Limit cycle based identification of two-input two-output systems with time delay

This paper presents an identification algorithm based on relay feedback approach for modelling and identification of a class of multivariable systems with time delay. Owing to nonlinear characteristics exhibited by relay, an unknown system under the asymmetrical relay feedback control yields the sustained oscillatory responses also known as limit cycle oscillations around the reference input. From the obtained system responses, a set of analytical expressions for frequency domain based parameter estimation of unknown system model parameters is proposed. To show the robustness of the proposed identification method when subjected to adverse effects of measurement noise due to presence of faulty sensors at the system output, a noise-free limit cycle measurements are recovered from a Fourier series based curve fitting method and further substituted in the derived set of analytical expressions for modelling and identification of two-input two-output systems in terms of second order plus time delay dynamics. Typical examples from the literature are included to validate the effectiveness and merit of the proposed identification algorithm.