rlocusplot

Root locus plot of dynamic system

Description

The rlocusplot function plots the root locus of a dynamic system model and returns an RLocusPlot 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.

To obtain feedback gains and complex root locations, use the rlocus function.

Creation

Syntax

rlp = rlocusplot(sys)

rlp = rlocusplot(sys1,sys2,...,sysN)

rlp = rlocusplot(sys1,LineSpec1,...,sysN,LineSpecN)

rlp = rlocusplot(___,k)

rlp = rlocusplot(___,plotoptions)

rlp = rlocusplot(parent,___)

Description

rlp = rlocusplot(sys) plots the root locus of the SISO dynamic system model sys and returns the corresponding chart object.

To produce a smooth plot, the rlocusplot function automatically selects a set of positive feedback gains.

rlp = rlocusplot(sys1,sys2,...,sysN) plots the root loci of multiple models on a single plot.

rlp = rlocusplot(sys1,LineSpec1,...,sysN,LineSpecN) sets the line style, marker type, and color for the plot of each system.

rlp = rlocusplot(___,k) plots responses for feedback gains specified in k. You can specify a frequency range or a vector of frequencies. You can use k with any of the input argument combinations in previous syntaxes.

rlp = rlocusplot(___,plotoptions) plots the root locus with the plotting options specified in plotoptions. Settings you specify in plotoptions override the plotting preferences for the current MATLAB^® session.

rlp = rlocusplot(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 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, 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.

LineSpec — Line style, marker, and color

string | character vector

Line style, marker, and color, specified as a string or character vector containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics. For example, specify the marker and omit the line style, then the plot shows only the marker and no line.

Example: '--or' is a red dashed line with circle markers.

Line Style	Description
"-"	Solid line
"--"	Dashed line
":"	Dotted line
"-."	Dash-dotted line

Marker	Description
"o"	Circle
"+"	Plus sign
"*"	Asterisk
"."	Point
"x"	Cross
"_"	Horizontal line
"|"	Vertical line
"s"	Square
"d"	Diamond
"^"	Upward-pointing triangle
"v"	Downward-pointing triangle
">"	Right-pointing triangle
"<"	Left-pointing triangle
"p"	Pentagram
"h"	Hexagram

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

k — Feedback gain values

vector

Feedback gain values that pertain to pole locations, specified as a vector. The feedback gains define the trajectory of the poles thereby affecting the shape of the root locus plot.

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 RLocusPlot Properties.

Responses — Model responses

RootLocusResponse object | array of RootLocusResponse objects

Model responses, specified as a RootLocusResponse 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 IOPZResponse 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 dynamic system model or array of dynamic system models.

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

FeedbackGainSpec — Dynamic system

vector

Feedback gain values that pertain to pole locations, specified as a vector. The feedback gains define the trajectory of the poles thereby affecting the shape of the root locus plot.

If you specify FeedbackGainSpec as empty, the software automatically selects a set of positive feedback gains that produce a smooth plot.

When you initially create a plot, FeedbackGainSpec matches the value you specify for k.

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

Plot Root Locus

Plot the root locus of a SISO dynamic system model.

sys = tf([2 5 1],[1 2 3]);
rlp = rlocusplot(sys);

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 rlocusplot 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.

  rlocusplot(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 rlocusplot function returns an RLocusPlot chart object. Previously, the rlocus 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 root locus plots to tiled chart layouts.

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

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

The following 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 root locus plot using the Children property of its parent figure.