PID tuning for integrating and unstable processes

A systematic PI and PID tuning method is developed for integrating and unstable processes. The method, based on a maximum peak-resonance specification, leads to simple tuning parameter expressions and is graphically supported by the Nichols chart. The common characteristic of integrating and processes is that their open-loop response, with the controller in cascade, has a phase maximum. The controller parameters are adjusted such that this maximum is located on the right-most point of the ellipse, corresponding to the maximum peak resonance on the Nichols chart. For these types of processes, making the open-loop frequency-response curve tangent to a specified ellipse is an efficient method of controlling the overshoot, the stability and the dynamics of the system. Charts that give the optimal peak resonance, according to the ITAE criterion, are given. The results obtained with this method are presented for typical design examples. A comparison of the performances of the proposed design settings with those given by earlier workers for unstable processes is presented.