Optimal Control of Induction Heating Processes

Transcription

1 Optimal Control of Induction Heating Processes Edgar Rapoport Vulia Pleshiutseua (löfh Taylor & Francis ^^ J Taylor & Francis Group Boca Raton London New York CRC is an imprint of the Taylor & Francis Group, an informa business

2 Table of Contents Chapter 1 Introduction to Theory and Industrial Application of Induction Heating Processes Short Description of Operating Principles of Induction Heaters on the Level of Basic Physical Laws B asic Electromagnetic Phenomena in Induction Heating Basic Thermal Phenomena in Induction Heating Mathematical Modeling of Induction Heating Processes Mathematical Modeling of Electromagnetic and Temperature Fields Basic Model of the Induction Heating Process Typical Industrial Applications and Fundamental Principles of Induction Mass Heating Design Approaches of Induction Mass Heating Technological Complex "Heater-Equipment for Metal Hot Working" Technological and Economic Advantages of Induction Heating 31 References 33 Chapter 2 Optimization Problems for Induction Heating Processes Overview of Induction Heating Prior to Metal Hot Working Operations as a Process under Control Cost Criteria Mathematical Models of a Heating Process Control Inputs Constraints Constraints on Control Inputs ' Technological Constraints on Temperature Distribution during the Heating Process Constraints Related to Specifics of Subsequent Metal Working Operations Disturbances Requirements of Final Temperature Distribution within Heated Workpieces General Problem of Time-Optimal Control Model Problems of Optimal Control Respective to Typical Cost Functions 66

3 2.9.1 Problem of Achieving Maximum Hearing Accuracy Problem of Minimum Power Consumption 69 References 72 Chapter 3 Method for Computation of Optimal Processes for Induction Heating of Metals Universal Properties of Temperature Distribution within Workpieces at End of Time-Optimal Induction Heating Processes Extended Discussion on Properties of Final Temperature Distribution for Time-Optimal Induction Heating Processes Typical Profiles of Final Temperature Distribution and Set of Equations for Computation of Optimal Control Parameters Computational Technique for Time-Optimal Control Processes Application of the Suggested Method to Model Problems Based on Typical Cost Functions Examples Solution of Time-Optimal Control Problem Solution of Minimum Power Consumption Problem General Problem of Parametrical Optimization of Induction Heating Processes 111 References 116 Chapter 4 Optimal Control of Static Induction Heating Processes Time-Optimal Control for Linear One-Dimensional Models of Static IHP with Consideration of Technological Restraints General Overview of Optimal Heating Power Control Power Control during the Holding Stage Computational Technique for Optimal Heating Modes, Taking into Consideration Technological Constraints Examples Time-Optimal Problem, Taking into Consideration the Billet Transportation to Metal Forming Operation Problem Statement Computational Technique for the "Transportation" Problem of Time-Optimal Heating Technological Constraints in "Transportation" Problem Examples Time-Optimal Heating under Incomplete Information with Respect to Controlled Systems Problem Statement Technique for Time-Optimal Problem Solution under Interval Uncertainties 168

4 4.4 Heating Process with Minimum Product Cost Problem of Metal Scale Minimization Overview of Optimal Heating Modes Two-Parameter Power Control Algorithm of Scale Minimization Minimization of Product Cost Optimal Control of Multidimensional Linear Models of Induction Heating Processes Linear Two-Dimensional Model of the Induction Heating Process Two-Dimensional Time-Optimal Control Problem Time-Optimal Control of Induction Heating for Cylindrical Billets Time-Optimal Control of Induction Heating of Rectangular-Shaped Workpieces Surface Heat-Generating Sources Optimization of Internal Source Heating Exploration of Three-Dimensional Optimization Problems for Induction Heating Optimal Control for Complicated Models of the Induction Heating Process Overview Approximate Method for Computation of the Optimal Induction Heating Process for Ferromagnetic Billets Optimal Control for Numerical Models of Induction Heating Processes 245 References 254 Chapter 5 Optimal Control of Progressive and Continuous Induction Heating Processes Optimization of Continuous Heaters at Steady-State Operating Conditions Overview of Typical Optimization Problems and Methods for Their Solution Design of Minimum Length Inductor Optimization of the Continuous Heating of Ferromagnetic Materials Optimization of the Continuous Heating Process Controlled by a Power Supply Voltage Optimization of Progressive Heaters at Steady-State Operating Conditions Key Features of Optimization Problems for Progressive Heaters 288

5 5.2.2 Optimization of Induction Heater Design and Operating Modes Optimal Control of a Single-Section Heater Two-Position Control of Slab Induction Heating 306 References 308 Chapter 6 Combined Optimization of Production Complex for Induction Billet Heating and Subsequent Metal Hot Forming Operations Mathematical Models of Controlled Processes General Problem of Optimization of a Technological Complex Maximum Productivity Problem for an Industrial Complex "Induction Heater-Extrusion Press" Multiparameter Statement of the Optimization Problem for Technological Complex "Heating-Hot Forming" Combined Optimization of Heating and Pressing Modes for Aluminum Alloy Billets Time-Optimal Heating Modes Time-Optimal Pressing Modes Temperature Distribution within Pressurized Metal Optimal Program of Extrusion Speed Variation Computational Results Optimization of Billet Gradient Heating About Optimal IHI Design in Technological Complex "Heating-Hot Forming" 334 References 339 Conclusion 341 Index 343