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Functional Observer-Based T–S Fuzzy Systems for Quadratic Stability of Power System Synchronous Generator

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Abstract

This paper presents the functional observer-based Takagi–Sugeno fuzzy controller to enhance the dynamic response of the synchronous generator infinite bus power system under low-frequency oscillations. The unmeasurable states of the synchronous generator are estimated by using minimum order functional observer. The T–S fuzzy controller rules are a function of the estimated states in which the functional observer based on T–S fuzzy conditions presented in rank equality form. The Lyapunov theory in the form of linear matrix inequalities (LMIs) represented here in this paper to synthesis the functional observer stability. Small disturbances are taken to simulate the synchronous generator oscillations. The results clearly show that our scheme is a better response when compared with the full observer-based T–S fuzzy system.

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References

  1. Begnini, M., Bertol, D.W., Martins, N.A.: Practical implementation of a simple and effective robust adaptive fuzzy variable structure trajectory tracking control for differential wheeled mobile robots. Int. J. Innov. Comput. Inform. Control 13(1), 341–364 (2017)

    Google Scholar 

  2. Li, S., Xiang, Z., Lin, H., Karimi, H.R.: State estimation on positive Markovian jump systems with timevarying delay and uncertain transition probabilities. Inform. Sci. 369, 251–266 (2016)

    Article  MathSciNet  Google Scholar 

  3. Shi, P., Zhang, Y., Chadli, M., Agarwal, R.K.: Mixed H-infinity and passive filtering for discrete fuzzy neural networks with stochastic jumps and time delays. IEEE Trans. Neural Netw. Learning Syst. 27(4), 903–909 (2016)

    Article  MathSciNet  Google Scholar 

  4. Sun, C., Wang, F., He, X.: Robust fault-tolerant control for fuzzy delay systems with unmeasurable premise variables via uncertain system approach. Int. J. Innov. Comput. Inform. Control 13(3), 823–846 (2017)

    Google Scholar 

  5. Zhong, Z., Zhu, Y., Lam, H.K.: Asynchronous piecewise output-feedback control for large-scale fuzzy systems via distributed event-triggering schemes. IEEE Trans. Fuzzy Syst. (2017). https://doi.org/10.1109/TFUZZ

    Article  Google Scholar 

  6. Cheng, J., Zhang, D., Qi, W., Cao, J., Shi, K.: Finite-time stabilization of T–S fuzzy semi-Markov switching systems: a coupling memory sampled-data control approach. J. Franklin Inst. (2019). https://doi.org/10.1016/j.jfranklin.2019.06.021

    Article  Google Scholar 

  7. Chang, X.H., Yang, G.H.: Nonfragile \({H_\infty }\) filtering of continuous-time fuzzy systems. IEEE Trans. Signal Process. 59(4), 1528–1538 (2011)

    Article  MathSciNet  Google Scholar 

  8. Chang, X.H., Yang, G.H.: Nonfragile filter design for T–S fuzzy systems in standard form. IEEE Trans. Ind. Elect. 61(7), 3448–3458 (2014)

    Article  Google Scholar 

  9. Peng, C., Ma, S., Xie, X.: Observer-based non-PDC control for networked T–S fuzzy systems with an event-triggered communication. IEEE Trans. Cybern. 47(8), 2279–2287 (2017)

    Article  Google Scholar 

  10. Aslam, M.S., Chen, Z.: Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise. Nonlinear Dyn. 95(4), 2923–2941 (2019)

    Article  Google Scholar 

  11. Pan, Y., Yang, G.H.: Event-triggered fuzzy control for nonlinear networked control systems. Fuzzy Sets Syst. 329, 91–107 (2017)

    Article  MathSciNet  Google Scholar 

  12. Johansen, T.A., Shorten, R., Murray-Smith, R.: On the interpretation and identification of dynamic Takagi–Sugeno fuzzy models. IEEE Trans. Fuzzy Syst. 8(3), 297–313 (2000)

    Article  Google Scholar 

  13. Chang, X.H., Yang, G.H.: A descriptor representation approach to observer-based \({H_\infty }\) control synthesis for discrete-time fuzzy systems. Fuzzy Sets Syst. 185, 38–51 (2011)

    Article  MathSciNet  Google Scholar 

  14. Chiu, C.S., Ouyang, Y.L.: Robust maximum power tracking control of uncertain photovoltaic systems: a unified T–S fuzzy model-based approach. IEEE Trans. Control Syst. Technol. 19(6), 1516–1526 (2011)

    Article  Google Scholar 

  15. Tanaka, K., Ikeda, T., Wang, H.O.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI based designs. IEEE Trans. Fuzzy Syst. 6(2), 250–265 (1998)

    Article  Google Scholar 

  16. Tanaka, K., Wang, H.O.: Fuzzy control systems design and analysis: a linear matrix inequality approach. Wiley, New York (2001). https://doi.org/10.1002/0471224596

    Book  Google Scholar 

  17. Zhang, J., Shi, P., Qiu, J., Nguang, S.K.: A novel observer-based output feedback controller design for discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst. 23(1), 223–229 (2015)

    Article  Google Scholar 

  18. Luenberger, D.G.: An introduction to observers. IEEE Trans. Autom. Control 16(6), 596–602 (1971)

    Article  MathSciNet  Google Scholar 

  19. Cheng, J., Park, J.H., Qi, W.: Hidden Markov model-based nonfragile state estimation of switched neural network with probabilistic quantized outputs. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2909748

    Article  Google Scholar 

  20. Huang, S., Karimi, H.R., Xiang, Z.: Mixed L1/L2 fault detection filter design for fuzzy positive linear systems with time-varying delays. IET Control Theory Appl. 8(12), 1023–1031 (2014)

    Article  MathSciNet  Google Scholar 

  21. Li, S., Xiang, Z., Lin, H., Karimi, H.R.: State estimation B on positive Markovian jump systems with timevarying delay and uncertain transition probabilities. Inform. Sci. 369, 251–266 (2016)

    Article  MathSciNet  Google Scholar 

  22. Zhang, K., Jiang, B., Shi, P.: Fault estimation observer design for discrete-time Takagi–Sugeno fuzzy systems based on piecewise Lyapunov functions. IEEE Trans. Fuzzy Syst. 20(1), 192–200 (2012)

    Article  Google Scholar 

  23. Cheng, J., Park, J.H., Zhao, X., Qi, W.: Static output feedback control of switched systems with quantization: a nonhomogeneous sojourn probability approach. Int. J. Robust Nonlinear Control (2019). https://doi.org/10.1002/rnc.4703

    Article  MathSciNet  MATH  Google Scholar 

  24. Darouach, M.: Existence and design of functional observers for linear systems. IEEE Trans. Autom. Control 45(5), 940–943 (2000)

    Article  MathSciNet  Google Scholar 

  25. Trinh, H., Fernando, T.: On the existence and design of functional observers for linear systems. In: The IEEE International conference on mechatronics and automation, pp. 1974–1979 Harbin, China (2007)

  26. Teh, P.S., Trinh, H.: Partial state and unknown input estimation for time-delay systems. Int. J. Syst. Sci. 43(4), 748–763 (2012)

    Article  MathSciNet  Google Scholar 

  27. Jennings, L.S., Fernando, T.L., Trinh, H.M.: Existence conditions for functional observability from an eigenspace perspective. IEEE Trans. Autom. Control 56(12), 2957–2961 (2010)

    Article  MathSciNet  Google Scholar 

  28. Fernando, T., Emami, K., Yu, S., Lu, H., Wong, K.P.: A novel quasi-decentralized functional observer approach to LFC of interconnected power systems. In: IEEE Transactions on Power Systems, 1–10 (2019)

  29. Alhelou, H.H., Hamedani, M.E.: A decentralized functional observer based optimal LFC considering unknown inputs, uncertainties and cyber-attacks. In: IEEE power and energy society general meeting (PESGM). pp. 1944–9933, Boston (2016)

  30. Ma, X.J., Sun, Z.Q.: Analysis and design of fuzzy reduced-dimensional observer and fuzzy functional observer. Fuzzy Sets Syst. 120, 35–63 (2001)

    Article  MathSciNet  Google Scholar 

  31. Fadali, M.S.: Fuzzy functional observers for dynamic TSK systems, In: The \(14^{th}\) IEEE international conference on fuzzy systems, pp. 389–394. Reno, Nevada, USA (2005)

  32. Najat, O., Rachid, A., Noureddine, E.: Quadratic stability of synchronous machine via Takagi-Sugeno fuzzy control, In: The international conference on multimedia computing and systems, pp. 1169–1174. Tangier, Morocco (2012)

  33. Islam, S.I., Lim, C.C., Shi, P.: Functional observer-based fuzzy controller design for continuous nonlinear systems. Int. J. Syst. Sci. 49(5), 1047–1060 (2018)

    Article  MathSciNet  Google Scholar 

  34. Thoma, M., Allgöwer, F., Morari, M.: Functional observers for dynamical systems. Springer, Berlin (2012)

    Google Scholar 

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Authors and Affiliations

  1. School of Automation, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, P.R. China

    Khaled Eltag & Ziran Chen

  2. School of Electrical and Information Engineering, Guangxi University of Science and Technology, Liuzhou, 545006, China

    Muhammad Shamrooz Aslam

Authors
  1. Khaled Eltag
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  2. Muhammad Shamrooz Aslam
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  3. Ziran Chen
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Correspondence to Khaled Eltag or Muhammad Shamrooz Aslam.

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Eltag, K., Aslam, M.S. & Chen, Z. Functional Observer-Based T–S Fuzzy Systems for Quadratic Stability of Power System Synchronous Generator. Int. J. Fuzzy Syst. 22, 172–180 (2020). https://doi.org/10.1007/s40815-019-00784-x

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  • DOI: https://doi.org/10.1007/s40815-019-00784-x

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