Auto-tuning of PID controllers for second order unstable process having dead time

An auto-tuning procedure for PID controllers for a more general class of unstable process that has second-order dynamics is presented. These second-order dynamics are represented by a model having both stable and unstable poles together with an apparent dead time, A biased relay feedback test is used to generate a constant limit cycle for identifying this model. Criterion to distinguish a second-order model from the first-order one is devised. Upon finishing the identification, simple tuning rules are provided to tune the parameters of PID controllers. These simple tuning rules are derived from the authors' previous work regarding controller design for open loop unstable processes.