Smoothed Functional Algorithm with Norm-limited Update Vector for Identification of Continuous-time Fractional-order Hammerstein Models

Abstract

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods.

Keywords:

• Smoothed functional algorithm
• Continuous-time
• Fractional-order
• Hammerstein model
• Variable identification

Acknowledgment

The highest gratitude is especially extended to the Ministry of Higher Education for the financial assistance provided under Fundamental Research Grant Scheme (FRGS) No. FRGS/1/2022/TK07/UMP/03/8 (University reference RDU220107). Heartfelt appreciation is further directed to University Malaysia Pahang for the monetary and resource assurances under its internal grants from the postgraduate research scheme (PGRS) (PGRS200350).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Malaysian Ministry of Higher Education and University Malaysia Pahang: [FRGS/1/2022/TK07/UMP/03/8 (University reference RDU220107), PGRS200350].

Notes on contributors

RenHao Mok

RenHaoMok is a PhD student in University Malaysia Pahang. He did researches regarding model-free optimization methods in his studies during master's degree. His areas of interest are automation, machine learning and IOT. Corresponding author: E-mail: [email protected].

Mohd Ashraf Ahmad

Mohd Ashraf Ahmad received his degree in BEng electrical mechatronics and master degree in MEng mechatronics and automatic control from University of Technology Malaysia (UTM) in 2006 and 2008, respectively. In 2015, he received PhD in informatics (systems science) from Kyoto University. Currently, he is a senior lecturer in the faculty of Electrical and Electronics Engineering Technology, University Malaysia Pahang (UMP). His current research interests are model-free control, control of mechatronic systems, non-linear system identification and vibration control. He has been serving as associate editor for the International Journal of Electrical and Computer Engineering since 2016, Applications of Modeling and Simulation since 2017, and Journal of Future Robot Life since 2019. E-mail: [email protected]