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Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method

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Abstract

In this study, we present a Takagi–Sugeno (T–S) fuzzy model for the modeling and stability analysis of oceanic structures. We design a nonlinear fuzzy controller based on a parallel distributed compensation (PDC) scheme and reformulate the controller design problem as a linear matrix inequalities (LMI) problem as derived from the fuzzy Lyapunov theory. The robustness design technique is adopted so as to overcome the modeling errors for nonlinear time-delay systems subject to external oceanic waves. The vibration of the oceanic structure, i.e., the mechanical motion caused by the force of the waves, is discussed analytically based on fuzzy logic theory and a mathematical framework. The end result is decay in the amplitude of the surge motion affecting the time-delay tension leg platform (TLP) system. The feedback gain of the fuzzy controller needed to stabilize the TLP system can be found using the Matlab LMI toolbox. This proposed method of fuzzy control is applicable to practical TLP systems. The simulation results show that not only can the proposed method stabilize the systems but that the controller design is also simplified. The effects of the amplitude damping of the surge motion on the structural response are obvious and work as expected due to the control force.

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Abbreviations

M :

Mass matrix of structure

C :

Damping coefficient matrix of structure

K :

Stiffness matrix of structure

R n :

Real vector space of dimension n

R n×m :

Real matrix space of dimension n × m

A T :

Transpose of matrix A

A > 0:

Matrix A is a positive definite matrix

A ≥ 0:

Matrix A is a positive semi-definite matrix

λ i (A):

i-th eigenvalue of the matrix A

References

  1. Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia

    MATH  Google Scholar 

  2. Chen BS, Tseng CS, Uang HJ (1999) Robustness design of nonlinear dynamic systems via fuzzy linear control. IEEE Trans Fuzzy Syst 7:571–585

    Article  Google Scholar 

  3. Chen CW (2011) Stability analysis and robustness design of nonlinear systems: an NN-based approach. Appl Soft Comput 11(2):2735–2742

    Article  Google Scholar 

  4. Chen CW (2006) Stability conditions of fuzzy systems and its application to structural and mechanical systems. Adv Eng Softw 37:624–629

    Article  Google Scholar 

  5. Chen CW (2009) The stability of an oceanic structure with T-S fuzzy models. Math Comput Simul 80:402–426

    Article  MATH  Google Scholar 

  6. Chen CW (2010) Fuzzy control of interconnected structural systems using the fuzzy Lyapunov method. J Vib Control. doi:10.1177/1077546310379625

  7. Chen CW (2010) Application of fuzzy-model-based control to nonlinear structural systems with time delay: an LMI method. J Vib Control 16:1651–1672

    Article  MathSciNet  Google Scholar 

  8. Chen CW (2010) Modeling and fuzzy PDC control and its application to an oscillatory TLP structure. Math Probl Eng Open Access J. doi:10.1155/2010/120403

  9. Chen CW, Chen PC (2010) GA-based adaptive neural network controllers for nonlinear systems. Int J Innov Comput Inf Control 6:1793–1803

    Google Scholar 

  10. Chen CW, Chen PC, Chiang WL (2010) Stabilization of adaptive neural network controllers for nonlinear structural systems using a singular perturbation approach. J Vib Control. doi:10.1177/1077546309352827

  11. Chen CW, Chiang WL, Tsai CH (2006) Fuzzy Lyapunov method for stability conditions of nonlinear systems. Int J Artif Intell Tools 15:163–171

    Article  Google Scholar 

  12. Chen CW, Lin CL, Tsai CH (2007) A novel delay-dependent criteria for time-delay T-S fuzzy systems using fuzzy Lyapunov method. Int J Artif Intell Tools 16:545–552

    Article  Google Scholar 

  13. Chen CW, Shen CW, Chen CY, Jeng MJ (2010) Stability analysis of an oceanic structure using the Lyapunov method. Eng Comput 27:186–204

    Article  Google Scholar 

  14. Chen CW, Chiang WL, Tsai CH et al (2006) Fuzzy Lyapunov method for stability conditions of nonlinear systems. Int J Artif Intell Tools 15:163–171

    Article  Google Scholar 

  15. Chen CW, Chiang WL, Hsiao FH (2004) Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems. Math Comput Simul 66:523–537

    Article  MathSciNet  MATH  Google Scholar 

  16. Chen CW, Wang HL, Liu FR, Chen TH (2010) Application of project cash management and control for infrastructure. J Mar Sci Technol 18:644–651

    Google Scholar 

  17. Chen CW, Yeh K, Chiang WL, Chen CY, Wu DJ (2007) Modeling, H ∞ control and stability analysis for structural systems using Takagi-Sugeno fuzzy model. J Vib Control 13:1519–1534

    Article  MathSciNet  MATH  Google Scholar 

  18. Chen CW, Yeh Ken, Liu FR (2009) Adaptive fuzzy sliding mode control for seismically excited bridges with lead rubber bearing isolation. Int J Uncertain Fuzziness Knowl Based Syst 17:705–727

    Article  MATH  Google Scholar 

  19. Chen CY, Shen CW, Chen CW, Liu KFR, Jeng MJ (2009) A stability criterion for time-delay tension leg platform systems subjected to external force. China Ocean Eng 23:49–57

    Google Scholar 

  20. Chen CW (2009) Modeling and control for nonlinear structural systems via a NN-based approach. Expert Syst Appl 36:4765–4772

    Article  Google Scholar 

  21. Chen CW, Wang MHL, Lin JW (2009) Managing target the cash balance in construction firms using a fuzzy regression approach. Int J Uncertain Fuzziness Knowl Based Syst 17:667–684

    Article  Google Scholar 

  22. Chen PC, Chen CW, Chiang WL, Lo DC (2011) GA-based decoupled adaptive FSMC for nonlinear systems by a singular perturbation scheme. Neural Comput Appl. doi:10.1007/s00521-011-0540-7

  23. Chen PC, Chen CW, Chiang WL (2008) GA-based fuzzy sliding mode controller for nonlinear systems. Math Probl Eng Open Access J. doi:10.1155/2008/325859

  24. Chen PC, Chen CW, Chiang WL, Yeh K (2009) A novel stability condition and its application to GA-based fuzzy control for nonlinear systems with uncertainty. J Mar Sci Technol 17:293–299

    Google Scholar 

  25. Chen PC, Chen CW, Chiang WL (2011) Linear matrix inequality conditions of nonlinear systems by genetic algorithm-based H ∞ adaptive fuzzy sliding mode controller. J Vib Control 17(2):163–173

    Article  Google Scholar 

  26. Chen PC, Chen CW, Chiang WL (2009) GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems. Expert Syst Appl 36:5872–5879

    Article  Google Scholar 

  27. Chen CY, Lin JW, Lee WI, Chen CW (2010) Fuzzy control for an oceanic structure: a case study in time-delay TLP system. J Vib Control 16:147–160

    Article  MathSciNet  Google Scholar 

  28. Cococcioni M, Guasqui P, Lazzerini B et al (2006) Identification of Takagi-Sugeno fuzzy systems based on multi-objective genetic algorithms. Lect Note Artif Int 3849:172–177

    Google Scholar 

  29. Hsiao FH, Chen CW, Liang YW, Xu SD, Chiang WL (2005) T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays. IEEE Trans Circuits Syst I Regul Pap 52:1883–1893

    Article  Google Scholar 

  30. Hsiao FH, Chen CW, Wu YH, Chiang WL (2005) Fuzzy controllers for nonlinear interconnected TMD systems with external force. J Chin Inst Eng 28:175–181

    Article  Google Scholar 

  31. Hsiao FH, Chiang WL, Chen CW, Xu SD, Wu SL (2005) Application and robustness design of fuzzy controller for resonant and chaotic systems with external disturbance. Int J Uncertain Fuzziness Knowl Based Syst 13:281–295

    Article  MathSciNet  MATH  Google Scholar 

  32. Hsiao FH, Hwang JD, Chen CW, Tsai ZR (2005) Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control. IEEE Trans Fuzzy Syst 13:152–163

    Article  Google Scholar 

  33. Hsieh TY, Wang MHL, Chen CW et al (2006) A new viewpoint of S-curve regression model and its application to construction management. Int J Artif Intell Tools 15:131–142

    Article  Google Scholar 

  34. Li X, de Souza CE (1997) Criteria for robust stability and stabilization of uncertain linear systems with state delay. Automatica 33:1657–1662

    Article  Google Scholar 

  35. Limanond S, Si J (1998) Neural-network-based control design: an LMI approach. IEEE Trans Neural Netw 9:1422–1429

    Article  Google Scholar 

  36. Lin ML, Chen CW (2010) Stability analysis of community and ecosystem hierarchies using the Lyapunov method. J Vib Control. doi:10.1177/1077546310385737

  37. Lin ML, Chen CW (2010) Application of fuzzy models for the monitoring of ecologically sensitive ecosystems in a dynamic semi-arid landscape from satellite imagery. Eng Comput 27:5–19

    Article  Google Scholar 

  38. Lin ML, Chen CW, Wang QB, Cao Y (2009) Fuzzy model-based assessment and monitoring of desertification using MODIS satellite imagery. Eng Comput 26:745–760

    Article  Google Scholar 

  39. Lu LT, Chiang WL, Tang JP et al (2003) Active control for a benchmark building under wind excitations. J Wind Eng Ind Aerodyn 91:469–493

    Article  Google Scholar 

  40. Lu LT, Chiang WL, Tang JP (1998) Application of model reduction and LQG/LTR robust control methodology in active structure control. J Eng Mech ASCE 124:446–454

    Article  Google Scholar 

  41. Sugeno M, Kang GT (1986) Fuzzy modeling and control of multilayer incinerator. Fuzzy Sets Syst 18:329–346

    Article  MATH  Google Scholar 

  42. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15:116–132

    MATH  Google Scholar 

  43. Tanaka K (1996) An approach to stability criteria of neural-network control systems. IEEE Trans Neural Netw 7:629–643

    Article  Google Scholar 

  44. Tanaka K (1995) Stability and stabilization of fuzzy-neural-linear control systems. IEEE Trans Fuzzy Syst 3:438–447

    Article  Google Scholar 

  45. Tanaka K, Wang HO (2001) Fuzzy control systems design and analysis. Wiley, New York

    Book  Google Scholar 

  46. Tanaka K, Sugeno M (1992) Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst 45:135–156

    Article  MathSciNet  MATH  Google Scholar 

  47. Tsai CH, Chen CW, Chiang WL, Lin ML (2008) Application of geographic information system to the allocation of disaster shelters via fuzzy models. Eng Comput Int J Comput Aided Eng Softw 25:86–100

    Google Scholar 

  48. Wang HO, Tanaka K, Griffin MF (1995) Parallel distributed compensation of nonlinear systems by Tanaka-Sugeno fuzzy model. Proc FUZZ IEEE/IFES’95 531–538

  49. Wang H, Tanaka OK, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and design issues. IEEE Trans Fuzzy Syst 4:14–23

    Article  Google Scholar 

  50. Yeh K, Chen CW (2010) Stability analysis of interconnected fuzzy systems using the fuzzy Lyapunov method. Math Probl Eng Open Access J. doi:10.1155/2010/734340

  51. Yeh K, Chen CY, Chen CW (2008) Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method. Appl Math Comput 205:568–577

    Article  MathSciNet  MATH  Google Scholar 

  52. Yeh K, Chiang WL, Juang DS (1996) Application of fuzzy control theory in active control of structures. Int J Uncertain Fuzziness Knowl Based Syst 4:255–274

    Article  MathSciNet  Google Scholar 

  53. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  54. Zhang ZY, Zhou HL, Liu SD et al (2006) An application of Takagi-Sugeno fuzzy system to the classification of cancer patients based on elemental contents in serum samples. Chemometr Intell Lab Syst 82:294–299

    Article  Google Scholar 

Download references

Acknowledgments

The author acknowledges the financial support from the National Science Council of Taiwan, R.O.C., under project number NSC 98-2221-E-366-006-MY2. The authors are also most grateful for the kind assistance of Prof. John MacIntyre, Chief-editor of Neural Computing & Applications, and the constructive suggestions of the anonymous reviewers all of which has led to the making of several corrections and suggestions that have greatly aided us in improving the presentation of this paper.

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  1. Institute of Maritime Information and Technology, National Kaohsiung Marine University, Kaohsiung, 80543, Taiwan

    Cheng-Wu Chen

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Correspondence to Cheng-Wu Chen.

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Chen, CW. Modeling, control, and stability analysis for time-delay TLP systems using the fuzzy Lyapunov method. Neural Comput & Applic 20, 527–534 (2011). https://doi.org/10.1007/s00521-011-0576-8

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