Analysis of Numerical Methods in Fractional Order Control Systems with Time Delay and Large Time Coefficient

Authors : Ali YUCE, Tufan DOĞRUER, Nusret TAN

Pages : 44-53

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Publication Date : 2018-12-15

Article Type : Research Paper

Abstract :In recent years, fractional calculus has been used frequently in the field of control engineering. One of the main reasons for this is that it models a real world more successfully. However, there are some disadvantages. First, it has complex and tedious mathematical calculations. Second, it does not has general analytical solutions. Namely, computing time responses of fractional order systems is still a big problem. Therefore, integer order approximation methods and some numerical methods are used for computation of impulse and step responses. Furthermore, computation accuracy and computation duration of time responses by using Matlab is also important because the computation duration may be too long for some systems such as systems with large time delay and large inertia. In this paper, computation duration and accuracy of time responses is investigated by testing different numerical approximation method for fractional order control systems with large time coefficient.
Keywords : Fractional order system, Grunwald Letnikov, Fourier series method, inverse Fourier transform method, Time delay, Time coefficient