National Instruments ICDM - Manuals

Contents Xmath Interactive Control Design Module x ni.com Chapter 13Multi-Loop Synthesis Multi-Loop Window Anatomy ...................................................................................... 13-1Setup and Synthesis Method ......................................................................

© National Instruments Corporation 1-1 Xmath Interactive Control Design Module 1 Introduction The Xmath Interactive Control Design Module (ICDM) is a complete library of classical and modern interactive control design functions that takes full advantage of Xmath’s powerful, object-oriented, graphica...

Chapter 1 Introduction © National Instruments Corporation 1-3 Xmath Interactive Control Design Module Commonly-Used Nomenclature This manual uses the following general nomenclature: • Matrix variables are generally denoted with capital letters; vectors are represented in lowercase. • G ( s ) is used...

Chapter 1 Introduction Xmath Interactive Control Design Module 1-4 ni.com MATRIXx Help Interactive Control Design Module function reference information is available in the MATRIXx Help . The MATRIXx Help includes all Interactive Control Design functions. Each topic explains a function’s inputs, outp...

© National Instruments Corporation 2-1 Xmath Interactive Control Design Module 2 Introduction to SISO Design Xmath provides a structure for system representation called a system object . This object includes system parameters in a data structure designed to reflect the way these systems are analyzed...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-3 Xmath Interactive Control Design Module • The closed-loop transfer function T is given by T = PC /(1 + PC ). T is the transfer function from r to y . • The characteristic polynomial of the system is defined as X = n c n p +...

Chapter 2 Introduction to SISO Design Xmath Interactive Control Design Module 2-4 ni.com These are briefly described in the following sections, and in more detail in later chapters. Several of these windows have different forms for SISO and MIMO design. This chapter restricts the discussion to the S...

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 contr...

Chapter 2 Introduction to SISO Design Xmath Interactive Control Design Module 2-6 ni.com The plant and the alternate plant have very different uses in ICDM, and therefore different data flow characteristics. The plant transfer function is read from Xmath into the ICDM Main window, and is then export...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-7 Xmath Interactive Control Design Module list. The current controller is the active or selected entry on the list of saved controllers. Only one synthesis window, or the History window, is allowed to be open at any given tim...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-9 Xmath Interactive Control Design Module controller. Using the Root Locus window, the user could reduce the controller to a PI controller by deleting poles and zeros, at which point the PID window can be opened, initialized ...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-11 Xmath Interactive Control Design Module Figure 2-4. Simple ICDM Session General Plotting Features All of the plots in the ICDM Main and other windows support several useful features: arbitrary re-ranging, zooming, data-vie...

Chapter 2 Introduction to SISO Design Xmath Interactive Control Design Module 2-12 ni.com window has an autoscale feature, which can be invoked by selecting Autoscale on the View or Plot menu of the window. When you invoke Autoscale, ICDM tries to assign some reasonable values to the slider and plot...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-13 Xmath Interactive Control Design Module poles and zeros are (and indeed, the only way on a black-and-white display) is to use data-viewing. As a general rule: To find out the meaning, purpose, or value of an object (pole, ...

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...

Chapter 2 Introduction to SISO Design © National Instruments Corporation 2-15 Xmath Interactive Control Design Module (if it was not already) but otherwise does not move. Thus, to make a pair of complex poles real, you first drag one of them near the real axis and release. Then you select one of the...

Chapter 2 Introduction to SISO Design Xmath Interactive Control Design Module 2-16 ni.com To add a pole-zero pair, click the Add Pair button, select the Add Pair entry on the Edit menu, or press <Ctrl-P> in the window. As with poles and zeros, the pole-zero pair you create will be either real ...

© National Instruments Corporation 3-1 Xmath Interactive Control Design Module 3 ICDM Main Window This chapter describes the use of the ICDM Main window, which is used to perform the following functions: • Communicate with Xmath—for example, transfer plants/controllers from/to Xmath • Display warnin...

Chapter 3 ICDM Main Window Xmath Interactive Control Design Module 3-2 ni.com • A line that identifies the type and source of the current controller. The source is either the currently active synthesis window or the history list. • A plotting area for the various plots. Figure 3-1. ICDM Main Window ...

Chapter 3 ICDM Main Window © National Instruments Corporation 3-3 Xmath Interactive Control Design Module Most Common Usage In most cases, you will read a plant from Xmath at the beginning of an ICDM design session, and write one or more controllers back to Xmath during or at the end of an ICDM desi...

Chapter 3 ICDM Main Window Xmath Interactive Control Design Module 3-4 ni.com to a simple transfer function representation, which means that you cannot read them back into the Pole Place, LQG, or synthesis windows because these types depend on the plant. Also, all synthesis windows will be reset to ...

Chapter 3 ICDM Main Window © National Instruments Corporation 3-5 Xmath Interactive Control Design Module ICDM Plots Various plots can be shown at the bottom of the main ICDM window. The Plot menu is used to select which plots are shown, and also to magnify a plot or set the plotting ranges. The use...

Chapter 3 ICDM Main Window Xmath Interactive Control Design Module 3-6 ni.com In the ICDM Main window, the Plot Choices dialog box is used to select any combination of the eight plots. This dialog box is modal so you cannot interact with any other Xmath window until you dismiss it. Ranges of Plots T...

Chapter 3 ICDM Main Window © National Instruments Corporation 3-7 Xmath Interactive Control Design Module Figure 3-3. ICDM Ranges Window Plot Magnify Windows In addition to the standard plotting features (zooming, data-viewing, and interactive re-ranging) described in the General Plotting Features s...

Chapter 3 ICDM Main Window Xmath Interactive Control Design Module 3-8 ni.com of Plots section. If another plot is subsequently selected for magnifying, it will replace the current plot in the plot magnify window. The Plot Magnify window is a separate window that shows one of the ICDM main plots. Th...

Chapter 3 ICDM Main Window © National Instruments Corporation 3-9 Xmath Interactive Control Design Module Selecting a Synthesis or History Window The Synthesis menu in the ICDM Main window is used to select which synthesis window will be active. If the current controller is compatible with the reque...

© National Instruments Corporation 4-1 Xmath Interactive Control Design Module 4 PID Synthesis This chapter discusses the PID Synthesis window. This window is used to synthesize various types of standard classical SISO controllers such as P, PI, PD, PID, lead-lag, and lag-lead. However, the controll...

Chapter 4 PID Synthesis Xmath Interactive Control Design Module 4-2 ni.com Toggling Controller Terms On and Off For each parameter, the toggle button at the left of the row is used to toggle the terms on and off. “On” means that the corresponding controller term appears in the overall controller tra...

Chapter 4 PID Synthesis Xmath Interactive Control Design Module 4-4 ni.com Notice that there are at least two other commonly used forms for a PID control law that differ from the one used in ICDM: and ICDM enforces a proper controller transfer function, that is, a finite high frequency gain. Therefo...

Chapter 4 PID Synthesis © National Instruments Corporation 4-5 Xmath Interactive Control Design Module Time Versus Frequency Parameters Notice that the sliders and variable-edit boxes use time parameters, whereas the Bode plot handles use frequencies, that is, the inverses of the time parameters. If...

Chapter 4 PID Synthesis Xmath Interactive Control Design Module 4-6 ni.com Derivative Term Normalization The derivative term is low-frequency normalized, which means that at low frequencies (below 1/ T diff ) it is nearly one, and so has little effect on the overall controller transfer function at l...

© National Instruments Corporation 5-1 Xmath Interactive Control Design Module 5 Root Locus Synthesis This chapter describes the user interface, terminology, and parameters used for root locus synthesis. Overview The Root Locus window performs two main functions: • Displays selected gain and phase c...

Chapter 5 Root Locus Synthesis © National Instruments Corporation 5-3 Xmath Interactive Control Design Module Edit menu or by typing the accelerators in the Root Locus window. A more detailed description appears following. The Root Locus Synthesis window is shown in Figure 5-1 with the standard (def...

Chapter 5 Root Locus Synthesis Xmath Interactive Control Design Module 5-4 ni.com Plotting Styles Selecting View»Locus Select or pressing <Ctrl-L> in the Root Locus window produces a dialog box in which the user can choose one of many possible plotting styles. In all cases, the (open-loop) con...

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 tr...

Chapter 5 Root Locus Synthesis Xmath Interactive Control Design Module 5-6 ni.com All of the plots support data viewing: click the right mouse button with the cursor positioned near a pole, zero, or one of the plots. This allows you to find the gain associated with a particular point on a phase cont...

Chapter 5 Root Locus Synthesis © National Instruments Corporation 5-7 Xmath Interactive Control Design Module Design This section gives short descriptions of how the Root Locus window can be used to design or analyze controllers. This section also provides some interpretations and describes some use...

Chapter 5 Root Locus Synthesis Xmath Interactive Control Design Module 5-8 ni.com Interpreting the Nonstandard Contour Plots The Root Locus window can display phase contours other than the standard 180 ° as well as various magnitude contour plots. The meaning of these curves is simple: if L ( s ) = ...

© National Instruments Corporation 6-1 Xmath Interactive Control Design Module 6 Pole Place Synthesis This chapter discusses the Pole Place Synthesis window, which is used to design a SISO controller by assigning the closed-loop poles. Pole Place operates in two modes: • Normal mode (integral action...

Chapter 6 Pole Place Synthesis Xmath Interactive Control Design Module 6-2 ni.com Figure 6-1. Pole Place Synthesis Window Pole Place Modes In Pole Place, the user selects either closed-loop poles (in normal mode) or 2 n + 1 closed-loop poles (in integral action mode). These poles uniquely determine ...

Chapter 6 Pole Place Synthesis © National Instruments Corporation 6-3 Xmath Interactive Control Design Module where d p ( s ) = s n + a 1 s n –1 + a 2 s n –2 + ... + a n n p ( s ) = b 0 s n + b 1 s n –1 + ... + ab n Notice that the order of the plant is n , and allow the possibility that the plant t...

Chapter 6 Pole Place Synthesis Xmath Interactive Control Design Module 6-4 ni.com We can write this polynomial equation as follows: These 2 n linear equations are solved to find the 2 n controller parameters x 1 , ..., x n and y 1 , ..., y n . Integral Action Mode The degree (number of poles) of the...

Chapter 6 Pole Place Synthesis © National Instruments Corporation 6-5 Xmath Interactive Control Design Module State-Space Interpretation In a state-space framework, it is common to classify the closed-loop poles as n “control eigenvalues” and n “estimator eigenvalues.” But, in fact, it makes no diff...

Chapter 6 Pole Place Synthesis Xmath Interactive Control Design Module 6-6 ni.com A circle of radius F avg also is displayed in the plot. You also can drag the circle to change F avg . Butterworth Configuration Click the Butterworth button to move the poles to a Butterworth configuration, preserving...

© National Instruments Corporation 7-1 Xmath Interactive Control Design Module 7 LQG Synthesis This chapter discusses the LQG Synthesis window, which is used to synthesize a linear quadratic Gaussian (LQG) controller for a SISO plant. If you select LQG synthesis with a MIMO plant, you will get the M...

Chapter 7 LQG Synthesis © National Instruments Corporation 7-3 Xmath Interactive Control Design Module If the decay rate is enabled, it is shown as a vertical line that can be dragged. – A plot showing the poles and zeros of the output weight transfer function. If weight zero editing is enabled, the...

Chapter 7 LQG Synthesis Xmath Interactive Control Design Module 7-4 ni.com Setup and Terminology The different modes are described using the following basic terminology: Figure 7-1 shows a block diagram with the basic setup for LQG synthesis, where u is the actuator signal (output of the controller)...

Chapter 7 LQG Synthesis © National Instruments Corporation 7-5 Xmath Interactive Control Design Module Integral Action When integral action is enabled, the controller minimizes a variation on the LQG cost: where As in the standard mode, the sensor noise parameter ν is the ratio of the sensor noise i...

Chapter 7 LQG Synthesis Xmath Interactive Control Design Module 7-6 ni.com Output Weight Editing When Weight Zero Edit is enabled, the LQG controller is based on , which is a filtered version of the plant output signal y . Without integral action, the controller minimizes the quantity: and with inte...

Chapter 7 LQG Synthesis © National Instruments Corporation 7-7 Xmath Interactive Control Design Module State-Space Interpretation In LQG theory, the closed-loop poles consist of n “optimal control eigenvalues” and n “estimator (Kalman filter) eigenvalues.” For multivariable systems, the optimal cont...

© National Instruments Corporation 8-1 Xmath Interactive Control Design Module 8 H-Infinity Synthesis This chapter describes the H ∞ Synthesis window used for SISO plants. The H ∞ Synthesis window is used to synthesize a central controller. Such controllers are sometimes called linear exponential qu...

Chapter 8 H-Infinity Synthesis © National Instruments Corporation 8-3 Xmath Interactive Control Design Module Opening the Synthesis Window The H ∞ window can only accept H ∞ controllers. If the current controller is of type H ∞ (perhaps from the History window) and the H ∞ window is opened, the curr...

Chapter 8 H-Infinity Synthesis Xmath Interactive Control Design Module 8-4 ni.com Figure 8-2. Block Diagram Showing the Basic Setup for H-Infinity Synthesis Figure 8-2 shows a block diagram with the basic setup for H ∞ synthesis where closed-loop transfer matrix H relates the two exogenous inputs w ...

Chapter 8 H-Infinity Synthesis Xmath Interactive Control Design Module 8-6 ni.com Manipulating the Design Parameters The parameters γ , ρ , and ν can be changed using the associated slider or variable edit box. If the user types in a value that is outside the current slider range, the slider range w...

© National Instruments Corporation 9-1 Xmath Interactive Control Design Module 9 History Window This chapter describes the History window used for SISO plants. The History window is used to display and manipulate the design history list, which is a list of controllers that have been explicitly saved...

Chapter 9 History Window Xmath Interactive Control Design Module 9-2 ni.com • A Variable-Edit box which shows which history list entry is active or currently selected. The selected entry is the controller exported to ICDM for plotting. • Buttons for manipulating the history list. Selecting the Activ...

Chapter 9 History Window © National Instruments Corporation 9-3 Xmath Interactive Control Design Module Deleting History List Entries Any number of designs on the history list can be deleted by selecting them and then clicking Delete . To renumber the remaining designs, you can select Edit»Renumber ...

Chapter 9 History Window Xmath Interactive Control Design Module 9-4 ni.com Using the History List The history list can be used in several ways. You can save controllers as “benchmarks” whose performance you want to match with a simpler controller. You also can save any promising designs that you fi...

© National Instruments Corporation 10-1 Xmath Interactive Control Design Module 10 Alternate Plant Window This chapter describes the form of the Alternate Plant window used for SISO design; refer to Chapter 11, Introduction to MIMO Design , for the form used for MIMO design. Role and Use of Plant an...

Chapter 10 Alternate Plant Window Xmath Interactive Control Design Module 10-2 ni.com Alternate Plant Window Anatomy The Alternate Plant window is shown in Figure 10-1. From top to bottom, it consists of: • A menu bar with Special , Edit , and View menus. • A toggle button for controlling whether th...

Chapter 10 Alternate Plant Window © National Instruments Corporation 10-3 Xmath Interactive Control Design Module Figure 10-1. Alternate Plant Window Opening the Alternate Plant Window When the Alternate Plant window is first opened, the alternate plant is initialized to the plant transfer function....

Chapter 10 Alternate Plant Window Xmath Interactive Control Design Module 10-4 ni.com Normalization The form of the transfer function of the alternate plant depends on the normalization selected. With high-frequency normalization, the alternate plant transfer function is: where K is the gain (shown ...

Chapter 10 Alternate Plant Window © National Instruments Corporation 10-5 Xmath Interactive Control Design Module You can switch between high frequency and DC normalization by clicking the appropriate buttons. If the alternate plant has a pole or zero at s = 0, then you cannot switch to DC normaliza...

Chapter 10 Alternate Plant Window Xmath Interactive Control Design Module 10-6 ni.com Ranges of Sliders and Plot To change the ranges of the Gain slider or the pole zero plot, select View»Ranges or press <Ctrl-R> in the Alternate Plant window. The slider range also will be changed automaticall...

© National Instruments Corporation 11-1 Xmath Interactive Control Design Module 11 Introduction to MIMO Design The following chapters describe the use of ICDM for MIMO design. NI assumes the reader is familiar with the use of ICDM for SISO design. In many cases, the texts describe the differences be...

Chapter 11 Introduction to MIMO Design Xmath Interactive Control Design Module 11-2 ni.com u denotes the plant input or actuator signal, which is a vector of size n u r denotes the reference or command input signal, which is a vector of size n y e denotes the error signal, which is a vector of size ...

Chapter 11 Introduction to MIMO Design © National Instruments Corporation 11-5 Xmath Interactive Control Design Module or disturbance rejection only on a subspace of dimension r , so do not be surprised if some (or many) diagonal entries of T are not one, or off diagonal entries are not zero. Finall...

Chapter 11 Introduction to MIMO Design Xmath Interactive Control Design Module 11-6 ni.com options, the user clicks the Show all options button after which the plot options window shown in Figure 11-3 opens. From this window, all transfer functions mentioned in the Transfer Functions section can be ...

Chapter 11 Introduction to MIMO Design © National Instruments Corporation 11-7 Xmath Interactive Control Design Module Notice that having the MIMO Plot window on the screen may increase the required computational response time of ICDM. Closing the window using the Special option of the MIMO Plot men...

Chapter 12 LQG/H-Infinity Synthesis © National Instruments Corporation 12-5 Xmath Interactive Control Design Module The weights ρ u , i , ρ y , j , ρ u , and ρ y are then replaced with noise variances ν u , i , ν y , j , ν u , and ν y . The noise level parameter in the main LQG/H ∞ window is related...

Chapter 12 LQG/H-Infinity Synthesis Xmath Interactive Control Design Module 12-6 ni.com value. If a lower bound on the minimal value of γ is known, it also is displayed. Figure 12-4. LQG/H-Infinity Performance Level Window Frequency Weights Window The Frequency Weights window is shown in Figure 12-5...

Chapter 12 LQG/H-Infinity Synthesis © National Instruments Corporation 12-7 Xmath Interactive Control Design Module Figure 12-5. LQG/H-Infinity Frequency Weights Window Synthesis Modes and Window Usage In addition to the standard LQG/H ∞ synthesis, any combination of three additional features is sup...

Chapter 12 LQG/H-Infinity Synthesis Xmath Interactive Control Design Module 12-8 ni.com Opening the LQG/H-Infinity Synthesis Window The LQG/H ∞ window can only accept LQG / H ∞ controllers. If the current controller is of type LQG / H ∞ (perhaps, from the History window) and the LQG/H ∞ window is op...

Chapter 12 LQG/H-Infinity Synthesis Xmath Interactive Control Design Module 12-12 ni.com Penalizing the “running integral” of the plant output forces the power spectral density of the plant output to vanish at zero frequency. In classical control terms, this forces a pole at s = 0 in the loop transf...

Chapter 12 LQG/H-Infinity Synthesis © National Instruments Corporation 12-13 Xmath Interactive Control Design Module The transfer functions W u, i and W y, j are the input and output weighting transfer functions, respectively. When W u, i = 1 and W u, j = 1, this reduces to the previously described ...

Chapter 12 LQG/H-Infinity Synthesis Xmath Interactive Control Design Module 12-16 ni.com Manipulating the Design Parameters Main Window The design parameters ρ and ν can be changed using the associated sliders or the variable edit boxes. If the user types in a value that is outside the current slide...

© National Instruments Corporation 13-1 Xmath Interactive Control Design Module 13 Multi-Loop Synthesis This chapter describes multi-loop synthesis. The Multi-Loop window is used to synthesize a MIMO controller using PID and Root Locus methods, applying them one-loop-at-a-time. In many practical ind...

Chapter 13 Multi-Loop Synthesis © National Instruments Corporation 13-3 Xmath Interactive Control Design Module Figure 13-2. Multi-Loop Gain and Phase Plots Added to the ICDM Main Window Setup and Synthesis Method This section describes the setup and synthesis method for multi-loop synthesis. Multi-...

Chapter 13 Multi-Loop Synthesis © National Instruments Corporation 13-7 Xmath Interactive Control Design Module Opening the Multi-Loop Synthesis Window The multi-loop window can accept any type of MIMO controller and will decompose it into its SISO components, one for each loop. Control loops are ca...

Chapter 13 Multi-Loop Synthesis Xmath Interactive Control Design Module 13-8 ni.com Editing and Deleting Loops When a loop is highlighted, it can be edited, deleted, disabled, or enabled. Here, “editing” means designing a SISO controller for the selected loop. The editing and deleting options are ac...

Appendix A Using an Xmath GUI Tool Xmath Interactive Control Design Module A-2 ni.com Figure A-1. Programmable GUI Examples Each demo has a Help menu in its menu bar, near the upper right side of the window. The Help messages explain how to interact with the demo and what it does. It may be helpful ...

Appendix A Using an Xmath GUI Tool © National Instruments Corporation A-3 Xmath Interactive Control Design Module Figure A-2. Programmable GUI Examples Do It Dialog GUI Functions Many functions are controlled by the left mouse button. For example, a button is activated or selected by pointing at the...

Appendix A Using an Xmath GUI Tool Xmath Interactive Control Design Module A-4 ni.com • A list is a vertical list of items (strings) that can be selected (highlighted). Depending on the application, a list can be configured to allow various types of selection: – A single-selection list allows only a...