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control.phaseplot.separatrices — Python Control Systems Library 0.10.2 documentation

control.phaseplot.separatrices(sys, pointdata, timedata=None, gridspec=None, zorder=None, ax=None, _check_kwargs=True, suppress_warnings=False, **kwargs)[source]

Plot separatrices in the phase plane.

This function plots separatrices for a two-dimensional state space system.

Parameters:

sysNonlinearIOSystem or callable(t, x, …)

I/O system or function used to generate phase plane data. If a function is given, the remaining arguments are drawn from the params keyword.

pointdatalist or 2D array

List of the form [xmin, xmax, ymin, ymax] describing the boundaries of the phase plot or an array of shape (N, 2) giving points of at which to plot the vector field.

timedataint or list of int

Time to simulate each streamline. If a list is given, a different time can be used for each initial condition in pointdata.

gridtypestr, optional

The type of grid to use for generating initial conditions: ‘meshgrid’ (default) generates a mesh of initial conditions within the specified boundaries, ‘boxgrid’ generates initial conditions along the edges of the boundary, ‘circlegrid’ generates a circle of initial conditions around each point in point data.

gridspeclist, optional

If the gridtype is ‘meshgrid’ and ‘boxgrid’, gridspec gives the size of the grid in the x and y axes on which to generate points. If gridtype is ‘circlegrid’, then gridspec is a 2-tuple specifying the radius and number of points around each point in the pointdata array.

paramsdict or list, optional

Parameters to pass to system. For an I/O system, params should be a dict of parameters and values. For a callable, params should be dict with key ‘args’ and value given by a tuple (passed to callable).

colormatplotlib color spec, optional

Plot the separatrices in the given color. If a single color specification is given, this is used for both stable and unstable separatrices. If a tuple is given, the first element is used as the color specification for stable separatrices and the second element for unstable separatrices.

axmatplotlib.axes.Axes, optional

Use the given axes for the plot, otherwise use the current axes.

Returns:

outlist of Line2D objects

Other Parameters:

rcParamsdict

Override the default parameters used for generating plots. Default is set by config.defaults['ctrlplot.rcParams'].

suppress_warningsbool, optional

If set to True, suppress warning messages in generating trajectories.

zorderfloat, optional

Set the zorder for the separatrices. In not specified, it will be automatically chosen by matplotlib.axes.Axes.plot.

Notes

The value of config.defaults['separatrices_radius'] is used to set the offset from the equilibrium point to the starting point of the separatix traces, in the direction of the eigenvectors evaluated at that equilibrium point.

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