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National Instruments ICDM LQG Synthesis Window, H-Infinity Synthesis Window, Alternate Plant Window, Key Transfer Functions and Data Flow in ICDM

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Chapter 2 Introduction to SISO Design

© National Instruments Corporation 2-5 Xmath Interactive Control Design Module

LQG Synthesis Window

The LQG Synthesis window synthesizes LQG controllers, and therefore

can be used only with strictly proper plants. The user can vary weights for

the ratio of control (input) to regulation (output) cost and the ratio of sensor

(output) noise power to process (input) noise power. Optionally, the user

can specify a guaranteed decay rate and integral time constant. By dragging

zeros on a symmetric root locus plot, the user can vary the state weighting

or perform LTR design.

There also is a MIMO LQG window, described in Chapter12,

LQG/H-Infinity Synthesis.

H-Infinity Synthesis Window

The H∞ Synthesis window synthesizes central H∞ controllers (also called

minimum entropy, risk sensitive, or LEQG controllers). The user can vary

weights for the ratio of control (input) to regulation (output) cost, the ratio

of sensor (output) noise power to process (input) noise power, and the risk

sensitivity or H∞ bound parameter γ. The user can vary the state weighting,

or equivalently, the output weight transfer function, by dragging zeros.

History Window

The History window is used to display and manipulate the design history

list, which is a list of controllers that have been explicitly saved during the

design process. The History window can be used to rapidly cycle through

and compare a subset of the saved designs. Any controller on the history

list can be recalled, and the design process continued.

Alternate Plant Window

The Alternate Plant window is used to study the robustness of a controller

to variations or changes in the plant. The user can interactively vary the

plant gain or dynamics, or add extra parasitic dynamics to the plant, see the

effect on the closed-loop system, and compare it to the nominal system.

Key Transfer Functions and Data Flow in ICDM

ICDM has three key transfer functions:

• The plant transfer function P

• The alternate plant transfer function Palt

• The current controller transfer function C

Contents

Main Page Important Information Warranty Copyright Trademarks Patents Conventions Contents Chapter 1 Introduction Chapter 2 Introduction to SISO Design Chapter 3 ICDM Main Window Chapter 4 PID Synthesis Chapter 5 Root Locus Synthesis Chapter 6 Pole Place Synthesis Chapter 7 LQG Synthesis Chapter 8 H-Infinity Synthesis Chapter 9 Chapter 10 Alternate Plant Window Chapter 11 Introduction to MIMO Design Chapter 12 LQG/H-Infinity Synthesis Page Introduction Using This Manual Document Organization Page Commonly-Used Nomenclature Related Publications MATRIXx Help ICDM Overview SISO Versus MIMO Design Starting ICDM Page Introduction to SISO Design SISO Design Overview Basic SISO Terminology Page Overview of ICDM ICDM Windows ICDM Main Window PID Synthesis Window Root Locus Synthesis Window Pole Place Synthesis Window LQG Synthesis Window H-Infinity Synthesis Window Alternate Plant Window Key Transfer Functions and Data Flow in ICDM Summary Origin of the Controller What the ICDM Main Window Plots Show Controller/Synthesis Window Compatibilities Page Using ICDM G G Page Zooming Data-Viewing Plots Interactive Plot Re-ranging Graphically Manipulating Poles and Zeros Editing Poles and Zeros Editing Poles and Zeros Graphically Complex Poles and Zeros Isolated Real Poles and Zeros Nonisolated Real Poles and Zeros and Almost Real Pairs Adding/Deleting Poles and Zeros Adding/Deleting Pole-Zero Pairs Page ICDM Main Window Communicating with Xmath Most Common Usage Default Plants Saving and Restoring an ICDM Session Reading Another Plant into ICDM Reading a Controller from Xmath into ICDM Writing the Plant Back to Xmath Writing the Alternate Plant back to Xmath Writing a Controller on the History List to Xmath ICDM Plots Selecting Plots Ranges of Plots Plot Magnify Windows Page Selecting a Synthesis or History Window Edit Menu PID Synthesis PID Controller Terms Toggling Controller Terms On and Off Page Opening the PID Synthesis Window Manipulating the Controller Parameters Time Versus Frequency Parameters Ranges of Sliders and Plots Controller Term Normalizations Integral Term Normalization Derivative Term Normalization Rolloff Term Normalization Root Locus Synthesis Overview Page Opening the Root Locus Synthesis Window Terminology Plotting Styles Phase Contours Magnitude Contours Slider and Plot Ranges Manipulating the Parameters Design Adding a Pole-Zero Pair Deleting Pole-Zero Pairs Interpreting the Nonstandard Contour Plots Page Pole Place Synthesis Pole Place Modes Normal Mode Integral Action Mode State-Space Interpretation Opening the Pole Place Window Manipulating the Closed-Loop Poles Time and Frequency Scaling Butterworth Configuration Editing the Closed-Loop Poles Slider and Plot Ranges LQG Synthesis LQG Synthesis Window Anatomy Page Synthesis Modes Opening the LQG Synthesis Window Setup and Terminology Standard LQG (All Toggle Buttons Off) Exponential Time Weighting Output Weight Editing State-Space Interpretation Manipulating the Design Parameters Graphically Page H-Infinity Synthesis H-Infinity Synthesis Window Anatomy Page Opening the Synthesis Window Setup and Synthesis Method Central H-Infinity Controller Output Weight Editing Manipulating the Weight Transfer Function Infeasible Parameter Values Page History Window Saving the Current Controller on the History List Opening the History Window History Window Anatomy Selecting the Active Controller Editing the Comments Deleting History List Entries To Continue Designing from a Saved Controller Cycling Through Designs Writing a Saved Design to Xmath Page Alternate Plant Window Role and Use of Plant and Alternate Plant Displaying the Alternate Plant Responses Alternate Plant Window Anatomy Page Normalization Manipulating the Parameters Using the Alternate Plant Window Robustness to Plant Variations Adding Unmodeled Dynamics Ranges of Sliders and Plot Introduction to MIMO Design Basic Terminology for MIMO Systems Feedback System Configuration Transfer Functions Page Page Overview of ICDM for MIMO Design ICDM MIMO Windows Main Window MIMO Plot Window Alternate Plant Window (MIMO Version) Page LQG/H-Infinity Synthesis LQG/H-Infinity Main Window LQG/H-Infinity Weights Window Page Page Decay Rate Window H-Infinity Performance Window Frequency Weights Window Synthesis Modes and Window Usage Opening the LQG/H-Infinity Synthesis Window Setup and Terminology Page Chapter 12 LQG/H-Infinity Synthesis Xmath Interactive Control Design Module 12-10 ni.com Figure 12-6. LQG/H-Infinity Control Design Configuration w How to Select w, u, y, and z H-Infinity Solution Page Main Window Page Multi-Loop Synthesis Multi-Loop Window Anatomy Page Setup and Synthesis Method Multi-Loop Versus Multivariable Design Page Page Page Opening the Multi-Loop Synthesis Window Designing a Multi-Loop Controller Graphical Editor Selecting and Deselecting Loops Editing and Deleting Loops Loop Gain Magnitude and Phase A Using an Xmath GUI Tool Overview Interacting with a GUI Application GUI Functions GUI Objects Page Page Page B Technical Support and Professional Services Index A B C D G H I K L R S T W Z