Analytical Determination of the Parameters of the Self-Tuning Circuit of the Traffic Control System on the Limit of Vibrational Stability

In the article the author analyzed the known simple types of self-tuning automatic control systems, the order of choosing the parameters of the main control circuit for a given structure and parameters of the self-tuning circuit. In the article the theory of P.L. Chebyshev's approximations for the study of control systems with limit cycle was used. The mathematical formulas give the possibility to construct a transitional process in a control system arising from parametric perturbations under initial conditions. The proposed method allows it possible to calculate the parameters and to simulate a specific control system.