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National Instruments 370760B-01 178 CHAPTER 4. DEMONSTRATION EXAMPLES

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178 CHAPTER 4. DEMONSTRATION EXAMPLES

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Contents

Main MATRIXx XmathTM X Manual MATRIXx Xmath Basics Page Important Information Warranty Copyright Trademarks Patents Contents Page Page Page Page Page Chapter 1 Introduction 1.1 Notation 1.2 Manual Outline 1.3 How to avoid really reading this Manual Chapter 2 Overview of the Underlying Theory 2.1 Introduction 2.1.1 Notation Page 2.1.2 An Introduction to Norms Page Page Page Page 2.2 Modeling Uncertain Systems 2.2.1 Perturbation Models for Robust Control Page Page Page 2.2.2 Linear Fractional Transformations Page Page Page Page 2.2.3 Assumptions on P,, and the unknown signals 2.2.4 Additional Perturbation Structures Page Page Page Page 2.2.5 Obtaining Robust Control Models for Physical Systems 2.3 Hand H2Design Methodologies Page 2.3.1 HDesign Overview 2.3.2 Assumptions for the HDesign Problem 2.3.3 A Brief Review of the Algebraic Riccati Equation Page Page 2.3.4 Solving the HDesign Problem for a Special Case Page 2.3.5 Further Notes on the HDesign Algorithm Page 2.3.6 H2Design Overview 2.3.7 Details of the H2Design Procedure Page 2.4 Analysis 2.4.1 Measures of Performance Page 2.4.2 Robust Stability and Page 2.4.3 Robust Performance 2.4.4 Properties of Page 2.4.5 The Main Loop Theorem Page 2.4.6 State-space Robustness Analysis Tests Page Page Page Page Page Page 2.4.7 Analysis with both Real and Complex Perturbations 2.5 Synthesis and D-KIteration 2.5.1 -Synthesis Page 2.5.2 The D-KIteration Algorithm Page Page Page 2.6 Model Reduction 2.6.1 Truncation and Residualization 2.6.2 Balanced Truncation Page Page 2.6.3 Hankel Norm Approximation Page Chapter 3 Functional Description of X 3.1 Introduction 3.2 Data Objects 3.2.1 Dynamic Systems Page 3.2.2 pdms Page Page 3.2.3 Subblocks: selecting input & outputs 3.2.4 Basic Functions Page Page 3.2.5 Continuous to Discrete Transformations 3.3 Matrix Information, Display and Plotting 3.3.1 Information Functions for Data Objects 3.3.2 Formatted Display Functions 3.3.3 Plotting Functions Page Page 3.4 System Response Functions 3.4.1 Creating Time Domain Signals 3.4.2 Dynamic System Time Responses Page Page 3.4.3 Frequency Responses Page 90 CHAPTER 3. FUNCTIONAL DESCRIPTION OF X 3.5 System Interconnection Page Page Page 3.6 H2and HAnalysis and Synthesis 3.6.1 Controller Synthesis Page Page 98 CHAPTER 3. FUNCTIONAL DESCRIPTION OF X The desired closed loop conguration is illustrated in Figure 3.6. Figure 3.6: Closed loop conguration Page Page Page Page Page Page 3.6.2 System Norm Calculations Page 3.7 Structured Singular Value () Analysis and Synthesis 3.7.1 Calculation of Page Page 3.7.2 The D-KIteration Page 3.7.3 Fitting DScales Page Page Page Page Page Page Page 3.7.4 Constructing Rational Perturbations 3.7.5 Block Structured Norm Calculations 3.8 Model Reduction 3.8.1 Truncation and Residualization 3.8.2 Balanced Realizations Page 3.8.3 Hankel Singular Value Approximation 126 CHAPTER 3. FUNCTIONAL DESCRIPTION OF X Magnitude Chapter 4 Demonstration Examples 4.1 The Himat Example 4.1.1 Problem Description 4.1.2 State-space Model of Himat Page Page 4.1.3 Creating a Weighted Interconnection Structure for Design Page 4.1.4 HDesign Page Page Page Page 4.1.5 AnalysisoftheH Page 4.1.6 Fitting D-scales for the D-KIteration Page 142 CHAPTER 4. DEMONSTRATION EXAMPLES 4.1.7 Design Iteration #2 Page Page 4.1.8 Simulation Comparison with a Loopshaping Controller Page Page 4.1. THE HIMATEXAMPLE 149 Page 4.1. THE HIMATEXAMPLE 151 Page 4.2 A Simple Flexible Structure Example 4.2.1 The Control Design Problem Page 4.2.2 Creating the Weighted Design Interconnection Structure Page Page Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 159 Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 161 4.2.3 Design of an HController Page 164 CHAPTER 4. DEMONSTRATION EXAMPLES 4.2.4 Robustness Analysis Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 167 4.2.5 D-KIteration Page 170 CHAPTER 4. DEMONSTRATION EXAMPLES Page 172 CHAPTER 4. DEMONSTRATION EXAMPLES 4.2.6 A Simulation Study 174 CHAPTER 4. DEMONSTRATION EXAMPLES Page 176 CHAPTER 4. DEMONSTRATION EXAMPLES Page 178 CHAPTER 4. DEMONSTRATION EXAMPLES Page 180 CHAPTER 4. DEMONSTRATION EXAMPLES Page 182 CHAPTER 4. DEMONSTRATION EXAMPLES Page 184 CHAPTER 4. DEMONSTRATION EXAMPLES Page Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 187 Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 189 Page 4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 191 Bibliography Page Page Page Page Page Page Chapter 6 Function Reference 6.1 XFunctions System building and interconnection Variable display and graphics Time response calculationsand pdm functions Page Page balmoore Page Page blknorm Page Page conpdm consys csum Page Page ctrlplot Page Page Page Page Page Page Page Page Page daug Page Page Page Page delsubstr Page tsys Page Page 242 Chapter 6. Function Reference Page 244 Chapter 6. Function Reference Page gstep 248 Chapter 6. Function Reference Page hinfnorm Page Page h2norm Page hinfsyn p k zw y u Page Page Page 262 Chapter 6. Function Reference Page Page Page Page hinfsyn 267 Page h2syn p k Page Page h2syn 273 Page Page Page Page 278 Chapter 6. Function Reference Page interp Page interp 283 Page mergeseg Page mergeseg 287 mkpert Page mkphase Page modalstate Page mu Page Page musynt Page Page Page musynfit 303 Page musynfit 305 Page musynfit 307 Page Page 310 Chapter 6. Function Reference Page 312 Chapter 6. Function Reference Page ophank Page ophank 317 Page orderstate Page Page randpdm Page Page randpert Page randsys Page Page 332 Chapter 6. Function Reference Page rifd Page Page sdtrsp Sys dSys Example: Page sdtrsp 343 Page simtransform Page Page spectrad Page sresidualize Page sresidualize 353 Page starp Page Page Page Page substr sysic Page trsp Page trsp 367 Page trsp 369 Page trsp 371 truncate Page sresidualize 375 Page 6.2 XSubroutines and Utilities hinfsyn subroutines mu subroutines blkbal Page Page Page Page riccati eig Page riccati schur Page Appendices A Translation Between Matlab -Tools and X A.1 Data Objects Page Page Page Page A.2 Matrix Information, Display and Plotting A.3 System Response Functions A.4 System Interconnection A.5 Model Reduction A.6 H2and HAnalysis and Synthesis A.7 Structured Singular Value() Analysis and Synthesis Page Page Page Technical Support and Professional Services