Relay based PI–PD design for stable and unstable FOPDT processes

A simple identification method based on relay feedback test is proposed for stable and unstable first order plus time delay (FOPDT) processes. Initially, a relay in parallel with a proportional controller is applied to an inner feedback controller-stabilized process on the usual manner to induce limit cycle output. From the measurements made on the limit cycle output, two parameters of the FOPDT process model are estimated. The steady state gain of the FOPDT process is assumed to be known a priori. Then, these parameters are used to design a two degree of freedom proportional-integral–proportional-derivative (PI–PD) controller based on the loop phase margin and gain margin criteria. Simulation examples illustrate the effectiveness and the simplicity of the proposed identification and control method.