Design and Analysis of Fractional Filters with Complex Orders

Bingi, Kishore; Devan, P. Arun Mozhi; Prusty, B Rajanarayan

doi:10.1109/icepe50861.2021.9404431

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…In Gilmutdinov et al, 9 their work was one of the pioneer studies on the possible realization of fractional order elements with complex fractional order. There has been recent renewed interest in studying these systems 10,11 particularly from a controller design perspective, 12,13 although there were also reports on complex‐order fractional filters in Bingi et al 14 and the modeling of biomedical signals 15 . Notably, and to the best of our knowledge, no circuit synthesis or design examples have yet been proposed for these systems, which is the main objective of this Letter.…”

Section: Introductionmentioning

confidence: 97%

On the possible realization of a complex‐order capacitive impedance and its applications

Elwakil

Psychalinos

Maundy

et al. 2022

Circuit Theory & Apps

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Summary The fractional‐order Laplace operator s±α=false(jωfalse)±α has been used in recent years in many applications including the synthesis of fractional‐order capacitors and inductors as well as in fractional‐order filter design. However, the synthesis and application of fractional‐order impedances with a complex‐order proportional to sfalse(α±jβfalse) have not received similar attention. In this work, we report on the possibility of synthesizing capacitive impedances with complex orders and explain the meaning of such impedances. Applications in realizing a complex order integrator and a complex order high‐pass filter are demonstrated supported by circuit simulation results.

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Section: Introductionmentioning

confidence: 97%

On the possible realization of a complex‐order capacitive impedance and its applications

Elwakil

Psychalinos

Maundy

et al. 2022

Circuit Theory & Apps

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“…Simulation of a third-generation CRONE controller was done to control a wind turbine [46]. Complex order approximation and design of complex order filters and differentiators were studied in [47], [48]. Complex order modelling in biomedical applications and tuning and control have also been studied [49], [50].…”

Section: Introductionmentioning

confidence: 99%

Design of an Optimal Fractional Complex Order PID Controller for Buck Converter

Warrier,

Shah

2023

Journal of Robotics and Control

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Dynamic and robust controllers are the inherent requirement of power electronic converters, which are subjected to dynamic variations and nonlinearities. The effectiveness of fractional order controllers in non-linear system control has been well-established by studies in the past few decades. Various forms of fractional order controllers have been used in power-electronic control. Recent research indicates that complex order controllers, extensions of fractional controllers, are more robust against uncertainties and non-linearities than their integer and fractional order counterparts. Though complex order controllers have been employed in various nonlinear plants, they have not been extensively tested on power electronic applications. Also, the design and tuning of the controller is difficult. This paper investigates the effectiveness of a complex order PID controller on a typical power electronic DC-DC buck converter for the first time. Two types of complex order controllers of the form PI^{a+ib}D^c and PI^{a+ib}D^{c+id} were designed for a power electronic buck converter. The complex order controllers were implemented in Simulink and the optimal tuning of the complex order controller parameters for various performance indices was performed using different optimization algorithms. The Cohort Intelligence algorithm was found to give the most optimal results. Both the complex controllers showed more robustness towards uncertainties than the linear and fractional PID controllers. The PI^{a+ib}D^c controller gave the smoothest and fastest response under non-linearities. The dynamic performance of the complex order controller is the best and can be expected to be useful for more power electronic applications.

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“…Recently, there has been increased research interest in the development of controllers, where the order of their respective stages is a complex number 3–11 . The transfer function of such controller is given by

C false(s false) = K_{p} + \frac{K_{i}}{s^{λ + j ϑ}} + K_{d} s^{μ + j ϕ}, 0 < λ, μ, ϑ, ϕ < 1,

where {

λ, μ

} and {

ϑ, ϕ

} are the real and imaginary parts of the orders, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…A possible solution is based on the least square iterative algorithm for fitting frequency response, which has already been employed in previous works 4–6 . But the problem there is that the derived integer‐order transfer functions are not realizable, due to the negative coefficients in their denominators.…”

Section: Introductionmentioning

confidence: 99%

“…A possible solution is based on the least square iterative algorithm for fitting frequency response, which has already been employed in previous works. [4][5][6] But the problem there is that the derived integer-order transfer functions are not realizable, due to the negative coefficients in their denominators. This problem will be overcome through the procedure introduced in this work, where after a detailed investigation, it was concluded that the order of approximation, as well as the frequency range, must be smaller than those considered in the aforementioned work, and this is not a problem when dealing with most controllers.…”

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confidence: 99%

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Complex‐order controller design examples and their implementation

Nako

Psychalinos

Elwakil

2023

Circuit Theory & Apps

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A systematic method for approximating the complex‐order Laplacian operator by realizable integer‐order transfer functions is presented in this work. The realization is performed by a simple structure where only one active element is used. Thanks to the employment of complex‐order impedances, both integrators and differentiators can be readily implemented by the same core simply by interchanging the associated impedance locations. The validity of the presented concept is verified through simulation and experimental results, using the OrCAD PSpice suite and a Field Programmable Analog array device.

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Design and Analysis of Fractional Filters with Complex Orders

Cited by 7 publications

References 12 publications

On the possible realization of a complex‐order capacitive impedance and its applications

On the possible realization of a complex‐order capacitive impedance and its applications

Design of an Optimal Fractional Complex Order PID Controller for Buck Converter

Complex‐order controller design examples and their implementation

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