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Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation

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  • Anitha Karthikeyan
  • Karthikeyan Rajagopal

Abstract

We investigate a specific smart grid system and its nonlinear properties. Lyapunov exponents are derived to prove the existence of chaos and bifurcation and bicoherence contours are investigated to show the parameter dependence and existence of quadratic nonlinearities, respectively. A fractional order model of the smart grid system (FOSG) is then derived and bifurcation of the FOSG system with variation in the commensurate fractional order of the system is investigated to show that largest Lyapunov exponent of the system exists in fractional order. Hence we proposed two different control methods to suppress the chaotic oscillations. In the first method we derive fractional order adaptive sliding mode control (FOASMC) algorithm to control chaotic oscillations and in the second method we used genetically optimized fractional order PID controllers (GAFOPID) for chaos control. Numerical simulations are conducted to show the effectiveness of the controllers and also to prove that GAFOPID controllers are more effective than FOASMC controllers for fractional order systems. The GAFOPID controllers are then realized in FPGA to show that the proposed methodology is hardware realizable.

Suggested Citation

  • Anitha Karthikeyan & Karthikeyan Rajagopal, 2017. "Chaos Control in Fractional Order Smart Grid with Adaptive Sliding Mode Control and Genetically Optimized PID Control and Its FPGA Implementation," Complexity, Hindawi, vol. 2017, pages 1-18, April.
    • Handle: RePEc:hin:complx:3815146
    DOI: 10.1155/2017/3815146
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    1. Chen, Hsien-Keng & Lin, Tsung-Nan & Chen, Juhn-Horng, 2005. "Dynamic analysis, controlling chaos and chaotification of a SMIB power system," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1307-1315.
    2. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
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    Cited by:

    1. Nazarimehr, Fahimeh & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Alsaedi, Ahmed & Pham, Viet-Thanh & Hayat, Tasawar, 2018. "Investigation of dynamical properties in a chaotic flow with one unstable equilibrium: Circuit design and entropy analysis," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 7-13.
    2. Wang, Cong & Zhang, Hong-li & Fan, Wen-hui & Ma, Ping, 2020. "Finite-time function projective synchronization control method for chaotic wind power systems," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

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