System identification with measurement noise compensation based on polynomial modulating function for fractional-order systems with a known time-delay

This study presents a system identification method based on polynomial modulating function for fractional-order systems with a known time-delay involving input and output noises in the time domain. Based on the polynomial modulating function and fractional-order integration by parts, the identified fractional-order differential equation is transformed into an algebraic equation. By using the numerical integral formula, the least squares form for the system identification is obtained. In order to reduce the effect of noises existing in the input and output measurements, the compensation method for the input and output noises is also studied by introducing an auxiliary high-order fractional-order system in the revised identification algorithm. Finally, the effectiveness of the proposed algorithm is verified by the simulation result of an illustrative example and the experimental result of temperature identification for a thermal system.