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Absolute control of chaotic responses in Robbins disc dynamo

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Abstract

Chaotic responses of Robbins disc dynamo are considered through boundedness and Lyapunov exponents to specify the place where the controller needed to be applied. In order to get the beneficial aspects in engineering of the Robbins disc dynamo, controller is calculated by using the concept of Lie derivative which is the most significant facet of control analytical technique. The necessary and sufficient conditions are confirmed, and a single input function controller u is constructed for linear and nonlinear output function. Robbins disc dynamo system is totally controlled for the required goals in both cases. To show the effectiveness of proposed control technique, a comparison with other techniques is presented in this article. Numerical simulation results confirm our analytical results.

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Acknowledgements

This work is partially supported by Higher Education Commission (HEC), Pakistan, under the programme 5856/Federal/NRPU/R&D/HEC/2016.

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Authors and Affiliations

  1. Institute of Space Technology, Islamabad, Pakistan

    Javeria Ayub, Muhammad Aqeel, Salman Ahmad & Zainab Rana

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  1. Javeria Ayub
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  2. Muhammad Aqeel
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  3. Salman Ahmad
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  4. Zainab Rana
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Correspondence to Javeria Ayub.

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Ayub, J., Aqeel, M., Ahmad, S. et al. Absolute control of chaotic responses in Robbins disc dynamo. Eur. Phys. J. Plus 135, 307 (2020). https://doi.org/10.1140/epjp/s13360-020-00316-9

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