Online tuning of controllers for an unstable FOPDT process

A single-relay feedback test can be used to identify exact model parameters of an unstable first-order plus delay (FOPDT) transfer function when a limit cycle exists. This is only true if the ratio of time delay to unstable time constant is less than 0.693. It is shown how adding an internal proportional (P) feedback can increase this value. The P controller parameter for the identification is set in terms of the steady-state gain of the process, which is assumed to be known a priori. The tuning of two types of controller is discussed: PI and PI-PD. Two methods of controller tuning are proposed; tuning formulas in terms of the plant model parameters; simple auto-tuning rules based on the single-relay feedback test, where necessary with the P feedback controller. It is also shown that a PD in the inner feedback loop gives a better control than a P controller suggested for controlling unstable process. The proposed identification and control methods are simple and give better performance than previous methods for unstable FOPDT processes.