New tuning formulae for the PI controller applied to processes with integral actions

A new model Gm(s), defined by the four measurable parameters ultimate gain, ultimate frequency, amplitude of ultimate oscillation and dead-time, is obtained from tangent to the Nyquist curve at the critical point. This model represents the generalization of the Ziegler-Nichols process dynamics characterization method, for a large class of stable, integrating and unstable processes Gp(s). In the present paper, by applying time and amplitude scaling technique to the model Gm(s), a new tuning formulae are developed for the PI controller. These tuning formulae guarantee almost optimal performance/robustness tradeoff for a large class of processes with integral action.