Modulating function-based system identification for a fractional-order system with a time delay involving measurement noise using least-squares method

This study proposes an identification algorithm for a time-delay fractional-order system with the measurement noise via the modulating function approach. The polynomial function is adopted as the modulating function, and the approach to determine the coefficients of the modulating function is provided. By the property of modulating function, the identified fractional-order equation is converted into an algebraic equation. By the recursive least squares estimation algorithm, the estimation method of coefficients is offered. Supposing that the measurement noise in the output signal is the Gauss white noise, a revised identification algorithm is proposed to compensate the effect of measurement noise. Finally, two examples are given to verify the effectiveness of the proposed method.