Auto-tuning and controller design for unstable time delay processes

A single relay feedback test is used to identify exact model parameters of unstable first order plus delay and second order plus delay transfer functions. It is shown that a limit cycle only exists if the time delay is less than a certain value and that this can be increased by adding PD feedback. A systematic PI-PD and PID controller tuning method, based on standard forms with a variable zero, is developed for unstable processes. The performance of the proposed controllers is shown to be superior to previous methods presented for unstable processes.