Analytical Expressions for Modeling and Control of Over-damped SOPDT Transfer Functions with NMP Zero Using Relay Feedback Test

The paper describes a relay feedback based algorithm for identification of over-damped second order plus dead time transfer functions with a NMP zero. Exact analytical expressions for system output under relay test and frequency response points are derived using a single run of biased relay test. Using the proposed method all five unkown parameters of the model can be driven simultaneously. The identified model is used for control applications. A standard PID controller by the direct synthesis approach is designed in order to provide a good disturbance rejection. Reforming the controller structure to a 2DOF one leads to a good set-point tracking also. The algorithm used for controller design lets a compromise between performance and robustness.