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Model-free control of unknown nonlinear systems using an iterative learning concept: theoretical development and experimental validation

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Abstract

In this paper, a newly developed adaptive model-free control method using an iterative learning control method based on a robust control design framework is discussed. Consequently, no system plant model is required for control design; only the inputs and outputs are used as controller input. Briefly, no assumption is required regarding the system plant model. In this contribution, a fully model-free control method is developed to be applied to unknown nonlinear SISO systems using (i) a modified model-free adaptive scheme to estimate the system local dynamics iteratively, (ii) an optimal weighting matrices design method based on a designable relationship between the system output to its input, and (iii) an iterative learning concept to generate a suitable control input according to the robust design framework. As an example, the task of perfect sinusoidal movement of a cart with a mounted inverted elastic cantilever beam is chosen to validate the performance of the proposed approach. The challenge is to realize the control in the presence of unknown nonlinear interaction of the flexible beam to the moving carts motion. To demonstrate effectiveness of the proposed method, the results obtained are compared with classical and well-known model-based control approaches.

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Acknowledgements

This research is partly supported by the German Academic Exchange Service (DAAD) through the Research Grants for Doctoral Candidates and Young Academics and Scientists.

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  1. Chair of Dynamics and Control, University of Duisburg-Essen, Lotharstr. 1-21, 47057, Duisburg, Germany

    Elmira Madadi & Dirk Söffker

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  1. Elmira Madadi
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  2. Dirk Söffker
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Correspondence to Elmira Madadi.

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Madadi, E., Söffker, D. Model-free control of unknown nonlinear systems using an iterative learning concept: theoretical development and experimental validation. Nonlinear Dyn 94, 1151–1163 (2018). https://doi.org/10.1007/s11071-018-4415-7

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  • DOI: https://doi.org/10.1007/s11071-018-4415-7

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