A procedure for tuning automatic controllers with determining a second-order plant model with time delay from two points of a complex frequency response

The problem of obtaining the mathematical model of a plant in the course of adaptively tuning the operating automatic closed-loop control systems is considered. A new method is proposed for calculating the parameters of a model with four free coefficients represented by two inertial sections with a time delay. The model parameters are calculated from the data of experiments on determining two points of a plant??s complex frequency response. The results from checking the performance of the method in combination with obtaining information on the plant dynamics by applying the Fourier transform to the impulse transient response of the system are presented. The PID controller is tuned using a parameter scanning algorithm with directly checking the amplitude-frequency response of the closed-loop system, using which the stability margin can be calculated and different quality criteria can be applied.