National-instruments Xmath Interactive Control Design Module ICDM Manuel d'utilisateur Page 51
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Chapter 5 Root Locus Synthesis
© National Instruments Corporation 5-5 Xmath Interactive Control Design Module
Phase Contours
For each of magnitude and phase contours, you can choose one of three
possible plotting styles.
• 180°
The plot shows the locus of points where the phase angle of the loop
transfer function is 180°. This yields a conventional root locus display.
This is the default phase contour plotting style. The plot shows the set
of all possible closed-loop pole locations as the gain is swept from
0to∞.
• 160° 200° 10°
The plot shows the loci of points where the phase angle of the loop
transfer function is 160°, 170°, 180°, 190°, or 200°. These plots show
the set of all possible closed-loop pole locations as the gain is swept
from 0 to and there is an additional phase shift of ±20°, ±10° in the
loop transfer function.
• None
No phase contours are plotted.
Magnitude Contours
•0 dB
The plot shows the locus of points where the magnitude of the loop
transfer function (including the delay, if applicable) is 0 dB.
• –2:2 dB
The plot shows the loci of points where the magnitude of the loop
transfer function is –2, –1, 0, +1, and +2 dB, respectively.
• None
No magnitude contours are plotted. This is the default magnitude
contour plotting style.
Notice that by selecting None for both phase and magnitude contours, the
plot shows only the controller and plant poles and zeros. This is useful for
graphically editing the controller poles and zeros.
If any phase contours are plotted, the closed-loop poles are shown (in blue
on a color display). They can be dragged along the 180° contour plot.
- 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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