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Optimal integer‐order transfer function approximation of linear time‐invariant fractional‐order systems (FOS) using a straight‐forward approach is proposed here. The error between the rational approximant and the FOS (commensurate/non‐commensurate/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 CBO‐optimised 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. [ABSTRACT FROM AUTHOR]

A new approach to determine the integer‐order transfer function approximation for α and α + β, where 0 < α, β < 1, fractional‐order analogue filters is presented. Reported works deal with this design problem by using techniques which are non‐optimal. The proposed designs with guaranteed stability are obtained by employing a global search optimisation algorithm called colliding bodies optimisation (CBO). The modelling error is iteratively minimised by CBO in the least‐squares sense directly in the frequency domain. The improved accuracy in the magnitude response of the proposed fractional‐order low pass filters, fractional‐order high pass filters, and fractional‐order band pass filters as compared to the designs based on the Matsuda and the continued fractions expansion‐based techniques is demonstrated. The efficacies of the proposed filters are also validated in SIMULINK platform. [ABSTRACT FROM AUTHOR]

Optimal integer‐order transfer function approximations to model the single fractance element‐based fractional‐order low‐pass filter (FLF) for any arbitrary order α, where, 0 < α < 1, is proposed here. First of all, the integer‐order filter coefficients for FLFs, with α varying from 0.01 to 0.99 in steps of 0.01, are directly obtained by using a metaheuristic algorithm called colliding bodies optimisation. For practical usability, the approximated FLF coefficients are explicitly provided in the form of analytical equations by employing a curve fitting on the optimised coefficients in the second step. The proposed approach provides a simpler design procedure in comparison to the reported literature which approximates the FLF by substituting an integer‐order rational approximation of the sα operator in the transfer function of the ideal FLF. Simulations confirm the superior modelling accuracy of the proposed design over the recent literature. [ABSTRACT FROM AUTHOR]

Optimal integer-order transfer function approximations to model the single fractance element-based fractional-order low-pass filter (FLF) for any arbitrary order α, where, 0 < α < 1, is proposed here. First of all, the integer-order filter coefficients for FLFs, with α varying from 0.01 to 0.99 in steps of 0.01, are directly obtained by using a metaheuristic algorithm called colliding bodies optimisation. For practical usability, the approximated FLF coefficients are explicitly provided in the form of analytical equations by employing a curve fitting on the optimised coefficients in the second step. The proposed approach provides a simpler design procedure in comparison to the reported literature which approximates the FLF by substituting an integer-order rational approximation of the sα operator in the transfer function of the ideal FLF. Simulations confirm the superior modelling accuracy of the proposed design over the recent literature. [ABSTRACT FROM AUTHOR]

This study presents a new approach to design fractional‐order low‐pass Butterworth filters (FOLPBF) in terms of integer‐order rational approximations meeting an accurate magnitude response. A parameter‐independent, metaheuristic optimisation algorithm called colliding bodies optimisation (CBO) is used for this purpose. The CBO‐based optimisation routine determines the optimal values of the coefficients for the proposed integer‐order models for the (1 + α), where, 0 < α < 1, order FOLPBFs. The performance of the proposed filter is examined concerning the passband and the stopband characteristics, solution quality robustness, and the convergence rate. The generic nature of the proposed design approach is also demonstrated. The roll‐off characteristics of the proposed higher orders of FOLPBFs exhibit accurate stopband attenuation behaviour. The proposed designs also achieve the best magnitude responses as compared with state‐of‐the‐art designs published in the recent literature. The proposed models can be practically implemented without using any fractance devices. [ABSTRACT FROM AUTHOR]

This study deals with the implementation of highly accurate, stable, minimum phase, and wideband fractional‐order digital differentiators (FODDs) in terms of infinite impulse response filters using an efficient evolutionary optimisation algorithm called adaptive Gbest‐guided gravitational search algorithm (GGSA). Performance evaluation of GGSA as compared with real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) based designs are carried out in terms of different magnitude and phase response error metrics, solution quality reliability, and convergence speed. Simulation results clearly demonstrate that GGSA significantly outperforms RGA, PSO, and DE in consistently achieving the most accurate FODDs in a computationally efficient manner. The proposed FODDs also significantly outperform all state‐of‐the‐art designs in terms of magnitude responses. [ABSTRACT FROM AUTHOR]

This study presents a novel approach to design wideband infinite impulse response fractional order digital integrators (FODIs) for the half and one‐fourth order integrators based on a parameter independent metaheuristic algorithm called colliding bodies optimisation (CBO). The performance of CBO‐based FODIs have been compared with the designs based on three well‐known benchmark evolutionary optimisation algorithms namely, real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) in terms of robustness, consistency, parameter sensitivity, convergence speed, and computational time. Simulations results confirm that the proposed CBO‐based designed FODIs achieve consistently superior magnitude responses in a computationally efficient manner as compared with the designs based on RGA, PSO, and DE. The proposed CBO‐based FODIs also significantly outperform all state‐of‐the‐art designs reported in literature in terms of two different magnitude response error metrics. This research work underlines the potential of CBO as an efficient optimisation tool for the design of accurate digital approximations to the fractional order integrators. [ABSTRACT FROM AUTHOR]