National Instruments Xmath Interactive Control Design Module ICDM Manuel d'utilisateur

NI MATRIXxTMXmathTM Interactive Control Design ModuleXmath Interactive Control Design ModuleApril 2007370754C-01

ContentsXmath Interactive Control Design Module x ni.comChapter 13Multi-Loop SynthesisMulti-Loop Window Anatomy...

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-6 ni.comvalue. If a lower bound on the minimal value of γ is known, it a

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-7 Xmath Interactive Control Design ModuleFigure 12-5. LQG/H-Infinity Frequen

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-8 ni.comOpening the LQG/H-Infinity Synthesis WindowThe LQG/H∞ window can

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-9 Xmath Interactive Control Design ModuleThe weighted output vector z consist

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-10 ni.comFigure 12-6. LQG/H-Infinity Control Design ConfigurationIn the

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-11 Xmath Interactive Control Design ModuleThe system equations of plant, filt

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-12 ni.comPenalizing the “running integral” of the plant output forces th

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-13 Xmath Interactive Control Design ModuleThe transfer functions Wu, i and Wy

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-14 ni.comBy clicking the button at the bottom of the Weights window, arb

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-15 Xmath Interactive Control Design ModuleHere is a square matrix such that

© National Instruments Corporation 1-1 Xmath Interactive Control Design Module1IntroductionThe Xmath Interactive Control Design Module (ICDM) is a com

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-16 ni.comManipulating the Design ParametersMain WindowThe design paramet

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-17 Xmath Interactive Control Design ModuleRangesTo change the ranges of the s

© National Instruments Corporation 13-1 Xmath Interactive Control Design Module13Multi-Loop SynthesisThis chapter describes multi-loop synthesis. The

Chapter 13 Multi-Loop SynthesisXmath Interactive Control Design Module 13-2 ni.comFigure 13-1. Multi-Loop Main WindowAfter the Multi-Loop window is o

Chapter 13 Multi-Loop Synthesis© National Instruments Corporation 13-3 Xmath Interactive Control Design ModuleFigure 13-2. Multi-Loop Gain and Phase

Chapter 13 Multi-Loop SynthesisXmath Interactive Control Design Module 13-4 ni.comone loop at a time. The loops that are not closed are considered to

Chapter 13 Multi-Loop Synthesis© National Instruments Corporation 13-5 Xmath Interactive Control Design ModuleFigure 13-4. Multi-Loop Configuration w

Chapter 13 Multi-Loop SynthesisXmath Interactive Control Design Module 13-6 ni.comFigure 13-5. Root Locus Window During the Multi-Loop DesignFigure 1

Chapter 13 Multi-Loop Synthesis© National Instruments Corporation 13-7 Xmath Interactive Control Design ModuleOpening the Multi-Loop Synthesis WindowT

Chapter 13 Multi-Loop SynthesisXmath Interactive Control Design Module 13-8 ni.comEditing and Deleting LoopsWhen a loop is highlighted, it can be edit

Chapter 1 IntroductionXmath Interactive Control Design Module 1-2 ni.com• Chapter 5, Root Locus Synthesis, describes the user interface, terminology,

© National Instruments Corporation A-1 Xmath Interactive Control Design ModuleAUsing an Xmath GUI ToolThis appendix describes the basics of using an X

Appendix A Using an Xmath GUI ToolXmath Interactive Control Design Module A-2 ni.comFigure A-1. Programmable GUI ExamplesEach demo has a Help menu in

Appendix A Using an Xmath GUI Tool© National Instruments Corporation A-3 Xmath Interactive Control Design ModuleFigure A-2. Programmable GUI Examples

Appendix A Using an Xmath GUI ToolXmath Interactive Control Design Module A-4 ni.com•A list is a vertical list of items (strings) that can be selected

Appendix A Using an Xmath GUI Tool© National Instruments Corporation A-5 Xmath Interactive Control Design Module• GUI windows might contain buttons th

Appendix A Using an Xmath GUI ToolXmath Interactive Control Design Module A-6 ni.comA slider might also appear like a bar graph. Its tip represents th

© National Instruments Corporation B-1 Xmath Interactive Control Design ModuleBTechnical Support and Professional ServicesVisit the following sections

© National Instruments Corporation I-1 Xmath Interactive Control Design ModuleIndexAactuatordisturbance signal, 11-2effort transfer function, 11-3loop

IndexXmath Interactive Control Design Module I-2 ni.comGgain loop, 2-2graphical editor, 13-1HHelp, 1-5help, technical support, B-1high-frequency norma

Index© National Instruments Corporation I-3 Xmath Interactive Control Design ModulePole PlaceModes, 6-2Synthesis window, 2-4, 6-1window, 2-8poles, 1-1

Chapter 1 Introduction© National Instruments Corporation 1-3 Xmath Interactive Control Design ModuleCommonly-Used NomenclatureThis manual uses the fol

Chapter 1 IntroductionXmath Interactive Control Design Module 1-4 ni.comMATRIXx HelpInteractive Control Design Module function reference information i

Chapter 1 Introduction© National Instruments Corporation 1-5 Xmath Interactive Control Design Module• Have a user’s understanding of Xmath (enough to

© National Instruments Corporation 2-1 Xmath Interactive Control Design Module2Introduction to SISO DesignXmath provides a structure for system repres

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-2 ni.comThe equations describing this system are as follows:where y den

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-3 Xmath Interactive Control Design Module• The closed-loop transfer function

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-4 ni.comThese are briefly described in the following sections, and in m

SupportWorldwide Technical Support and Product Informationni.comNational Instruments Corporate Headquarters11500 North Mopac Expressway Austin, Texas

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-5 Xmath Interactive Control Design ModuleLQG Synthesis WindowThe LQG Synthes

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-6 ni.comThe plant and the alternate plant have very different uses in I

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-7 Xmath Interactive Control Design Modulelist. The current controller is the

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-8 ni.comwindow. Thus, the Root Locus Synthesis window can be used to in

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-9 Xmath Interactive Control Design Modulecontroller. Using the Root Locus wi

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-10 ni.comFigure 2-3 shows a simplified schematic representation of the

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-11 Xmath Interactive Control Design ModuleFigure 2-4. Simple ICDM SessionGe

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-12 ni.comwindow has an autoscale feature, which can be invoked by selec

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-13 Xmath Interactive Control Design Modulepoles and zeros are (and indeed, t

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-14 ni.comcontains variable edit boxes for the value of the pole or zero

Important InformationWarrantyThe media on which you receive National Instruments software are warranted not to fail to execute programming instructio

Chapter 2 Introduction to SISO Design© National Instruments Corporation 2-15 Xmath Interactive Control Design Module(if it was not already) but otherw

Chapter 2 Introduction to SISO DesignXmath Interactive Control Design Module 2-16 ni.comTo add a pole-zero pair, click the Add Pair button, select the

© National Instruments Corporation 3-1 Xmath Interactive Control Design Module3ICDM Main WindowThis chapter describes the use of the ICDM Main window,

Chapter 3 ICDM Main WindowXmath Interactive Control Design Module 3-2 ni.com• A line that identifies the type and source of the current controller. Th

Chapter 3 ICDM Main Window© National Instruments Corporation 3-3 Xmath Interactive Control Design ModuleMost Common UsageIn most cases, you will read

Chapter 3 ICDM Main WindowXmath Interactive Control Design Module 3-4 ni.comto a simple transfer function representation, which means that you cannot

Chapter 3 ICDM Main Window© National Instruments Corporation 3-5 Xmath Interactive Control Design ModuleICDM PlotsVarious plots can be shown at the bo

Chapter 3 ICDM Main WindowXmath Interactive Control Design Module 3-6 ni.comIn the ICDM Main window, the Plot Choices dialog box is used to select any

Chapter 3 ICDM Main Window© National Instruments Corporation 3-7 Xmath Interactive Control Design ModuleFigure 3-3. ICDM Ranges WindowPlot Magnify Wi

Chapter 3 ICDM Main WindowXmath Interactive Control Design Module 3-8 ni.comof Plots section. If another plot is subsequently selected for magnifying,

ConventionsThe following conventions are used in this manual:» The » symbol leads you through nested menu items and dialog box options to a final acti

Chapter 3 ICDM Main Window© National Instruments Corporation 3-9 Xmath Interactive Control Design ModuleSelecting a Synthesis or History WindowThe Syn

© National Instruments Corporation 4-1 Xmath Interactive Control Design Module4PID SynthesisThis chapter discusses the PID Synthesis window. This wind

Chapter 4 PID SynthesisXmath Interactive Control Design Module 4-2 ni.comToggling Controller Terms On and OffFor each parameter, the toggle button at

Chapter 4 PID Synthesis© National Instruments Corporation 4-3 Xmath Interactive Control Design ModuleFigure 4-1. PID Synthesis WindowAs an example, s

Chapter 4 PID SynthesisXmath Interactive Control Design Module 4-4 ni.comNotice that there are at least two other commonly used forms for a PID contro

Chapter 4 PID Synthesis© National Instruments Corporation 4-5 Xmath Interactive Control Design ModuleTime Versus Frequency ParametersNotice that the s

Chapter 4 PID SynthesisXmath Interactive Control Design Module 4-6 ni.comDerivative Term NormalizationThe derivative term is low-frequency normalized,

© National Instruments Corporation 5-1 Xmath Interactive Control Design Module5Root Locus SynthesisThis chapter describes the user interface, terminol

Chapter 5 Root Locus SynthesisXmath Interactive Control Design Module 5-2 ni.comFigure 5-1. Root Locus Synthesis WindowThe Root Locus Synthesis windo

Chapter 5 Root Locus Synthesis© National Instruments Corporation 5-3 Xmath Interactive Control Design ModuleEdit menu or by typing the accelerators in

© National Instruments Corporation v Xmath Interactive Control Design ModuleContentsChapter 1IntroductionUsing This Manual...

Chapter 5 Root Locus SynthesisXmath Interactive Control Design Module 5-4 ni.comPlotting StylesSelecting View»Locus Select or pressing <Ctrl-L>

Chapter 5 Root Locus Synthesis© National Instruments Corporation 5-5 Xmath Interactive Control Design ModulePhase ContoursFor each of magnitude and ph

Chapter 5 Root Locus SynthesisXmath Interactive Control Design Module 5-6 ni.comAll of the plots support data viewing: click the right mouse button wi

Chapter 5 Root Locus Synthesis© National Instruments Corporation 5-7 Xmath Interactive Control Design ModuleDesignThis section gives short description

Chapter 5 Root Locus SynthesisXmath Interactive Control Design Module 5-8 ni.comInterpreting the Nonstandard Contour PlotsThe Root Locus window can di

Chapter 5 Root Locus Synthesis© National Instruments Corporation 5-9 Xmath Interactive Control Design ModuleFigure 5-3. Root Locus Synthesis Window w

© National Instruments Corporation 6-1 Xmath Interactive Control Design Module6Pole Place SynthesisThis chapter discusses the Pole Place Synthesis win

Chapter 6 Pole Place SynthesisXmath Interactive Control Design Module 6-2 ni.comFigure 6-1. Pole Place Synthesis WindowPole Place ModesIn Pole Place,

Chapter 6 Pole Place Synthesis© National Instruments Corporation 6-3 Xmath Interactive Control Design Modulewheredp(s)=sn+ a1sn–1+ a2sn–2+...+annp(s)=

Chapter 6 Pole Place SynthesisXmath Interactive Control Design Module 6-4 ni.comWe can write this polynomial equation as follows:These 2n linear equat

ContentsXmath Interactive Control Design Module vi ni.comGraphically Manipulating Poles and Zeros...

Chapter 6 Pole Place Synthesis© National Instruments Corporation 6-5 Xmath Interactive Control Design ModuleState-Space InterpretationIn a state-space

Chapter 6 Pole Place SynthesisXmath Interactive Control Design Module 6-6 ni.comA circle of radius Favg also is displayed in the plot. You also can dr

© National Instruments Corporation 7-1 Xmath Interactive Control Design Module7LQG SynthesisThis chapter discusses the LQG Synthesis window, which is

Chapter 7 LQG SynthesisXmath Interactive Control Design Module 7-2 ni.comFigure 7-1. LQG Synthesis Window• A control panel used to graphically edit t

Chapter 7 LQG Synthesis© National Instruments Corporation 7-3 Xmath Interactive Control Design ModuleIf the decay rate is enabled, it is shown as a ve

Chapter 7 LQG SynthesisXmath Interactive Control Design Module 7-4 ni.comSetup and TerminologyThe different modes are described using the following ba

Chapter 7 LQG Synthesis© National Instruments Corporation 7-5 Xmath Interactive Control Design ModuleIntegral ActionWhen integral action is enabled, t

Chapter 7 LQG SynthesisXmath Interactive Control Design Module 7-6 ni.comOutput Weight EditingWhen Weight Zero Edit is enabled, the LQG controller is

Chapter 7 LQG Synthesis© National Instruments Corporation 7-7 Xmath Interactive Control Design ModuleState-Space InterpretationIn LQG theory, the clos

Chapter 7 LQG SynthesisXmath Interactive Control Design Module 7-8 ni.comRangesTo change the ranges of the sliders or plots, select View»Ranges or ent

Contents© National Instruments Corporation vii Xmath Interactive Control Design ModuleChapter 5Root Locus SynthesisOverview...

© National Instruments Corporation 8-1 Xmath Interactive Control Design Module8H-Infinity SynthesisThis chapter describes the H∞ Synthesis window used

Chapter 8 H-Infinity SynthesisXmath Interactive Control Design Module 8-2 ni.comFigure 8-1. H-Infinity Synthesis Window

Chapter 8 H-Infinity Synthesis© National Instruments Corporation 8-3 Xmath Interactive Control Design ModuleOpening the Synthesis WindowThe H∞ window

Chapter 8 H-Infinity SynthesisXmath Interactive Control Design Module 8-4 ni.comFigure 8-2. Block Diagram Showing the Basic Setup for H-Infinity Synt

Chapter 8 H-Infinity Synthesis© National Instruments Corporation 8-5 Xmath Interactive Control Design ModuleIf either of these singular values is equa

Chapter 8 H-Infinity SynthesisXmath Interactive Control Design Module 8-6 ni.comManipulating the Design ParametersThe parameters γ, ρ, and ν can be ch

Chapter 8 H-Infinity Synthesis© National Instruments Corporation 8-7 Xmath Interactive Control Design ModuleRangesTo change the ranges of the sliders

© National Instruments Corporation 9-1 Xmath Interactive Control Design Module9History WindowThis chapter describes the History window used for SISO p

Chapter 9 History WindowXmath Interactive Control Design Module 9-2 ni.com• A Variable-Edit box which shows which history list entry is active or curr

Chapter 9 History Window© National Instruments Corporation 9-3 Xmath Interactive Control Design ModuleDeleting History List EntriesAny number of desig

ContentsXmath Interactive Control Design Module viii ni.comManipulating the Design Parameters...

Chapter 9 History WindowXmath Interactive Control Design Module 9-4 ni.comUsing the History ListThe history list can be used in several ways. You can

© National Instruments Corporation 10-1 Xmath Interactive Control Design Module10Alternate Plant WindowThis chapter describes the form of the Alternat

Chapter 10 Alternate Plant WindowXmath Interactive Control Design Module 10-2 ni.comAlternate Plant Window AnatomyThe Alternate Plant window is shown

Chapter 10 Alternate Plant Window© National Instruments Corporation 10-3 Xmath Interactive Control Design ModuleFigure 10-1. Alternate Plant WindowOp

Chapter 10 Alternate Plant WindowXmath Interactive Control Design Module 10-4 ni.comNormalizationThe form of the transfer function of the alternate pl

Chapter 10 Alternate Plant Window© National Instruments Corporation 10-5 Xmath Interactive Control Design ModuleYou can switch between high frequency

Chapter 10 Alternate Plant WindowXmath Interactive Control Design Module 10-6 ni.comRanges of Sliders and PlotTo change the ranges of the Gain slider

© National Instruments Corporation 11-1 Xmath Interactive Control Design Module11Introduction to MIMO DesignThe following chapters describe the use of

Chapter 11 Introduction to MIMO DesignXmath Interactive Control Design Module 11-2 ni.comu denotes the plant input or actuator signal, which is a vect

Chapter 11 Introduction to MIMO Design© National Instruments Corporation 11-3 Xmath Interactive Control Design ModuleThe standard feedback system has

Contents© National Instruments Corporation ix Xmath Interactive Control Design ModuleChapter 11Introduction to MIMO DesignBasic Terminology for MIMO S

Chapter 11 Introduction to MIMO DesignXmath Interactive Control Design Module 11-4 ni.comNotice that in the SISO case, these “complementary pairs” of

Chapter 11 Introduction to MIMO Design© National Instruments Corporation 11-5 Xmath Interactive Control Design Moduleor disturbance rejection only on

Chapter 11 Introduction to MIMO DesignXmath Interactive Control Design Module 11-6 ni.comoptions, the user clicks the Show all options button after wh

Chapter 11 Introduction to MIMO Design© National Instruments Corporation 11-7 Xmath Interactive Control Design ModuleNotice that having the MIMO Plot

Chapter 11 Introduction to MIMO DesignXmath Interactive Control Design Module 11-8 ni.complants. Therefore, the (MIMO) Alternate Plant window looks ve

© National Instruments Corporation 12-1 Xmath Interactive Control Design Module12LQG/H-Infinity SynthesisThis chapter describes the MIMO LQG/H∞ Synthe

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-2 ni.comFigure 12-1. LQG/H-Infinity Main Window• A pull-down menu for f

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-3 Xmath Interactive Control Design Moduledescriptions are for the control cos

Chapter 12 LQG/H-Infinity SynthesisXmath Interactive Control Design Module 12-4 ni.com• A table with ny rows with, in each row:– A toggle button to in

Chapter 12 LQG/H-Infinity Synthesis© National Instruments Corporation 12-5 Xmath Interactive Control Design ModuleThe weights ρu, i, ρy, j, ρu,andρy a