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Limit cycle prediction of a neurocontrol vehicle system based on gain-phase margin analysis

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Abstract

Based on some useful frequency domain methods, this paper proposes a systematic procedure to address the limit cycle prediction of a neural vehicle control system with adjustable parameters. A simple neurocontroller can be linearized by using describing function method firstly. According to the classical method of parameter plane, the stability of linearized system with adjustable parameters is then considered. In addition, gain margin and phase margin for limit cycle generation are also analyzed by adding a gain-phase margin tester into open loop system. Computer simulations show the efficiency of this approach.

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References

  1. Gelb A, Velde WEV (1968) Multiple input describing functions and nonlinear system design. McGraw-Hill, New York

    MATH  Google Scholar 

  2. Siljak DD (1969) Nonlinear systems—the parameter analysis and design. Wiley, New York

    MATH  Google Scholar 

  3. Han KW (1977) Nonlinear control systems—some practical methods. Academic Cultural Company, California

    MATH  Google Scholar 

  4. Miller RK, Michel AN, Krenz GS (1983) On the stability of limit cycles in nonlinear feedback systems: analysis using describing functions. IEEE Trans Circuits Syst CAS-30(9):684–696

    Article  MathSciNet  Google Scholar 

  5. Krenz GS, Miller RK (1986) Qualitative analysis of oscillations in nonlinear control Systems: a describing function approach. IEEE Trans Circuits Syst CAS-33(5):562–566

    Article  MathSciNet  Google Scholar 

  6. Chung SC, Huang SR, Huang JS, Lee EC (2001) Applications of describing functions to estimate the performance of nonlinear inductance. IEE Proc Sci Meas Technol 148(3):108–114

    Article  Google Scholar 

  7. Amato F, Iervolino R, Scala S, Verde L (2001) Category II pilot in–the-loop oscillations analysis from robust stability methods. J Guid Control Dyn 24(3):531–538

    Article  Google Scholar 

  8. Wang QG, Zou B, Lee TH, Bi Q (1997) Auto-tuning of multivariable PID controllers from decentralized relay feedback. Automatica 33(3):319–330

    Article  MATH  MathSciNet  Google Scholar 

  9. Ackermann J, Bunte T (1997) Actuator rate limits in robust car steering control. In: Proceedings of the IEEE conference on decision and control, pp 4726–4731

  10. Gordillo F, Aracil J, Alamo T (1997) Determining limit cycles in fuzzy control systems. In: Proceedings of the IEEE international conference on fuzzy systems, pp 193–198

  11. Kim E, Lee H, Park M (2000) Limit-cycle prediction of a fuzzy control system based on describing function method. IEEE Trans Fuzzy Syst 8(1):11–21

    Article  MathSciNet  Google Scholar 

  12. Delgado A (1998) Stability analysis of neurocontrol systems using a describing function. In: Proceedings of the international joint conference on neural networks, pp 2126–2130

  13. Delgado A, Warwick K, Kambhampati C (1998) Limit cycles in neurocontrolled minirobots. In: Proceedings of the UKACC international conference control, pp 173–177

  14. Siljak DD (1989) Parameter space methods for robust control design: a guide tour. IEEE Trans Automat Contr 34(7):674–688

    Article  MATH  MathSciNet  Google Scholar 

  15. Han KW, Thaler GJ (1966) Control system analysis and design using a parameter space method. IEEE Trans Automat Contr 11(3):560–563

    Article  Google Scholar 

  16. Ackermann J (1980) Parameter space design of robust control systems. IEEE Trans Automat Contr 25(6):1058–1072

    Article  MATH  Google Scholar 

  17. Cavallo A, Maria GE, Verde L (1992) Robust control systems: a parameter space design. J Guid Control Dyn 15(5):1207–1215

    Article  Google Scholar 

  18. Chang CH, Han KW (1990) Gain margins and phase margins for control systems with adjustable parameters. J Guid Control Dyn 13(3):404–408

    Article  MATH  Google Scholar 

  19. Chang CH, Han KW (1989) Gain margin and phase margin analysis of a nuclear reactor control system with multiple transport lags. IEEE Trans Nucl Sci 36(4):1418–1425

    Article  Google Scholar 

  20. Shenton AT, Shafiei Z (1994) Relative stability for control systems with adjustable parameters. J Guid Control Dyn 17(2):304–310

    Article  MATH  Google Scholar 

  21. Chang CH, Chang MK (1994) Analysis of gain margins and phase margins of a nonlinear reactor control system. IEEE Trans Nucl Sci 41(4):1686–1691

    Article  Google Scholar 

  22. Chang MK, Chang CH, Han KW (1993) Gain margins and phase margins for nonlinear control systems with adjustable parameters. In: Proceedings of the IEEE transaction industry and application society conference, pp 2123–2130

  23. Chang YC, Han KW (1998) Analysis of limit cycles for a low flying vehicle with three nonlinearities. J Actual Probl Aviat Aerosp Syst 6(2):38–50

    MathSciNet  Google Scholar 

  24. Wu BF, Perng JW, Chin HI (2005) Limit cycle analysis of nonlinear sampled-data systems by gain-phase margin approach. J Franklin Inst 342(2):175–192

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, 70, Lienhai Road, Kaohsiung, 80424, Taiwan, ROC

    Jau-Woei Perng

  2. Department of Electronic Engineering, Chienkuo Technology University, No. 1, Chieh Shou N. Rd, Changhua City, Taiwan, ROC

    Li-Shan Ma

  3. Institute of Electrical Control Engineering, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu, 300, Taiwan, ROC

    Li-Shan Ma & Bing-Fei Wu

Authors
  1. Jau-Woei Perng
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  2. Li-Shan Ma
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  3. Bing-Fei Wu
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Correspondence to Jau-Woei Perng.

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Perng, JW., Ma, LS. & Wu, BF. Limit cycle prediction of a neurocontrol vehicle system based on gain-phase margin analysis. Neural Comput & Applic 19, 565–571 (2010). https://doi.org/10.1007/s00521-009-0319-2

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  • DOI: https://doi.org/10.1007/s00521-009-0319-2

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