Closed-Form Analytical Formulation for Riemann–Liouville-Based Fractional-Order Digital Differentiator Using Fractional Sample Delay Interpolation

2021 ◽  
Author(s):  
Anmol Gupta ◽  
Sanjay Kumar
Keyword(s):  
Closed Form ◽  
Fractional Order ◽  
Analytical Formulation ◽  
Digital Differentiator

Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

2018 ◽  
Vol 27 (08) ◽  
pp. 1850129 ◽  
Author(s):  
Shibendu Mahata ◽  
Suman Kumar Saha ◽  
Rajib Kar ◽  
Durbadal Mandal
Keyword(s):  
Fractional Order ◽  
Optimization Technique ◽  
Phase Response ◽  
Computational Time ◽  
Infinite Impulse Response ◽  
Flower Pollination Algorithm ◽  
Solution Quality ◽  
Digital Differentiator ◽  
Flower Pollination ◽  
Real Coded Genetic Algorithm

This paper presents an efficient approach to design wideband, accurate, stable, and minimum-phase fractional-order digital differentiators (FODDs) in terms of the infinite impulse response (IIR) filters using an evolutionary optimization technique called flower pollination algorithm (FPA). The efficiency comparisons of FPA with real-coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE)-based designs are conducted with respect to different magnitude and phase response error metrics, parametric and nonparametric statistical hypotheses tests, computational time, and fitness convergence. Exhaustive simulation results clearly demonstrate that FPA significantly outperforms RGA, PSO, and DE in attaining the best solution quality consistently. Extensive analysis is also conducted in order to determine the role of control parameters of FPA on the performance of the designed FODDs. The proposed FPA-based FODDs outperform all the designs published in the recent literature with respect to the magnitude responses and also achieve a competitive performance in terms of the phase response.

Liquid Container Filling and Charging

1976 ◽  
Vol 98 (2) ◽  
pp. 730-732
Author(s):  
R. H. Nunn ◽  
E. J. Gibson
Keyword(s):  
Closed Form ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Experimental Results ◽  
Simple Analytical Model ◽  
Liquid Slug ◽  
Analytical Formulation ◽  
Closed Form Solutions

A simple analytical model has been developed to describe the dynamic behavior of a liquid slug as it is rapidly and suddenly rammed into a receiving chamber. Useful closed-form solutions are obtained from approximate versions of the governing relationships. Experimental results indicate the essential correctness of the analytical formulation.

Optimal and accurate design of fractional‐order digital differentiator – an evolutionary approach

2017 ◽  
Vol 11 (2) ◽  
pp. 181-196 ◽  
Author(s):  
Shibendu Mahata ◽  
Suman Kumar Saha ◽  
Rajib Kar ◽  
Durbadal Mandal
Keyword(s):  
Fractional Order ◽  
Evolutionary Approach ◽  
Digital Differentiator ◽  
Accurate Design

An efficient design of finite impulse response — Fractional-order differentiator using shuffled frog leaping algorithm heuristic

2019 ◽  
Vol 18 (01) ◽  
pp. 1941005
Author(s):  
G. S. S. S. S. V. Krishna Mohan ◽  
Yarravarapu Srinivasa Rao
Keyword(s):  
Signal Processing ◽  
Impulse Response ◽  
Fractional Order ◽  
Finite Impulse Response ◽  
Fitness Function ◽  
Infinite Length ◽  
Shuffled Frog Leaping Algorithm ◽  
Digital Differentiator ◽  
Shuffled Frog Leaping ◽  
Fractional Order Differentiator

A fractional-order digital differentiator is employed for the calculation of a time-derivative of the applied signal. In the recent few decades, this particular concept of a fractional derivative has been gaining a lot of attention in various applications concerning engineering, technology and science that includes image processing along with automatic control. Once there has been an effective use for this continuous-time Fractional-Order Differentiator (FOD), the trend in its research is primarily toward using a discrete-time fractional differentiator. All these conventional techniques tend to make use of a unimodal function for approximating an ideal FOD. For these techniques, there is a minimization of the fitness function that is accomplished by the algorithms which are based on the gradient. The fractional-order circuits along with their systems include an emerging area that has a high level of potential in aspects such as the biomedical instrumentation, control or signal processing. A digital differentiator is a tool that is extremely helpful in the determination and estimation of time derivatives of any given signal. Irrespective of the actual type of filter chosen (the Finite Impulse Response (FIR) or the Infinite-Length Impulse Response (IIR)), it is critical to bring down the complexity of computation needed for the implementation of the filter for a certain bandwidth and error of approximation. A metaheuristic algorithm normally has some advantages in the solving of problems which are Non-Deterministic Polynomial (NP)-hard. The Shuffled Frog Leaping Algorithm (SFLA) has been a new heuristic algorithm proposed in this work for the determination of optimal coefficients of the problem of FIR-FOD. A design for fractional-order-based digital differentiator is not a very important topic in research and signal processing.

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