of the system and the final state in a fixed time. It is shown that, regardless of the initial state of the system, it is possible to calculate optimal control, but only for the case of unlimited resources. Pontryagin’s maximum principle is used as an optimality criterion. Based on the obtained optimal control, the synthesis of a sequential correcting device is realized - the transfer function coefficients of the correcting device of the structural diagram are determined.