TCM Modeling and Control in Literature

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Table of contents

Chapter 1 General Introduction 
Chapter 2 Cold Rolling of Steel 
2.1 Introduction
2.2 Process Overview
2.3 TCM Modeling and Control in Literature
2.3.1 Roll Force and Torque Mathematical models
2.3.2 Tandem Cold Mill Modeling and Control
2.4 Conclusion
Chapter 3 Mathematical Preliminaries 
3.1 Introduction
3.2 Linear Quadratic Regulation
3.3 Stability
3.3.1 Basic Definitions
3.3.2 Lyapunov’s Direct Method for Stability
3.4 Stability of Time Delay Systems
3.4.1 Time Delay Systems in Brief
3.4.2 Stability Concept for General TDS
3.4.2.1 Lyapunov-Krasovskii Direct Method
3.4.3 Stability of Linear Systems with Time-Varying Delays
3.4.4 Stabilization of Linear Systems with Time-Varying Delays
3.5 Stability of Singular Systems
3.5.1 Singular Systems in Brief
3.5.2 Preliminaries on Singular Systems
3.5.3 Stability of Linear Singular Systems
3.5.4 Stabilization of Linear Singular Systems
3.6 Stability of Time Delay Singular Systems
3.6.1 Preliminaries of Time Delay Singular Systems
3.6.2 Stability of Time Delay Singular System
3.6.3 Stabilization of Time Delay Singular System
3.7 Conclusion
Chapter 4 Tandem Cold Mill : Model and Current Control Strategy 
4.1 Introduction
4.2 Description of the Tandem Stand
4.2.1 Stand Actuator
4.2.2 Stand Motor
4.2.3 Yield Stress Model
4.2.4 Sims’ Gauge Relation
4.2.5 Mass Flow Conservation
4.2.6 Strip Exit Speed
4.2.7 Interstand Tension
4.2.8 Interstand Transport Delay
4.2.9 Rolling Force Model
4.3 TCM Multivariable Model
4.3.1 Exit Thickness Integral Action
4.3.2 Multivariable Non-linear Descriptor Model
4.4 TCM Linearized Model
4.4.1 TCM Time Delay Singular System
4.5 Current Multi-loop PID Control for Tandem Process
4.6 Conclusion
Chapter 5 State Feedback Control for TCM Process 
5.1 Introduction
5.2 Existence and Uniqueness of Solution
5.3 Controller Synthesis Paradigm
5.3.1 Formulation of Controller Synthesis as a Constrained Optimization Problem
5.3.2 Process Performance translated as a Quadratic Cost
5.3.3 Stability and Performance Optimization via Lyapunov-Krasovskii Functional
5.3.4 Control solution of the Optimization Synthesis Problem
5.4 State Feedback Synthesis
5.4.1 Controller Synthesis via LMI Problem
5.4.2 Majorant Minimization
5.4.3 Numerical example
5.5 TCM Controller Synthesis
5.5.1 Controller Tuning
5.6 Conclusion
Chapter 6 Dynamic Output Feedback Control for TCM Process 
6.1 Introduction
6.2 Output Feedback Synthesis
6.2.1 Problem Formulation
6.2.2 Closed Loop System Model
6.2.3 Control Design : Synthesis Analysis
6.2.4 LMI formulation of the Synthesis Problem
6.3 Dynamic Output Feedback Feasibility Problem
6.3.1 Controller Synthesis via LMI Feasibility Problem
6.3.2 Numerical example
6.4 DOF Synthesis for the TCM Process
6.5 Conclusion
Chapter 7 General Conclusion 
References