This PR implements time response plots for the various simulation routines in python-control via a new functiontime_response_plot() and via theplot() method on theTimeResponseData class. This is aligned with the new plotting paradigm in#645.

Examples (from the user documentation):

Input/output time responses are produced using one of several python-control functions:forced_response,impulse_response,initial_response(),input_output_response(), andstep_response(). Each of these return aTimeResponseData object, which contains the time, input, state, and output vectors associated with the simulation. Time response data can be plotted with thetime_response_plot() function, which is also available as theplot() 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:

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

time, outputs, inputs = response.time, response.outputs, response.inputsfig, 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 theimpulse_response() andstep_response() commands, the inputs are not shown. This behavior can be changed using theplot_inputs keyword. It is also possible to combine multiple lines onto a single graph, using either theoverlay_signals keyword (which puts all outputs out a single graph and all inputs on a single graph) or theoverlay_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, usingplot_input=True andoverlay_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 theforced_response() or theinput_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 ofplot_inputs=’overlay’ as well as the ability to reposition the legends using thelegend_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_traces(    [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 thecombine_traces() function.

Additional customization is possible using theinput_props,output_props andtrace_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 ['-', '--']])