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Chapter 12 LQG/H-Infinity Synthesis
Xmath Interactive Control Design Module 12-16 ni.com
Manipulating the Design Parameters
Main Window
The design parameters ρ and ν can be changed using the associated sliders
or the variable edit boxes. If the user types in a value that is outside the
current slider range, the slider range will automatically adjust. Notice that
the slider positions in the Weights window are simultaneously updated
when the ρ and ν sliders are moved. The user can change the ranges for the
sliders using the Ranges window.
The parameters T
int
and a can be manipulated using the sliders or variable
edit boxes provided the associated toggle button is On. If the toggle button
is Off, then the slider and variable edit box are insensitive; you cannot drag
the slider handle, and you cannot type into the variable edit box.
When the toggle buttons are turned On again, the parameters are restored
to their previous (or default) values.
The design parameters also can be manipulated graphically.
• When the Decay Rate toggle button is on, a dashed line appears in the
Decay Rate window, showing ℜs = a. The user can drag this line left
and right to set the Decay Rate parameter.
•When Weight Edit is enabled, the user can graphically manipulate the
poles and zeros of the weight transfer functions or on the plot labeled
Weight Poles & Zeros. Refer to the Editing Poles and Zeros
Graphically section of Chapter 2, Introduction to SISO Design, for
a general discussion of how to move, add, delete, or edit these zeros
graphically.
• When the H∞ performance level toggle button is enabled, the user
can graphically manipulate γ by moving the dashed line in the
H∞ Performance window vertically.
- NI MATRIXx 1
- Important Information 3
- Conventions 4
- Chapter 3 6
- Chapter 4 6
- Chapter 11 9
- Chapter 12 9
- LQG/H-Infinity Synthesis 9
- Contents 10
- Introduction 11
- Chapter 1 Introduction 12
- Commonly-Used Nomenclature 13
- Related Publications 13
- ICDM Overview 14
- Introduction to SISO Design 16
- Overview of ICDM 18
- ICDM Main Window 19
- PID Synthesis Window 19
- Root Locus Synthesis Window 19
- Pole Place Synthesis Window 19
- LQG Synthesis Window 20
- H-Infinity Synthesis Window 20
- History Window 20
- Alternate Plant Window 20
- Origin of the Controller 21
- Using ICDM 24
- General Plotting Features 26
- Ranges of Plots and Sliders 26
- Data-Viewing Plots 27
- Interactive Plot Re-ranging 28
- Editing Poles and Zeros 28
- Complex Poles and Zeros 29
- Isolated Real Poles and Zeros 29
- Communicating with Xmath 33
- Most Common Usage 34
- Default Plants 34
- Chapter 3 ICDM Main Window 35
- ICDM Plots 36
- Selecting Plots 36
- Ranges of Plots 37
- Plot Magnify Windows 38
- Edit Menu 40
- PID Synthesis 41
- Chapter 4 PID Synthesis 42
- Ranges of Sliders and Plots 45
- Integral Term Normalization 45
- Derivative Term Normalization 46
- Rolloff Term Normalization 46
- Root Locus Synthesis 47
- Terminology 49
- Plotting Styles 50
- Phase Contours 51
- Magnitude Contours 51
- Manipulating the Parameters 52
- Adding a Pole-Zero Pair 53
- Deleting Pole-Zero Pairs 53
- Pole Place Synthesis 56
- Pole Place Modes 57
- Normal Mode 58
- Integral Action Mode 59
- State-Space Interpretation 60
- Opening the Pole Place Window 60
- Time and Frequency Scaling 60
- Butterworth Configuration 61
- Editing the Closed-Loop Poles 61
- Slider and Plot Ranges 61
- LQG Synthesis 62
- Chapter 7 LQG Synthesis 63
- Synthesis Modes 64
- Output Weight Editing 67
- R in the LQG window 69
- window 69
- H-Infinity Synthesis 70
- Opening the Synthesis Window 72
- Central H-Infinity Controller 73
- Infeasible Parameter Values 75
- Editing the Comments 78
- Deleting History List Entries 79
- Cycling Through Designs 79
- Using the History List 80
- Normalization 84
- Adding Unmodeled Dynamics 85
- Ranges of Sliders and Plot 86
- Introduction to MIMO Design 87
- Transfer Functions 88
- ICDM MIMO Windows 91
- MIMO Plot Window 92
- LQG/H-Infinity Weights Window 96
- Decay Rate Window 99
- H-Infinity Performance Window 99
- Frequency Weights Window 100
- Setup and Terminology 102
- Integral Action 105
- Exponential Time Weighting 106
- Weight Editing 106
- How to Select w, u, y, and z 107
- H-Infinity Solution 108
- Main Window 110
- in the LQG window 111
- Multi-Loop Synthesis 112
- Setup and Synthesis Method 114
- Graphical Editor 118
- Editing and Deleting Loops 119
- Loop Gain Magnitude and Phase 119
- Using an Xmath GUI Tool 120
- GUI Functions 122
- GUI Objects 122
- and the left mouse button 123
- Technical Support and 126
- Professional Services 126
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