Plotting data

The Python Control Toolbox contains a number of functions for plotting input/output responses in the time and frequency domain, root locus diagrams, and other standard charts used in control system analysis. While some legacy functions do both analysis and plotting, the standard pattern used in the toolbox is to provide a function that performs the basic computation (e.g., time or frequency response) and returns and object representing the output data. A separate plotting function, typically ending in _plot is then used to plot the data. The plotting function is also available via the plot() method of the analysis object, allowing the following type of calls:

step_response(sys).plot()
frequency_response(sys).plot()  # implementation pending
nyquist_curve(sys).plot()       # implementation pending
rootlocus_curve(sys).plot()     # implementation pending

Time response data

Input/output time responses are produced one of several python-control functions: forced_response(), impulse_response(), initial_response(), input_output_response(), step_response(). Each of these return a TimeResponseData object, which contains the time, input, state, and output vectors associated with the simulation. Time response data can be plotted with the time_response_plot() function, which is also available as the plot() method. For example, the step response for a two-input, two-output can be plotted using the commands:

sys_mimo = ct.tf2ss(
    [[[1], [0.1]], [[0.2], [1]]],
    [[[1, 0.6, 1], [1, 1, 1]], [[1, 0.4, 1], [1, 2, 1]]], name="MIMO")
response = step_response(sys)
response.plot()

which produces the following plot:

The TimeResponseData object can also be used to access the data from the simulation:

time, outputs, inputs = response.time, response.outputs, response.inputs
fig, axs = plt.subplots(2, 2)
for i in range(2):
    for j in range(2):
        axs[i, j].plot(time, outputs[i, j])

A number of options are available in the plot method to customize the appearance of input output data. For data produced by the impulse_response() and step_response() commands, the inputs are not shown. This behavior can be changed using the plot_inputs keyword. It is also possible to combine multiple lines onto a single graph, using either the overlay_signals keyword (which puts all outputs out a single graph and all inputs on a single graph) or the overlay_traces keyword, which puts different traces (e.g., corresponding to step inputs in different channels) on the same graph, with appropriate labeling via a legend on selected axes.

For example, using plot_input=True and overlay_signals=True yields the following plot:

ct.step_response(sys_mimo).plot(
  plot_inputs=True, overlay_signals=True,
  title="Step response for 2x2 MIMO system " +
  "[plot_inputs, overlay_signals]")

Input/output response plots created with either the forced_response() or the input_output_response() functions include the input signals by default. These can be plotted on separate axes, but also “overlaid” on the output axes (useful when the input and output signals are being compared to each other). The following plot shows the use of plot_inputs=’overlay’ as well as the ability to reposition the legends using the legend_map keyword:

timepts = np.linspace(0, 10, 100)
U = np.vstack([np.sin(timepts), np.cos(2*timepts)])
ct.input_output_response(sys_mimo, timepts, U).plot(
    plot_inputs='overlay',
    legend_map=np.array([['lower right'], ['lower right']]),
    title="I/O response for 2x2 MIMO system " +
    "[plot_inputs='overlay', legend_map]")

Another option that is available is to use the transpose keyword so that instead of plotting the outputs on the top and inputs on the bottom, the inputs are plotted on the left and outputs on the right, as shown in the following figure:

U1 = np.vstack([np.sin(timepts), np.cos(2*timepts)])
resp1 = ct.input_output_response(sys_mimo, timepts, U1)

U2 = np.vstack([np.cos(2*timepts), np.sin(timepts)])
resp2 = ct.input_output_response(sys_mimo, timepts, U2)

ct.combine_time_responses(
    [resp1, resp2], trace_labels=["Scenario #1", "Scenario #2"]).plot(
        transpose=True,
        title="I/O responses for 2x2 MIMO system, multiple traces "
        "[transpose]")

This figure also illustrates the ability to create “multi-trace” plots using the combine_time_responses() function. The line properties that are used when combining signals and traces are set by the input_props, output_props and trace_props parameters for time_response_plot().

Additional customization is possible using the input_props, output_props, and trace_props keywords to set complementary line colors and styles for various signals and traces:

out = ct.step_response(sys_mimo).plot(
    plot_inputs='overlay', overlay_signals=True, overlay_traces=True,
    output_props=[{'color': c} for c in ['blue', 'orange']],
    input_props=[{'color': c} for c in ['red', 'green']],
    trace_props=[{'linestyle': s} for s in ['-', '--']])

Plotting functions

time_response_plot(data, *fmt[, ax, ...])	Plot the time response of an input/output system.
combine_time_responses(response_list[, ...])	Combine multiple individual time responses into a multi-trace response.
get_plot_axes(line_array)	Get a list of axes from an array of lines.