Charef Approximation Method for Fractional Order System Models Using Hybrid Fmincon Mayfly Optimization Algorithm
| International Journal of Electronics and Communication Engineering |
| © 2024 by SSRG - IJECE Journal |
| Volume 11 Issue 10 |
| Year of Publication : 2024 |
| Authors : Sanjay Ambadas Patil, Uday Pandit Khot |
10.14445/23488549/IJECE-V11I10P115
How to Cite?
Sanjay Ambadas Patil, Uday Pandit Khot, "Charef Approximation Method for Fractional Order System Models Using Hybrid Fmincon Mayfly Optimization Algorithm," SSRG International Journal of Electronics and Communication Engineering, vol. 11, no. 10, pp. 186-201, 2024. Crossref, https://doi.org/10.14445/23488549/IJECE-V11I10P115
Abstract:
Fractional order calculus in modelling and control applications has been increasingly popular in every scientific field due to its versatility and superiority in various instances. These methods present advantages in frequency response approximation. However, real-world engineering applications require more accurate time responses to implement FO operators. Consequently, the article proposed FO systems’ rational integer order approximate transfer function. This will positively contribute to the realization performance of FO system models in real-world applications. A pole and zero model of the Charef rational approximation method is proposed on a fractional-order transfer function. The poles of the approximate model are unrelated to the order of the integrator. This feature shows the benefits of extending the algorithm to the systems containing various fractional orders. Moreover, numerical examples are given to show the wide applicability of this method and to illustrate the acceptable accuracy for approximations. Further, time responses of FMINCON-based FO derivative models are improved by the Mayfly Optimization Algorithm (MOA). This study analyses the convergence behaviour and magnitude error metrics of the different order FO to improve magnitude response. In addition, the research proposed to optimize the Simulated Annealing (SA) algorithm for the determination of optimal hyper-parameters with custom target values to improve magnitude response. The proposed work is implemented using Matlab software. The analysis process involves selecting key parameters such as fractional order, optimization algorithm settings, and convergence criteria. Validation methods include comparing the results from the proposed approaches with analytical solutions and employing metrics like magnitude error to assess accuracy. The numerical simulations of various test cases are conducted to confirm the effectiveness and robustness of the model. Comparing the analytical and actual solutions demonstrates that the proposed approaches effectively and efficiently investigate complicated nonlinear models. Furthermore, the proposed methodologies control and manipulate the achieved better solutions in a very useful way, providing a simple process to adjust and control the convergence regions of the series solution.
Keywords:
Fractional Order System, Charef Approximation, FMINCON, Mayfly Optimization, Magnitude Error Metrics, Simulated Annealing, and Hyper-Parameters.
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