Optimal approximation of fractional‐order systems with model validation using CFOA

Abstract

Optimal integer-order transfer function approximation of linear time-invariant fractional-order systems (FOS) using a straightforward approach is proposed here. The error between the rational approximant and the FOS (commensurate/noncommensurate/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 CBOoptimised 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.

Optimal approximation of asymmetric type fractional‐order bandpass Butterworth filter using decomposition technique

“…For the FOBBF characterized by 1, the highest powers of the numerator and denominator of the theoretical FO model are ( n 2 + β ) and ( n 1 + n 2 + α + β ), respectively; for α = β = 1, the orders are ( n 2 + 1) and ( n 1 + n 2 + 2). Previous works (e.g., Mahata et al 12,13 ) have shown that optimization techniques achieve better or comparable modeling accuracy with a lower design order as compared with the substitution method. Hence, a starting value of M = ( n 2 + 1) and N = ( n 1 + n 2 + 2) was used to approximate the characteristics of the proposed FOBBF.…”

On the Design of Power Law Filters and Their Inverse Counterparts

“…CFOAs are popular analog signal processing integrated circuits that offer a high slew rate, gain-bandwidth decoupling, and smaller power consumption compared to operational amplifiers [59]. Due to their versatility, CFOAs have been widely employed to implement FO filters [19,32,41,51,60].…”

“…Another design strategy that involves the approximation of FO filter characteristics using the integer order transfer function was also reported in the literature [27]. The integer order approximant can be realized using the field programmable analog array [28], voltage mode operational amplifier [29], switched capacitor [30], operational transconductance amplifier (OTA) [31], and current feedback operational amplifier (CFOA) [32].…”

Electronically Controlled Power-Law Filters Realizations

“…The replacement of the Laplacian operator by its fractional-order counterpart (i.e., s → s α , where 0 < α < 1) has been broadly utilized for transposing integer-order transfer functions into the fractional-order domain [1]. Therefore, the rational approximation of the resulted fractional-order filter functions has gained a significant research interest [2][3][4][5][6].…”