This paper presents a new practical method for PI or PID industrial regu-lator optimal adjustments.This method is well feasible for off-line theoreticaladjustment of a control system and provided for closed loop identification withon-line regulator tuning.The proposed algorithm is based on approximationinversion of s-domain disturbance property of a control system by shiftedChebyshev's series.The PI or PID regulator parameter optimization usings-domain approximation representation of time-domain performance index of acontrol system is exclusively discussed with an example of using the algorit-hm.The introduced method is proved convenient to industrial process withhigh-order mathematical model.And it has both theoretical and engineeringsignificance.