Finite-dimensional Thermal-electromagnetic Coupled Modeling And Robust Control For Temperature In Microwave Heating Process

As a novel energy carrier,microwave has been shown the great application values in domestic and industrical fields.Compared with the traditional heating process,microwave has revealed some remarkable features,such as energy conservation and saving time,because it can penetrate the most of dielectric media and immediately transform as thermal energy.With mightily approving of sustainable conception by the world,more and more researchers pay attention to the microwave energy technology.Moreover,as a means of new thermotechnical process,it has greatly affected the technical reform in heat treatment field.However,scholars from all over the world have found that when dielectric media are exposed by unreasonable microwave power,it is inevitable to appear uneven heating phenomenon.Without an effective regulation strategy,the local overheating problems will lead thermal runaway,i.e.,burning,explosion and blasting boiling,which may destroy magnetron,transmission line and heated media.In order to realize the safe,efficient and reliable application,it is significant for us to avoid local overheating in microwave heating process.The solutions of aforementioned problem are that based on the mechanism model and the information of detection in spatial domain,the power control strategy can be designed to track the expected global or local temperature rise curve.This dissertation is supported by a subtopic of the National Basic Research Program of China(973 Program)“Load characteristics based online intelligent control theory and key technologies for microwave source”.This dissertation mainly focuses two critical problems,i.e.,modeling and control,in the microwave heating process.Firstly,the relationships between the electromagnetic and thermodynamic field are explicitly revealed by discussing the evolution and coupled mechanism to propose the microwave heating temperature model with the explicit dissipated power.Subsequently,the spectral Galerkin method is improved to facilitate the controller design.Finally,receding horizon robust control strategy is proposed to solve the relationship of constrained input,boundary perturbation and higher performance requirements.The main work and relevant results of this dissertation include the following four parts:(1)Based on the coupled mechanism of microwave heating dielectric media,microwave heating model can be divided into electromagnetic and thermodynamic submodels,which can be described by the different mathematical formations.Comapared with the traditional heating method,the thermodynamic submodel is usually modeled by the partial differential equation(PDE)models with nonhomogeneous term,which can not only describe the phenomenon of thermal conduction and convection,but also consider the energy transformation between the electromagnetism and heat.In the case of temperature-independent or temperature-dependent permittivity,dominant mode analysis method and spatial discretization method is generalized to obtain an approximate microwave heating temperature model with the explicit dissipated power.(2)Supposing that the microwave heating PDE model is known,it is still difficult for us to readily design controller due to the infinite-dimensional characteristics of the spatial differential operator.With the help of the steady and unsteady characteristics for the nonhomogeneous Neumann boundary conditions,this dissertation derives an equivalence PDE model with homogeneous Neumann boundary condition to overcome above obstruction.And then,the finite-dimensional microwave heating ordinary differential equation(ODE)model is proposed for approximately describing temperature distribution by applying spectral method and Galerkin truncation theory.However,the meshing strategy in numerical simulation of microwave heating Debye media does not match the meshless feature of the proposed ODE model.In particular,the serial solution strategy about time-varying electromagnetic submodel and finite-dimensional ODE model is proposed by applying the local feedback information from the method of spatial discretization.(3)In the case of unknown heat spots,the finite-dimensional ODE model can be transformed into finite-dimensional error model,which means that tracking problem is firstly transformed into the stabilization problem.Subsquently,this dissertation analyzes the stabilization of bounded disturbance problem for microwave heating Debye media and non-Debye media,respectively.Then,with the framework of linear matrix inequation(LMI),receding horizon H∞ and improved H∞ temperature spectra control strategies are proposed by combining constrained robust optimization theory.Moreover,the receding horizon H∞ guaranteed cost control is proposed in order to improve the dynamic performance of closed-loop system and weaken input oscillation.(4)In the case of known heat spots,the problem of temperature tracking is analyzed and discussed for monitoring high-temperature area.With the help of discrete and augmented models,the proposed control strategy can be generalized to discrete time domain.Without loss of generality,the same performance indexes,i.e.,H∞ norm and guaranteed cost function,are introduced to solve the certain or uncertain problem.Therefore,this dissertation also proposes receding horizon H∞,improved receding horizon H∞ and receding horizon H∞ guaranteed cost temperature tracking control strategy.Moreover,the numerical comparisons and simulation analysis indeedly demonstrate that the modeling methodologies of microwave heating are effective and the design strategies of tracking controller are feasible.They will provide a novel solution idea and a solid theoretical foundation for the safe,efficient and reliable microwave heating industrical application.