Combining differential evolution and particle swarm optimization to tune and realize fractional-order controllers

Mathematical and Computer Modelling of Dynamical Systems

Volumn 19, Issue 3, 2013, Pages 277-299

  Maione, Guido ^a   Punzi, Antonio ^b  

^a POLITECNICO DI BARI   (Italy)

^b ISS Innovative Software Services GmbH   (Germany)

Author keywords

differential evolution; fractional order controllers; non integer order differintegrators; particle swarm optimization; rational approximation; tuning

Indexed keywords

DIFFERENTIAL EVOLUTION; DIFFERENTIAL EVOLUTION AND PARTICLE SWARM OPTIMIZATIONS; DIFFERINTEGRATORS; FRACTIONAL-ORDER CONTROLLERS; FREQUENCY DOMAIN SIMULATION; PERFORMANCE SPECIFICATIONS; PROPORTIONAL , INTEGRAL AND DERIVATIVE CONTROLLERS; RATIONAL APPROXIMATIONS;

CHAOS THEORY; TUNING;

PARTICLE SWARM OPTIMIZATION (PSO);

EID: 84876291135     PISSN: 13873954     EISSN: 17445051     Source Type: Journal    
DOI: 10.1080/13873954.2012.745006     Document Type: Article

References (59)

1. Yamamoto, S. and Hashimoto, I. Recent status and future needs: The view from Japanese industry. Proceedings of the 4th International Conference on Chemical Process Control CPC IV. February17-221991, South Padre Island, TX. Edited by: Arkun, Y. and Ray, W.H. pp.1-28. New York: American Institute of Chemical Engineers.
2. Chen, Y.Q. and Moore, K.L. 2005. Relay feedback tuning of robust PID controllers with iso-damping property. IEEE Trans. Syst. Man Cybern. B Cybern, 35: 23-31.
3. μ controllers. Proceedings of the 36th IEEE Conference on Decision and Control. December10-121997, San Diego, CA. Edited by: Michel, A.N. pp.4985-4990. Piscataway, NJ: IEEE Press.
4. Chen, Y.Q. Ubiquitous fractional order controls?. Proceedings of the Second IFAC Workshop on Fractional Differentiation and its Applications (IFAC FDA'06). July19-212006, Porto, Portugal. Edited by: Oustaloup, A. Vol. 2, pp.168-173. Elsevier, Amsterdam: The Institute of Engineering of Porto (ISEP). part 1
5. Oldham, K.B. and Spanier, J. 1974. The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order, Vol. 111, New York and London: Academic Press. Mathematics in Science and Engineering
6. Podlubny, I. 1999. Fractional Differential Equations, San Diego: Academic Press.
7. West, B.J., Bologna, M. and Grigolini, P. 2003. Physics of Fractal Operators, New York: Institute for Nonlinear Science, Springer-Verlag.
8. Magin, R.L. 2004. Fractional calculus in bioengineering-Parts 1, 2, 3. Crit. Rev. Biomed. Eng, 32: 1-377.
9. Koeller, R.C. 1984. Application of fractional calculus to the theory of viscoelasticity. ASME J. Appl. Mech, 51(2): 299-307.
10. Manabe, S. 1961. The non-integer integral and its application to control systems. Jap. Inst. Electr. Eng. J, 6(3/4): 83-87.
11. Das, S. and Pan, I. 2012. Fractional Order Signal Processing: Introductory Concepts and Applications, Berlin: Springer Briefs in Applied Science and Technology, Springer.
12. Arena, P., Caponetto, R., Fortuna, L. and Porto, D. 2000. Nonlinear noninteger order circuits and systems-An introduction, in World Scientific Series on Nonlinear Science, Series A, Edited by: Chua, L. Vol. 38, Singapore: World Scientific.
13. Caponetto, R., Fortuna, L. and Porto, D. 2004. A new tuning strategy for non-integer order PID controller. Proceedings of the First IFAC Workshop on Fractional Differentiation and its Application. July19-212004, France. Edited by: Le Mehauté, A., Tenreiro Machado, J. A., Trigeassou, J.C. and Sabatier, J. pp.168-173. ENSEIRB, Bordeaux.
14. Cao, J.Y. and Cao, B.G. 2006. Design of fractional order controller based on particle swarm optimization. Int. J. Contr. Automat. Syst, 4: 775-781.
15. Maione, G., Punzi, A. and Li, K. 2012. Using swarm intelligence for optimization of parameters in approximations of fractional-order operators (accepted), in Swarm Intelligence in Electrical and Electronic Engineering, Edited by: Fornarelli, G. and Mescia, L. Hershey, PA: IGI Global.
16. ν. Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications (FDA 2012). May14-172012, Nanjing, China. Edited by: Chen, W., Sun, H.G. and Baleanu, D. pp.1942-1948. Hohai University.
17. Heaviside, O. 1894. Electromagnetic Theory, Vol. II, London: "The Electrician" Printing and Publishing Co., Ltd.
18. Baleanu, D., Diethelm, K., Scalas, E. and Trujillo, J.J. 2012. Fractional Calculus-Models and Numerical Methods, Vol. 3, London: World Scientific. CNC Series on Complexity, Nonlinearity and Chaos
19. Hilfer, R. 2000. Applications of Fractional Calculus in Physics, Singapore: World Scientific.
20. Oldham, K.B. 2010. Fractional differential equations in electrochemistry. Adv. Eng. Softw, 41: 9-12.
21. Torvik, P.J. and Bagley, R.L. 1984. On the appearance of the fractional derivative in behaviour of real materials. J. Appl. Mech., Trans. ASME, 51(2): 294-298.
22. Bagley, R.L. and Calico, R.A. 1991. Fractional-order state equations for the control of viscoelastic damped structures. J. Guid. Contr. Dynam, 14: 304-311.
23. Borredon, L., Henry, B. and Wearne, S. 1999. Differentiating the non-differentiable-Fractional calculus. Parabola, 35(2): 9-19.
24. Mainardi, F. 1996. Fractional relaxation-oscillation and fractional diffusion wave phenomena. Chaos Solitons Fractals, 7: 1461-1477.
25. Duarte, F.B., Tenreiro Machado, J.A. and Monteiro Duarte, G. 2010. Dynamics of the Dow Jones and the NASDAQ stock indexes. Nonlin. Dyn, 61: 691-705.
26. Saravanan, R. and McWilliams, J.C. 1998. Advective ocean-atmosphere interaction: An analytical stochastic model with implications for decadal variability. J. Clim, 11: 165-188.
27. Anastasio, T.J. 1994. The fractional-order dynamics of brainstem vestibulo-oculomotor neurons. Biol. Cybernet, 72: 69-79.
28. Hartley, T.T., Lorenzo, C.F. and Qammar, H.K. 1995. Chaos in fractional order Chua's system. IEEE Trans. Circ. Syst.-Part I, 42: 485-490.
29. Bode, H.W. 1945. Network Analysis and Feedback Amplifier Design, New York: Van Nostrand.
30. Tustin, A. The design of systems for automatic control of the position of massive objects. Proc. Inst. Electr. Eng. 105. pp.1-57. Part C, Suppl. No. 1
31. Oustaloup, A. 1991. La Commande CRONE. Commande Robuste d'Ordre Non Entièr, Paris: Editions Hermès.
32. Oustaloup, A., Mathieu, B. and Lanusse, P. 1995. The CRONE control of resonant plants: Application to a flexible transmission. Eur. J. Contr, 1: 113-121.
33. Oustaloup, A., Moreau, X. and Nouillant, M. 1996. The CRONE suspension. Contr. Eng. Pract, 4: 1101-1108.
34. Oustaloup, A., Sabatier, J., Lanusse, P., Malti, R., Melchior, P., Moreau, X. and Moze, M. An overview of the CRONE approach in system analysis, modeling and identification, observation and control. Proceedings of the 17th IFAC World Congress. July6-112008, Seoul, Korea. Edited by: Chung, M.J. and Misra, P. pp.14254-14265. Elsevier, Amsterdam
35. Storn, R. and Price, K.V. 1997. Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim, 11: 341-359.
36. μ controllers with an improved differential evolution. Eng. Appl. Artif. Intell, 22: 343-350.
37. Price, K.V., Storn, R.M. and Lampinen, J.A. 2005. Differential Evolution-A Practical Approach to Global Optimization, Berlin: Springer.
38. Das, S., Konar, A. and Chakraborty, U.K. Two improved differential evolution schemes for faster global search. ACM-SIGEVO Proceedings of Genetic and Evolutionary Computation Conference. June25-292005, Washington, DC, USA. pp.991-998. New York: ACM Press.
39. Tenreiro Machado, J.A. 2010. Optimal tuning of fractional controllers using genetic algorithms. Nonlin. Dyn, 62: 447-452.
40. Xue, D., Zhao, C. and Chen, Y.Q. Fractional order PID control of a dc-motor with elastic shaft: A case study. Proceedings of the 2006 American Control Conference. June14-16, Minneapolis, MN, USA. pp.3182-3187. Piscataway, NJ: IEEE Press.
41. Petráš, I. 2009. Fractional-order feedback control of a dc-motor. J. Electr. Eng, 60: 117-128.
42. Li, H., Luo, Y. and Chen, Y.Q. 2010. A fractional order proportional and derivative (FOPD) motion controller: Tuning rule and experiments. IEEE Trans. Contr. Syst. Tech, 18: 516-520.
43. Vinagre, B.M., Podlubny, I., Hernandez, A. and Feliu, V. 2000. Some approximations of fractional order operators used in control theory and applications. J. Frac. Calc. Appl. Anal, 3: 231-248.
44. Chen, Y.Q., Vinagre, B.M. and Podlubny, I. 2004. Continued fraction expansion approaches to discretizing fractional order derivatives-An expository review. Nonlin. Dyn., Special Issue on Fractional Derivatives and Their Applications, 38: 155-170.
45. Barbosa, R.S., Tenreiro Machado, J.A. and Silva, M.F. 2006. Time domain design of fractional differintegrators using least squares. Signal Process, 86: 2567-2581.
46. Maione, G. 2011. High-speed digital realizations of fractional operators in the delta domain. IEEE Trans. Autom. Control, 56: 697-702.
47. Maione, G. Conditions for a class of rational approximants of fractional differentiators/integrators to enjoy the interlacing property. Proceedings of the 18th IFAC World Congress (IFAC WC 2011). 28 August-2 September2011, Milan, Italy. Edited by: Bittanti, S., Cenedese, A. and Zampieri, S. Vol. 18, Elsevier, Amsterdam: Università Cattolica del Sacro Cuore. part 1
48. Maione, G. 2012. Thiele's continued fractions in digital implementation of noninteger differintegrators. Signal Image Video Process, 6: 401-410. Special Issue: Fractional signals and systems (C. M. Ionescu, J. Sabatier, J. A. Tenreiro Machado, eds.)
49. Horowitz, I. 1963. Synthesis of Feedback Systems, New York, London: Academic Press.
50. Sidi, M.J. 2001. Design of Robust Control Systems: From Classical to Modern Practical Approaches, Malbar, FL: Krieger Publishing Company.
51. Kennedy, J. and Eberhart, R.C. Particle swarm optimization. Proceedings of the 4th IEEE International Conference on Neural Networks. 27 November-1 December1995, Perth, Australia. Vol. 4, pp.1942-1948. Washington, DC: IEEE Press.
52. Clerc, M. and Kennedy, J. 2002. The particle swarm-Explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evolut. Comput, 6: 58-73.
53. Shi, Y. and Eberhart, R.C. A modified particle swarm optimizer. Proceedings of IEEE World Congress on Computational Intelligence, The 1998 IEEE International Conference on Evolutionary Computation. May4-91998, Anchorage, AK, USA. Edited by: Simpson, P.C. pp.69-73. Piscataway, NJ: IEEE Press.
54. Shi, Y. and Eberhart, R.C. Empirical study of particle swarm optimization. Proceedings of the IEEE 1999 Congress on Evolutionary Computation. July6-91999, Washington, DC, USA. Edited by: Angeline, P.J., Michalewicz, Z., Schoenauer, M., Yao, X. and Zalzala, A. Vol. 3, pp.1945-1950. Piscataway, NJ: IEEE Press.
55. van den Bergh, F. and Engelbrecht, A.P. 2006. A study of particle swarm optimization particle trajectories. Inf. Sci, 176: 937-971.
56. Chao, O. and Weixing, L. Comparison between PSO and GA for parameters optimization of PID controllers. Proceedings of the 2006 IEEE International Conference on Mechatronics and Automation. June25-282006, Luoyang, China. pp.2471-2475. Piscataway, NJ: IEEE Press.
57. Poli, R. An analysis of publications on particle swarm optimization applications. Tech. Rep. CSM-469. 2007. Department of Computer Science, University of Essex, Colchester, UK, May
58. Eberhart, R.C. and Shi, Y. Comparing inertia weights and constriction factors in particle swarm optimization. Proceedings of the 2000 Congress on Evolutionary Computation. July16-192000, San Diego, CA, USA. Edited by: Zalzala, A., Fonseca, C., Kim, J.H., Smith, A. and Yao, X. pp.84-88. Piscataway, NJ: IEEE Press.
59. Maione, G. 2008. Continued fractions approximation of the impulse response of fractional order dynamic dystems. IET Contr. Theory Appl, 2: 564-572.