Abstract
In this paper, a finite-dimensional ordinary differential equation (ODE) model is proposed for predicting the temperature profile with microwave heating to accomplish lower computing complexity. The traditional parabolic partial different equation (PDE) model with integrating Maxwell's equation and heat transport equation is not suitable for designing the on-line controller. Based on the obstruction, using an auxiliary function derives an intermediate model, which is analyzed and discussed for model reduction by employing the parameter separation method and Galerkin's method. The simulation experiments on one-dimensional waveguide and cavity demonstrate that the proposed approximate model is effective.
Highlights
Microwave applications for thermal purposes have obtained vast application in domestic usage and are attracting much attention in industrial applications over several decades [5]
In order to obtain the temperature profile from above equations, traditional analytical methods are hardly to get its closedform solution, which promotes the development of numerical methods, such as, Finite Element Method (FEM), Finite-Different Time-Domain (FDTD) method, Moment of Method (MoM), Finite-Volume Time-Domain (FVTD) method and Transmission Line Matrix (TLM) method [18, 19, 26]
We focus on developing a novel approximate nonlinear temperature model for one-dimensional microwave heating with mixed or nonhomogeneous boundary conditions
Summary
Microwave applications for thermal purposes have obtained vast application in domestic usage and are attracting much attention in industrial applications over several decades [5]. From the view of cybernetics, the main characteristics of the microwave heating process are that the outputs, inputs, state variables and parameters are changing with the time domain and spatial domain That is another insufficient for the traditional PDE model to directly design the close-loop controllers [20]. While the nonhomogeneous or mixed boundary condition is another important factor to influence the efficiency of heating and it is difficult to obtain eigenfunctions of spatial differential operator directly To solve these problems, the research efforts focus on applying an auxiliary function to achieve a more complicated equivalent PDE, including the states of microwave irradiation and heat transfer, and the information of boundary conditions. In order to verify the nonlinear model, the results of traditional model are simulated in some points by Matlab to contrast with the novel model in Section 4, whose results demonstrate that the methodology could provide important guarantee for control algorithm in the step
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