Abstract
Fractional-order filter functions are generalization of rational filter functions, which includes integer order filter functions. Fractional-order filters present advantages of more options in frequency selectivity properties of filters compared to integer order counterparts. This study presents an application of Particle Swarm Optimization (PSO) for IIR filter discretization of fractional-order continuous filter functions. The proposed method enforces particles to search in stable filter search regions and ensures the stability of optimized IIR filter functions that approximate to amplitude response of continues fractional-order filter functions. In this chapter, illustrative filter discretization examples are demonstrated to show results of PSO algorithm and these results are compared with results of Continued Fraction Expansion (CFE) approximation method. Stop band approximation performance is very substantial for band reject filter design. We observed that proposed discretization method can provide better approximation to the amplitude response of fractional-order filter functions at the stop bands compared to CFE approximation method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ates, A., Kavuran, G., Alagoz, B.B., Yeroglu, C.: Improvement of IIR filter discretization for fractional order filter by discrete stochastic optimization. In: 39th International Conference on Telecommunications and Signal Processing, 2016, Vienna (2016)
Ates, A., Alagoz, B.B., Kavuran, G., Yeroglu, C.: Implementation of fractional order filters discretized by modified fractional order darwinian particle swarm optimization. Measurement. 107, 53–164 (2017)
Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Berlin (2008)
Das, S., Majumder, B., Pakhira, A., Pan, I., Gupta, A.: Optimizing continued fraction expansion based IIR realization of fractional order differ-integrators with genetic algorithm. In: 2011 International Conference on Process Automation, Control and Computing (PACC). IEEE, Coimbatore (2011)
Radwan, A.G., Soliman, A.M., Elwakil, A.S.: First-order filters generalized to the fractional domain. J. Circuit Syst. Comp. 17(1), 55–66 (2008)
Freeborn, T., Maundy, B., Elwakil, A.S.: Approximated fractional order Chebyshev lowpass filters. Math. Probl. Eng. 2015, 1–7 (2015)
Chen, Y.Q., Moore, K.L.: Discretization schemes for fractional-order differentiators and integrators. IEEE Trans. Circuit Syst-I. 49(3), 363–367 (2002)
Chen, Y.Q., Vinagre, B.M., Podlubny, I.: Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review. Nonlinear Dyn. 38, 155–170 (2004)
Ren, J., Sun, Z.Z., Dai, W., Cole, K.S., Cole, R.H.: New approximations for solving the caputo-type fractional partial differential equations. Appl. Math. Model. 40(4), 2625–2636 (2016)
Tseng, C.: Design of FIR and IIR fractional order Simpson digital integrators. Signal Process. 87(5), 1045–1057 (2007)
Valerio, D., Costa, J.S.: Time-domain implementation of fractional order controllers. IEEE Proc. Control Theory Appl. 152(5), 539–552 (2005)
Vinagre, B.M., Chen, Y.Q., Petras, I.: Two direct Tustin discretization methods for fractional-order differentiator/integrator. J. Franklin Inst. 340(5), 349–362 (2003)
Zhe, G., Liao, X.: Rational approximation for fractional-order system by particle swarm optimization. Nonlinear Dyn. 67(2), 1387–1395 (2012)
Valle, Y.D., Venayagamoorthy, G.K., Mohagheghi, S., Hernandez, J.C., Harley, R.: Particle swarm optimization: basic concepts, variants and applications in power systems. IEEE Trans. Evol. Comput. 2(2), 171–195 (2008)
Saha, S.K., Kar, R., Mandal, D., Ghoshal, S.P.: Optimal IIR filter design using novel particle swarm optimization technique. 2012. Int. J. Circuits Syst. Signal Process. 6(2), 151–162 (2012)
Heris, M.K.: Particle Swarm Optimization in Matlab. http://yarpiz.com/ (2017). Accessed in Feb 2017
Acknowledgments
This study is based upon works from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Imik, O., Alagoz, B.B., Ates, A., Yeroglu, C. (2019). Fractional Order Filter Discretization by Particle Swarm Optimization Method. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-91065-9_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91064-2
Online ISBN: 978-3-319-91065-9
eBook Packages: EngineeringEngineering (R0)