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Dergiler / Journal of New Results in Science / 2018 / Cilt: 7 - Sayı: 3

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

Ali YUCE
Tufan DOĞRUER
Nusret TAN
Sayfa
44–53
Yayın Tarihi
2018-12-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In recent years, fractional calculus has been used frequently in the field of control engineering.
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Temel Bulgular & Veri:One of the main reasons for this is that it models a real world more successfully.
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Sonuç & Katkı: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.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fractional order system · Grunwald-Letnikov · Fourier series method

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.

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Bu Makaleye Atıf Yap

YUCE, A., DOĞRUER, T., TAN, N. (2018). Analysis of Numerical Methods in Fractional Order Control Systems with Time Delay and Large Time Coefficient. Journal of New Results in Science, Cilt: 7 - Sayı: 3, 44–53. https://ajindex.com/articles/777846

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Kaynakça (5)

  1. Atherton, D. P., Tan, N., Yüce, A. 2014. Methods for computing the time response of fractional-order systems. IET Control Theory & Applications, 9(6), 817-830.
  2. Chen, Y., Petras, I., Xue, D. 2009. Fractional order control-a tutorial. Paper presented at the American Control Conference, 2009. ACC'09., 1397-1411.
  3. Das, S. 2007. Functional Fractional Calculus for System Identification and Controls: Springer Publishing Company, Incorporated. Diethelm, K. 2010. The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type: Springer Science & Business Media. Fei, D., Yongjie, Z. 2014. Research on a new feedforward controller of main steam temperature system. Paper presented at the Information and Automation (ICIA), 2014 IEEE International Conference on, 295-300.
  4. Ibrahim, D. 2002. Microcontroller-based temperature monitoring and control: Elsevier. Monje, C. A., Chen, Y., Vinagre, B. M., Xue, D., Feliu-Batlle, V. 2010. Fractional-order systems and controls: fundamentals and applications: Springer Science & Business Media. Nonnenmacher, T., Glöckle, W. 1991. A fractional model for mechanical stress relaxation. Philosophical magazine letters, 64(2), 89-93.
  5. Podlubny, I. 1998. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Vol. 198): Elsevier. Weilbeer, M. 2005. Efficient numerical methods for fractional differential equations and their analytical background: Papierflieger. Xue, D., Chen, Y., Atherton, D. 2009. Linear feedback control: analysis and design with MATLAB. Society for Industrial and Applied Mathematics. Yüce, A., Tan, N. 2017. Examining of Numerical Methods in Time Response Analysis of Fractional Order Systems with Long Settling Time Paper presented at the International Symposium on Mathematical Methods in Engineering (MME2017) (Abstract Book), Ankara.