Nonlinear Dynamics

, Volume 94, Issue 2, pp 1151–1163 | Cite as

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

  • Elmira MadadiEmail author
  • Dirk Söffker
Original Paper


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.


Model-free control approach Adaptive iterative learning control Unknown nonlinear dynamical system 



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

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Chair of Dynamics and ControlUniversity of Duisburg-EssenDuisburgGermany

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