A metaheuristic optimization approach to discretize the fractional order Laplacian operator without employing a discretization operator

Abstract A single-step procedure to obtain first and higher order discrete-time models in terms of infinite impulse response templates of the fractional order Laplacian operator s α , where 0 α 1 , is proposed in this paper. The Moth Flame Optimization (MFO) algorithm based rational approximations are generated using a discretization operator-free method. Solution accuracy and the convergence performance of MFO are extensively compared with several other advanced evolutionary algorithms. Simulations justify the improved modelling accuracy of the proposed models over the recently published designs. The effects due to the finite word length leading to truncated filter coefficients are also considered, and the design stability robustness is demonstrated. The efficacy of the proposed model as a fractional order proportional-derivative controller is also validated.