Parameter identification of fractional order linear system based on Haar wavelet operational matrix
Yuanlu Li1, Xiao Meng2, Bochao Zheng1
1B-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.
ISA Transactions
|September 9, 2015
Summary
This study introduces a novel method for identifying fractional order linear systems using time-domain input-output data. The Haar wavelet approach efficiently converts fractional order differential equations into algebraic equations for parameter determination.
Area of Science:
- Control Systems Engineering
- Applied Mathematics
- Dynamical Systems Theory
Background:
- Fractional order systems offer more accurate modeling of dynamical systems compared to traditional integer order models.
- Developing effective methods for identifying these fractional order models remains an active research area.
Purpose of the Study:
- To propose and validate a novel time-domain identification method for fractional order linear systems.
- To provide a practical approach for obtaining fractional order models from system data.
Main Methods:
- Utilizing Haar wavelets to represent input-output signals in the time domain.
- Transforming fractional order differential equations into fractional order integral equations.
- Employing the Haar wavelet operational matrix for fractional order integration to convert the system into algebraic equations.
Main Results:
- The proposed method successfully transforms fractional order systems into solvable algebraic equations.
- System parameters are determined by minimizing the error between the actual and identified system outputs.
- Numerical simulations demonstrate the efficiency of the methodology for both integral and fractional order systems.
Conclusions:
- The Haar wavelet-based identification method is an efficient technique for determining fractional order linear systems.
- This approach simplifies the complex process of fractional order system identification.
- The validated methodology contributes to the advancement of fractional order system modeling.
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