Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem

Luo, Dongsheng; Wei, Wei; Liao, Yumei; Deng, Hongyong

doi:10.1007/s10957-019-01559-y

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…For temperature control in the microwave heating process, Luo et al 17 explored the bang‐bang property and the existence of a solution of time optimal control for a specific class microwave heating problem. However, the form of its optimal control existence is obtained with certain given assumptions and has not been verified by professional simulation software.…”

Section: Introductionmentioning

confidence: 99%

Research on temperature uniformity optimization of microwave heating Debye media based on MDADT

Yang

Xiao

Cheng

et al. 2022

Int J RF Mic Comp-Aid Eng

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In the microwave heating process, the uneven temperature distribution is not conducive to improving the quality characteristics of the media. This article proposes a model-dependent average dwell time (MDADT) switching control method for the uneven temperature distribution of the Debye medium during microwave heating. First, a mathematical model of microwave heating switching control is established. Next, according to the mathematical model, the sufficient and necessary conditions for Lyapunov stability in the MDADT microwave heating process are given, which enables the microwave input power to coordinate with the model-dependent average dwell time. Last, numerical simulations of microwave heating SiC show that the proposed method can improve the temperature uniformity of the media and reduce the energy consumption, which indicates the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Research on temperature uniformity optimization of microwave heating Debye media based on MDADT

Yang

Xiao

Cheng

et al. 2022

Int J RF Mic Comp-Aid Eng

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show abstract

Optimal control for a phase field model of melting arising from inductive heating

Xiong¹,

Wei²,

Zhou³

et al. 2021

MATH

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<abstract><p>Due to its unique performance of high efficiency, fast heating speed and low power consumption, induction heating is widely and commonly used in many applications. In this paper, we study an optimal control problem arising from a metal melting process by using a induction heating method. Metal melting phenomena can be modeled by phase field equations. The aim of optimization is to approximate a desired temperature evolution and melting process. The controlled system is obtained by coupling Maxwell's equations, heat equation and phase field equation. The control variable of the system is the external electric field on the local boundary. The existence and uniqueness of the solution of the controlled system are showed by using Galerkin's method and Leray-Schauder's fixed point theorem. By proving that the control-to-state operator $ P $ is weakly sequentially continuous and Fréchet differentiable, we establish an existence result of optimal control and derive the first-order necessary optimality conditions. This work improves the limitation of the previous control system which only contains heat equation and phase field equation.</p></abstract>

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Bang-Bang Property of Time Optimal Control for a Kind of Microwave Heating Problem

Cited by 2 publications

References 23 publications

Research on temperature uniformity optimization of microwave heating Debye media based on MDADT

Research on temperature uniformity optimization of microwave heating Debye media based on MDADT

Optimal control for a phase field model of melting arising from inductive heating

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