New improved fractional order differentiator models based on optimized digital differentiators

Different evolutionary algorithms (EAs), namely, particle swarm optimization (PSO), genetic algorithm (GA), and PSO-GA hybrid optimization, have been used to optimize digital differential operators so that these can be better fitted to exemplify their new improved fractional order differentiator counterparts. First, the paper aims to provide efficient 2nd and 3rd order operators in connection with process of minimization of error fitness function by registering mean, median, and standard deviation values in different random iterations to ascertain the best results among them, using all the abovementioned EAs. Later, these optimized operators are discretized for half differentiator models for utilizing their restored qualities inhibited from their optimization. Simulation results present the comparisons of the proposed half differentiators with the existing and amongst different models based on 2nd and 3rd order optimized operators. Proposed half differentiators have been observed to approximate the ideal half differentiator and also outperform the existing ones reasonably well in complete range of Nyquist frequency.