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From fuzzy center average defuzzifier (CAD) to fuzzy lookup table controller (FLTC) with an efficient Heaviside search algorithm (HSA)

  • Chi-Hsu WangEmail author
  • Kar-Chun Hor
Original Article
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Abstract

This paper proposes an alternate interpretation of the traditional lookup table controller via the center average defuzzifier (CAD) in fuzzy set theory with a set of disjoint block pulse membership functions (DBPMFs). The DBPMFs with CAD can be proved to be equivalent to the traditional fuzzy lookup table controller (FLTC). Further, a new Heaviside search algorithm (HSA) is also proposed to implement the FLTC in a more efficient way. The HSA is to find the indices for every fuzzy input variable independently, in order to speed up the table-searching process. The computational complexity of our new HSA is far less than the complexity of the traditional linear search algorithm (LSA), where HSA is the sum of Ri, where Ri is the number of membership functions for ith input variable in FLTC. The average computational complexity in LSA is the product of Ri divided by 2. The HSA also reduces the complexity of coding significantly in the same order as the comparison of computation complexities between HSA and LSA. The balancing of the inverted pendulum system is adopted as the benchmark to show the feasibility and efficiency of this new FLTC and HSA.

Keywords

Fuzzy logic controller (FLC) Fuzzy lookup table controller (FLTC) Heaviside search algorithm (HSA) Inverted pendulum system (IPS) 
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Notes

Acknowledgements

This work was supported by the Ministry of Science and Technology of Taiwan, R.O.C., under Award Number 106-2221-E-062.

References

  1. 1.
    Sugeno M (1985) Industrial applications of fuzzy control. Elsevier, AmsterdamzbMATHGoogle Scholar
  2. 2.
    Yager RR, Zadeh LA (1992) An introduction to fuzzy logic applications in intelligent systems. Kluwer Academic, BostonCrossRefzbMATHGoogle Scholar
  3. 3.
    Wang C-H, Huang D-Y (2013) A new intelligent fuzzy controller for nonlinear hysteretic electronic throttle in modern intelligent automobiles. IEEE Trans Ind Electron 60(l6):2332–2345CrossRefGoogle Scholar
  4. 4.
    Ray KS, Majumder DD (1985) Fuzzy logic control of a nonlinear multivariable steam generating unit using decoupling theory. IEEE Trans Syst Man Cybern 4:539–558CrossRefGoogle Scholar
  5. 5.
    Ali MH, Murata T, Tamura J (2004) The effect of temperature rise of the fuzzy logic-controlled braking resistors on transient stability. IEEE Trans Power Syst 19(2):1085–1095CrossRefGoogle Scholar
  6. 6.
    Schouten NJ, Salman MA, Kheir NA (2002) Fuzzy logic control for parallel hybrid vehicles. IEEE Trans Control Syst Technol 10(3):460–468CrossRefGoogle Scholar
  7. 7.
    Duan X-G, Deng H, Li H-X (2013) A saturation-based tuning method for fuzzy PID controller. IEEE Trans Ind Electron 60(11):5177–5185CrossRefGoogle Scholar
  8. 8.
    Gil P, Lucena C, Cardoso A, Palma LB (2015) Gain tuning of fuzzy PID controllers for MIMO systems: a performance-driven approach. IEEE Trans Fuzzy Syst 23(4):757–768CrossRefGoogle Scholar
  9. 9.
    Tang K-S, Man KF, Chen G, Kwong S (2001) An optimal fuzzy PID controller. IEEE Trans Ind Electron 48(4):757–765CrossRefGoogle Scholar
  10. 10.
    Meza JL, Santibáñez V, Soto R, Llama MA (2012) Fuzzy self-tuning PID semiglobal regulator for robot manipulators. IEEE Trans Ind Electron 59(6):2709–2717CrossRefGoogle Scholar
  11. 11.
    Choi HH, Yun HM, Kim Y (2015) Implementation of evolutionary fuzzy PID speed controller for PM synchronous motor. IEEE Trans Industr Inform 11(2):540–547CrossRefGoogle Scholar
  12. 12.
    Leu Y-G, Lee T-T, Wang W-Y (1999) Observer-based adaptive fuzzy-neural control for unknown nonlinear dynamical systems. IEEE Trans Syst Man Cybern B Cybern 29(5):583–591CrossRefGoogle Scholar
  13. 13.
    Wang C-H, Liu H-L, Lin T-C (2001) Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems. In: The 10th IEEE international conference on fuzzy systems, 2001. IEEE, pp 622–625Google Scholar
  14. 14.
    Wai R-J, Muthusamy R (2014) Design of fuzzy-neural-network-inherited backstepping control for robot manipulator including actuator dynamics. IEEE Trans Fuzzy Syst 22(4):709–722CrossRefGoogle Scholar
  15. 15.
    Shen J-C (2001) Fuzzy neural networks for tuning PID controller for plants with underdamped responses. IEEE Trans Fuzzy Syst 9(2):333–342CrossRefGoogle Scholar
  16. 16.
    Pomares H, Rojas I, Ortega J, Gonzalez J, Prieto A (2000) A systematic approach to a self-generating fuzzy rule-table for function approximation. IEEE Trans Syst Man Cybern B Cybern 30(3):431–447CrossRefGoogle Scholar
  17. 17.
    Brando G, Dannier A, Del Pizzo A, Rizzo R, Spina I (2015) Generalised look-up table concept for direct torque control in induction drives with multilevel inverters. IET Electr Power Appl 9(8):556–567CrossRefGoogle Scholar
  18. 18.
    Rad AB, Chan P, Lo WL, Mok C (2003) An online learning fuzzy controller. IEEE Trans Ind Electron 50(5):1016–1021CrossRefGoogle Scholar
  19. 19.
    Meher PK (2010) An optimized lookup-table for the evaluation of sigmoid function for artificial neural networks. In: 18th IEEE/IFIP on VLSI system on chip conference (VLSI-SoC), 2010. IEEE, pp 91–95Google Scholar
  20. 20.
    Razali AM, Rahman M, George G, Rahim NA (2015) Analysis and design of new switching lookup table for virtual flux direct power control of grid-connected three-phase PWM AC–DC converter. IEEE Trans Ind Appl 51(2):1189–1200CrossRefGoogle Scholar
  21. 21.
    Hwang C-L (2008) Microprocessor-based fuzzy decentralized control of 2-D piezo-driven systems. IEEE Trans Ind Electron 55(3):1411–1420CrossRefGoogle Scholar
  22. 22.
    Wang L-X (1997) A course in fuzzy systems. Prentice-Hall International, Inc, Upper Saddle RiverGoogle Scholar
  23. 23.
    Wang CH, Wen JS (2008) On the equivalence of a table lookup (TL) technique and fuzzy neural network (FNN) with block pulse membership functions (BPMFs) and its application to water injection control of an automobile. IEEE Trans Syst Man Cybern Part C Appl Rev 38(4):574–580CrossRefGoogle Scholar
  24. 24.
    Hester JH, Hirschberg D (1985) Self-organizing linear search. ACM Comput Surv 17(3):295–311CrossRefGoogle Scholar
  25. 25.
    Afaq N, Asghar S, Abbasi AR, Wallam F, Saeed Q (2015) Low-cost hardware & control design of an inverted pendulum using conventional, fuzzy and hybrid techniques. In: 12th international conference on electrical engineering/electronics, computer, telecommunications and information technology (ECTI-CON), 2015. IEEE, pp 1–6Google Scholar
  26. 26.
    Jung S, Cho H-T, Hsia TC (2007) Neural network control for position tracking of a two-axis inverted pendulum system: experimental studies. IEEE Trans Neural Netw 18(4):1042–1048CrossRefGoogle Scholar
  27. 27.
    Wai R-J, Chang L-J (2006) Stabilizing and tracking control of nonlinear dual-axis inverted-pendulum system using fuzzy neural network. IEEE Trans Fuzzy Syst 14(1):145–168CrossRefzbMATHGoogle Scholar
  28. 28.
    Huang C-H, Wang W-J, Chiu C-H (2011) Design and implementation of fuzzy control on a two-wheel inverted pendulum. IEEE Trans Ind Electron 58(7):2988–3001CrossRefGoogle Scholar
  29. 29.
    Ohta T, Murakami T (2009) A stabilization control of bilateral system with time delay by vibration index—application to inverted pendulum control. IEEE Trans Ind Electron 56(5):1595–1603CrossRefGoogle Scholar
  30. 30.
    Chiu C-H (2010) The design and implementation of a wheeled inverted pendulum using an adaptive output recurrent cerebellar model articulation controller. IEEE Trans Ind Electron 57(5):1814–1822CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Hunan University of TechnologyZhuzhouChina
  2. 2.National Chiao Tung UniversityHsinchuTaiwan
  3. 3.College of Electrical and Computer EngineeringNational Chiao Tung UniversityHsinchuTaiwan

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