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National Instruments ICDM Editing Poles and Zeros Graphically, Complex Poles and Zeros, Isolated Real Poles and Zeros, Nonisolated Real Poles and Zeros and Almost Real Pairs

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Chapter 2 Introduction to SISO Design

Xmath Interactive Control Design Module 2-14 ni.com

contains variable edit boxes for the value of the pole or zero (the real and

imaginary part when the pole or zero is complex) and, if appropriate, its

multiplicity. After you enter new values, you can select OK, which will

make the changes and dismiss the dialog box, or Cancel, which will

dismiss the dialog box without making the changes.

The values you type in will not be accepted if they are invalid—for

example, a negative multiplicity for a pole or zero.

Editing Poles and Zeros Graphically

The easiest way to change a pole or zero is to grab it by clicking the left

mouse button and dragging it to the desired location. You can only drag

poles and zeros in “sensible” ways. For example, you cannot drag a single

real pole or zero off the real axis to a complex location. More precisely, the

dragging of poles and zeros works as described in the following sections.

Complex Poles and Zeros

If the pole or zero that you grab is complex, then the complex conjugate

pole or zero will automatically move as required. In this case you can drag

the pole or zero in any direction.

Isolated Real Poles and Zeros

If the pole or zero that you grab is real and not very close to another real

pole or zero, then the pole or zero motion will be constrained to the real

axis. You cannot drag the pole or zero off the real axis.

Nonisolated Real Poles and Zeros and Almost Real Pairs

If a pair of nearby poles or zeros is very near the real axis—that is, two

nearby real poles or zeros, or a pair of complex poles and zeros with very

small imaginary part—then the dragging motion will depend on how you

originally drag the poles or zeros. If you drag it up or down, then the pair

acts as a complex pair and there is no constraint on how you can drag it. For

example, two real poles that are very close to each other can be split into a

complex pair by grabbing either one and dragging it away from the real

axis. On the other hand, if you drag the selected pole or zero left or right,

then the pair act as a real pair—the selected pole or zero then can be

dragged only along the real axis, and the other pole or zero becomes real

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