Identification scheme for fractional Hammerstein models with the delayed Haar wavelet

• Published in: IEEE/CAA journal of automatica sinica Vol. 7; no. 3; pp. 882 - 891
• Main Authors: Kothari, Kajal, Mehta, Utkal, Prasad, Vineet, Vanualailai, Jito
• Format: Journal Article
• Language: English
• Published: Piscataway Chinese Association of Automation (CAA) 01-05-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Biological system modeling; Complexity; Complexity theory; Computational modeling; Delay effects; Integrated circuit modeling; Linear systems; Mathematical models; Matrix methods; Nonlinearity; Numerical models; Parameter estimation; Parameter identification; Robustness (mathematics); Step response; Transfer functions; Wavelet analysis
• ISSN: 2329-9266; 2329-9274
• DOI: 10.1109/JAS.2020.1003093

The parameter identification of a nonlinear Hammerstein-type process is likely to be complex and challenging due to the existence of significant nonlinearity at the input side. In this paper, a new parameter identification strategy for a block-oriented Hammerstein process is proposed using the Haar wavelet operational matrix &#x0028 HWOM &#x0029 . To determine all the parameters in the Hammerstein model, a special input excitation is utilized to separate the identification problem of the linear subsystem from the complete nonlinear process. During the first test period, a simple step response data is utilized to estimate the linear subsystem dynamics. Then, the overall system response to sinusoidal input is used to estimate nonlinearity in the process. A single-pole fractional order transfer function with time delay is used to model the linear subsystem. In order to reduce the mathematical complexity resulting from the fractional derivatives of signals, a HWOM based algebraic approach is developed. The proposed method is proven to be simple and robust in the presence of measurement noises. The numerical study illustrates the efficiency of the proposed modeling technique through four different nonlinear processes and results are compared with existing methods.