pzplot

Plot pole-zero map of dynamic system

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.

The figure shows pole-zero maps for a continuous-time (left) and discrete-time (right) linear time-variant model. The maps use x and o represent poles and zeros, respectively.

• 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 the pzmap function.

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.

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

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

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. You can use plotoptions with any of the input argument combinations in previous syntaxes.

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

sys — Dynamic system

dynamic system model | model array

Dynamic system, specified as a SISO or MIMO dynamic system model or array of dynamic system models. You can use these types of dynamic systems:

• Continuous-time or discrete-time numeric LTI models, such as tf, zpk, or ss models.

• Sparse state-space models, such as sparss or mechss models.

• Generalized or uncertain LTI models such as genss 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 (System Identification Toolbox), idss (System Identification Toolbox), or idproc (System Identification Toolbox) models. Using identified models requires System Identification Toolbox™ software.

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

ColorSpec — Color

"r" | "g" | "b" | ...

Color, specified as one of these values.

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

plotoptions — Pole-zero plot options

pzoptions object

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 — Parent graphics container

Figure object | TiledChartLayout object | UIFigure object | UIGridLayout object | UIPanel object | UITab object | Axes object | UIAxes object

Parent graphics container, specified as one of these objects:

• Figure

• TiledChartLayout

• UIFigure

• UIGridLayout

• UIPanel

• UITab

You can also specify parent as an Axes or UIAxes object, which sets the plot parent to the parent of the specified axes object.

Properties

Note

The properties listed here are only a subset. For a complete list, see PZPlot Properties.

Responses — Model responses

PZResponse object | array of PZResponse objects

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 these properties.

SourceData — Source data

structure

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

Model — Dynamic system

dynamic system model | model array

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

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

Name — Response name

string | character vector

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

Visible — Response visibility

"on" (default) | on/off logical value

Response visibility, specified as one of these 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.

LegendDisplay — Option to list response in legend

"on" (default) | on/off logical value

Option to list the response in the legend, specified as one of these 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.

Color — Plot color

RGB triplet | hexadecimal color code | color name

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. This table lists these colors and their corresponding RGB triplets and hexadecimal color codes.

Color Name	RGB Triplet	Hexadecimal 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

MarkerSize — Marker size

positive scalar

Marker size, specified as a positive scalar.

LineWidth — Line width

positive scalar

Line width, specified as a positive scalar.

TimeUnit — Time units

"seconds" | "milliseconds" | "minutes" | ...

Time units, specified as one of these 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.

FrequencyUnit — Frequency units

"Hz" | "rad/s" | "rpm" | ...

Frequency units, specified as one of these 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.

Visible — Chart visibility

"on" (default) | on/off logical value

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

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

• "off", 0, or false — Hide the chart without deleting it. You can still 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

addResponse

Add dynamic system response to existing response plot

Examples

Pole-Zero Plot with Custom Plot Title

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

$$sys\left(s\right)=\frac{2s^2+5s+1}{s^2+3s+5}.$$

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

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];

Pole-Zero Plot of Multiple Models

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');

Pole-Zero Plot with Custom Options

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

$$sys\left(s\right)=\frac{2s^2+5s+1}{s^2+3s+5}.$$

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);

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.

More About

Pole-Zero Plot Grid Lines

To plot lines of constant damping ratio (ζ) and natural frequency (w_n in the s-plane or z-plane, enable the GridVisible property of the chart object. Alternatively, you can use the grid command or right-click the plot area and select Grid.

The type of grid displayed in the plot depends on the time-domain of the plotted responses.

• For z-plane grids, you can specify the grid sample time (T_s) using the GridSampleTime property of the chart object. The w_n grid lines depend on the T_s. Therefore, you must specify T_s to plot specific w_n values. If you do not specify T_s, the plot uses normalized factors of w_n/T_s.

• The default s-plane grid plots lines for ζ from 0 to 1 in steps of 0.1 and w_n from 0 to 10 rad/sec in steps of one rad/sec.

• The default z-plane grid plots lines for ζ from 0 to 1 in steps of 0.1 and w_n from 0 to π/T_s in steps of 0.1*π/T_s.

• To specify ζ and w_n values, set the GridDampingSpec and GridFrequencySpec properties of the chart object.

Tips

• Plots created using pzplot do not support multiline titles or labels specified as string arrays or cell arrays of character vectors. To specify multiline titles and labels, use a single string with a newline character.

  impulseplot(sys)
  title("first line" + newline + "second line");

Version History

Introduced before R2006a

R2024b: Improved customization workflows and integration with MATLAB plotting tools

Starting in R2024b, the pzplot function returns a PZPlot chart object. Previously, the pzplot function returned a handle to the resulting plot.

The new chart object allows you to customize your plot using dot notation.

The new chart object also improves integration with MATLAB plotting tools. For example:

• You can now add PZ plots to tiled chart layouts.

• Saving and loading a parent figure now maintains full plot interactivity.

• You can add a response to your PZ plot using the new addResponse function.

These functionality changes might require updates to your code:

• The gca function now returns the chart object rather than an axes within the plot.

• You can no longer access the graphics objects within a PZ plot using the Children property of its parent figure.