Optimal Control of Induction Heating: Theory and Application

2011 ◽  
pp. 153-173
Author(s):  
Darya Filatova ◽  
Marek Grzywaczewski
Keyword(s):  
Optimal Control ◽  
Induction Heating

Power formulation for the optimal control of an industrial induction heating process for thixoforming

2004 ◽  
Vol 19 (1-4) ◽  
pp. 51-56 ◽  
Author(s):  
Alexandre Masserey ◽  
Jacques Rappaz ◽  
Roland Rozsnyo ◽  
Rachid Touzani
Keyword(s):  
Optimal Control ◽  
Induction Heating ◽  
Heating Process

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

2022 ◽  
Vol 7 (1) ◽  
pp. 121-142
Author(s):  
Zonghong Xiong ◽  
◽  
Wei Wei ◽  
Ying Zhou ◽  
Yue Wang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Field Equation ◽  
Heat Equation ◽  
Induction Heating ◽  
Phase Field ◽  
Control Variable ◽  
Melting Process ◽  
Inductive Heating ◽  
Controlled System ◽  
Metal Melting

<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>

scholarly journals Two-channel time-optimal control of induction heating process with maximum temperature constraint

2020 ◽  
Vol 28 (2) ◽  
pp. 41-58
Author(s):  
Natalya A. Il`ina
Keyword(s):  
Optimal Control ◽  
Temperature Field ◽  
Temperature Distribution ◽  
Induction Heating ◽  
Time Optimal Control ◽  
Maximum Temperature ◽  
Heating Process ◽  
Problem Of Time ◽  
Control Actions ◽  
Time Optimal

The formulation and method of solution of the problem of time-optimal control of induction heating process of an unlimited plate with two control actions on the value of internal heat sources with technological constraint in relation to a one-dimensional model of the temperature field are proposed. The problem is solved under the conditions of a given accuracy of uniform approximation of the final temperature distribution over the thickness of the plate to the required. The method of finite integral transformations is used to search for the input-output characteristics of an object with distributed parameters with two control actions. The preliminary parameterization of control actions based on analytical optimality conditions in the form of the Pontryagin maximum principle is used. At the next stage reduction is performed to the problem of semi-infinite optimization, the solution of which is found using the alternance method. The alternance properties of the final resulting temperature state at the end of the optimal process lead to a basic system of relations, which, if there is additional information about the shape of the temperature distribution curve, is reduced to a system of equations that can be solved. An example of solving the problem of time-optimal control of temperature field of an unlimited plate with two offices is carried out in two stages. At first stage the case of induction heating without maximum temperature constraints is considered, at the second stage is carried out on the basis of the results of the first stage to obtain the solution subject to the limitation on the maximum temperature of the heated billet.

Numerical analysis and optimal control of induction heating hardening

2010 ◽  
Author(s):  
Bogdan Gilev ◽  
Andrey Yonchev ◽  
Dimitar Penev ◽  
George Venkov ◽  
Vesela Pasheva ◽  
...  
Keyword(s):  
Optimal Control ◽  
Numerical Analysis ◽  
Induction Heating

scholarly journals Numerical investigation of optimal control of induction heating processes

2001 ◽  
Vol 25 (8) ◽  
pp. 697-712 ◽  
Author(s):  
Olivier Bodart ◽  
Anne-Valérie Boureau ◽  
Rachid Touzani
Keyword(s):  
Optimal Control ◽  
Numerical Investigation ◽  
Induction Heating

Optimal Control of an Induction Heating Process for Thixoforming

2004 ◽  
Vol 40 (3) ◽  
pp. 1664-1671 ◽  
Author(s):  
A. Masserey ◽  
J. Rappaz ◽  
R. Rozsnyo ◽  
R. Touzani
Keyword(s):  
Optimal Control ◽  
Induction Heating ◽  
Heating Process
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