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370760B-01
164 CHAPTER 4. DEMONSTRATION EXAMPLES
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164
CHAPTER 4.
DEMONSTRATION EXAMPLES
Frequency
10 100
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1000
Magnitude
0.001
0.01
0.1
0.0001
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Controller: Khinf
Frequency
10 100
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1000
Phase (degrees)
-50
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200
Contents
Main
MATRIXx
XmathTM X Manual
MATRIXx Xmath Basics
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Important Information
Warranty
Copyright
Trademarks
Patents
Contents
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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
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2.1.2 An Introduction to Norms
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2.2 Modeling Uncertain Systems
2.2.1 Perturbation Models for Robust Control
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2.2.2 Linear Fractional Transformations
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2.2.3 Assumptions on P,, and the unknown signals
2.2.4 Additional Perturbation Structures
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2.2.5 Obtaining Robust Control Models for Physical Systems
2.3 Hand H2Design Methodologies
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2.3.1 HDesign Overview
2.3.2 Assumptions for the HDesign Problem
2.3.3 A Brief Review of the Algebraic Riccati Equation
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2.3.4 Solving the HDesign Problem for a Special Case
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2.3.5 Further Notes on the HDesign Algorithm
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2.3.6 H2Design Overview
2.3.7 Details of the H2Design Procedure
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2.4 Analysis
2.4.1 Measures of Performance
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2.4.2 Robust Stability and
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2.4.3 Robust Performance
2.4.4 Properties of
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2.4.5 The Main Loop Theorem
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2.4.6 State-space Robustness Analysis Tests
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2.4.7 Analysis with both Real and Complex Perturbations
2.5 Synthesis and D-KIteration
2.5.1 -Synthesis
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2.5.2 The D-KIteration Algorithm
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2.6 Model Reduction
2.6.1 Truncation and Residualization
2.6.2 Balanced Truncation
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2.6.3 Hankel Norm Approximation
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Chapter 3
Functional Description of X
3.1 Introduction
3.2 Data Objects
3.2.1 Dynamic Systems
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3.2.2 pdms
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3.2.3 Subblocks: selecting input & outputs
3.2.4 Basic Functions
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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
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3.4 System Response Functions
3.4.1 Creating Time Domain Signals
3.4.2 Dynamic System Time Responses
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3.4.3 Frequency Responses
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90 CHAPTER 3. FUNCTIONAL DESCRIPTION OF X
3.5 System Interconnection
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3.6 H2and HAnalysis and Synthesis
3.6.1 Controller Synthesis
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98 CHAPTER 3. FUNCTIONAL DESCRIPTION OF X
The desired closed loop conguration is illustrated in Figure 3.6.
Figure 3.6: Closed loop conguration
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3.6.2 System Norm Calculations
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3.7 Structured Singular Value () Analysis and Synthesis
3.7.1 Calculation of
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3.7.2 The D-KIteration
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3.7.3 Fitting DScales
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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
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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
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4.1.3 Creating a Weighted Interconnection Structure for Design
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4.1.4 HDesign
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4.1.5 AnalysisoftheH
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4.1.6 Fitting D-scales for the D-KIteration
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142 CHAPTER 4. DEMONSTRATION EXAMPLES
4.1.7 Design Iteration #2
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4.1.8 Simulation Comparison with a Loopshaping Controller
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4.1. THE HIMATEXAMPLE 149
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4.1. THE HIMATEXAMPLE 151
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4.2 A Simple Flexible Structure Example
4.2.1 The Control Design Problem
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4.2.2 Creating the Weighted Design Interconnection Structure
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 159
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 161
4.2.3 Design of an HController
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164 CHAPTER 4. DEMONSTRATION EXAMPLES
4.2.4 Robustness Analysis
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 167
4.2.5 D-KIteration
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170 CHAPTER 4. DEMONSTRATION EXAMPLES
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172 CHAPTER 4. DEMONSTRATION EXAMPLES
4.2.6 A Simulation Study
174 CHAPTER 4. DEMONSTRATION EXAMPLES
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176 CHAPTER 4. DEMONSTRATION EXAMPLES
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178 CHAPTER 4. DEMONSTRATION EXAMPLES
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180 CHAPTER 4. DEMONSTRATION EXAMPLES
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182 CHAPTER 4. DEMONSTRATION EXAMPLES
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184 CHAPTER 4. DEMONSTRATION EXAMPLES
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 187
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 189
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4.2. A SIMPLE FLEXIBLE STRUCTURE EXAMPLE 191
Bibliography
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Chapter 6
Function Reference
6.1 XFunctions
System building and interconnection
Variable display and graphics
Time response calculationsand pdm functions
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balmoore
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blknorm
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conpdm
consys
csum
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ctrlplot
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daug
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delsubstr
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tsys
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242 Chapter 6. Function Reference
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244 Chapter 6. Function Reference
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gstep
248 Chapter 6. Function Reference
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hinfnorm
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h2norm
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hinfsyn
p k
zw y u
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262 Chapter 6. Function Reference
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hinfsyn 267
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h2syn
p k
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h2syn 273
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278 Chapter 6. Function Reference
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interp
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interp 283
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mergeseg
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mergeseg 287
mkpert
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mkphase
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modalstate
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mu
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musynt
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musynfit 303
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musynfit 305
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musynfit 307
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310 Chapter 6. Function Reference
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312 Chapter 6. Function Reference
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ophank
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ophank 317
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orderstate
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randpdm
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randpert
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randsys
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332 Chapter 6. Function Reference
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rifd
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sdtrsp
Sys dSys
Example:
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sdtrsp 343
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simtransform
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spectrad
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sresidualize
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sresidualize 353
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starp
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substr
sysic
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trsp
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trsp 367
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trsp 369
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trsp 371
truncate
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sresidualize 375
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6.2 XSubroutines and Utilities
hinfsyn subroutines
mu subroutines
blkbal
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riccati eig
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riccati schur
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Appendices
A Translation Between Matlab -Tools and X
A.1 Data Objects
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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
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Technical Support and Professional Services
164 CHAPTER 4. DEMONSTRATION EXAMPLES164 CHAPTER 4. DEMONSTRATION EXAMPLES