Qualitative properties and stability analysis of the mathematical model for a DC-DC electric circuit
E.V. Chistyakova, D.N. Sidorov, A.V. Domyshev, V.F. Chistyakov
TL;DR
This paper presents a mathematical analysis of a simplified DC-DC converter model with a PID regulator, focusing on its solvability and stability using advanced differential equations theory.
Contribution
It introduces a novel approach to analyze the stability of a singular differential equation model of a DC-DC converter with a PID regulator.
Findings
Proves solvability of the model
Establishes stability conditions
Provides theoretical insights into system behavior
Abstract
This paper describes a simplified model of an electric circuit with a DC-DC converter and a PID-regulator as a system of integral differential equations with an identically singular matrix multiplying the higher derivative of the desired vector-function. We use theoretical results on integral and differential equations and their systems to prove solvability of such a model and analyze its stability.
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Taxonomy
TopicsElectric Power Systems and Control · Induction Heating and Inverter Technology · Diverse Industrial Engineering Technologies