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control.root_locus_plot — Python Control Systems Library 0.10.2 documentation

control.root_locus_plot(sysdata, gains=None, grid=None, plot=None, **kwargs)[source]

Root locus plot.

Calculate the root locus by finding the roots of 1 + k * G(s) where G is a linear system and k varies over a range of gains.

Parameters:

sysdataPoleZeroMap or LTI object or list

Linear input/output systems (SISO only, for now).

gainsarray_like, optional

Gains to use in computing plot of closed-loop poles. If not given, gains are chosen to include the main features of the root locus map.

xlimtuple or list, optional

Set limits of x axis (see matplotlib.axes.Axes.set_xlim).

ylimtuple or list, optional

Set limits of y axis (see matplotlib.axes.Axes.set_ylim).

plotbool, optional

(legacy) If given, root_locus_plot returns the legacy return values of roots and gains. If False, just return the values with no plot.

gridbool or str, optional

If True plot omega-damping grid, if False show imaginary axis for continuous-time systems, unit circle for discrete-time systems. If ‘empty’, do not draw any additional lines. Default value is set by config.defaults['rlocus.grid'].

initial_gainfloat, optional

Mark the point on the root locus diagram corresponding to the given gain.

colormatplotlib color spec, optional

Specify the color of the markers and lines.

Returns:

cpltControlPlot object

Object containing the data that were plotted. See ControlPlot for more detailed information.

cplt.linesarray of list of matplotlib.lines.Line2D

The shape of the array is given by (nsys, 3) where nsys is the number of systems or responses passed to the function. The second index specifies the object type:

• lines[idx, 0]: poles

• lines[idx, 1]: zeros

• lines[idx, 2]: loci

cplt.axes2D array of matplotlib.axes.Axes

Axes for each subplot.

cplt.figurematplotlib.figure.Figure

Figure containing the plot.

cplt.legend2D array of matplotlib.legend.Legend

Legend object(s) contained in the plot.

roots, gainsndarray

(legacy) If the plot keyword is given, returns the closed-loop root locations, arranged such that each row corresponds to a gain, and the array of gains (same as gains keyword argument if provided).

Other Parameters:

axmatplotlib.axes.Axes, optional

The matplotlib axes to draw the figure on. If not specified and the current figure has a single axes, that axes is used. Otherwise, a new figure is created.

labelstr or array_like of str, optional

If present, replace automatically generated label(s) with the given label(s). If sysdata is a list, strings should be specified for each system.

legend_locint or str, optional

Include a legend in the given location. Default is ‘center right’, with no legend for a single response. Use False to suppress legend.

show_legendbool, optional

Force legend to be shown if True or hidden if False. If None, then show legend when there is more than one line on the plot or legend_loc has been specified.

titlestr, optional

Set the title of the plot. Defaults to plot type and system name(s).

Notes

The root_locus_plot function calls matplotlib.pyplot.axis(‘equal’), which means that trying to reset the axis limits may not behave as expected. To change the axis limits, use matplotlib.pyplot.gca().axis(‘auto’) and then set the axis limits to the desired values.

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