Fractional order integrator/differentiator: FPGA implementation and FOPID controller application


This paper introduces two FPGA based design approaches of the fractional order integrator and differentiator using Grünwald Letnikov (GL) definition where fixed window and linear approximation approaches are considered. The main advantage of the linear approximation method is that it reduces the huge memory of the fractional order systems. One of the top applications of fractional calculus is the fractional order Proportional Integral Derivative (FOPID) controller. It has gained a great attention in academic studies and in industrial applications. The proposed approaches have been used as building blocks to implement FOPID controller. Oscilloscope experimental results for several cases are presented for GL and the fractional order PID controller. The proposed designs have been implemented based on Verilog Hardware Description Language (HDL) and realized on Nexys 4 Artix-7 FPGA XC7A100T. Moreover, a comparison between the proposed FPGA Implementation results for the GL operator and previous work has been investigated. © 2018 Elsevier GmbH


Tolba M.F., AboAlNaga B.M., Said L.A., Madian A.H., Radwan A.G.


FPGA; Fractional order; Grünwald-Letnikov; Integrators

Document Type



AEU – International Journal of Electronics and Communications, Vol. 98, PP. 220 to 229, Doi: 10.1016/j.aeue.2018.10.007

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