Optimizing Continued Fraction Expansion Based IIR Realization of Fractional Order Differ-Integrators with Genetic Algorithm

Das, Saptarshi; Majumder, Basudev; Pakhira, Anindya; Pan, Indranil; Das, Shantanu; Gupta, Amitava

doi:10.1109/pacc.2011.5979043

Cited by 17 publications

(14 citation statements)

References 23 publications

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“…In the parameterized Al-Alaoui transform, the parameter δ could be adjusted to achieve certain optimal digital filter approximation of the fractional-order operator. An objective function is defined in [7], which is to obtain the optimal IIR-type digital filter realization by minimizing the weighted sum of the discrepancies between the responses of the continuous time fractional order filter and its approximate digital filter realization.…”

Section: Discretization Of Fractional-order Operator With Different Omentioning

confidence: 99%

“…Zhu and Zou propose an improved recursive algorithm for fractional-order system solution based on PSE and Tustin operator [6]. Miladinovic and his colleagues use genetic algorithm to minimize the deviation in magtitude and phase responses between the original fractional order element and the rationalized discrete time filter in IIR structure [7]. The discretization methods for fractional-order differentiator are compared based on Tustin operator and three different expansion algorithms in [8].…”

Section: Introductionmentioning

confidence: 99%

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Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders

Zhang¹,

Song²,

Zhao³

et al. 2017

ICA

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This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operator, Tustin operator and Al-Alaoui operator). However, the following simulation results show that the optimal variable parameters are different for different fractional orders. Then the weighted square integral index about the magtitude and phase is defined as the objective functions to achieve the optimal variable parameter for different fractional orders. Finally, the simulation results demonstrate that there are great differences on the optimal variable parameter for differential and integral operators with different fractional orders, which should be attracting more attentions in the design of digital fractional order controller.

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Section: Discretization Of Fractional-order Operator With Different Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders

Zhang¹,

Song²,

Zhao³

et al. 2017

ICA

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“…In the literature, several existing techniques vastly used for direct discretization are power series expansion (PSE) [8,9], continued fraction expansion (CFE) [10][11][12][13][14][15][16][17][18], Taylor series expansion (TSE) [19][20][21][22][23], and numerical integration formulae. The resulting rational approximations can be cut short to any arbitrary 'N' number of terms, which gives the order of resultant fractional order differentiators (FODs) and fractional order integrators (FOIs) after the truncation process.…”

Section: Introductionmentioning

confidence: 99%

Approximations of higher-order fractional differentiators and integrators using indirect discretization

Yadav¹,

Gupta²

2015

Turk J Elec Eng & Comp Sci

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This paper describes new approximations of fractional order integrators (FOIs) and fractional order differentiators (FODs) by using a continued fraction expansion-based indirect discretization scheme. Different tenth-order fractional blocks have been derived by applying three different s-to-z transforms described earlier by Al-Alaoui, namely new two-segment, four-segment, and new optimized four-segment operators. A new addition has been done in the new optimized four-segment operator by modifying it by the zero reflection method. All proposed half (s ±1/2 ) and one-fourth

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“…The main novelty proposed by this paper is to put together unique combination of optimized integer order operators and an accurate approximation technique for configuring their efficient fractional order (fo) operators. The current scenario of design methods for deriving optimal operators [33][34][35][36][37][38][39][40][41], is cumulatively proceeding towards "not so distant" phase of perfect optimization with negligible errors. So, another motivating point behind the approach proposed in this paper is to trespass all disadvantages of existing conventional design methods of FOIs by using refined capabilities of an efficient optimization scheme.…”

Section: Introductionmentioning

confidence: 99%

“…In recent novel advancements, different optimization algorithms, namely, Linear Programming (LP) [33,34], Genetic Algorithm (GA) [35][36][37], Simulated Annealing (SA) [38,39], and pole-zero (PZ) optimization [40,41], have been used for obtaining more refined integer order differintegrators. Jain et al [35] have recently derived optimal models of recursive DIs and DDs by GA algorithm while Upadhyay [41] has developed these operators by analyzing poles and zeros of existing recursive DDs by PZ optimization technique for obtaining better results for frequency responses over wideband of complete frequency spectrum.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

Gupta

Yadav

2013

Journal of Optimization

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Second and third order digital integrators (DIs) have been optimized first using Particle Swarm Optimization (PSO) with minimized error fitness function obtained by registering mean, median, and standard deviation values in different random iterations. Later indirect discretization using Continued Fraction Expansion (CFE) has been used to ascertain a better fitting of proposed integer order optimized DIs into their corresponding fractional counterparts by utilizing their refined properties, now restored in them due to PSO algorithm. Simulation results for the comparisons of the frequency responses of proposed 2nd and 3rd order optimized DIs and proposed discretized mathematical models of half integrators based on them, with their respective existing operators, have been presented. Proposed integer order PSO optimized integrators as well as fractional order integrators (FOIs) have been observed to outperform the existing recently published operators in their respective domains reasonably well in complete range of Nyquist frequency.

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Optimizing Continued Fraction Expansion Based IIR Realization of Fractional Order Differ-Integrators with Genetic Algorithm

Cited by 17 publications

References 23 publications

Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders

Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders

Approximations of higher-order fractional differentiators and integrators using indirect discretization

Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

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