Relaxed Ziegler-Nichols Closed Loop Tuning of PI Controllers” Skogestad, S. Simple analytic rules for model reduction and pid controller tuning

A modification of the PI setting of the Ziegler-Nichols closed loop tuning method is proposed. The modifi-cation is based on a combination of the Skogestad SIMC tuning formulas for “integrator plus time-delay” processes with the Ziegler-Nichols tuning formulas assuming that the process is modeled as an “inte-grator plus time-delay ” process. The resulting PI settings provide improved stability margins compared with those obtained with the original Ziegler-Nichols PI settings. Compared with the well-known Tyreus-Luyben PI settings, the proposed PI settings give improved disturbance compensation. For processes with zero or a negligible time-delay, but with some lags in the form of time-constants, tuning based on ultimate gain and ultimate period may give poor results. Successful PI settings for such processes are proposed