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Research Papers

Fractional Order Control of Fractional Diffusion Systems Subject to Input Hysteresis

[+] Author and Article Information
Necati Özdemir1

Department of Mathematics, Balikesir University, 10145 Balikesir, Turkeynozdemir@balikesir.edu.tr

Beyza Billur İskender

Department of Mathematics, Balikesir University, 10145 Balikesir, Turkeybiskender@balikesir.edu.tr

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(2), 021002 (Feb 09, 2010) (5 pages) doi:10.1115/1.4000791 History: Received January 30, 2009; Revised May 20, 2009; Published February 09, 2010; Online February 09, 2010

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 PID controllers are analyzed in comparison with integer order PID controllers by simulation results, and it is shown that the fractional order controllers are more advantageous than the integer ones.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

The PIλDμ control of the fractional order system with input hysteresis

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Figure 2

Duhem hysteresis

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Figure 3

Comparison of the analytical and the numerical solution of the system 18 for α=1

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Figure 4

Contribution of the number of eigenvalues

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Figure 5

The PIλDμ and the PID control of the system 18

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Figure 6

The PIλ and the PI control of the system 18

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Figure 7

The PDμ and the PD control of the system 18

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