Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

Jarosław Smoczek

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 4, page 749-759
  • ISSN: 1641-876X

Abstract

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A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.

How to cite

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Jarosław Smoczek. "Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control." International Journal of Applied Mathematics and Computer Science 23.4 (2013): 749-759. <http://eudml.org/doc/262528>.

@article{JarosławSmoczek2013,
abstract = {A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.},
author = {Jarosław Smoczek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {interval mathematics; pole placement method; evolutionary algorithm; fuzzy logic; TSK controller; anti-sway crane control},
language = {eng},
number = {4},
pages = {749-759},
title = {Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control},
url = {http://eudml.org/doc/262528},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Jarosław Smoczek
TI - Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 4
SP - 749
EP - 759
AB - A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.
LA - eng
KW - interval mathematics; pole placement method; evolutionary algorithm; fuzzy logic; TSK controller; anti-sway crane control
UR - http://eudml.org/doc/262528
ER -

References

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  1. Auernig, J.W. and Troger, H. (1987). Time optimal control of overhead cranes with hoisting of the load, Automatica 23(4): 437-447. Zbl0617.93040
  2. Bańka, S., Dworak, P. and Jaroszewski, K. (2013). Linear adaptive structure for control of a nonlinear MIMO dynamic plant, International Journal of Applied Mathematics and Computer Science 23(1): 47-63, DOI: 10.2478/amcs-2013-0005. Zbl1293.93428
  3. Benhidjeb, A. and Gissinger, G.L. (1995). Fuzzy control of an overhead crane performance comparison with classic control, Control Engineering Practice 3(12): 1687-1696. 
  4. Chang, C.-Y. (2006). The switching algorithm for the control of overhead crane, Neural Computing and Applications 15(3-4): 350-358. 
  5. Chang, C.-Y. (2007). Adaptive fuzzy controller of the overhead crane with nonlinear disturbances, IEEE Transactions on Industrial Informatics 3(2): 164-172. 
  6. Chapellat, H., Keel, L.H. and Bhattacharyya, S.P. (1994). External robustness properties of multilinear interval systems, Automatica 30(6): 1037-1042. Zbl0800.93283
  7. Dahleh, M., Tesi, A. and Vicino, A. (1993). An overview of extremal properties for robust control of interval plants, Automatica 29(3): 707-721. Zbl0771.93064
  8. De Jong, K.A., Spears, W.M. and Gordon, D.F. (1993). Using genetic algorithms for concept learning, Machine Learning 13(2-3): 161-188. 
  9. Fang, Y., Ma, B., Wang, P. and Zhang, X. (2012). A motion planning-based adaptive control method for an underactuated crane system, IEEE Transactions on Control Systems Technology 20(1): 241-248. 
  10. Filipic, B., Urbancic, T. and Krizman, V. (1999). A combined machine learning and genetic algorithm approach to controller design, Engineering Applications of Artificial Intelligence 12(4): 401-409. 
  11. Hsu, C.-C., Chang, S.-C. and Yu, C.-Y. (2007). Tolerance design of robust controllers for uncertain interval systems based on evolutionary algorithms, IET Control Theory and Applications 1(1): 244-252. 
  12. Hyla, P. (2012). The crane control systems: A survey, Proceedings of the 17th IFAC International Conference on Methods and Models in Automation and Robotics MMAR, Międzyzdroje, Poland, pp. 505-509. 
  13. Kang, Z., Fujii, S., Zhou, C. and Ogata, K. (1999). Adaptive control of a planar gantry crane by the switching of controllers, Transactions of Society of Instrument and Control Engineers 35(2): 253-261. 
  14. Karajgikar, A., Vaughan, J. and Singhose, W. (2011). Double-pendulum crane operator performance comparing pd-feedback control and input shaping, Proceedings of the ECCOMAS Thematic Conference on Advances in Compuational Multibody Dynamics, Brussels, Belgium, pp. 1-14. 
  15. Kharitonov, V.L. (1978). Asymptotic stability of an equilibrium position of a family of systems of linear differential equations, Differential'nye Uravneniya 14(11): 2086-2088. 
  16. Kijima, Y., Ohtsubo, R., Yamada, S. and Fujikawa, H. (1995). An optimization of fuzzy controller and it's application to overhead crane, Proceedings of the IEEE IECON 21st International Conference on Industrial Electronics, Control, and Instrumentation, Tokyo, Japan, pp. 1508-1513. 
  17. Kimiaghalam, B., Homaifar, A., Bikdash, M. and Dozier, G. (1999). Genetic algorithms solution for unconstrained optimal crane control, Proceedings of the IEEE Congress on Evolutionary Computation, Washington, DC, USA, pp. 2124-2130. 
  18. Kimiaghalan, B., Homaifar, A., Bikdash, M. and Sayyarrodsari, B. (2002). Genetic algorithm based gain scheduling, Proceedings of the Congress on Evolutionary Computation, Greensboro, NC, USA, pp. 540-545. 
  19. Kluska, J. (2006). Transformation lemma on analytical modeling via Takagi-Sugeno fuzzy system and its applications, 8th International Conference on Artificial Intelligence and Soft Computing (ICAISC 2006), Zakopane, Poland, pp. 230-239. 
  20. Kluska, J. (2009). Analytical Methods in Fuzzy Modeling and Control, Studies in Fuzziness and Soft Computing, Vol. 241, Springer-Verlag, Berlin/Heidelberg. Zbl1226.93002
  21. Lee, C.-H., Lee, Y.-H. and Teng, C.-C. (2002). A novel robust PID controllers design by fuzzy neural network, Proceedings of the American Control Conference, Anchorage, AK, USA, pp. 1561-1566. 
  22. Li, X. and Yu, W. (2012). Anti-swing control for an overhead crane with fuzzy compensation, Intelligent Automation and Soft Computing 18(1): 1-11. 
  23. Liu, D., Yi, J. and Tan, M. (2002). Proposal of GA-based two-stage fuzzy control of overhead crane, Proceedings of the IEEE Conference on Computers, Communications, Control and Power Engineering, Beijing, China, pp. 1721-1724. 
  24. Liu, D., Yi, J., Zhao, D. and Wang, W. (2005). Adaptive sliding mode fuzzy control for a two-dimensional overhead crane, Mechatronics 15(5): 505-522. 
  25. Mahfouf, M., Kee, C.H., Abbod, M.F. and Linkens, D.A. (2000). Fuzzy logic-based anti-sway control design for overhead cranes, Neural Computing and Applications 9(1): 38-43. 
  26. Mallan, S., Milanese, M. and Taragna, M. (1997). Robust analysis and design of control systems using interval arithmetic, Automatica 33(7): 1363-1372. Zbl0890.93034
  27. McNichols, H. and Fadali, M.S. (2003). Selecting operating points for discrete-time gain scheduling, Computers and Electrical Engineering 29(2): 289-301. Zbl1006.93550
  28. Mendez, J.A., Acosta, L., Moreno, L., Torres, S. and Marichal, G.N. (1999). An application of a neural self-tuning controller to an overhead crane, Neural Computing and Applications 8(2): 143-150. 
  29. Michalewicz, Z. and Janikow, C.Z. (1991). Handling constraints in genetic algorithm, Proceedings of the 4th International Conference on Genetic Algorithms, San Diego, CA, USA, pp. 151-157. 
  30. Moon, M.S., VanLandingham, H.F. and Beliveau, Y.J. (1996). Fuzzy time optimal control of crane load, Proceedings of the 35th Conference on Decision and Control, Kobe, Japan, pp. 1127-1132. 
  31. Moore, R. (1966). Interval Analysis, Prentice-Hall, Englewood Cliffs, NJ. Zbl0176.13301
  32. Moustafa, K. A. F. (2001). Reference trajectory tracking of overhead cranes, Journal of Dynamic Systems, Measurement, and Control 123(1): 139-141. 
  33. Nakazono, K., Ohnisihit, K. and Kinjot, H. (2007). Load swing suppression in jib crane systems using a genetic algorithm-trained neuro-controller, Proceedings of the International Conference on Mechatronics, Kumamoto, Japan, pp. 1-4. 
  34. Oh, S.-K., Pedrycz, W., Rho, S.-B. and Ahn, T.-C. (2004). Parameter estimation of fuzzy controller and its application to inverted pendulum, Engineering Applications of Artificial Intelligence 17(1): 37-60. 
  35. Sadati, N. and Hooshmand, A. (2006). Design of a gain-scheduling anti-sway controller for tower cranes using fuzzy clustering techniques, Proceedings of the International Conference on Computational Intelligence for Modeling, Control and Automation, Sydney, Australia, p. 172. 
  36. Sakawa, Y. and Shindo, Y. (1982). Optimal control of container cranes, Automatica 18(3): 257-266. Zbl0488.93021
  37. Singer, N., Singhose, W. and Kriikku, E. (1997). An input shaping controller enabling cranes to move without sway, Proceedings of the American Nuclear Society 7th Topical Meeting on Robotics and Remote Systems, Augusta, GA, USA, pp. 225-231. 
  38. Smalko, Z. and Szpytko, J. (2009). Safety in engineering practice, Proceedings of the 17th European Safety and Reliability Conference ESREL, Valencia, Spain, pp. 1231-1237. 
  39. Smith, S.F. (1980). A Learning System Based on Genetic Adaptive Algorithms, Ph.D. thesis, University of Pittsburgh, Pittsburgh, PA. 
  40. Smoczek, J. and Szpytko, J. (2008). A mechatronics approach in intelligent control systems of the overhead traveling cranes prototyping, Information Technology and Control 37(2): 154-158. 
  41. Smoczek, J. and Szpytko, J. (2010). Fuzzy logic approach to the gain scheduling crane control system, Proceedings of the 15th IFAC International Conference on Methods and Models in Automation and Robotics MMAR, Międzyzdroje, Poland, pp. 261-266. 
  42. Smoczek, J. and Szpytko, J. (2011). Design of a fuzzy gain scheduling controller for the anti-sway crane system, Proceedings of the 26th ISPE International Conference on CAD/CAM, Robotics and Factories of the Future, CARSFOF, Kuala Lumpur, Malaysia, pp. 809-818. 
  43. Solihin, M.I., Wahyudi and Legowo, A. (2010). Fuzzy-tuned antiswing control of automatic gantry crane, Journal of Vibration and Control 16(1): 127-145. Zbl1269.70051
  44. Sugeno, M. and Kang, G.T. (1988). Structure identification of fuzzy model, Fuzzy Sets and Systems 28(1): 15-33. Zbl0652.93010
  45. Szpytko, J. and Wozniak, D.A. (2007). To keep operational potential of transport device e-based on reliability indicators, Proceedings of the European Safety and Reliability Conference ESREL, Stavanger, Norway, pp. 2377-2384. 
  46. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its application to modeling and control, IEEE Transactions on Systems, Man and Cybernetics 15(1): 116-132. Zbl0576.93021
  47. Trabia, M.B., Renno, J.M. and Moustafa, K.A.F. (2008). Generalized design of an anti-swing fuzzy logic controller for an overhead crane with hoist, Journal of Vibration and Control 14(3): 319-346. Zbl1229.70087
  48. Warmus, M. (1956). Calculus of approximations, Bulletin de l'Academie Polonaise des Sciences IV(5): 253-259. Zbl0071.12503
  49. Yi, J., Yubazaki, N. and Hirota, K. (2003). Anti-swing and positioning control of overhead traveling crane, Information Sciences 155(1-2): 19-42. 
  50. Young, R.C. (1931). The algebra of many-valued quantities, Mathematische Annalen 104(1): 260-290. Zbl0001.01102
  51. Yu, W., Moreno-Armendariz, A. and Rodriguez, F.O. (2011). Stable adaptive compensation with fuzzy CMAC for an overhead crane, Information Sciences 181(21): 4895-4907. Zbl1250.70015
  52. Zubowicz, T. and Brdyś, M.A. (2013). Stability of softly switched multiregional dynamic output controllers with a static antiwindup filter: A discrete-time case, International Journal of Applied Mathematics and Computer Science 23(1): 65-73, DOI: 10.2478/amcs-2013-0006. Zbl1293.93583

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