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EID estimator-based modified repetitive control for singular systems with time-varying delay

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Abstract

This paper investigates the disturbance rejection for a modified repetitive control system (MRCS) that is described by a class of linear singular systems in the presence of external disturbances and time-varying delay. In particular, an equivalent-input-disturbance (EID)-based estimator is included in the MRCS to compensate both periodic and aperiodic disturbances which yields an EID-based MRCS. More precisely, the incorporation of the EID-based estimator into the control input enables rejection of all types of disturbances in MRCS and tracking of a periodic reference input is archived via a repetitive controller. Attention is focused on the state-feedback repetitive controller design which not only guarantees the regular, impulse free, and asymptotic stability of the closed-loop singular MRCS, but also provides an optimized upper bound of the time-varying delay. Based on Lyapunov stability theory and utilizing some advanced mathematical techniques, a new set of delay-dependent sufficient conditions is presented in terms of linear matrix inequalities for obtaining the required result. Then, an explicit expression for the desired state-feedback repetitive control law is developed. Further, the obtained results are validated through two numerical examples in the simulation section.

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Acknowledgements

The work of R. Sakthivel was supported by Samsung Research Fund, Sungkyunkwan University, 2016.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    R. Sakthivel

  2. Department of Mathematics, Anna University Regional Campus, Coimbatore, 641046, India

    S. Mohanapriya, P. Selvaraj & S. Marshal Anthoni

  3. Department of Mechanical Engineering, Politecnico di Milano, 20156, Milan, Italy

    H. R. Karimi

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  1. R. Sakthivel
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  2. S. Mohanapriya
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  3. P. Selvaraj
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  4. H. R. Karimi
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  5. S. Marshal Anthoni
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Correspondence to R. Sakthivel or H. R. Karimi.

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Sakthivel, R., Mohanapriya, S., Selvaraj, P. et al. EID estimator-based modified repetitive control for singular systems with time-varying delay. Nonlinear Dyn 89, 1141–1156 (2017). https://doi.org/10.1007/s11071-017-3506-1

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  • DOI: https://doi.org/10.1007/s11071-017-3506-1

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