Efficient design of wideband digital fractional order differentiators and integrators using multi-verse optimizer

• Published in: Applied soft computing Vol. 93; p. 106340
• Main Authors: Ali, Talal Ahmed Ali, Xiao, Zhu, Mirjalili, Seyedali, Havyarimana, Vincent
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-08-2020
• Subjects: [formula omitted]-norm; Digital fractional order differentiator; Digital fractional order integrator; Genetic Algorithm; Metaheuristic; Multi-verse optimizer; Optimization; Particle Swarm Optimization; L1-norm; Multi-verse optimizer; Digital fractional order integrator; Metaheuristic; Genetic Algorithm; Digital fractional order differentiator; Particle Swarm Optimization; Optimization
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2020.106340

In this paper, a novel method is proposed based on combining L1-norm optimally criterion with a recently-proposed metaheuristic called multi-verse optimizer (MVO) to design 2nd–4th order stable, minimum phase and wideband infinite impulse response (IIR) digital fractional order differentiators (DFODs) for the fractional order differentiators (FODs) of one-half, one-third and one-fourth order. To confirm the superiority of the proposed approach, we conduct comparisons of the MVO-based designs with the real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO)-based designs in terms of accuracy, robustness, consistency, and efficiency. The transfer functions of the proposed designs are inverted to obtain new models of digital fractional order integrators (DFOIs) of the same order. A comparative study of the frequency responses of the proposed digital fractional order differentiators and integrators with the ones of the existing models is then conducted. The results demonstrate that the proposed designs yield the optimal magnitude responses in terms of absolute magnitude error (AME) with flat response profiles.
•L1-norm approximation error combined with multi-verse optimizer is proposed for infinite impulse response digital fractional order integrator design.•Multi-verse optimizer (MVO) is used to estimate the global optimum.•Digital fractional order differentiators are derived from their integrators counterparts.•Extensive simulations confirm the superiority of the proposed designs of digital fractional order integrators and differentiators.•A standard time domain function is employed to further illustrate the effectiveness of the proposed approach.