An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer
System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory met...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/6/460 |
| _version_ | 1827737221885591552 |
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| author | Ali Yüce |
| author_facet | Ali Yüce |
| author_sort | Ali Yüce |
| collection | DOAJ |
| description | System identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model. |
| first_indexed | 2024-03-11T02:27:05Z |
| format | Article |
| id | doaj.art-0d205b35dca1487789571876442d4f54 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T02:27:05Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-0d205b35dca1487789571876442d4f542023-11-18T10:29:37ZengMDPI AGFractal and Fractional2504-31102023-06-017646010.3390/fractalfract7060460An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium OptimizerAli Yüce0Department of Electrical and Electronics Engineering, Faculty of Engineering and Natural Sciences, Malatya Turgut Ozal University, Malatya 44200, TurkeySystem identification is an important methodology used in control theory and constitutes the first step of control design. It is known that many real systems can be better characterized by fractional-order models. However, it is often quite complex and difficult to apply classical control theory methods analytically for fractional-order models. For this reason, integer-order models are generally considered in classical control theory. In this study, an alternative approximation method is proposed for fractional-order models. The proposed method converts a fractional-order transfer function directly into an integer-order transfer function. The proposed method is based on curve fitting that uses a quadratic system model and Equilibrium Optimizer (EO) algorithm. The curve fitting is implemented based on the unit step response signal. The EO algorithm aims to determine the optimal coefficients of integer-order transfer functions by minimizing the error between general parametric quadratic model and objective data. The objective data are unit step response of fractional-order transfer functions and obtained by using the Grünwald-Letnikov (GL) method in the Fractional-Order Modeling and Control (FOMCON) toolbox. Thus, the coefficients of an integer-order transfer function most properly can be determined. Some examples are provided based on different fractional-order transfer functions to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of time and frequency responses. It is seen that the proposed method exhibits better model approximation performance and provides a lower order model.https://www.mdpi.com/2504-3110/7/6/460fractional-order modelsinteger-order approximation methodsquadratic systemsGrünwald-Letnikovequilibrium optimizer algorithm |
| spellingShingle | Ali Yüce An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer Fractal and Fractional fractional-order models integer-order approximation methods quadratic systems Grünwald-Letnikov equilibrium optimizer algorithm |
| title | An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer |
| title_full | An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer |
| title_fullStr | An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer |
| title_full_unstemmed | An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer |
| title_short | An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer |
| title_sort | approximation method for fractional order models using quadratic systems and equilibrium optimizer |
| topic | fractional-order models integer-order approximation methods quadratic systems Grünwald-Letnikov equilibrium optimizer algorithm |
| url | https://www.mdpi.com/2504-3110/7/6/460 |
| work_keys_str_mv | AT aliyuce anapproximationmethodforfractionalordermodelsusingquadraticsystemsandequilibriumoptimizer AT aliyuce approximationmethodforfractionalordermodelsusingquadraticsystemsandequilibriumoptimizer |