Relay based identification of processes with time delay

General analytical expressions are derived from the analysis of half cycle of the relay response curve for identification of a class of processes with time delay. Using these expressions the parameters of open loop stable, unstable and integrating transfer function models may be estimated making simple measurements on the half cycle of the oscillation. For the first time, the time delay parameter of the process model is calculated from the second derivative of the half cycle data. Models with up to four parameters can be identified by means of a single symmetrical relay experiment. The robustness of the technique is assessed against two forms of introduced error: measurement errors and load disturbances. The limit cycle data in the presence of measurement noise and load disturbance are obtained using the Fourier series based curve fitting with the options of non-linear least squares method and the resetting of the relay height, respectively. Simulation examples illustrate the effectiveness and the simplicity of the proposed method for identification of processes with time delay.