A new view to Ziegler–Nichols step response tuning method: Analytic non-fragility justification

Recently, exploiting the centroids of stability regions (admissible regions) to be used in tuning two-parameter controllers has been considered as an approach to obtain non-fragile two-parameter controllers. Such an approach can be extended for three-dimensional stability spaces (admissible spaces) by considering the center of mass of these spaces in tuning three-parameter controllers. In this paper, the mentioned approach is used to tune PID controllers for controlling integrator plus dead-time (IPDT) and first order plus dead-time (FOPDT) processes. It is shown that the tuning method resulted from this approach is very similar to the Ziegler–Nichols step response tuning method. Consequently, this paper presents an analytic non-fragility justification for the mentioned tuning method.

► The idea of using centroids in tuning is extended for 3D stability spaces.
► This extended idea is applied in tuning PIDs for IPDT and FOPDT processes.
► An analytic non-fragility justification is found for the ZN tuning method.