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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 597236, 9 pages
Research Article

Robust Nonlinear Control with Compensation Operator for a Peltier System

1School of Electrical and Information Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China
2Department of Electrical and Electronic Engineering, Tokyo University of Agriculture and Technology, Tokyo 183-8538, Japan

Received 19 February 2014; Revised 4 June 2014; Accepted 26 June 2014; Published 9 July 2014

Academic Editor: Asier Ibeas

Copyright © 2014 Sheng-Jun Wen 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.


Robust nonlinear control with compensation operator is presented for a Peltier actuated system, where the compensation operator is designed by using a predictive model on heat radiation. For the Peltier system, the heat radiation is related to the fourth power of temperature. So, the heat radiation is affected evidently by the temperature when it is high and temperature difference between the system and environment is large. A new nonlinear model with the heat radiation is set up for the system according to some thermal conduction laws. To ensure robust stability of the nonlinear system, operator based robust right coprime factorization design is considered. Also, a compensation operator based on a predictive model is proposed to cancel effect of the heat radiation, where the predictive model is set up by using radial basis kernel function based SVM (support vector machine) method. Finally, simulation results are given to show the effectiveness of the proposed scheme.