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

Year 2018, Volume: 7 Issue: 3, 44 - 53, 15.12.2018

Ali Yuce Tufan Doğruer Nusret Tan

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.

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