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pzplot

Plot pole-zero map of dynamic system

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    Description

    The pzplot function plots the pole-zero map of a dynamic system model and returns a PZPlot chart object. To customize the plot, modify the properties of the chart object using dot notation. For more information, see Customize Linear Analysis Plots at Command Line (Control System Toolbox).

    The following figure shows pole-zero maps for a continuous-time (left) and discrete-time (right) linear time-variant model.

    • In continuous-time systems, all the poles on the complex s-plane must be in the left-half plane (blue region) to ensure stability. The system is marginally stable if distinct poles lie on the imaginary axis, that is, the real parts of the poles are zero.

    • In discrete-time systems, all the poles in the complex z-plane must lie inside the unit circle (blue region). The system is marginally stable if it has one or more poles lying on the unit circle.

    To obtain pole and zero locations, use pzmap.

    Creation

    Syntax

    pzp = pzplot(sys)
    pzp = pzplot(sys1,sys2,...,sysN)
    pzp = pzplot(sys1,ColorSpec1,...,sysN,ColorSpecN)
    pzp = pzplot(___,plotoptions)
    pzp = pzplot(parent,___)

    Description

    pzp = pzplot(sys) plots the poles and transmission zeros of the dynamic system model sys and returns the corresponding chart object. In the plot, x and o represent poles and zeros, respectively.

    example

    pzp = pzplot(sys1,sys2,...,sysN) displays the poles and transmission zeros of multiple models on a single plot.

    example

    pzp = pzplot(sys1,ColorSpec1,...,sysN,ColorSpecN) sets the color for the plot of each system.

    example

    pzp = pzplot(___,plotoptions) plots the poles and transmission zeros with the plotting options specified in plotoptions. Settings you specify in plotoptions override the plotting preferences for the current MATLAB® session.

    example

    pzp = pzplot(parent,___) plots the poles and zeros in the specified parent graphics container, such as a Figure or TiledChartLayout, and sets the Parent property. Use this syntax when you want to create a plot in a specified open figure or when creating apps in App Designer.

    Input Arguments

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    Dynamic system, specified as a SISO or MIMO dynamic system model or array of dynamic system models. Dynamic systems that you can use include:

    • Continuous-time or discrete-time numeric LTI models, such as tf (Control System Toolbox), zpk (Control System Toolbox), or ss (Control System Toolbox) models.

    • Sparse state-space models, such as sparss (Control System Toolbox) or mechss (Control System Toolbox) models.

    • Generalized or uncertain LTI models such as genss (Control System Toolbox) or uss (Robust Control Toolbox) models. Using uncertain models requires Robust Control Toolbox™ software.

      • For tunable control design blocks, the function evaluates the model at its current value to plot the response.

      • For uncertain control design blocks, the function plots the nominal value and random samples of the model.

    • Identified LTI models, such as idtf, idss, or idproc models.

    If sys is an array of models, the plot shows responses of all models in the array on the same axes.

    Color, specified as one of the following values.

    ColorDescription
    "r"red
    "g"green
    "b"blue
    "c"cyan
    "m"magenta
    "y"yellow
    "k"black
    "w"white

    Pole-zero plot options, specified as a pzoptions object. You can use these options to customize the PZ plot appearance. Settings you specify in plotoptions override the preference settings for the current MATLAB session.

    Parent container of the chart, specified as one of the following objects:

    • Figure

    • TiledChartLayout

    • UIFigure

    • UIGridLayout

    • UIPanel

    • UITab

    Properties

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    Note

    The properties listed here are only a subset. For a complete list, see PZPlot Properties (Control System Toolbox).

    Model responses, specified as a PZResponse object or an array of such objects. Use this property to modify the dynamic system model or appearance for each response in the plot. Each PZResponse object has the following fields.

    Source data for the response, specified as a structure with the following fields.

    Dynamic system, specified as a SISO or MIMO dynamic system model or array of dynamic system models.

    When you initially create a plot, Model matches the value you specify for sys.

    Response name, specified as a string or character vector and stored as a string.

    Response visibility, specified as one of the following logical on/off values:

    • "on", 1, or true — Display the response in the plot.

    • "off", 0, or false — Do not display the response in the plot.

    The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.

    Option to list response in legend, specified as one of the following logical on/off values:

    • "on", 1, or true — List the response in the legend.

    • "off", 0, or false — Do not list the response in the legend.

    The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.

    Plot color, specified as an RGB triplet or a hexadecimal color code and stored as an RGB triplet.

    Alternatively, you can specify some common colors by name. The following table lists these colors and their corresponding RGB triplets and hexadecimal color codes.

    Color NameRGB TripletHexadecimal Color Code

    "red" or "r"

    		[1 0 0]#FF0000

    "green" or "g"

    		[0 1 0]#00FF00

    "blue" or "b"

    		[0 0 1]#0000FF

    "cyan" or "c"

    		[0 1 1]#00FFFF

    "magenta" or "m"

    		[1 0 1]#FF00FF

    "yellow" or "y"

    		[1 1 0]#FFFF00

    "black" or "k"

    		[0 0 0]#000000

    "white" or "w"

    		[1 1 1]#FFFFFF

    Marker size, specified as a positive scalar.

    Line width, specified as a positive scalar.

    Time units, specified as one of the following values:

    • "nanoseconds"

    • "microseconds"

    • "milliseconds"

    • "seconds"

    • "minutes"

    • "hours"

    • "days"

    • "weeks"

    • "months"

    • "years"

    Dependencies

    By default, the response uses the time units of the plotted linear system. You can override the default units by specifying toolbox preferences. For more information, see Specify Toolbox Preferences for Linear Analysis Plots.

    Frequency units, specified as one of the following values:

    • "Hz"

    • "rad/s"

    • "rpm"

    • "kHz"

    • "MHz"

    • "GHz"

    • "rad/nanosecond"

    • "rad/microsecond"

    • "rad/millisecond"

    • "rad/minute"

    • "rad/hour"

    • "rad/day"

    • "rad/week"

    • "rad/month"

    • "rad/year"

    • "cycles/nanosecond"

    • "cycles/microsecond"

    • "cycles/millisecond"

    • "cycles/hour"

    • "cycles/day"

    • "cycles/week"

    • "cycles/month"

    • "cycles/year"

    Dependencies

    By default, the response uses the frequency units of the plotted linear system. You can override the default units by specifying toolbox preferences. For more information, see Specify Toolbox Preferences for Linear Analysis Plots.

    Chart visibility, specified as one of the following logical on/off values:

    • "on", 1, or true — Display the chart.

    • "off", 0, or false — Hide the chart without deleting it. You still can access the properties of chart when it is not visible.

    The value is stored as an on/off logical value of type matlab.lang.OnOffSwitchState.

    Object Functions

    addResponseAdd dynamic system response to existing response plot

    Examples

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    This example uses:

    Open Live Script

    Plot the poles and zeros of the continuous-time system represented by the following transfer function:

    sys(s)=2s2+5s+1s2+3s+5.

    sys = tf([2 5 1],[1 3 5]);
pzp = pzplot(sys);
grid on

    MATLAB figure

    Turning on the grid displays lines of constant damping ratio (zeta) and lines of constant natural frequency (wn). This system has two real zeros, marked by o on the plot. The system also has a pair of complex poles, marked by x.

    Change the color of the plot title.

    pzp.Title.Color = [1 0 0];

    MATLAB figure

    Open Live Script

    For this example, load a 3-by-1 array of transfer function models.

    load('tfArrayMargin.mat','sys');
size(sys)
    3x1 array of transfer functions.
Each model has 1 outputs and 1 inputs.

    Plot the poles and zeros of the model array. Define the colors for each model. For this example, use red for the first model, green for the second, and blue for the third model in the array.

    pzplot(sys(:,:,1),'r',sys(:,:,2),'g',sys(:,:,3),'b');

    MATLAB figure

    Open Live Script

    Plot the poles and zeros of the continuous-time system represented by the following transfer function with a custom option set:

    sys(s)=2s2+5s+1s2+3s+5.

    Create the custom option set using pzoptions.

    plotoptions = pzoptions;

    For this example, specify the grid to be visible.

    plotoptions.Grid = 'on';

    Use the specified options to create a pole-zero map of the transfer function.

    h = pzplot(tf([2 5 1],[1 3 5]),plotoptions);

    MATLAB figure

    Turning on the grid displays lines of constant damping ratio (zeta) and lines of constant natural frequency (wn). This system has two real zeros, marked by o on the plot. The system also has a pair of complex poles, marked by x.

    Tips

    • Use sgrid or zgrid to plot lines of constant damping ratio and natural frequency in the s-plane or z-plane, respectively.

    Version History

    Introduced before R2006a

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    See Also

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