National Instruments Xmath Interactive Control Design Module ICDM User Manual download pdf (Page 43)

Chapter 4 PID Synthesis

Figure 4-1. PID Synthesis Window

As an example, suppose that the P and I toggle buttons are on, and the D

and HF rolloff buttons are off. The controller transfer function will then

have the following form:

Cs() K

= 1 sT

int

⁄()+

1 2 ... 38 39 40 41 42 43 44 45 46 47 48 ... 128 129

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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National Instruments Xmath Interactive Control Design Module ICDM User Manual Page 43

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