PID tuning using B-parabolas: A tool to translate time domain performance specification into frequency domain performance measures

The paper presents a novel frequency domain PID tuning method to achieve specified maximum overshoot and settling time of the closed-loop step response. The method is applicable for linear stable single-input single-output (SISO) systems even if the mathematical model of the plant is unknown. Tuning rule parameters are based on one suitably chosen point of the plant frequency response obtained by sine-wave signal with specified excitation frequency, and the required stability margin. The main result provided is construction of empirical charts that help converting time-domain performance specifications (in terms of maximum overshoot and settling time) into corresponding frequency domain performance measures (stability margins). The method is applicable for systematic shaping of the closed-loop response of the plant. The new approach has been verified on a set of benchmark examples.