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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 610490, 11 pages
Research Article

The Application of MPC in Microwave Heating Process Based on Model Constructed by Lambert’s Law Combined with Temperature

1School of Automation, Chongqing University, Chongqing 400044, China
2Key Laboratory of Dependable Service Computing in Cyber Physical Society, MOE, Chongqing 400044, China
3School of Software Engineering, Chongqing University, Chongqing 400044, China

Received 13 October 2014; Revised 23 January 2015; Accepted 23 January 2015

Academic Editor: B. Rush Kumar

Copyright © 2015 Jianshuo Li 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.


Microwave heating has been the research hot spot for many years. It has the capability of volumetric heating, which makes it save energy and time compared to traditional heating by conduction. A lot of work has been done to easily and exactly describe power distribution in the heating material. Maxwell’s equations and Lambert’s law are the most common ways. Maxwell’s equation is complicated and hard to apply, while Lambert’s law ignores the temperature influence. For material thickness less than penetration depth, only Maxwell’s equation can accurately solve power distribution. For large thickness material, Lambert’s law combined with regional temperature proposed in this paper can be more precise than only Lambert’s law. But there also exist some differences. To precisely control the heating process and make the whole process safe, this paper proposes the use of model predictive control (MPC) algorithm to make the maximum temperature follow a preset reference trajectory. The simulation results demonstrate that the algorithm can well control the heating process with little difference between the reference trajectory and the practical output.