Parameter identification of fractional order linear system based on Haar wavelet operational matrix.
Fractional order systems can be more adequate for the description of dynamical systems than integer order models, however, how to obtain fractional order models are still actively exploring. In this paper, an identification method for fractional order linear system was proposed. This is a method based on input-output data in time domain. The input and output signals are represented by Haar wavelet, and then fractional order systems described by fractional order differential equations are transformed into fractional order integral equations. Taking use of the Haar wavelet operational matrix of the fractional order integration, the fractional order linear system can easily be converted into a system of algebraic equation. Finally, the parameters of the fractional order system are determined by minimizing the errors between the output of the real system and that of the identified system. Numerical simulations, involving integral and fractional order systems, confirm the efficiency of the above methodology.
B-DAT, School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China; Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China. Electronic address: lyl_nuist@nuist.edu.cn.
Yuanlu
Y
Li
Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China. Electronic address: 1725932714@qq.com.
Xiao
X
Meng
B-DAT, School of Information and Control, Nanjing University of Information Science & Technology, Nanjing 210044, China; Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China. Electronic address: zhengbochao81@126.com.
Bochao
B
Zheng
Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology, Nanjing University of Information Science & Technology, Nanjing 210044, China. Electronic address: dingyaqing@163.com.
Yaqing
Y
Ding
Fractional order system; Haar wavelet; Operational matrix; System identification