Implementation of fractional order integrator/differentiator on field programmable gate array

Abstract

Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractional calculus i.e. fractional integrator and derivative, using Grünwald–Letnikov definition, on field programmable gate array (FPGA) in LabVIEW environment. The simulation and hardware implementation results for fractional order integrator and derivative of sinusoid and square waveform signals for some selected fractional orders have been presented. A close agreement between the simulated and the experimental results demonstrated the suitability of FPGA device in fractional order control and signal processing applications. LabVIEW being one of the finest tools for measurement and control, and signal processing applications the fractional order operator implementation is expected to further enhance the capability of the tool to cater to the needs of advanced experimental research employing fractional order operators.

Keywords

• Fractional order integrator
• Fractional order differentiator
• FPGA
• Virtual instrumentation