Optimal Control of Induction Heating Processes

by Rapoport; Edgar

• ISBN13: 9780849337543
• ISBN10: 0849337542
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-07-07
• Publisher: CRC Press

Summary

This book introduces new approaches to solving optimal control problems in induction heating process applications. Optimal Control of Induction Heating Processes demonstrates how to apply and use new optimization techniques for different types of induction heating installations.

Table of Contents

Introduction to Theory and Industrial Application of Induction Heating Processes	p. 1
Short Description of Operating Principles of Induction heaters on the Level of Basic Physical Laws	p. 1
Basic Electromagnetic Phenomena in Induction Heating	p. 1
Basic Thermal Phenomena in Induction Heating	p. 5
Mathematical Modeling of Induction Heating Processes	p. 7
Mathematical Modeling of Electromagnetic and Temperature Fields	p. 8
Basic Model of the Induction Heating Process	p. 12
Typical Industrial Applications and Fundamental Principles of Induction Mass Heating	p. 19
Design Approaches of Induction Mass Heating	p. 25
Technological Complex "Heater-Equipment for Metal Hot Working"	p. 29
Technological and Economic Advantages of Induction Heating	p. 31
References	p. 33
Optimization Problems for Induction Heating Processes	p. 35
Overview of Induction Heating Prior to Metal Hot Working Operations as a Process under Control	p. 35
Cost Criteria	p. 38
Mathematical Models of a Heating Process	p. 41
Control Inputs	p. 45
Constraints	p. 49
Constraints on Control Inputs	p. 50
Technological Constraints on Temperature Distribution during the Heating Process	p. 51
Constraints Related to Specifics of Subsequent Metal Working Operations	p. 53
Disturbances	p. 54
Requirements of Final Temperature Distribution within Heated Workpieces	p. 57
General Problem of Time-Optimal Control	p. 59
Model Problems of Optimal Control Respective to Typical Cost Functions	p. 66
Problem of Achieving Maximum Heating Accuracy	p. 66
Problem of Minimum Power Consumption	p. 69
References	p. 72
Method for Computation of Optimal Processes for Induction Heating of Metals	p. 73
Universal Properties of Temperature Distribution within Workpieces at End of Time-Optimal Induction Heating Processes	p. 73
Extended Discussion on Properties of Final Temperature Distribution for Time-Optimal Induction Heating Processes	p. 79
Typical Profiles of Final Temperature Distribution and Set of Equations for Computation of Optimal Control Parameters	p. 82
Computational Technique for Time-Optimal Control Processes	p. 90
Application of the Suggested Method to Model Problems Based on Typical Cost Functions	p. 97
Examples	p. 101
Solution of Time-Optimal Control Problem	p. 101
Solution of Minimum Power Consumption Problem	p. 110
General Problem of Parametrical Optimization of Induction Heating Processes	p. 111
References	p. 116
Optimal Control of Static Induction Heating Processes	p. 119
Time-Optimal Control for Linear One-Dimensional Models of Static IHP with Consideration of Technological Restraints	p. 119
General Overview of Optimal Heating Power Control	p. 120
Power Control during the Holding Stage	p. 127
Computational Technique for Optimal Heating Modes, Taking into Consideration Technological Constraints	p. 131
Examples	p. 140
Time-Optimal Problem, Taking into Consideration the Billet Transportation to Metal Forming Operation	p. 142
Problem Statement	p. 142
Computational Technique for the "Transportation" Problem of Time-Optimal Heating	p. 149
Technological Constraints in "Transportation" Problem	p. 156
Examples	p. 163
Time-Optimal Heating under Incomplete Information with Respect to Controlled Systems	p. 165
Problem Statement	p. 166
Technique for Time-Optimal Problem Solution under Interval Uncertainties	p. 168
Heating Process with Minimum Product Cost	p. 174
Problem of Metal Scale Minimization	p. 176
Overview of Optimal Heating Modes	p. 176
Two-Parameter Power Control Algorithm of Scale Minimization	p. 178
Minimization of Product Cost	p. 187
Optimal Control of Multidimensional Linear Models of Induction Heating Processes	p. 192
Linear Two-Dimensional Model of the Induction heating Process	p. 193
Two-Dimensional Time-Optimal Control Problem	p. 198
Time-Optimal Control of Induction Heating for Cylindrical Billets	p. 200
Time-Optimal Control of Induction Heating of Rectangular-Shaped Workpieces	p. 215
Surface Heat-Generating Sources	p. 215
Optimization of Internal Source Heating	p. 231
Exploration of Three-Dimensional Optimization Problems for Induction Heating	p. 236
Optimal Control for Complicated Models of the Induction Heating Process	p. 240
Overview	p. 240
Approximate Method for Computation of the Optimal Induction Heating Process for Ferromagnetic Billets	p. 242
Optimal Control for Numerical Models of Induction Heating Processes	p. 245
References	p. 254
Optimal Control of Progressive and Continuous Induction Heating Processes	p. 257
Optimization of Continuous Heaters at Steady-State Operating Conditions	p. 258
Overview of Typical Optimization Problems and Methods for Their Solution	p. 258
Design of Minimum Length Inductor	p. 263
Optimization of the Continuous Heating of Ferromagnetic Materials	p. 273
Optimization of the Continuous Heating Process Controlled by a Power Supply Voltage	p. 281
Optimization of Progressive Heaters at Steady-State Operating Conditions	p. 288
Key Features of Optimization Problems for Progressive Heaters	p. 288
Optimization of Induction Heater Design and Operating Modes	p. 290
Optimal Control of a Single-Section Heater	p. 298
Two-Position Control of Slab Induction Heating	p. 306
References	p. 308
Combined Optimization of Production Complex for Induction Billet Heating and Subsequent Metal Hot Forming Operations	p. 309
Mathematical Models of Controlled Processes	p. 310
General Problem of Optimization of a Technological Complex	p. 315
Maximum Productivity Problem for an Industrial Complex "Induction heater-Extrusion Press"	p. 317
Multiparameter Statement of the Optimization Problem for Technological Complex "Heating-Hot Forming"	p. 322
Combined Optimization of Heating and Pressing Modes for Aluminum Alloy Billets	p. 325
Time-Optimal Heating Modes	p. 325
Time-Optimal Pressing Modes	p. 325
Temperature Distribution within Pressurized Metal	p. 327
Optimal Program of Extrusion Speed Variation	p. 329
Computational Results	p. 330
Optimization of Billet Gradient Heating	p. 332
About Optimal IHI Design in Technological Complex "Heating-Hot Forming"	p. 334
References	p. 339
Conclusion	p. 341
Index	p. 343
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