Design of a Low-pass Filter from Fractional Chebyshev Polynomials

This paper introduces a novel magnitude approximation for the fractional-order Chebyshev low-pass filter. The proposed magnitude response is constructed from the fractional Chebyshev polynomials originating from the series solution of fractional-order Chebyshev differential equation. The transfer function of the fractional-order Sallen-Key biquad is used as a prototype for the approximation. To identify the coefficients of the Sallen-Key topology, the flower pollination algorithm (FPA) is used to minimize an objective function representing the sum of relative magnitude error. The optimization problem is executed in MATLAB, and stable solutions are chosen for the implementation. Two different cases are investigated corresponding to filter orders 1.8 and 2.7. LT-Spice is used for circuit simulations, and the Valsa approach is used for fractional-order capacitor approximation. The original magnitude response is compared with the optimized one and the circuit simulation results, and this comparison shows a magnitude error less than 2%. © 2021 IEEE.

Time-domain Li-ion Battery Modeling under Staircase Charging and Discharging

Parameter identification of Li-ion battery models is important for efficiently charge and discharge the most widely used energy storage devices. In this work, we propose a simplified battery model with a parameter identification method for time-domain charging and discharging. Staircase PotentioElectrochemical Impedance Spectroscopy technique (SPEIS) is chosen to characterize the batteries during charging and discharging cycles at different voltage steps values. Marine Predator Algorithm (MPA) is used to identify the proposed model parameters on two commercial Li-ion coin-shaped batteries. The proposed model shows very good matching with the experiments with absolute current error less than 10 4. Hence, the proposed model can be used for real-time applications to predict the battery’s behavior under different operating conditions. © 2021 IEEE.

Low pass filter design based on fractional power chebyshev polynomial

This paper introduces the design procedure for the low pass filter based on Chebyschev polynomials of fractional power of any order. The filter order is considered in intervals of width two. Only the first two intervals are considered along with their pole locus produced by varying the filter order and the magnitude response. A general formula for constructing the filter from its s-plane poles is suggested. Numerical analysis and circuit simulations using MATLAB and Advanced Design System (ADS) based on the proposed design procedure are presented. Good matching between the circuit simulation and the numerical analysis is obtained which proves the reliability of the proposed design procedure. © 2015 IEEE.

Charging and discharging RC? circuit under Riemann-Liouville and Caputo fractional derivatives

In this paper, the effect of non-zero initial condition on the time domain responses of fractional-order systems using Caputo and Riemann-Liouville (RL) fractional definitions are discussed. Analytical formulas were derived for the step and square wave responses of fractional-order RC? circuit under RL and Caputo operators for non-zero initial condition. Moreover, a simulation scheme for fractional state-space systems with non-zero initial condition is introduced. © 2016 IEEE.