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Mathematical Problems in Engineering
Volume 2016, Article ID 2926914, 11 pages
Research Article

Smooth Adaptive Internal Model Control Based on Model for Nonlinear Systems with Dynamic Uncertainties

1Engineering Research Institute, University of Science and Technology Beijing, Beijing 100083, China
2School of Automation & Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received 22 June 2016; Accepted 27 September 2016

Academic Editor: Tarek Ahmed-Ali

Copyright © 2016 Li Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An improved smooth adaptive internal model control based on model control method is presented to simplify modeling structure and parameter identification for a class of uncertain dynamic systems with unknown model parameters and bounded external disturbances. Differing from traditional adaptive methods, the proposed controller can simplify the identification of time-varying parameters in presence of bounded external disturbances. Combining the small gain theorem and the virtual equivalent system theory, learning rate of smooth adaptive internal model controller has been analyzed and the closed-loop virtual equivalent system based on discrete model has been constructed as well. The convergence of this virtual equivalent system is proved, which further shows the convergence of the complex closed-loop discrete model system. Finally, simulation and experimental results on a typical nonlinear dynamic system verified the feasibility of the proposed algorithm. The proposed method is shown to have lighter identification burden and higher control accuracy than the traditional adaptive controller.