Modeling of stable and unstable second order systems with time delay

Estimation of stable and unstable second order plus time delay (SOPDT) process model parameters is proposed in this paper by using relay with hysteresis and describing function approximation (DFA) technique. The process models concerned in this paper are assumed to have only real poles. Relay with hysteresis reduces the effect of measurement noise on process model parameters. DFA technique is used to derive mathematical expressions to identify the unknown model parameters. Measurement noise which is an important issue in real time systems, may lead to inaccurate estimation of process model parameters. The effectiveness of the proposed method is studied in the noisy environment. For denoising, Fourier series based curve fitting technique is used. The general usefulness of the proposed method is validated with simulation results.