Use of squared magnitude function in approximation and hardware implementation of SISO fractional order system

Khanra, Munmun; Pal, Jayanta; Biswas, Karabi

doi:10.1016/j.jfranklin.2013.05.001

Cited by 15 publications

(27 citation statements)

References 32 publications

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“…(iv) A 7th-order CBO-based approximant provides an improved solution quality in comparison with the 11-order model for the oscillatory FOS reported in [22]. (v) While Khanra et al's technique [23] is based on a frequencydomain curve-fitting approach, however, the coefficients of the rational approximant are not directly determined. Rather, a linear equation was solved to find the coefficients of the IOTF from the optimal frequency points.…”

Section: Introductionmentioning

confidence: 99%

“…Rather, a linear equation was solved to find the coefficients of the IOTF from the optimal frequency points. Hence, Khanra et al's technique [23] can be considered as a two-step design technique. Moreover, Khanra et al [23] used a differentiator circuit to realise a zero lying on the real axis of the s-plane.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, Khanra et al's technique [23] can be considered as a two-step design technique. Moreover, Khanra et al [23] used a differentiator circuit to realise a zero lying on the real axis of the s-plane. As pointed out in [23], such circuits might be prone to noise problems.…”

Section: Introductionmentioning

confidence: 99%

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Optimal approximation of fractional‐order systems with model validation using CFOA

Mahata

Kar

Mandal

2019

IET signal process.

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Optimal integer-order transfer function approximation of linear time-invariant fractional-order systems (FOS) using a straightforward approach is proposed here. The error between the rational approximant and the FOS (commensurate/noncommensurate/oscillatory types etc.) is minimised directly in the frequency domain, subject to design stability constraints, by using the colliding bodies optimisation (CBO) algorithm. Comparisons with other well-known metaheuristics regarding the computational time and the design effort expended in parameter tuning justify the efficiency of the proposed method. The CBOoptimised models achieve a superior solution quality regarding both the magnitude and phase responses in comparison to the reported literature. Analogue circuit implementations of the models using the current feedback operational amplifier are also presented. Simulations carried out in OrCAD PSPICE environment validate the practical efficacy of the proposed models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal approximation of fractional‐order systems with model validation using CFOA

Mahata

Kar

Mandal

2019

IET signal process.

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“…[3][4][5][6] Some methods are available that can be used to compute the integer-order approximation of fractional operator. 3,[24][25][26][27][28] The approach to realize analog fractional systems is available in the literature. [25][26][27] Adhikary et al 29 reviewed some significant research work, along with their success and limitations, in the field of fractional circuit realization.…”

Section: Introductionmentioning

confidence: 99%

Unique fractional calculus engineering laboratory for learning and research

Khubalkar

Junghare

Aware

et al. 2018

The International Journal of Electrical Engineering & Educa

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In this paper, a novel prototype laboratory is presented for engineering education, in which experiments are based on the fractional calculus. The prototypes of analog and digital fractional-order proportional-integral-derivative (PID) controllers are built in the laboratory. These fractional-order PID controllers are applied to linear and nonlinear plants to demonstrate the effectiveness of fractional-order calculus in real time. These experiments are designed, developed, and implemented on the analog and digital platforms. These controllers are integrated to control the DC motor, brushless DC motor, and magnetic levitation modules through hardware-in-loop as well as stand-alone systems. The analog type of fractional-order PID implementation is carried out by using passive components (i.e. resistances and capacitances) with an operational amplifier. However, real-time digital implementation is carried out using field-programmable gate array and digital signal processor. This paper describes how the experiments on fractional calculus can be tailored for graduate, undergraduate students’ education and extended for research in this emerging area.

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“…The continuous fraction expansion of (1 + s ±1 ) ± α , α ∈(0,1) and elliptical functions for the equiripple approximation of ± α 90° is used in . In , an approximation is obtained by comparing the square magnitude of the candidate approximate transfer function and the actual fractional order transfer function, at some frequency points in the desired frequency band. The frequency points in the desired frequency range are selected by using a genetic algorithim.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Getting Rational Approximation for Fractional Order Differintegrals

Dhabale¹,

Dive²,

Aware³

et al. 2015

Asian Journal of Control

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In this paper a new algorithm is presented to calculate the poles and zeros to approximate a fractional order (FO) differintegral (s±α,α∈(0,1)) by a rational function on a finite frequency band ω∈(ωl,ωh). The constant phase property of the FO differintegral is the basis for development of the algorithm. Interlacing of real poles and zeros is used to achieve the constant phase. The calculations are done using the asymptotic Bode phase plot. A brief investigation is made to get a good approximation for the Bode phase plot. Two design parameters are introduced to keep the average phase close to the desired phase angle and to keep the error within the allowed bounds. A study is done to empirically understand the relationship between the error and the design parameters. The results thus obtained help in the further calculations. The algorithm is computationally simple and inexpensive, and gives a fairly good approximation of fractance frequency response on the specified frequency band.

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Use of squared magnitude function in approximation and hardware implementation of SISO fractional order system

Cited by 15 publications

References 32 publications

Optimal approximation of fractional‐order systems with model validation using CFOA

Optimal approximation of fractional‐order systems with model validation using CFOA

Unique fractional calculus engineering laboratory for learning and research

A New Method for Getting Rational Approximation for Fractional Order Differintegrals

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