PID Controller Fast Tuning Method

The tuning method presented in the article belongs to the group of frequency -response methods.Only simple explicit formulas are used in a single tuning cycle.The input quantities are r0 -P -controller gain and two arbitrary frequencies out of three (f1, f2, f0), where f1 is the lower and f2 is the upper frequency of the P -controller interval (3 or 1 dB) and f0 is the geometric mean (scale, norm) frequency.The calculated quantities are r-1, r1, where r-1 is I -controller gain and r1 is D -controller gain.The formulas used provide accurate output values, unlike the relationships valid for asymptotic estimates.Asymptotic estimates are very inaccurate for relatively narrow (f2 -f1) intervals of the P -controller.The published method is valid for an ideal PID controller.Using a similar procedure, analogous relations can be derived even if a simple filter is used in the D -controller branch.