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 un stable process that has second-order dynamics is presented. These second-or der dynamics are represented by a model having both stable and unstable pol es together with an apparent dead time, A biased relay feedback test is use d to generate a constant limit cycle for identifying this model. Criterion to distinguish a second-order model from the first-order one is devised. Up on finishing the identification, simple tuning rules are provided to tune t he parameters of PID controllers. These simple tuning rules are derived fro m the authors' previous work regarding controller design for open loop unst able processes.