Non-singleton General Type-2 Fuzzy Control for a Two-Wheeled Self-Balancing Robot

  • Tao Zhao
  • Qian Yu
  • Songyi DianEmail author
  • Rui Guo
  • Shengchuan Li


This paper presents several non-singleton general type-2 fuzzy logic controllers (NGT2FLCs) for an under-actuated mobile two-wheeled self-balancing robot to improve the anti-interference capability of the system. Four kinds of fuzzifiers, including singleton fuzzifier, type-1 non-singleton fuzzifier, interval type-2 non-singleton fuzzifier and general type-2 non-singleton fuzzifier, are considered to construct different general type-2 fuzzy logic controllers (GT2FLCs). In order to show the superiority of the GT2FLCs, three kinds of interval type-2 fuzzy logic controllers (IT2FLCs), including singleton IT2FLCs, type-1 non-singleton IT2FLCs (N1IT2FLCs) and interval type-2 non-singleton IT2FLCs (N2IT2FLCs), are also presented. A comparative study between singleton fuzzy controllers and non-singleton fuzzy controllers, and IT2FLCs and GT2FLCs is also shown. All simulation results show that the performance of non-singleton fuzzy logic controllers is better than that of singleton fuzzy logic controllers. The NGT2FLCs get the best performance in the presence of uncertainties and external disturbances.


Mobile two-wheeled self-balancing robot Non-singleton interval type-2 fuzzy logic controllers Non-singleton general type-2 fuzzy logic controllers External disturbances 



This work is supported by the National Key R&D Program of China (2018YFB1307402) and the National Natural Science Foundation of China (61703291).


  1. 1.
    Sepúlveda, R., Castillo, O., Melin, P., et al.: Experimental study of intelligent controllers under uncertainty using type-1 and type-2 fuzzy logic. Inf. Sci. 177(10), 2023–2048 (2007)CrossRefGoogle Scholar
  2. 2.
    Zhai, D., Mendel, J.M.: Uncertainty measures for general type-2 fuzzy sets. Inf. Sci. 181(3), 503–518 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Runkler, T.A., Chen, C., John, R.: Type reduction operators for interval type–2 defuzzification. Inf. Sci. 467, 464–476 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Zhao, T., Liu, J., Dian, S.: Finite-time control for interval type-2 fuzzy time-delay systems with norm-bounded uncertainties and limited communication capacity. Inf. Sci. 483, 153–173 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Tong, S., Sun, K., Sui, S.: Observer-based adaptive fuzzy decentralized optimal control design for strict-feedback nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 26(2), 569–584 (2018)CrossRefGoogle Scholar
  6. 6.
    Li, Y., Li, K., Tong, S.: Finite-time adaptive fuzzy output feedback dynamic surface control for MIMO nonstrict feedback systems. IEEE Trans. Fuzzy Syst. 27(1), 96–110 (2019)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Li, Y., Tong, S.: Adaptive fuzzy control with prescribed performance for block-triangular-structured nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1153–1163 (2018)CrossRefGoogle Scholar
  8. 8.
    Wagner, C., Hagras, H.: Toward general type-2 fuzzy logic controllers based on zslices. IEEE Trans. Fuzzy Syst. 18(4), 637–660 (2010)CrossRefGoogle Scholar
  9. 9.
    MéNdez, G.M., De Los Angeles HernáNdez, M.: Hybrid learning mechanism for interval A2-C1 type-2 non-singleton type-2 Takagi–Sugeno–Kang fuzzy logic controllers. Inf. Sci. 220, 149–169 (2013)CrossRefGoogle Scholar
  10. 10.
    Castillo, O., Melin, P.: Recent Advances in Interval Type-2 Fuzzy Systems, pp. 5–6. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  11. 11.
    Martínez-Soto, R., Castillo, O., Castro, J.R.: Genetic algorithm optimization for type-2 non-singleton fuzzy logic controllers. In: Castillo, O., Melin, P., Pedrycz, W., Kacprzyk, J. (eds.) Recent Advances on Hybrid Approaches for Designing Intelligent Systems, pp. 3–18. Springer, Cham (2014)CrossRefGoogle Scholar
  12. 12.
    Wu, D., Mendel, J.M.: Similarity measures for closed general type-2 fuzzy sets: overview, comparisons, and a geometric approach. IEEE Trans. Fuzzy Syst. 27(3), 515–526 (2019)CrossRefGoogle Scholar
  13. 13.
    Zhai, D., Hao, M., Mendel, J.M.: A non-singleton interval type-2 fuzzy logic system for universal image noise removal using quantum-behaved particle swarm optimization. In: IEEE International Conference on Fuzzy Systems, pp. 957–964. IEEE (2011)Google Scholar
  14. 14.
    Pourabdollah, A., Wagner, C., Smith, M., et al.: Real-world utility of non-singleton fuzzy logic controllers: a case of environmental management. In: IEEE International Conference on Fuzzy Systems. IEEE (2015)Google Scholar
  15. 15.
    Kulkarni, S., Agrawal, R.: Determining the optimal fuzzifier range for alpha-planes of general type-2 fuzzy sets. In: 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1–8. IEEE (2018)Google Scholar
  16. 16.
    Castillo, O., Atanassov, K.: Comments on fuzzy sets, interval type-2 fuzzy sets, general type-2 fuzzy sets and intuitionistic fuzzy sets. In: Melliani, S., Castillo, O. (eds.) Recent Advances in Intuitionistic Fuzzy Logic Systems, pp. 35–43. Springer, Cham (2019)CrossRefGoogle Scholar
  17. 17.
    Chen, Y., Wang, D.: Forecasting by designing Mamdani general type-2 fuzzy logic systems optimized with quantum particle swarm optimization algorithms. Trans. Inst. Meas. Control (2019). Google Scholar
  18. 18.
    Castillo, O., Amador-Angulo, L., Castro, J.R., et al.: A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems. Inf. Sci. 354, 257–274 (2016)CrossRefGoogle Scholar
  19. 19.
    Castillo, O., Amador-Angulo, L.: A generalized type-2 fuzzy logic approach for dynamic parameter adaptation in bee colony optimization applied to fuzzy controller design. Inf. Sci. 460–461, 476–496 (2018)CrossRefGoogle Scholar
  20. 20.
    Castillo, O., Cervantes, L., Soria, J., et al.: A generalized type-2 fuzzy granular approach with applications to aerospace. Inf. Sci. 354, 165–177 (2016)CrossRefGoogle Scholar
  21. 21.
    Mohammadzadeh, A., Kayacan, E.: A non-singleton type-2 fuzzy neural network with adaptive secondary membership for high dimensional applications. Neurocomputing 338, 63–71 (2019)CrossRefGoogle Scholar
  22. 22.
    Ruiz-Garcia, G., Hagras, H., Pomares, H., et al.: Towards a fuzzy logic system based on general forms of interval type-2 fuzzy sets. IEEE Trans. Fuzzy Syst. (2019). zbMATHGoogle Scholar
  23. 23.
    Sv, A.K., Srivatsa, S.K.: An image fusion technique based on sparse wavelet transform and non-singleton type-2 FNN techniques. TAGA J. 14, 76–86 (2018)Google Scholar
  24. 24.
    Huang, J., Ding, F., Fukuda, T., et al.: Modeling and velocity control for a novel narrow vehicle based on mobile wheeled inverted pendulum. IEEE Trans. Control Syst. Technol. 21(5), 1607–1617 (2013)CrossRefGoogle Scholar
  25. 25.
    Ri, S.H., Huang, J., Wang, Y., et al.: Terminal sliding mode control of mobile wheeled inverted pendulum system with nonlinear disturbance observer. Math. Probl. Eng. 2014, 1–8 (2014)CrossRefzbMATHGoogle Scholar
  26. 26.
    Huang, J., Ri, S., Liu, L., et al.: Nonlinear disturbance observer-based dynamic surface control of mobile wheeled inverted pendulum. IEEE Trans. Control Syst. Technol. 23(6), 2400–2407 (2015)CrossRefGoogle Scholar
  27. 27.
    Huang, C.H., Wang, W.J., Chiu, C.H.: Design and implementation of fuzzy control on a two-wheel inverted pendulum. IEEE Trans. Ind. Electron. 58(7), 2988–3001 (2011)CrossRefGoogle Scholar
  28. 28.
    El-Bardini, M., El-Nagar, A.M.: Interval type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system. ISA Trans. 53(3), 732–743 (2014)CrossRefGoogle Scholar
  29. 29.
    Cervantes, L., Castillo, O.: Type-2 fuzzy logic aggregation of multiple fuzzy controllers for airplane flight control. Inf. Sci. 324, 247–256 (2015)CrossRefGoogle Scholar
  30. 30.
    Mohammadzadeh, A., Ghaemi, S., Kaynak, O., et al.: Observer-based method for synchronization of uncertain fractional order chaotic systems by the use of a general type-2 fuzzy system. Appl. Soft Comput. 49, 544–560 (2016)CrossRefGoogle Scholar
  31. 31.
    Mendel, J.M.: Uncertain rule-based fuzzy logic system: introduction and new directions, 2nd edn, pp. 617–673. Springer, New York (2017)CrossRefGoogle Scholar
  32. 32.
    Mendel, J.M., Liu, F., Zhai, D.: α-Plane representation for type-2 fuzzy sets: theory and applications. IEEE Trans. Fuzzy Syst. 17(5), 1189–1207 (2009)CrossRefGoogle Scholar
  33. 33.
    Zhai, D., Mendel, J.M.: Comment on “toward general type-2 fuzzy logic controllers based on zSlices”. IEEE Trans. Fuzzy Syst. 20(5), 996–997 (2012)CrossRefGoogle Scholar
  34. 34.
    Wagner, C., Hagras, H.: zSlices based general type-2 fuzzy sets and systems. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds.) Advances in Type-2 Fuzzy Sets and Systems, pp. 65–80. Springer, New York (2013)CrossRefGoogle Scholar
  35. 35.
    Wu, D.: Approaches for reducing the computational cost of interval type-2 fuzzy logic controllers: overview and comparisons. IEEE Trans. Fuzzy Syst. 21(1), 80–99 (2013)CrossRefGoogle Scholar
  36. 36.
    Huang, J., Ri, M.H., Wu, D., et al.: Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum. IEEE Trans. Fuzzy Syst. 26(4), 2030–2038 (2018)CrossRefGoogle Scholar
  37. 37.
    Nie, M., Tan, W.W.: Towards an efficient type-reduction method for interval type-2 fuzzy logic controllers. In: IEEE International Conference on Fuzzy Systems, 2008. FUZZ-IEEE 2008. (IEEE World Congress on Computational Intelligence), pp. 1425–1432. IEEE (2008)Google Scholar
  38. 38.
    Chan, R.P.M., Stol, K.A., Halkyard, C.R.: Review of modelling and control of two-wheeled robots. Annu. Rev. Control 37(1), 89–103 (2013)CrossRefGoogle Scholar
  39. 39.
    Muhammad, M., Buyamin, S., Ahmad, M.N., et al.: Takagi–Sugeno fuzzy modeling of a two-wheeled inverted pendulum robot. J. Intell. Fuzzy Syst. 25(3), 535–546 (2013)MathSciNetGoogle Scholar
  40. 40.
    Chang, X.H.: Robust nonfragile filtering of fuzzy systems with linear fractional parametric uncertainties. IEEE Trans. Fuzzy Syst. 20(6), 1001–1011 (2012)CrossRefGoogle Scholar
  41. 41.
    Xie, X.P., Yue, D., Peng, C.: Multi-instant observer design of discrete-time fuzzy systems: a ranking-based switching approach. IEEE Trans. Fuzzy Syst. 25(5), 1281–1292 (2017)CrossRefGoogle Scholar
  42. 42.
    Li, H.Y., Yin, S., Pan, Y.N., Lam, H.K.: Model reduction for interval type-2 Takagi–Sugeno fuzzy systems. Automatica 61, 308–314 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Lam, H.K., Li, H.Y., Deters, C., Secco, E.L., Wurdemann, H.A., Althoefer, K.: Control design for interval type-2 fuzzy systems under imperfect premise matching. IEEE Trans. Ind. Electron. 16(2), 956–968 (2014)CrossRefGoogle Scholar
  44. 44.
    Zhao, T., Dian, S.: State feedback control for interval type-2 fuzzy systems with time-varying delay and unreliable communication links. IEEE Trans. Fuzzy Syst. 26(2), 951–966 (2018)CrossRefGoogle Scholar
  45. 45.
    Zhao, T., Dian, S.: Fuzzy dynamic output feedback H∞ control for continuous-time TS fuzzy systems under imperfect premise matching. ISA Trans. 70, 248–259 (2017)CrossRefGoogle Scholar
  46. 46.
    Zhao, T., Dian, S.: Delay-dependent stabilization of discrete-time interval type-2 T–S fuzzy systems with time-varying delay. J. Franklin Inst. 354(3), 1542–1567 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Kumbasar, T., Hagras, H.: Big Bang-Big Crunch optimization based interval type-2 fuzzy PID cascade controller design strategy. Inf. Sci. 282, 277–295 (2014)CrossRefGoogle Scholar
  48. 48.
    Lam, H.K., Li, H., Liu, H.: Stability analysis and control synthesis for fuzzy-observer-based controller of nonlinear systems: a fuzzy-model-based control approach. IET Control Theory Appl. 7(5), 663–672 (2013)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Lee, C.H., Chang, F.Y., Lin, C.M.: An efficient interval type-2 fuzzy CMAC for chaos time-series prediction and synchronization. IEEE Trans. Cybern 44(3), 329–341 (2014)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  • Tao Zhao
    • 1
  • Qian Yu
    • 1
  • Songyi Dian
    • 1
    Email author
  • Rui Guo
    • 2
  • Shengchuan Li
    • 3
  1. 1.College of Electrical Engineering and Information TechnologySichuan UniversityChengduChina
  2. 2.State Grid Shandong Electric Power CompanyJinanChina
  3. 3.Electric Power Research Institute of State Grid Liaoning Electric Power Co., LtdShenyangChina

Personalised recommendations