This paper concerns the control of a time fractional diffusion system defined in the Riemann–Liouville sense. It is assumed that the system is subject to hysteresis nonlinearity at its input, where the hysteresis is mathematically modeled with the Duhem operator. To compensate the effects of hysteresis nonlinearity, a fractional order Proportional+Integral+Derivative (PID) controller is designed by minimizing integral square error. For numerical computation, the Riemann–Liouville fractional derivative is approximated by the Grünwald–Letnikov approach. A set of algebraic equations arises from this approximation, which can be solved numerically. Performance of the fractional order controllers are analyzed in comparison with integer order controllers by simulation results, and it is shown that the fractional order controllers are more advantageous than the integer ones.
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e-mail: nozdemir@balikesir.edu.tr
e-mail: biskender@balikesir.edu.tr
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April 2010
Research Papers
Fractional Order Control of Fractional Diffusion Systems Subject to Input Hysteresis
Necati Özdemir,
Necati Özdemir
Department of Mathematics,
e-mail: nozdemir@balikesir.edu.tr
Balikesir University
, 10145 Balikesir, Turkey
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Beyza Billur İskender
Beyza Billur İskender
Department of Mathematics,
e-mail: biskender@balikesir.edu.tr
Balikesir University
, 10145 Balikesir, Turkey
Search for other works by this author on:
Necati Özdemir
Department of Mathematics,
Balikesir University
, 10145 Balikesir, Turkeye-mail: nozdemir@balikesir.edu.tr
Beyza Billur İskender
Department of Mathematics,
Balikesir University
, 10145 Balikesir, Turkeye-mail: biskender@balikesir.edu.tr
J. Comput. Nonlinear Dynam. Apr 2010, 5(2): 021002 (5 pages)
Published Online: February 9, 2010
Article history
Received:
January 30, 2009
Revised:
May 20, 2009
Online:
February 9, 2010
Published:
February 9, 2010
Citation
Özdemir, N., and İskender, B. B. (February 9, 2010). "Fractional Order Control of Fractional Diffusion Systems Subject to Input Hysteresis." ASME. J. Comput. Nonlinear Dynam. April 2010; 5(2): 021002. https://doi.org/10.1115/1.4000791
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