Rational Approximation and Analog Realization of Fractional Order Transfer Function with Multiple Fractional Powered Terms

Khanra, Munmun; Pal, Jayanta; Biswas, Karabi

doi:10.1002/asjc.565

Cited by 22 publications

(19 citation statements)

References 44 publications

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“…Now comparing with the other approximation methods like Charef [38], Oustaloup [39] and Xue [19], these methods require a higher order of the polynomial and the phase error obtained is also greater than 1 • . Considering the analog realization in [40], it requires three resistors, two capacitors and one op-amp for one pole-zero implementation. For that case, the phase error >1 • and the realization have issues in low frequency operation.…”

Section: Fractional Pimentioning

confidence: 99%

“…Also, in optimal pole-zero analog implementation, it requires three resistors, one op-amp and one capacitor for one pole-zero combination. Thus, it requires fewer components in comparison to the implementation published in [40]. Because of the above advantages, we will use the same for analog implementation of the fractional PID controller.…”

Section: Fractional Pimentioning

confidence: 99%

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Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor

2020

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In this paper, the performance of an analog PI λ D μ controller is done for speed regulation of a DC motor. The circuits for the fractional integrator and differentiator of PI λ D μ controller are designed by optimal pole-zero interlacing algorithm. The performance of the controller is compared with another PI λ D μ controller—in which the fractional integrator circuit employs a solid-state fractional capacitor. It can be verified from the results that using PI λ D μ controllers, the speed response of the DC motor has improved with reduction in settling time ( T s ), steady state error (SS error) and % overshoot (% M p ).

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Section: Fractional Pimentioning

confidence: 99%

Section: Fractional Pimentioning

confidence: 99%

Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor

2020

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“…To further demonstrate the effectiveness of the proposed approach, a fractional-order transfer function (FOTF) reported by Khanra et al (2011;2013) is considered. The FOTF in polynomial form with fractional powers is R(s) = s + 1 10s 3.2 + 185s 2.5 + 288s 0.7 + 1 .…”

Section: Fractional-order Transfer Function (Fotf)mentioning

confidence: 99%

“…This extended method is focused on improving the accuracy of the original proposal. Other approximation algorithms based on the stability boundary locus (Deniz et al, 2016), the vector fitting method (Du et al, 2017), the time moments approach (Khanra et al, 2013), the state space approach (Poinot and Trigeassou, 2003;Krajewski and Viaro, 2011) and the frequency distribution mode (Wei et al, 2014b) have been proposed, too. A key issue with these methods is that they are quite complex and hence difficult to implement.…”

Section: Introductionmentioning

confidence: 99%

Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

Bingi

Ibrahim

Karsiti

et al. 2019

International Journal of Applied Mathematics and Computer Science

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Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results. stable performance, especially for higher-order systems. Moreover, the controller can easily attain the iso-damping property (Monje et al., 2010; Shah and Agashe, 2016). It should be noted that seven different configurations can be achieved with the PI λ D μ controller (i.e., P, PI, PI λ , PD, PD μ , PID and PI λ D μ ) (Xue et al., 2007;Xue, 2017;Monje et al., 2010;Kishore et al., 2018; Shah and Agashe, 2016). However, a key issue with the practical realization or equivalent circuit implementation of such controllers in a finite-dimensional integer-order system is the approximation of the fractional-order parameters. This has generated a lot of interest among researchers recently.For effective approximation of a fractional-order integrator and differentiator in the PI λ D μ controller,

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“…Partial fraction expansion of this approximant transfer function, results in an expression representing: (i) impedance of series combination of N þ 1 parallel RC networks, for Àve a; and (ii) admittance of parallel combination of N þ 1 series RC networks, for positive a. Khanra et al (2013) have demonstrated the realization of fractor Ks a where a can be any arbitrary real 1 There is a difference between FOE and FO system (FOS). FOE is typically the realization of single fractional operator where FOS may include multiple.…”

Section: Realization Of Multi-component Foementioning

confidence: 99%

Realization of Fractional Order Elements

et al. 2017

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Fractional order (FO) element (FOE) is the building block for realization of FO systems, an important research domain. However, the realization of FO system is still a challenge. Till date, no FOE or fractor is available in the market. However, many researchers have developed various types of FOE, multi-component and single component, over past 50 years or more. This paper reviews some significant research work, along with their success and limitations, in the field of FOE realization. Also, it discusses the chronological development and a brief comparative study to present an overall idea on current stage of FOE research to the readers.

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Rational Approximation and Analog Realization of Fractional Order Transfer Function with Multiple Fractional Powered Terms

Cited by 22 publications

References 44 publications

Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor

Hardware Implementation and Performance Study of Analog PIλDμ Controllers on DC Motor

Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

Realization of Fractional Order Elements

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