IDEAS home Printed from https://ideas.repec.org/a/hin/complx/3815146.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/3815146.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/3815146.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/3815146?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Shahverdiev, E.M. & Hashimova, L.H. & Hashimova, N.T., 2008. "Chaos synchronization in some power systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 827-834.
    4. Xiaodong Wang & Caiqin Song, 2019. "Analysis on Nonlinear Dynamic Characteristic of Synchronous Generator Rotor System," Complexity, Hindawi, vol. 2019, pages 1-14, January.
    5. Chenhui Wang, 2016. "Adaptive Fuzzy Control for Uncertain Fractional-Order Financial Chaotic Systems Subjected to Input Saturation," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-17, October.
    6. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    7. Li, Ruoxia & Gao, Xingbao & Cao, Jinde, 2019. "Non-fragile state estimation for delayed fractional-order memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 221-233.
    8. Taneco-Hernández, Marco Antonio & Vargas-De-León, Cruz, 2020. "Stability and Lyapunov functions for systems with Atangana–Baleanu Caputo derivative: An HIV/AIDS epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. Bei Zhang & Yonghui Xia & Lijuan Zhu & Haidong Liu & Longfei Gu, 2019. "Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    10. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    11. Yuwen Dong & Shuai Song & Xiaona Song & Inés Tejado, 2024. "Observer-Based Adaptive Fuzzy Quantized Control for Fractional-Order Nonlinear Time-Delay Systems with Unknown Control Gains," Mathematics, MDPI, vol. 12(2), pages 1-24, January.
    12. Li, Fan & Liu, Shuai & Li, Xiaola, 2023. "Effect of phase shift on the dynamics of a single-machine infinite-bus power system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    13. Xu, Quan & Xu, Xiaohui & Zhuang, Shengxian & Xiao, Jixue & Song, Chunhua & Che, Chang, 2018. "New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 552-566.
    14. Li, Yaguang & Sun, Chunhua & Ling, Haifeng & Lu, An & Liu, Yezheng, 2020. "Oligopolies price game in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:3815146. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.