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

ABSTRACT

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.

KEYWORDS:

• Fractional-order systems
• system identification
• modulating function
• measurement noise
• least squares estimation
• time-delay

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant Number 61304094]; the Scientific Research Fund of Liaoning Provincial Education Department, China [Grant Number L2015194].

Notes on contributors

Zhe Gao

Zhe Gao received his B.S. degree from Shenyang Ligong University, Shenyang, China in 2006. He received his M.S. degree from Northeastern University, Shenyang, China in 2008. Then, he received his Ph.D. degree in Control Theory and Control Engineering from Beijing Institute of Technology, Beijing, China in 2012. He is currently an associate professor in the Department of Electrical Engineering and Automation, College of Light Industry, Liaoning Univeristy, Shenyang, China. His research interests include identification and control for fractional-order systems, sliding mode control and robust control.