Optimal design of FIR fractional order differentiator using cuckoo search algorithm

• Published in: Expert systems with applications Vol. 42; no. 7; pp. 3433 - 3449
• Main Authors: Kumar, Manjeet, Rawat, Tarun Kumar
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2015
• Subjects: Computer simulation; Convergence; Cuckoo search algorithm; Design engineering; Differentiators; Fractional order differentiator; Genetic algorithm; Genetic algorithms; Interpolation; Lévy flight; Meta-heuristics; Optimization; Search algorithms; Fractional order differentiator; Cuckoo search algorithm; Genetic algorithm; Meta-heuristics; Lévy flight
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2014.12.020

•A novel weighted least square (WLS) fitness function is adopted.•The proposed method outperforms the GA in terms magnitude and phase error.•The proposed method is superior to the interpolation based methods.•Fast convergence rate is achieved. In this paper, a new meta-heuristic optimization algorithm, called cuckoo search algorithm (CSA) is applied to determine the optimal coefficients of the finite impulse response-fractional order differentiator (FIR-FOD) problem. CSA is based on lifestyle and unique parasitic behavior in egg laying and breeding of some cuckoo species along with Lévy flight behavior of some birds and fruit flies. The CSA is capable of solving linear and nonlinear optimization problems. The proposed CSA method prevents the local minima problem encountered in conventional FIR-FOD design method. A novel weighted least square (WLS) fitness function is adopted to improve the response of the FOD to a great extent. The proposed CSA based method has alleviated from inherent drawbacks of premature convergence and stagnation unlike genetic algorithm (GA). To verify the effectiveness of the proposed FIR-FOD based on the cuckoo search algorithm, different set of initial population is tested by simulation. Simulation results affirm that the proposed fractional order differentiator design approach using CSA outperforms the genetic algorithm in terms design accuracy (magnitude and phase error), fast convergence rate and optimal solution. The simulation results confirmed that the proposed FOD using CSA outperforms the FOD designed using evolutionary algorithm like GA and conventional FOD design methods such as radial basis function (RBF) interpolation method and DCT interpolation method.