Partial fraction expansion–based realizations of fractional‐order differentiators and integrators using active filters

2019 ◽  
Vol 47 (4) ◽  
pp. 513-531 ◽  
Author(s):  
Panagiotis Bertsias ◽  
Costas Psychalinos ◽  
Brent J. Maundy ◽  
Ahmed S. Elwakil ◽  
Ahmed G. Radwan
Keyword(s):  
Fractional Order ◽  
Active Filters ◽  
Partial Fraction ◽  
Partial Fraction Expansion

An experimental analog circuit realization of Matsuda’s approximate fractional-order integral operators for industrial electronics

2021 ◽  
Author(s):  
Murat Koseoglu ◽  
Furkan Nur Deniz ◽  
Baris Baykant Alagoz ◽  
Ali Yuce ◽  
Nusret Tan
Keyword(s):  
Fractional Order ◽  
Analog Circuit ◽  
Low Cost ◽  
Electric Circuit ◽  
Partial Fraction ◽  
Circuit Realization ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Performance Improvements ◽  
Low Pass

Abstract Analog circuit realization of fractional order (FO) elements is a significant step for the industrialization of FO control systems because of enabling a low-cost, electric circuit realization by means of standard industrial electronics components. This study demonstrates an effective operational amplifier-based analog circuit realization of approximate FO integral elements for industrial electronics. To this end, approximate transfer function models of FO integral elements, which are calculated by using Matsuda’s approximation method, are decomposed into the sum of low-pass filter forms according to the partial fraction expansion. Each partial fraction term is implemented by using low-pass filters and amplifier circuits, and these circuits are combined with a summing amplifier to compose the approximate FO integral circuits. Widely used low-cost industrial electronics components, which are LF347N opamps, resistor and capacitor components, are used to achieve a discrete, easy-to-build analog realization of the approximate FO integral elements. The performance of designed circuit is compared with performance of Krishna’s FO circuit design and performance improvements are shown. The study presents design, performance validation and experimental verification of this straightforward approximate FO integral realization method.

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