Your browser does not support JavaScript!
http://iet.metastore.ingenta.com
1887

access icon free Optimal design of wideband fractional order digital integrator using symbiotic organisms search algorithm

Optimal design of digital rational approximations with α-dependant coefficients to model the fractional order integrator of any arbitrary order α, where α ε (0, 1), is presented in this work. The analytical expressions of the coefficients for the proposed fractional order digital integrators (FODIs) are derived by a two-step method: (a) the coefficients of FODIs for α varying from 0.01 to 0.99 in steps of 0.01 are determined by a meta-heuristic optimisation algorithm called symbiotic organisms search (SOS) and (b) curve fitting is applied on the SOS-optimised coefficients to obtain their generalised expressions. Previous works dealing with the design of FODI based on various meta-heuristic optimisers have considered only a few specific fractional orders; hence, the practical usability of such designs is restricted. This gap provides the motivation for conducting this research. Design quality robustness and convergence consistency of SOS are extensively compared with three other well-known meta-heuristic algorithms. The superior modelling accuracy of the proposed designs is justified by comparing with the recent literature. Simulation results validate the effectiveness of the proposed models as a fractional order proportional–integral controller.

References

    1. 1)
      • 14. Vinagre, B.M., Podlubny, I., Hernandez, A., et al: ‘Some approximations of fractional order operators used in control theory and applications’, J. Fract. Calculus Appl. Anal., 2000, 3, (3), pp. 231248.
    2. 2)
      • 22. Gupta, M., Yadav, R.: ‘Design of improved fractional order integrators using indirect discretization method’, Int. J. Comput. Appl., 2012, 59, (14), pp. 1924.
    3. 3)
      • 30. Kennedy, J., Eberhart, R.: ‘Particle swarm optimization’. Proc. 4th IEEE Int. Conf. on Neural Networks, 1995, vol. 4, pp. 19421948.
    4. 4)
      • 41. Pal, P.S., Kar, R., Mandal, D., et al: ‘An efficient identification approach for stable and unstable nonlinear systems using colliding bodies optimization algorithm’, ISA Trans., 2015, 59, pp. 85104.
    5. 5)
      • 20. Krishna, B.T.: ‘Studies of fractional order differentiators and integrators: a survey’, Signal Process., 2011, 91, (3), pp. 386426.
    6. 6)
      • 42. Derrac, J., Garcia, S., Hui, S., et al: ‘Analyzing convergence performance of evolutionary algorithms: a statistical approach’, Inf. Sci., 2014, 289, pp. 4158.
    7. 7)
      • 26. Cheng, M.Y., Prayogo, D.: ‘Symbiotic organisms search: a new metaheuristic optimization algorithm’, Comput. Struct., 2014, 139, pp. 98112.
    8. 8)
      • 17. Romero, M., de Madrid, A.P., Manoso, C., et al: ‘IIR approximations to the fractional differentiator/integrator using Chebyshev polynomials theory’, ISA Trans., 2013, 52, (4), pp. 461468.
    9. 9)
      • 7. Mohan, P.V.A., Ramachandran, V., Swamy, M.N.S.: ‘Switched capacitor filters: theory, analysis, and design’ (Prentice Hall PTR, New Jersey, USA, 1995).
    10. 10)
      • 34. Cheng, M.-Y., Chiu, C.-K., Chiu, Y.-F., et al: ‘SOS optimization model for bridge life cycle risk evaluation and maintenance strategies’, J. Chin. Inst. Civil. Hydraul. Eng., 2014, 26, (4), pp. 293308.
    11. 11)
      • 12. Visweswaran, G.S., Varshney, P., Gupta, M.: ‘New approach to realize fractional power in z-domain at low frequency’, IEEE Trans. Circuits Syst. II, 2011, 58, (3), pp. 179183.
    12. 12)
      • 39. Mahata, S., Saha, S.K., Kar, R., et al: ‘Optimal and accurate design of fractional order digital differentiator – an evolutionary approach’, IET Signal Process., 2017, 11, (2), pp. 181196.
    13. 13)
      • 38. Abdullahi, M., Ngadi, M.A., Abdulhamid, S.M.: ‘Symbiotic organism search optimization based task scheduling in cloud computing environment’, Future Gener. Comput. Syst., 2016, 56, pp. 640650.
    14. 14)
      • 15. Tseng, C.C.: ‘Design of FIR and IIR fractional order Simpson digital integrators’, Signal Process., 2007, 87, (5), pp. 10451057.
    15. 15)
      • 36. Tran, D.H., Cheng, M.Y., Prayogo, D.: ‘A novel multiple objective symbiotic organisms search (MOSOS) for time–cost–labor utilization tradeoff problem’, Knowl. Based Syst., 2016, 94, pp. 132145.
    16. 16)
      • 9. Al-Alaoui, M.A.: ‘Discretization methods of fractional parallel PID controllers’. Proc. 16th Int. Conf. on Electronic Circuits and Systems (ICECS), 2009, pp. 327330.
    17. 17)
      • 13. Vinagre, B.M., Chen, Y.Q., Petras, I.: ‘Two direct Tustin discretization methods for fractional-order differentiator/integrator’, J. Frankl. Inst., 2003, 340, (5), pp. 349362.
    18. 18)
      • 29. Holland, J.H.: ‘Adaptation in natural and artificial systems’ (MIT Press, Cambridge, 1992).
    19. 19)
      • 16. Chen, Y.Q., Moore, K.L.: ‘Discretization schemes for fractional-order differentiators and integrators’, IEEE Trans. Circuits Syst. I, Fundam. Theor. Appl., 2002, 49, (3), pp. 363367.
    20. 20)
      • 4. Mocak, J., Janiga, I., Rievaj, M.: ‘The use of fractional differentiation or integration for signal improvement’, Meas. Sci. Rev., 2007, 7, (5), pp. 3942.
    21. 21)
      • 5. Bruton, L.T.: ‘Low-sensitivity digital ladder filters’, IEEE Trans. Circuits Syst., 1975, 22, (3), pp. 168176.
    22. 22)
      • 43. Abramowitz, M., Stegun, I.A.: ‘Handbook of mathematical functions’ (Dover Publications, New York, 1974).
    23. 23)
      • 23. Gupta, M., Yadav, R.: ‘Optimization of integer order integrators for deriving improved models of their fractional counterparts’, J. Optim., 2013, 2013, (article id: 142390), pp. 111.
    24. 24)
      • 33. Cheng, M.Y., Prayogo, D., Tran, D.H.: ‘Optimizing multiple-resources leveling in multiple projects using discrete symbiotic organisms search’, J. Comput. Civil Eng., 2015, 30, (3), pp. 19.
    25. 25)
      • 40. Mahata, S., Saha, S.K., Kar, R., et al: ‘Optimal design of wideband digital integrators and differentiators using hybrid flower pollination algorithm’, Soft Comput., 2017, doi. 10.1007/s00500-017-2595-6.
    26. 26)
      • 11. Chen, Y.Q., Vinagre, B.M., Podlubny, I.: ‘Continued fraction expansion approaches to discretizing fractional order derivatives – an expository review’, Nonlinear Dyn., 2004, 38, (1–4), pp. 155170.
    27. 27)
      • 25. Das, S., Majumder, B., Pakhira, A., et al: ‘Optimizing continued fraction expansion based IIR realization of fractional order differ-integrators with genetic algorithm’. Proc. Int. Conf. on Process Automation, Control and Computing, Coimbatore, India, 2011, pp. 16.
    28. 28)
      • 1. Oldham, K.B., Spanier, J.: ‘The fractional calculus’ (Academic Press, New York, 1974).
    29. 29)
      • 31. Storn, R., Price, K.: ‘Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces’, J. Glob. Optim., 1997, 11, (4), pp. 341359.
    30. 30)
      • 28. Kemp, R.: ‘Fundamentals of the average case analysis of particular algorithms’ (John Wiley & Sons Ltd and B.G. Teubner, New York, 1984).
    31. 31)
      • 3. Wu, J.-X., Li, C.-M., Ho, Y.-R., et al: ‘Peripheral arterial stenosis screening with a fractional-order integrator and info-gap decision-making’, IEEE Sens. J., 2016, 16, (8), pp. 26912700.
    32. 32)
      • 10. Ferdi, Y.: ‘Computation of fractional order derivative and integral via power series expansion and signal modeling’, Nonlinear Dyn., 2006, 46, (1–2), pp. 115.
    33. 33)
      • 27. Bosman, P.A.N.: ‘On gradients and hybrid evolutionary algorithms for real-valued multiobjective optimization’, IEEE Trans. Evol. Comput., 2012, 16, (1), pp. 5169.
    34. 34)
      • 24. Yadav, R., Gupta, M.: ‘New improved fractional order integrators using PSO optimization’, Int. J. Electron., 2015, 102, (3), pp. 490499.
    35. 35)
      • 19. Krishna, B.T., Reddy, K.V.V.S.: ‘Design of fractional order digital differentiators and integrators using indirect discretization’, Fract. Calc. Appl. Anal., 2008, 11, (2), pp. 143151.
    36. 36)
      • 6. Davis, R., Trick, T.: ‘Optimum design of low-pass switched capacitor ladder filters’, IEEE Trans. Circuits Syst., 1980, 27, (6), pp. 522527.
    37. 37)
      • 8. Laker, K., Ghausi, M.: ‘Modern filter design: active RC and switched capacitor’ (SciTech Publishing Inc., North Carolina, USA, 2003).
    38. 38)
      • 21. Yadav, R., Gupta, M.: ‘Approximations of higher-order fractional differentiators and integrators using indirect discretization’, Turk. J. Electr. Eng. Comput. Sci., 2015, 23, (3), pp. 666680.
    39. 39)
      • 18. Barbosa, R.S., Machado, J.A.T., Silva, M.F.: ‘Time domain design of fractional differintegrators using least-squares’, Signal Process., 2006, 86, (10), pp. 25672581.
    40. 40)
      • 32. Saha, D., Datta, A., Das, P.: ‘Optimal coordination of directional overcurrent relays in power systems using symbiotic organism search optimisation technique’, IET Gener. Transm. Distrib., 2016, 10, (11), pp. 26812688.
    41. 41)
      • 35. Panda, A., Pani, S.: ‘A symbiotic organisms search algorithm with adaptive penalty function to solve multi-objective constrained optimization problems’, Appl. Soft Comput., 2016, 46, pp. 344360.
    42. 42)
      • 37. Secui, D.C.: ‘A modified symbiotic organisms search algorithm for large scale economic dispatch problem with valve-point effects’, Energy, 2016, 113, pp. 366384.
    43. 43)
      • 44. Castillo-Garcia, F.J., Millan-Rodriguez, A.S., Feliu-Batlle, V., et al: ‘Fractional-order PI control of first order plants with guaranteed time specifications’, J. Appl. Math, 2015, 2013, (article ID 197186), pp. 111.
    44. 44)
      • 2. West, B.J., Bologna, M., Grigolini, P.: ‘Physics of fractal operators’ (Springer Verlag, New York, 2003).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cds.2017.0162
Loading

Related content

content/journals/10.1049/iet-cds.2017.0162
pub_keyword,iet_inspecKeyword,pub_concept
6
6
Loading
This is a required field
Please enter a valid email address