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Robust limit cycle control for finite-time generation of sustained oscillations in nonlinear systems with mixed dead-zone and saturation

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  • Azhdari, Meysam
  • Binazadeh, Tahereh

Abstract

This paper suggests a novel limit cycle control technique, based on the finite-time stability scheme, for producing sustained oscillations in a class of nonlinear complex systems. The considered systems are constrained to input dead-zone and saturation simultaneously and suffer from non-vanishing perturbations due to model uncertainties, and external disturbances. For this purpose, an innovative sliding manifold is proposed based on the topology of the wanted limit cycle which provides the conditions for developing the finite time stability concept for limit sets. With the aid of the finite-time command filter and the cooperation of the sliding mode control (SMC) method with the backstepping technique, a robust controller is constructed which guarantees the finite-time convergence of phase trajectories of the closed-loop system toward the wanted limit cycle. This leads to the creation of sustained oscillations, with the desirable amplitude and frequency, in the system's output. The stability analysis is proved based on the Lyapunov approach through the set stability concept. Finally, the effectiveness of the suggested methodology is confirmed by a variety of simulations.

Suggested Citation

  • Azhdari, Meysam & Binazadeh, Tahereh, 2023. "Robust limit cycle control for finite-time generation of sustained oscillations in nonlinear systems with mixed dead-zone and saturation," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011505
    DOI: 10.1016/j.chaos.2023.114248
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    References listed on IDEAS

    as
    1. Meysam Azhdari & Tahereh Binazadeh, 2021. "Output tracker design for uncertain nonlinear sandwich systems with sandwiched dead-zone nonlinearity based on adaptive finite-time control," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(3), pages 596-611, February.
    2. Azhdari, Meysam & Binazadeh, Tahereh, 2022. "A novel adaptive SMC strategy for sustained oscillations in nonlinear sandwich systems based on stable limit cycle approach," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Hakimi, A.R. & Azhdari, M. & Binazadeh, T., 2021. "Limit cycle oscillator in nonlinear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    4. Zare, Shahryar & Tavakolpour-Saleh, A.R. & Binazadeh, T., 2023. "Analytical investigation of free piston Stirling engines using practical stability method," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Sweetha, S. & Panneerselvam, V. & Tatar, N. & Sakthivel, R., 2023. "Observer-based control for nonlinear neutral type stochastic model with fractional Gaussian noise and input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. T. Binazadeh & A. R. Hakimi, 2020. "Adaptive generation of limit cycles in a class of nonlinear systems with unknown parameters and dead-zone nonlinearity," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(15), pages 3134-3145, November.
    7. Qian Wang & Chuang Gao & Yang Cui & Li-Bing Wu, 2022. "Adaptive control-based barrier Lyapunov functions for strict-feedback stochastic nonlinear systems with input saturation and dead zone," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(15), pages 3165-3176, November.
    8. Iqbal, Muhammad & Rehan, Muhammad & Hong, Keum-Shik & Khaliq, Abdul & Saeed-ur-Rehman,, 2015. "Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 158-169.
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