Engineering Mechanics

Proceedings Vol. 31 (2025)

ENGINEERING MECHANICS 2025

Copyright © 2025 Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague

 

Čech V.
pages 45 - 48, full text

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.

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