Series Optimized Fractional Order Low Pass Butterworth Filter

Abstract

The design and realization of fractional-order low-pass Butterworth filter (FOLPBF) for order (1 + α), with 0 < α < 1, optimized using a speed enhanced series combination of two meta-heuristic algorithms, namely cuckoo search algorithm (CSA) and interior search algorithm (ISA), is presented in this paper. This method optimizes both the gain and phase for the FOLPBF with respect to the ideal second-order Butterworth filter. The improvement in CSA → ISA series algorithm is established over standalone optimization using CSA and ISA on the basis of gain error, roll-off error, 3 dB frequency error, magnitude error [including passband error (PE) and stopband error (SE)], phase error, and convergence rate. The performance of the series optimization is demonstrated to be superior to the optimization techniques used in previous literature in terms of roll-off error, 3 dB frequency error, PE, SE, phase error and speed. The transient responses achieved with CSA → ISA series optimization is compared with the ideal response using Simulink simulations.