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    An Approximation Method for Fractional-Order Models Using Quadratic Systems and Equilibrium Optimizer
    (Mdpi, 2023) Yuce, Ali
    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 Grunwald-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.
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    Analytical Design of PI Controller for First Order Transfer Function Plus Time Delay: Stability Triangle Approach
    (Ieee-Inst Electrical Electronics Engineers Inc, 2023) Yuce, Ali
    In this study, proportional-integral (PI) controller design with a geometric approach for first order time-delayed systems is presented. This method can be expressed as an improved version of the weighted geometric center method. The method is based on calculating the center of gravity of a stability triangle selected inside the stability boundary locus (SBL). Stability boundary is determined along the (k(p), k(i)) axes with the SBL. A stability triangle is formed with the two boundary points of the SBL intersecting the k(p) axis for k(i) = 0 and the point corresponding to the weighted geometric center value of the angular frequency. The center of gravity of the determined stability triangle gives the optimum PI control gains. Also, an analytical solution method for the PI controller design is presented. The proposed method (stability triangle) is examined on numerical examples. The time response performances of the controller calculated with the proposed method and the controllers calculated using the weighted geometric center method were compared. In addition, the comparisons of the PI controller determined by the proposed method and the different controllers selected in the neighborhood of this point are included. Comparisons with the studies in the literature including the PI controller design of the time-delayed first-order open-loop unstable transfer function are presented. As a result, it has been seen that the proposed method determines the parameters that provide optimum system performance in the tested region.
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    System Identification Based on Experimental Technique Using Stability Boundary Locus Method for Linear Fractional Order Systems
    (Springer Heidelberg, 2024) Yuce, Ali
    Fractional calculus is an important mathematical tool that is widely used in control systems. It is established in the literature that fractional order models are more accurate and more effective in system modelling. In this study, an alternative and novel technique is proposed to identify the fractional order time-delayed model of an unknown system. The method is based on obtaining the approximate stability boundary locus (SBL) curve of the unknown system by applying three different experimental tests. Three points on the SBL curve are determined by the experimental tests and then the parameters of the fractional order time-delayed model are computed by solving the nonlinear systems of equation. The system model with double fractional order element plus a time delay is obtained using the proposed method. The proposed method is explained through simulations on a twin rotor system. The proposed method is also used in model order reduction calculation of the higher order transfer functions.