diff --git a/control/__init__.py b/control/__init__.py
index 9781ab80e..120d16325 100644
--- a/control/__init__.py
+++ b/control/__init__.py
@@ -77,6 +77,10 @@
from .xferfcn import *
from .frdata import *
+# Time responses and plotting
+from .timeresp import *
+from .timeplot import *
+
from .bdalg import *
from .delay import *
from .descfcn import *
@@ -91,7 +95,6 @@
from .rlocus import *
from .statefbk import *
from .stochsys import *
-from .timeresp import *
from .ctrlutil import *
from .canonical import *
from .robust import *
diff --git a/control/config.py b/control/config.py
index 987693c2d..1ed8b5dd5 100644
--- a/control/config.py
+++ b/control/config.py
@@ -135,6 +135,9 @@ def reset_defaults():
from .optimal import _optimal_defaults
defaults.update(_optimal_defaults)
+ from .timeplot import _timeplot_defaults
+ defaults.update(_timeplot_defaults)
+
def _get_param(module, param, argval=None, defval=None, pop=False, last=False):
"""Return the default value for a configuration option.
diff --git a/control/nlsys.py b/control/nlsys.py
index c540decb6..f11d08a31 100644
--- a/control/nlsys.py
+++ b/control/nlsys.py
@@ -1488,6 +1488,7 @@ def ufun(t):
return TimeResponseData(
t_eval, y, None, u, issiso=sys.issiso(),
output_labels=sys.output_labels, input_labels=sys.input_labels,
+ title="Input/output response for " + sys.name, sysname=sys.name,
transpose=transpose, return_x=return_x, squeeze=squeeze)
# Create a lambda function for the right hand side
@@ -1567,7 +1568,8 @@ def ivp_rhs(t, x):
return TimeResponseData(
soln.t, y, soln.y, u, issiso=sys.issiso(),
output_labels=sys.output_labels, input_labels=sys.input_labels,
- state_labels=sys.state_labels,
+ state_labels=sys.state_labels, sysname=sys.name,
+ title="Input/output response for " + sys.name,
transpose=transpose, return_x=return_x, squeeze=squeeze)
diff --git a/control/tests/kwargs_test.py b/control/tests/kwargs_test.py
index 1abc7547e..19f4bb627 100644
--- a/control/tests/kwargs_test.py
+++ b/control/tests/kwargs_test.py
@@ -26,6 +26,7 @@
import control.tests.statefbk_test as statefbk_test
import control.tests.stochsys_test as stochsys_test
import control.tests.trdata_test as trdata_test
+import control.tests.timeplot_test as timeplot_test
@pytest.mark.parametrize("module, prefix", [
(control, ""), (control.flatsys, "flatsys."), (control.optimal, "optimal.")
@@ -74,7 +75,8 @@ def test_kwarg_search(module, prefix):
# @parametrize messes up the check, but we know it is there
pass
- elif source and source.find('unrecognized keyword') < 0:
+ elif source and source.find('unrecognized keyword') < 0 and \
+ source.find('unexpected keyword') < 0:
warnings.warn(
f"'unrecognized keyword' not found in unit test "
f"for {name}")
@@ -161,7 +163,21 @@ def test_matplotlib_kwargs(function, nsysargs, moreargs, kwargs, mplcleanup):
function(*args, **kwargs, unknown=None)
+@pytest.mark.parametrize(
+ "function", [control.time_response_plot, control.TimeResponseData.plot])
+def test_time_response_plot_kwargs(function):
+ # Create a system for testing
+ response = control.step_response(control.rss(4, 2, 2))
+
+ # Call the plotting function normally and make sure it works
+ function(response)
+ # Now add an unrecognized keyword and make sure there is an error
+ with pytest.raises(AttributeError,
+ match="(has no property|unexpected keyword)"):
+ function(response, unknown=None)
+
+
#
# List of all unit tests that check for unrecognized keywords
#
@@ -185,6 +201,7 @@ def test_matplotlib_kwargs(function, nsysargs, moreargs, kwargs, mplcleanup):
'gangof4_plot': test_matplotlib_kwargs,
'input_output_response': test_unrecognized_kwargs,
'interconnect': interconnect_test.test_interconnect_exceptions,
+ 'time_response_plot': timeplot_test.test_errors,
'linearize': test_unrecognized_kwargs,
'lqe': test_unrecognized_kwargs,
'lqr': test_unrecognized_kwargs,
@@ -230,6 +247,7 @@ def test_matplotlib_kwargs(function, nsysargs, moreargs, kwargs, mplcleanup):
'StateSpace.__init__': test_unrecognized_kwargs,
'StateSpace.sample': test_unrecognized_kwargs,
'TimeResponseData.__call__': trdata_test.test_response_copy,
+ 'TimeResponseData.plot': timeplot_test.test_errors,
'TransferFunction.__init__': test_unrecognized_kwargs,
'TransferFunction.sample': test_unrecognized_kwargs,
'optimal.OptimalControlProblem.__init__':
diff --git a/control/tests/timeplot_test.py b/control/tests/timeplot_test.py
new file mode 100644
index 000000000..7cdde5c54
--- /dev/null
+++ b/control/tests/timeplot_test.py
@@ -0,0 +1,511 @@
+# timeplot_test.py - test out time response plots
+# RMM, 23 Jun 2023
+
+import pytest
+import control as ct
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+import numpy as np
+
+from control.tests.conftest import slycotonly
+
+# Detailed test of (almost) all functionality
+#
+# The commented out rows lead to very long testing times => these should be
+# used only for developmental testing and not day-to-day testing.
+@pytest.mark.parametrize(
+ "sys", [
+ # ct.rss(1, 1, 1, strictly_proper=True, name="rss"),
+ ct.nlsys(
+ lambda t, x, u, params: -x + u, None,
+ inputs=1, outputs=1, states=1, name="nlsys"),
+ # ct.rss(2, 1, 2, strictly_proper=True, name="rss"),
+ ct.rss(2, 2, 1, strictly_proper=True, name="rss"),
+ # ct.drss(2, 2, 2, name="drss"),
+ # ct.rss(2, 2, 3, strictly_proper=True, name="rss"),
+ ])
+# @pytest.mark.parametrize("transpose", [False, True])
+# @pytest.mark.parametrize("plot_inputs", [False, None, True, 'overlay'])
+# @pytest.mark.parametrize("plot_outputs", [True, False])
+# @pytest.mark.parametrize("overlay_signals", [False, True])
+# @pytest.mark.parametrize("overlay_traces", [False, True])
+# @pytest.mark.parametrize("second_system", [False, True])
+# @pytest.mark.parametrize("fcn", [
+# ct.step_response, ct.impulse_response, ct.initial_response,
+# ct.forced_response])
+@pytest.mark.parametrize( # combinatorial-style test (faster)
+ "fcn, pltinp, pltout, cmbsig, cmbtrc, trpose, secsys",
+ [(ct.step_response, False, True, False, False, False, False),
+ (ct.step_response, None, True, False, False, False, False),
+ (ct.step_response, True, True, False, False, False, False),
+ (ct.step_response, 'overlay', True, False, False, False, False),
+ (ct.step_response, 'overlay', True, True, False, False, False),
+ (ct.step_response, 'overlay', True, False, True, False, False),
+ (ct.step_response, 'overlay', True, False, False, True, False),
+ (ct.step_response, 'overlay', True, False, False, False, True),
+ (ct.step_response, False, False, False, False, False, False),
+ (ct.step_response, None, False, False, False, False, False),
+ (ct.step_response, 'overlay', False, False, False, False, False),
+ (ct.step_response, True, True, False, True, False, False),
+ (ct.step_response, True, True, False, False, False, True),
+ (ct.step_response, True, True, False, True, False, True),
+ (ct.step_response, True, True, True, False, True, True),
+ (ct.step_response, True, True, False, True, True, True),
+ (ct.impulse_response, False, True, True, False, False, False),
+ (ct.initial_response, None, True, False, False, False, False),
+ (ct.initial_response, False, True, False, False, False, False),
+ (ct.initial_response, True, True, False, False, False, False),
+ (ct.forced_response, True, True, False, False, False, False),
+ (ct.forced_response, None, True, False, False, False, False),
+ (ct.forced_response, False, True, False, False, False, False),
+ (ct.forced_response, True, True, True, False, False, False),
+ (ct.forced_response, True, True, True, True, False, False),
+ (ct.forced_response, True, True, True, True, True, False),
+ (ct.forced_response, True, True, True, True, True, True),
+ (ct.forced_response, 'overlay', True, True, True, False, True),
+ (ct.input_output_response,
+ True, True, False, False, False, False),
+ ])
+
+def test_response_plots(
+ fcn, sys, pltinp, pltout, cmbsig, cmbtrc,
+ trpose, secsys, clear=True):
+ # Figure out the time range to use and check some special cases
+ if not isinstance(sys, ct.lti.LTI):
+ if fcn == ct.impulse_response:
+ pytest.skip("impulse response not implemented for nlsys")
+
+ # Nonlinear systems require explicit time limits
+ T = 10
+ timepts = np.linspace(0, T)
+
+ elif isinstance(sys, ct.TransferFunction) and fcn == ct.initial_response:
+ pytest.skip("initial response not tested for tf")
+
+ else:
+ # Linear systems figure things out on their own
+ T = None
+ timepts = np.linspace(0, 10) # for input_output_response
+
+ # Save up the keyword arguments
+ kwargs = dict(
+ plot_inputs=pltinp, plot_outputs=pltout, transpose=trpose,
+ overlay_signals=cmbsig, overlay_traces=cmbtrc)
+
+ # Create the response
+ if fcn is ct.input_output_response and \
+ not isinstance(sys, ct.NonlinearIOSystem):
+ # Skip transfer functions and other non-state space systems
+ return None
+ if fcn in [ct.input_output_response, ct.forced_response]:
+ U = np.zeros((sys.ninputs, timepts.size))
+ for i in range(sys.ninputs):
+ U[i] = np.cos(timepts * i + i)
+ args = [timepts, U]
+
+ elif fcn == ct.initial_response:
+ args = [T, np.ones(sys.nstates)] # T, X0
+
+ elif not isinstance(sys, ct.lti.LTI):
+ args = [T] # nonlinear systems require final time
+
+ else: # step, initial, impulse responses
+ args = []
+
+ # Create a new figure (in case previous one is of the same size) and plot
+ if not clear:
+ plt.figure()
+ response = fcn(sys, *args)
+
+ # Look for cases where there are no data to plot
+ if not pltout and (
+ pltinp is False or response.ninputs == 0 or
+ pltinp is None and response.plot_inputs is False):
+ with pytest.raises(ValueError, match=".* no data to plot"):
+ out = response.plot(**kwargs)
+ return None
+ elif not pltout and pltinp == 'overlay':
+ with pytest.raises(ValueError, match="can't overlay inputs"):
+ out = response.plot(**kwargs)
+ return None
+ elif pltinp in [True, 'overlay'] and response.ninputs == 0:
+ with pytest.raises(ValueError, match=".* but no inputs"):
+ out = response.plot(**kwargs)
+ return None
+
+ out = response.plot(**kwargs)
+
+ # Make sure all of the outputs are of the right type
+ nlines_plotted = 0
+ for ax_lines in np.nditer(out, flags=["refs_ok"]):
+ for line in ax_lines.item():
+ assert isinstance(line, mpl.lines.Line2D)
+ nlines_plotted += 1
+
+ # Make sure number of plots is correct
+ if pltinp is None:
+ if fcn in [ct.forced_response, ct.input_output_response]:
+ pltinp = True
+ else:
+ pltinp = False
+ ntraces = max(1, response.ntraces)
+ nlines_expected = (response.ninputs if pltinp else 0) * ntraces + \
+ (response.noutputs if pltout else 0) * ntraces
+ assert nlines_plotted == nlines_expected
+
+ # Save the old axes to compare later
+ old_axes = plt.gcf().get_axes()
+
+ # Add additional data (and provide info in the title)
+ if secsys:
+ newsys = ct.rss(
+ sys.nstates, sys.noutputs, sys.ninputs, strictly_proper=True)
+ if fcn not in [ct.initial_response, ct.forced_response,
+ ct.input_output_response] and \
+ isinstance(sys, ct.lti.LTI):
+ # Reuse the previously computed time to make plots look nicer
+ fcn(newsys, *args, T=response.time[-1]).plot(**kwargs)
+ else:
+ # Compute and plot new response (time is one of the arguments)
+ fcn(newsys, *args).plot(**kwargs)
+
+ # Make sure we have the same axes
+ new_axes = plt.gcf().get_axes()
+ assert new_axes == old_axes
+
+ # Make sure every axes has more than one line
+ for ax in new_axes:
+ assert len(ax.get_lines()) > 1
+
+ # Update the title so we can see what is going on
+ fig = out[0, 0][0].axes.figure
+ fig.suptitle(
+ fig._suptitle._text +
+ f" [{sys.noutputs}x{sys.ninputs}, cs={cmbsig}, "
+ f"ct={cmbtrc}, pi={pltinp}, tr={trpose}]",
+ fontsize='small')
+
+ # Get rid of the figure to free up memory
+ if clear:
+ plt.clf()
+
+
+def test_axes_setup():
+ get_plot_axes = ct.timeplot.get_plot_axes
+
+ sys_2x3 = ct.rss(4, 2, 3)
+ sys_2x3b = ct.rss(4, 2, 3)
+ sys_3x2 = ct.rss(4, 3, 2)
+ sys_3x1 = ct.rss(4, 3, 1)
+
+ # Two plots of the same size leaves axes unchanged
+ out1 = ct.step_response(sys_2x3).plot()
+ out2 = ct.step_response(sys_2x3b).plot()
+ np.testing.assert_equal(get_plot_axes(out1), get_plot_axes(out2))
+ plt.close()
+
+ # Two plots of same net size leaves axes unchanged (unfortunately)
+ out1 = ct.step_response(sys_2x3).plot()
+ out2 = ct.step_response(sys_3x2).plot()
+ np.testing.assert_equal(
+ get_plot_axes(out1).reshape(-1), get_plot_axes(out2).reshape(-1))
+ plt.close()
+
+ # Plots of different shapes generate new plots
+ out1 = ct.step_response(sys_2x3).plot()
+ out2 = ct.step_response(sys_3x1).plot()
+ ax1_list = get_plot_axes(out1).reshape(-1).tolist()
+ ax2_list = get_plot_axes(out2).reshape(-1).tolist()
+ for ax in ax1_list:
+ assert ax not in ax2_list
+ plt.close()
+
+ # Passing a list of axes preserves those axes
+ out1 = ct.step_response(sys_2x3).plot()
+ out2 = ct.step_response(sys_3x1).plot()
+ out3 = ct.step_response(sys_2x3b).plot(ax=get_plot_axes(out1))
+ np.testing.assert_equal(get_plot_axes(out1), get_plot_axes(out3))
+ plt.close()
+
+ # Sending an axes array of the wrong size raises exception
+ with pytest.raises(ValueError, match="not the right shape"):
+ out = ct.step_response(sys_2x3).plot()
+ ct.step_response(sys_3x1).plot(ax=get_plot_axes(out))
+ sys_2x3 = ct.rss(4, 2, 3)
+ sys_2x3b = ct.rss(4, 2, 3)
+ sys_3x2 = ct.rss(4, 3, 2)
+ sys_3x1 = ct.rss(4, 3, 1)
+
+
+@slycotonly
+def test_legend_map():
+ 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 = ct.step_response(sys_mimo)
+ response.plot(
+ legend_map=np.array([['center', 'upper right'],
+ [None, 'center right']]),
+ plot_inputs=True, overlay_signals=True, transpose=True,
+ title='MIMO step response with custom legend placement')
+
+
+def test_combine_time_responses():
+ sys_mimo = ct.rss(4, 2, 2)
+ timepts = np.linspace(0, 10, 100)
+
+ # Combine two response with ntrace = 0
+ U = np.vstack([np.sin(timepts), np.cos(2*timepts)])
+ resp1 = ct.input_output_response(sys_mimo, timepts, U)
+
+ U = np.vstack([np.cos(2*timepts), np.sin(timepts)])
+ resp2 = ct.input_output_response(sys_mimo, timepts, U)
+
+ combresp1 = ct.combine_time_responses([resp1, resp2])
+ assert combresp1.ntraces == 2
+ np.testing.assert_equal(combresp1.y[:, 0, :], resp1.y)
+ np.testing.assert_equal(combresp1.y[:, 1, :], resp2.y)
+
+ # Combine two responses with ntrace != 0
+ resp3 = ct.step_response(sys_mimo, timepts)
+ resp4 = ct.step_response(sys_mimo, timepts)
+ combresp2 = ct.combine_time_responses([resp3, resp4])
+ assert combresp2.ntraces == resp3.ntraces + resp4.ntraces
+ np.testing.assert_equal(combresp2.y[:, 0:2, :], resp3.y)
+ np.testing.assert_equal(combresp2.y[:, 2:4, :], resp4.y)
+
+ # Mixture
+ combresp3 = ct.combine_time_responses([resp1, resp2, resp3])
+ assert combresp3.ntraces == resp3.ntraces + resp4.ntraces
+ np.testing.assert_equal(combresp3.y[:, 0, :], resp1.y)
+ np.testing.assert_equal(combresp3.y[:, 1, :], resp2.y)
+ np.testing.assert_equal(combresp3.y[:, 2:4, :], resp3.y)
+ assert combresp3.trace_types == [None, None] + resp3.trace_types
+ assert combresp3.trace_labels == \
+ [resp1.title, resp2.title] + resp3.trace_labels
+
+ # Rename the traces
+ labels = ["T1", "T2", "T3", "T4"]
+ combresp4 = ct.combine_time_responses(
+ [resp1, resp2, resp3], trace_labels=labels)
+ assert combresp4.trace_labels == labels
+
+ # Automatically generated trace label names and types
+ resp5 = ct.step_response(sys_mimo, timepts)
+ resp5.title = "test"
+ resp5.trace_labels = None
+ resp5.trace_types = None
+ combresp5 = ct.combine_time_responses([resp1, resp5])
+ assert combresp5.trace_labels == [resp1.title] + \
+ ["test, trace 0", "test, trace 1"]
+ assert combresp4.trace_types == [None, None, 'step', 'step']
+
+ with pytest.raises(ValueError, match="must have the same number"):
+ resp = ct.step_response(ct.rss(4, 2, 3), timepts)
+ combresp = ct.combine_time_responses([resp1, resp])
+
+ with pytest.raises(ValueError, match="trace labels does not match"):
+ combresp = ct.combine_time_responses(
+ [resp1, resp2], trace_labels=["T1", "T2", "T3"])
+
+ with pytest.raises(ValueError, match="must have the same time"):
+ resp = ct.step_response(ct.rss(4, 2, 3), timepts/2)
+ combresp6 = ct.combine_time_responses([resp1, resp])
+
+
+@slycotonly
+def test_linestyles():
+ # Check to make sure we can change line styles
+ 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")
+ out = ct.step_response(sys_mimo).plot('k--', plot_inputs=True)
+ for ax in np.nditer(out, flags=["refs_ok"]):
+ for line in ax.item():
+ assert line.get_color() == 'k'
+ assert line.get_linestyle() == '--'
+
+ 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 ['-', '--']])
+
+ assert out.shape == (1, 1)
+ lines = out[0, 0]
+ assert lines[0].get_color() == 'blue' and lines[0].get_linestyle() == '-'
+ assert lines[1].get_color() == 'orange' and lines[1].get_linestyle() == '-'
+ assert lines[2].get_color() == 'red' and lines[2].get_linestyle() == '-'
+ assert lines[3].get_color() == 'green' and lines[3].get_linestyle() == '-'
+ assert lines[4].get_color() == 'blue' and lines[4].get_linestyle() == '--'
+ assert lines[5].get_color() == 'orange' and lines[5].get_linestyle() == '--'
+ assert lines[6].get_color() == 'red' and lines[6].get_linestyle() == '--'
+ assert lines[7].get_color() == 'green' and lines[7].get_linestyle() == '--'
+
+
+def test_rcParams():
+ sys = ct.rss(2, 2, 2)
+
+ # Create new set of rcParams
+ my_rcParams = {
+ 'axes.labelsize': 10,
+ 'axes.titlesize': 10,
+ 'figure.titlesize': 12,
+ 'legend.fontsize': 10,
+ 'xtick.labelsize': 10,
+ 'ytick.labelsize': 10,
+ }
+
+ # Generate a figure with the new rcParams
+ out = ct.step_response(sys).plot(rcParams=my_rcParams)
+ ax = out[0, 0][0].axes
+ fig = ax.figure
+
+ # Check to make sure new settings were used
+ assert ax.xaxis.get_label().get_fontsize() == 10
+ assert ax.yaxis.get_label().get_fontsize() == 10
+ assert ax.title.get_fontsize() == 10
+ assert ax.xaxis._get_tick_label_size('x') == 10
+ assert ax.yaxis._get_tick_label_size('y') == 10
+ assert fig._suptitle.get_fontsize() == 12
+
+def test_relabel():
+ sys1 = ct.rss(2, inputs='u', outputs='y')
+ sys2 = ct.rss(1, 1, 1) # uses default i/o labels
+
+ # Generate a plot with specific labels
+ ct.step_response(sys1).plot()
+
+ # Generate a new plot, which overwrites labels
+ out = ct.step_response(sys2).plot()
+ ax = ct.get_plot_axes(out)
+ assert ax[0, 0].get_ylabel() == 'y[0]'
+
+ # Regenerate the first plot
+ plt.figure()
+ ct.step_response(sys1).plot()
+
+ # Generate a new plt, without relabeling
+ out = ct.step_response(sys2).plot(relabel=False)
+ ax = ct.get_plot_axes(out)
+ assert ax[0, 0].get_ylabel() == 'y'
+
+
+def test_errors():
+ sys = ct.rss(2, 1, 1)
+ stepresp = ct.step_response(sys)
+ with pytest.raises(AttributeError,
+ match="(has no property|unexpected keyword)"):
+ stepresp.plot(unknown=None)
+
+ with pytest.raises(AttributeError,
+ match="(has no property|unexpected keyword)"):
+ ct.time_response_plot(stepresp, unknown=None)
+
+ with pytest.raises(ValueError, match="unrecognized value"):
+ stepresp.plot(plot_inputs='unknown')
+
+ for kw in ['input_props', 'output_props', 'trace_props']:
+ propkw = {kw: {'color': 'green'}}
+ with pytest.warns(UserWarning, match="ignored since fmt string"):
+ out = stepresp.plot('k-', **propkw)
+ assert out[0, 0][0].get_color() == 'k'
+
+if __name__ == "__main__":
+ #
+ # Interactive mode: generate plots for manual viewing
+ #
+ # Running this script in python (or better ipython) will show a
+ # collection of figures that should all look OK on the screeen.
+ #
+
+ # In interactive mode, turn on ipython interactive graphics
+ plt.ion()
+
+ # Start by clearing existing figures
+ plt.close('all')
+
+ # Define a set of systems to test
+ sys_siso = ct.tf2ss([1], [1, 2, 1], name="SISO")
+ 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")
+
+ # Define and run a selected set of interesting tests
+ # def test_response_plots(
+ # fcn, sys, plot_inputs, plot_outputs, overlay_signals,
+ # overlay_traces, transpose, second_system, clear=True):
+ N, T, F = None, True, False
+ test_cases = [
+ # response fcn system in out cs ct tr ss
+ (ct.step_response, sys_siso, N, T, F, F, F, F), # 1
+ (ct.step_response, sys_siso, T, F, F, F, F, F), # 2
+ (ct.step_response, sys_siso, T, T, F, F, F, T), # 3
+ (ct.step_response, sys_siso, 'overlay', T, F, F, F, T), # 4
+ (ct.step_response, sys_mimo, F, T, F, F, F, F), # 5
+ (ct.step_response, sys_mimo, T, T, F, F, F, F), # 6
+ (ct.step_response, sys_mimo, 'overlay', T, F, F, F, F), # 7
+ (ct.step_response, sys_mimo, T, T, T, F, F, F), # 8
+ (ct.step_response, sys_mimo, T, T, T, T, F, F), # 9
+ (ct.step_response, sys_mimo, T, T, F, F, T, F), # 10
+ (ct.step_response, sys_mimo, T, T, T, F, T, F), # 11
+ (ct.step_response, sys_mimo, 'overlay', T, T, F, T, F), # 12
+ (ct.forced_response, sys_mimo, N, T, T, F, T, F), # 13
+ (ct.forced_response, sys_mimo, 'overlay', T, F, F, F, F), # 14
+ ]
+ for args in test_cases:
+ test_response_plots(*args, clear=F)
+
+ #
+ # Run a few more special cases to show off capabilities (and save some
+ # of them for use in the documentation).
+ #
+
+ test_legend_map() # show ability to set legend location
+
+ # Basic step response
+ plt.figure()
+ ct.step_response(sys_mimo).plot()
+ plt.savefig('timeplot-mimo_step-default.png')
+
+ # Step response with plot_inputs, overlay_signals
+ plt.figure()
+ ct.step_response(sys_mimo).plot(
+ plot_inputs=True, overlay_signals=True,
+ title="Step response for 2x2 MIMO system " +
+ "[plot_inputs, overlay_signals]")
+ plt.savefig('timeplot-mimo_step-pi_cs.png')
+
+ # Input/output response with overlaid inputs, legend_map
+ plt.figure()
+ 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]")
+ plt.savefig('timeplot-mimo_ioresp-ov_lm.png')
+
+ # Multi-trace plot, transpose
+ plt.figure()
+ U = np.vstack([np.sin(timepts), np.cos(2*timepts)])
+ resp1 = ct.input_output_response(sys_mimo, timepts, U)
+
+ U = np.vstack([np.cos(2*timepts), np.sin(timepts)])
+ resp2 = ct.input_output_response(sys_mimo, timepts, U)
+
+ 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]")
+ plt.savefig('timeplot-mimo_ioresp-mt_tr.png')
+
+ plt.figure()
+ 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 ['-', '--']])
+ plt.savefig('timeplot-mimo_step-linestyle.png')
diff --git a/control/timeplot.py b/control/timeplot.py
new file mode 100644
index 000000000..6409a6660
--- /dev/null
+++ b/control/timeplot.py
@@ -0,0 +1,808 @@
+# timeplot.py - time plotting functions
+# RMM, 20 Jun 2023
+#
+# This file contains routines for plotting out time responses. These
+# functions can be called either as standalone functions or access from the
+# TimeDataResponse class.
+#
+# Note: It might eventually make sense to put the functions here
+# directly into timeresp.py.
+
+import numpy as np
+import matplotlib as mpl
+import matplotlib.pyplot as plt
+from os.path import commonprefix
+from warnings import warn
+
+from . import config
+
+__all__ = ['time_response_plot', 'combine_time_responses', 'get_plot_axes']
+
+# Default font dictionary
+_timeplot_rcParams = mpl.rcParams.copy()
+_timeplot_rcParams.update({
+ 'axes.labelsize': 'small',
+ 'axes.titlesize': 'small',
+ 'figure.titlesize': 'medium',
+ 'legend.fontsize': 'x-small',
+ 'xtick.labelsize': 'small',
+ 'ytick.labelsize': 'small',
+})
+
+# Default values for module parameter variables
+_timeplot_defaults = {
+ 'timeplot.rcParams': _timeplot_rcParams,
+ 'timeplot.trace_props': [
+ {'linestyle': s} for s in ['-', '--', ':', '-.']],
+ 'timeplot.output_props': [
+ {'color': c} for c in [
+ 'tab:blue', 'tab:orange', 'tab:green', 'tab:pink', 'tab:gray']],
+ 'timeplot.input_props': [
+ {'color': c} for c in [
+ 'tab:red', 'tab:purple', 'tab:brown', 'tab:olive', 'tab:cyan']],
+ 'timeplot.time_label': "Time [s]",
+}
+
+# Plot the input/output response of a system
+def time_response_plot(
+ data, *fmt, ax=None, plot_inputs=None, plot_outputs=True,
+ transpose=False, overlay_traces=False, overlay_signals=False,
+ legend_map=None, legend_loc=None, add_initial_zero=True,
+ trace_labels=None, title=None, relabel=True, **kwargs):
+ """Plot the time response of an input/output system.
+
+ This function creates a standard set of plots for the input/output
+ response of a system, with the data provided via a `TimeResponseData`
+ object, which is the standard output for python-control simulation
+ functions.
+
+ Parameters
+ ----------
+ data : TimeResponseData
+ Data to be plotted.
+ ax : array of Axes
+ The matplotlib Axes to draw the figure on. If not specified, the
+ Axes for the current figure are used or, if there is no current
+ figure with the correct number and shape of Axes, a new figure is
+ created. The default shape of the array should be (noutputs +
+ ninputs, ntraces), but if `overlay_traces` is set to `True` then
+ only one row is needed and if `overlay_signals` is set to `True`
+ then only one or two columns are needed (depending on plot_inputs
+ and plot_outputs).
+ plot_inputs : bool or str, optional
+ Sets how and where to plot the inputs:
+ * False: don't plot the inputs
+ * None: use value from time response data (default)
+ * 'overlay`: plot inputs overlaid with outputs
+ * True: plot the inputs on their own axes
+ plot_outputs : bool, optional
+ If False, suppress plotting of the outputs.
+ overlay_traces : bool, optional
+ If set to True, combine all traces onto a single row instead of
+ plotting a separate row for each trace.
+ overlay_signals : bool, optional
+ If set to True, combine all input and output signals onto a single
+ plot (for each).
+ transpose : bool, optional
+ If transpose is False (default), signals are plotted from top to
+ bottom, starting with outputs (if plotted) and then inputs.
+ Multi-trace plots are stacked horizontally. If transpose is True,
+ signals are plotted from left to right, starting with the inputs
+ (if plotted) and then the outputs. Multi-trace responses are
+ stacked vertically.
+ *fmt : :func:`matplotlib.pyplot.plot` format string, optional
+ Passed to `matplotlib` as the format string for all lines in the plot.
+ **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
+ Additional keywords passed to `matplotlib` to specify line properties.
+
+ Returns
+ -------
+ out : array of list of Line2D
+ Array of Line2D objects for each line in the plot. The shape of
+ the array matches the subplots shape and the value of the array is a
+ list of Line2D objects in that subplot.
+
+ Additional Parameters
+ ---------------------
+ add_initial_zero : bool
+ Add an initial point of zero at the first time point for all
+ inputs with type 'step'. Default is True.
+ input_props : array of dicts
+ List of line properties to use when plotting combined inputs. The
+ default values are set by config.defaults['timeplot.input_props'].
+ legend_map : array of str, option
+ Location of the legend for multi-trace plots. Specifies an array
+ of legend location strings matching the shape of the subplots, with
+ each entry being either None (for no legend) or a legend location
+ string (see :func:`~matplotlib.pyplot.legend`).
+ legend_loc : str
+ Location of the legend within the axes for which it appears. This
+ value is used if legend_map is None.
+ output_props : array of dicts
+ List of line properties to use when plotting combined outputs. The
+ default values are set by config.defaults['timeplot.output_props'].
+ relabel : bool, optional
+ By default, existing figures and axes are relabeled when new data
+ are added. If set to `False`, just plot new data on existing axes.
+ time_label : str, optional
+ Label to use for the time axis.
+ trace_props : array of dicts
+ List of line properties to use when plotting combined outputs. The
+ default values are set by config.defaults['timeplot.trace_props'].
+
+ Notes
+ -----
+ 1. A new figure will be generated if there is no current figure or
+ the current figure has an incompatible number of axes. To
+ force the creation of a new figures, use `plt.figure()`. To reuse
+ a portion of an existing figure, use the `ax` keyword.
+
+ 2. The line properties (color, linestyle, etc) can be set for the
+ entire plot using the `fmt` and/or `kwargs` parameter, which
+ are passed on to `matplotlib`. When combining signals or
+ traces, the `input_props`, `output_props`, and `trace_props`
+ parameters can be used to pass a list of dictionaries
+ containing the line properties to use. These input/output
+ properties are combined with the trace properties and finally
+ the kwarg properties to determine the final line properties.
+
+ 3. The default plot properties, such as font sizes, can be set using
+ config.defaults[''timeplot.rcParams'].
+
+ """
+ from .iosys import InputOutputSystem
+ from .timeresp import TimeResponseData
+
+ #
+ # Process keywords and set defaults
+ #
+
+ # Set up defaults
+ time_label = config._get_param(
+ 'timeplot', 'time_label', kwargs, _timeplot_defaults, pop=True)
+ timeplot_rcParams = config._get_param(
+ 'timeplot', 'rcParams', kwargs, _timeplot_defaults, pop=True)
+
+ if kwargs.get('input_props', None) and len(fmt) > 0:
+ warn("input_props ignored since fmt string was present")
+ input_props = config._get_param(
+ 'timeplot', 'input_props', kwargs, _timeplot_defaults, pop=True)
+ iprop_len = len(input_props)
+
+ if kwargs.get('output_props', None) and len(fmt) > 0:
+ warn("output_props ignored since fmt string was present")
+ output_props = config._get_param(
+ 'timeplot', 'output_props', kwargs, _timeplot_defaults, pop=True)
+ oprop_len = len(output_props)
+
+ if kwargs.get('trace_props', None) and len(fmt) > 0:
+ warn("trace_props ignored since fmt string was present")
+ trace_props = config._get_param(
+ 'timeplot', 'trace_props', kwargs, _timeplot_defaults, pop=True)
+ tprop_len = len(trace_props)
+
+ # Set the title for the data
+ title = data.title if title == None else title
+
+ # Determine whether or not to plot the input data (and how)
+ if plot_inputs is None:
+ plot_inputs = data.plot_inputs
+ if plot_inputs not in [True, False, 'overlay']:
+ raise ValueError(f"unrecognized value: {plot_inputs=}")
+
+ #
+ # Find/create axes
+ #
+ # Data are plotted in a standard subplots array, whose size depends on
+ # which signals are being plotted and how they are combined. The
+ # baseline layout for data is to plot everything separately, with
+ # outputs and inputs making up the rows and traces making up the
+ # columns:
+ #
+ # Trace 0 Trace q
+ # +------+ +------+
+ # | y[0] | ... | y[0] |
+ # +------+ +------+
+ # :
+ # +------+ +------+
+ # | y[p] | ... | y[p] |
+ # +------+ +------+
+ #
+ # +------+ +------+
+ # | u[0] | ... | u[0] |
+ # +------+ +------+
+ # :
+ # +------+ +------+
+ # | u[m] | ... | u[m] |
+ # +------+ +------+
+ #
+ # A variety of options are available to modify this format:
+ #
+ # * Omitting: either the inputs or the outputs can be omitted.
+ #
+ # * Combining: inputs, outputs, and traces can be combined onto a
+ # single set of axes using various keyword combinations
+ # (overlay_signals, overlay_traces, plot_inputs='overlay'). This
+ # basically collapses data along either the rows or columns, and a
+ # legend is generated.
+ #
+ # * Transpose: if the `transpose` keyword is True, then instead of
+ # plotting the data vertically (outputs over inputs), we plot left to
+ # right (inputs, outputs):
+ #
+ # +------+ +------+ +------+ +------+
+ # Trace 0 | u[0] | ... | u[m] | | y[0] | ... | y[p] |
+ # +------+ +------+ +------+ +------+
+ # :
+ # :
+ # +------+ +------+ +------+ +------+
+ # Trace q | u[0] | ... | u[m] | | y[0] | ... | y[p] |
+ # +------+ +------+ +------+ +------+
+ #
+ # This also affects the way in which legends and labels are generated.
+
+ # Decide on the number of inputs and outputs
+ ninputs = data.ninputs if plot_inputs else 0
+ noutputs = data.noutputs if plot_outputs else 0
+ ntraces = max(1, data.ntraces) # treat data.ntraces == 0 as 1 trace
+ if ninputs == 0 and noutputs == 0:
+ raise ValueError(
+ "plot_inputs and plot_outputs both False; no data to plot")
+ elif plot_inputs == 'overlay' and noutputs == 0:
+ raise ValueError(
+ "can't overlay inputs with no outputs")
+ elif plot_inputs in [True, 'overlay'] and data.ninputs == 0:
+ raise ValueError(
+ "input plotting requested but no inputs in time response data")
+
+ # Figure how how many rows and columns to use + offsets for inputs/outputs
+ if plot_inputs == 'overlay' and not overlay_signals:
+ nrows = max(ninputs, noutputs) # Plot inputs on top of outputs
+ noutput_axes = 0 # No offset required
+ ninput_axes = 0 # No offset required
+ elif overlay_signals:
+ nrows = int(plot_outputs) # Start with outputs
+ nrows += int(plot_inputs == True) # Add plot for inputs if needed
+ noutput_axes = 1 if plot_outputs and plot_inputs is True else 0
+ ninput_axes = 1 if plot_inputs is True else 0
+ else:
+ nrows = noutputs + ninputs # Plot inputs separately
+ noutput_axes = noutputs if plot_outputs else 0
+ ninput_axes = ninputs if plot_inputs else 0
+
+ ncols = ntraces if not overlay_traces else 1
+ if transpose:
+ nrows, ncols = ncols, nrows
+
+ # See if we can use the current figure axes
+ fig = plt.gcf() # get current figure (or create new one)
+ if ax is None and plt.get_fignums():
+ ax = fig.get_axes()
+ if len(ax) == nrows * ncols:
+ # Assume that the shape is right (no easy way to infer this)
+ ax = np.array(ax).reshape(nrows, ncols)
+ elif len(ax) != 0:
+ # Need to generate a new figure
+ fig, ax = plt.figure(), None
+ else:
+ # Blank figure, just need to recreate axes
+ ax = None
+
+ # Create new axes, if needed, and customize them
+ if ax is None:
+ with plt.rc_context(timeplot_rcParams):
+ ax_array = fig.subplots(nrows, ncols, sharex=True, squeeze=False)
+ fig.set_tight_layout(True)
+ fig.align_labels()
+
+ else:
+ # Make sure the axes are the right shape
+ if ax.shape != (nrows, ncols):
+ raise ValueError(
+ "specified axes are not the right shape; "
+ f"got {ax.shape} but expecting ({nrows}, {ncols})")
+ ax_array = ax
+
+ #
+ # Map inputs/outputs and traces to axes
+ #
+ # This set of code takes care of all of the various options for how to
+ # plot the data. The arrays output_map and input_map are used to map
+ # the different signals that are plotted onto the axes created above.
+ # This code is complicated because it has to handle lots of different
+ # variations.
+ #
+
+ # Create the map from trace, signal to axes, accounting for overlay_*
+ output_map = np.empty((noutputs, ntraces), dtype=tuple)
+ input_map = np.empty((ninputs, ntraces), dtype=tuple)
+
+ for i in range(noutputs):
+ for j in range(ntraces):
+ signal_index = i if not overlay_signals else 0
+ trace_index = j if not overlay_traces else 0
+ if transpose:
+ output_map[i, j] = (trace_index, signal_index + ninput_axes)
+ else:
+ output_map[i, j] = (signal_index, trace_index)
+
+ for i in range(ninputs):
+ for j in range(ntraces):
+ signal_index = noutput_axes + (i if not overlay_signals else 0)
+ trace_index = j if not overlay_traces else 0
+ if transpose:
+ input_map[i, j] = (trace_index, signal_index - noutput_axes)
+ else:
+ input_map[i, j] = (signal_index, trace_index)
+
+ #
+ # Plot the data
+ #
+ # The ax_output and ax_input arrays have the axes needed for making the
+ # plots. Labels are used on each axes for later creation of legends.
+ # The gneric labels if of the form:
+ #
+ # signal name, trace label, system name
+ #
+ # The signal name or tracel label can be omitted if they will appear on
+ # the axes title or ylabel. The system name is always included, since
+ # multiple calls to plot() will require a legend that distinguishes
+ # which system signals are plotted. The system name is stripped off
+ # later (in the legend-handling code) if it is not needed, but must be
+ # included here since a plot may be built up by multiple calls to plot().
+ #
+
+ # Reshape the inputs and outputs for uniform indexing
+ outputs = data.y.reshape(data.noutputs, ntraces, -1)
+ if data.u is None or not plot_inputs:
+ inputs = None
+ else:
+ inputs = data.u.reshape(data.ninputs, ntraces, -1)
+
+ # Create a list of lines for the output
+ out = np.empty((nrows, ncols), dtype=object)
+ for i in range(nrows):
+ for j in range(ncols):
+ out[i, j] = [] # unique list in each element
+
+ # Utility function for creating line label
+ def _make_line_label(signal_index, signal_labels, trace_index):
+ label = "" # start with an empty label
+
+ # Add the signal name if it won't appear as an axes label
+ if overlay_signals or plot_inputs == 'overlay':
+ label += signal_labels[signal_index]
+
+ # Add the trace label if this is a multi-trace figure
+ if overlay_traces and ntraces > 1 or trace_labels:
+ label += ", " if label != "" else ""
+ if trace_labels:
+ label += trace_labels[trace_index]
+ elif data.trace_labels:
+ label += data.trace_labels[trace_index]
+ else:
+ label += f"trace {trace_index}"
+
+ # Add the system name (will strip off later if redundant)
+ label += ", " if label != "" else ""
+ label += f"{data.sysname}"
+
+ return label
+
+ # Go through each trace and each input/output
+ for trace in range(ntraces):
+ # Plot the output
+ for i in range(noutputs):
+ label = _make_line_label(i, data.output_labels, trace)
+
+ # Set up line properties for this output, trace
+ if len(fmt) == 0:
+ line_props = output_props[
+ i % oprop_len if overlay_signals else 0].copy()
+ line_props.update(
+ trace_props[trace % tprop_len if overlay_traces else 0])
+ line_props.update(kwargs)
+ else:
+ line_props = kwargs
+
+ out[output_map[i, trace]] += ax_array[output_map[i, trace]].plot(
+ data.time, outputs[i][trace], *fmt, label=label, **line_props)
+
+ # Plot the input
+ for i in range(ninputs):
+ label = _make_line_label(i, data.input_labels, trace)
+
+ if add_initial_zero and data.ntraces > i \
+ and data.trace_types[i] == 'step':
+ x = np.hstack([np.array([data.time[0]]), data.time])
+ y = np.hstack([np.array([0]), inputs[i][trace]])
+ else:
+ x, y = data.time, inputs[i][trace]
+
+ # Set up line properties for this output, trace
+ if len(fmt) == 0:
+ line_props = input_props[
+ i % iprop_len if overlay_signals else 0].copy()
+ line_props.update(
+ trace_props[trace % tprop_len if overlay_traces else 0])
+ line_props.update(kwargs)
+ else:
+ line_props = kwargs
+
+ out[input_map[i, trace]] += ax_array[input_map[i, trace]].plot(
+ x, y, *fmt, label=label, **line_props)
+
+ # Stop here if the user wants to control everything
+ if not relabel:
+ return out
+
+ #
+ # Label the axes (including trace labels)
+ #
+ # Once the data are plotted, we label the axes. The horizontal axes is
+ # always time and this is labeled only on the bottom most column. The
+ # vertical axes can consist either of a single signal or a combination
+ # of signals (when overlay_signal is True or plot+inputs = 'overlay'.
+ #
+ # Traces are labeled at the top of the first row of plots (regular) or
+ # the left edge of rows (tranpose).
+ #
+
+ # Time units on the bottom
+ for col in range(ncols):
+ ax_array[-1, col].set_xlabel(time_label)
+
+ # Keep track of whether inputs are overlaid on outputs
+ overlaid = plot_inputs == 'overlay'
+ overlaid_title = "Inputs, Outputs"
+
+ if transpose: # inputs on left, outputs on right
+ # Label the inputs
+ if overlay_signals and plot_inputs:
+ label = overlaid_title if overlaid else "Inputs"
+ for trace in range(ntraces):
+ ax_array[input_map[0, trace]].set_ylabel(label)
+ else:
+ for i in range(ninputs):
+ label = overlaid_title if overlaid else data.input_labels[i]
+ for trace in range(ntraces):
+ ax_array[input_map[i, trace]].set_ylabel(label)
+
+ # Label the outputs
+ if overlay_signals and plot_outputs:
+ label = overlaid_title if overlaid else "Outputs"
+ for trace in range(ntraces):
+ ax_array[output_map[0, trace]].set_ylabel(label)
+ else:
+ for i in range(noutputs):
+ label = overlaid_title if overlaid else data.output_labels[i]
+ for trace in range(ntraces):
+ ax_array[output_map[i, trace]].set_ylabel(label)
+
+ # Set the trace titles, if needed
+ if ntraces > 1 and not overlay_traces:
+ for trace in range(ntraces):
+ # Get the existing ylabel for left column
+ label = ax_array[trace, 0].get_ylabel()
+
+ # Add on the trace title
+ if trace_labels:
+ label = trace_labels[trace] + "\n" + label
+ elif data.trace_labels:
+ label = data.trace_labels[trace] + "\n" + label
+ else:
+ label = f"Trace {trace}" + "\n" + label
+
+ ax_array[trace, 0].set_ylabel(label)
+
+ else: # regular plot (outputs over inputs)
+ # Set the trace titles, if needed
+ if ntraces > 1 and not overlay_traces:
+ for trace in range(ntraces):
+ if trace_labels:
+ label = trace_labels[trace]
+ elif data.trace_labels:
+ label = data.trace_labels[trace]
+ else:
+ label = f"Trace {trace}"
+
+ with plt.rc_context(timeplot_rcParams):
+ ax_array[0, trace].set_title(label)
+
+ # Label the outputs
+ if overlay_signals and plot_outputs:
+ ax_array[output_map[0, 0]].set_ylabel("Outputs")
+ else:
+ for i in range(noutputs):
+ ax_array[output_map[i, 0]].set_ylabel(
+ overlaid_title if overlaid else data.output_labels[i])
+
+ # Label the inputs
+ if overlay_signals and plot_inputs:
+ label = overlaid_title if overlaid else "Inputs"
+ ax_array[input_map[0, 0]].set_ylabel(label)
+ else:
+ for i in range(ninputs):
+ label = overlaid_title if overlaid else data.input_labels[i]
+ ax_array[input_map[i, 0]].set_ylabel(label)
+
+ #
+ # Create legends
+ #
+ # Legends can be placed manually by passing a legend_map array that
+ # matches the shape of the suplots, with each item being a string
+ # indicating the location of the legend for that axes (or None for no
+ # legend).
+ #
+ # If no legend spec is passed, a minimal number of legends are used so
+ # that each line in each axis can be uniquely identified. The details
+ # depends on the various plotting parameters, but the general rule is
+ # to place legends in the top row and right column.
+ #
+ # Because plots can be built up by multiple calls to plot(), the legend
+ # strings are created from the line labels manually. Thus an initial
+ # call to plot() may not generate any legends (eg, if no signals are
+ # combined nor overlaid), but subsequent calls to plot() will need a
+ # legend for each different line (system).
+ #
+
+ # Figure out where to put legends
+ if legend_map is None:
+ legend_map = np.full(ax_array.shape, None, dtype=object)
+ if legend_loc == None:
+ legend_loc = 'center right'
+ if transpose:
+ if (overlay_signals or plot_inputs == 'overlay') and overlay_traces:
+ # Put a legend in each plot for inputs and outputs
+ if plot_outputs is True:
+ legend_map[0, ninput_axes] = legend_loc
+ if plot_inputs is True:
+ legend_map[0, 0] = legend_loc
+ elif overlay_signals:
+ # Put a legend in rightmost input/output plot
+ if plot_inputs is True:
+ legend_map[0, 0] = legend_loc
+ if plot_outputs is True:
+ legend_map[0, ninput_axes] = legend_loc
+ elif plot_inputs == 'overlay':
+ # Put a legend on the top of each column
+ for i in range(ntraces):
+ legend_map[0, i] = legend_loc
+ elif overlay_traces:
+ # Put a legend topmost input/output plot
+ legend_map[0, -1] = legend_loc
+ else:
+ # Put legend in the upper right
+ legend_map[0, -1] = legend_loc
+ else: # regular layout
+ if (overlay_signals or plot_inputs == 'overlay') and overlay_traces:
+ # Put a legend in each plot for inputs and outputs
+ if plot_outputs is True:
+ legend_map[0, -1] = legend_loc
+ if plot_inputs is True:
+ legend_map[noutput_axes, -1] = legend_loc
+ elif overlay_signals:
+ # Put a legend in rightmost input/output plot
+ if plot_outputs is True:
+ legend_map[0, -1] = legend_loc
+ if plot_inputs is True:
+ legend_map[noutput_axes, -1] = legend_loc
+ elif plot_inputs == 'overlay':
+ # Put a legend on the right of each row
+ for i in range(max(ninputs, noutputs)):
+ legend_map[i, -1] = legend_loc
+ elif overlay_traces:
+ # Put a legend topmost input/output plot
+ legend_map[0, -1] = legend_loc
+ else:
+ # Put legend in the upper right
+ legend_map[0, -1] = legend_loc
+
+ # Create axis legends
+ for i in range(nrows):
+ for j in range(ncols):
+ ax = ax_array[i, j]
+ # Get the labels to use
+ labels = [line.get_label() for line in ax.get_lines()]
+
+ # Look for a common prefix (up to a space)
+ common_prefix = commonprefix(labels)
+ last_space = common_prefix.rfind(', ')
+ if last_space < 0 or plot_inputs == 'overlay':
+ common_prefix = ''
+ elif last_space > 0:
+ common_prefix = common_prefix[:last_space]
+ prefix_len = len(common_prefix)
+
+ # Look for a common suffice (up to a space)
+ common_suffix = commonprefix(
+ [label[::-1] for label in labels])[::-1]
+ suffix_len = len(common_suffix)
+ # Only chop things off after a comma or space
+ while suffix_len > 0 and common_suffix[-suffix_len] != ',':
+ suffix_len -= 1
+
+ # Strip the labels of common information
+ if suffix_len > 0:
+ labels = [label[prefix_len:-suffix_len] for label in labels]
+ else:
+ labels = [label[prefix_len:] for label in labels]
+
+ # Update the labels to remove common strings
+ if len(labels) > 1 and legend_map[i, j] != None:
+ with plt.rc_context(timeplot_rcParams):
+ ax.legend(labels, loc=legend_map[i, j])
+
+ #
+ # Update the plot title (= figure suptitle)
+ #
+ # If plots are built up by multiple calls to plot() and the title is
+ # not given, then the title is updated to provide a list of unique text
+ # items in each successive title. For data generated by the I/O
+ # response functions this will generate a common prefix followed by a
+ # list of systems (e.g., "Step response for sys[1], sys[2]").
+ #
+
+ if fig is not None and title is not None:
+ # Get the current title, if it exists
+ old_title = None if fig._suptitle is None else fig._suptitle._text
+ new_title = title
+
+ if old_title is not None:
+ # Find the common part of the titles
+ common_prefix = commonprefix([old_title, new_title])
+
+ # Back up to the last space
+ last_space = common_prefix.rfind(' ')
+ if last_space > 0:
+ common_prefix = common_prefix[:last_space]
+ common_len = len(common_prefix)
+
+ # Add the new part of the title (usually the system name)
+ if old_title[common_len:] != new_title[common_len:]:
+ separator = ',' if len(common_prefix) > 0 else ';'
+ new_title = old_title + separator + new_title[common_len:]
+
+ # Add the title
+ with plt.rc_context(timeplot_rcParams):
+ fig.suptitle(new_title)
+
+ return out
+
+
+def combine_time_responses(response_list, trace_labels=None, title=None):
+ """Combine multiple individual time responses into a multi-trace response.
+
+ This function combines multiple instances of :class:`TimeResponseData`
+ into a multi-trace :class:`TimeResponseData` object.
+
+ Parameters
+ ----------
+ response_list : list of :class:`TimeResponseData` objects
+ Reponses to be combined.
+ trace_labels : list of str, optional
+ List of labels for each trace. If not specified, trace names are
+ taken from the input data or set to None.
+
+ Returns
+ -------
+ data : :class:`TimeResponseData`
+ Multi-trace input/output data.
+
+ """
+ from .timeresp import TimeResponseData
+
+ # Save the first trace as the base case
+ base = response_list[0]
+
+ # Process keywords
+ title = base.title if title is None else title
+
+ # Figure out the size of the data (and check for consistency)
+ ntraces = max(1, base.ntraces)
+
+ # Initial pass through trace list to count things up and do error checks
+ for response in response_list[1:]:
+ # Make sure the time vector is the same
+ if not np.allclose(base.t, response.t):
+ raise ValueError("all responses must have the same time vector")
+
+ # Make sure the dimensions are all the same
+ if base.ninputs != response.ninputs or \
+ base.noutputs != response.noutputs or \
+ base.nstates != response.nstates:
+ raise ValueError("all responses must have the same number of "
+ "inputs, outputs, and states")
+
+ ntraces += max(1, response.ntraces)
+
+ # Create data structures for the new time response data object
+ inputs = np.empty((base.ninputs, ntraces, base.t.size))
+ outputs = np.empty((base.noutputs, ntraces, base.t.size))
+ states = np.empty((base.nstates, ntraces, base.t.size))
+
+ # See whether we should create labels or not
+ if trace_labels is None:
+ generate_trace_labels = True
+ trace_labels = []
+ elif len(trace_labels) != ntraces:
+ raise ValueError(
+ "number of trace labels does not match number of traces")
+ else:
+ generate_trace_labels = False
+
+ offset = 0
+ trace_types = []
+ for response in response_list:
+ if response.ntraces == 0:
+ # Single trace
+ inputs[:, offset, :] = response.u
+ outputs[:, offset, :] = response.y
+ states[:, offset, :] = response.x
+ offset += 1
+
+ # Add on trace label and trace type
+ if generate_trace_labels:
+ trace_labels.append(response.title)
+ trace_types.append(
+ None if response.trace_types is None else response.types[0])
+
+ else:
+ # Save the data
+ for i in range(response.ntraces):
+ inputs[:, offset, :] = response.u[:, i, :]
+ outputs[:, offset, :] = response.y[:, i, :]
+ states[:, offset, :] = response.x[:, i, :]
+
+ # Save the trace labels
+ if generate_trace_labels:
+ if response.trace_labels is not None:
+ trace_labels.append(response.trace_labels[i])
+ else:
+ trace_labels.append(response.title + f", trace {i}")
+
+ offset += 1
+
+ # Save the trace types
+ if response.trace_types is not None:
+ trace_types += response.trace_types
+ else:
+ trace_types += [None] * response.ntraces
+
+ return TimeResponseData(
+ base.t, outputs, states, inputs, issiso=base.issiso,
+ output_labels=base.output_labels, input_labels=base.input_labels,
+ state_labels=base.state_labels, title=title, transpose=base.transpose,
+ return_x=base.return_x, squeeze=base.squeeze, sysname=base.sysname,
+ trace_labels=trace_labels, trace_types=trace_types,
+ plot_inputs=base.plot_inputs)
+
+
+# Create vectorized function to find axes from lines
+def get_plot_axes(line_array):
+ """Get a list of axes from an array of lines.
+
+ This function can be used to return the set of axes corresponding to
+ the line array that is returned by `time_response_plot`. This is useful for
+ generating an axes array that can be passed to subsequent plotting
+ calls.
+
+ Parameters
+ ----------
+ line_array : array of list of Line2D
+ A 2D array with elements corresponding to a list of lines appearing
+ in an axes, matching the return type of a time response data plot.
+
+ Returns
+ -------
+ axes_array : array of list of Axes
+ A 2D array with elements corresponding to the Axes assocated with
+ the lines in `line_array`.
+
+ Notes
+ -----
+ Only the first element of each array entry is used to determine the axes.
+
+ """
+ _get_axes = np.vectorize(lambda lines: lines[0].axes)
+ return _get_axes(line_array)
diff --git a/control/timeresp.py b/control/timeresp.py
index defdbdf4e..bc13ad0d1 100644
--- a/control/timeresp.py
+++ b/control/timeresp.py
@@ -81,6 +81,7 @@
from . import config
from .exception import pandas_check
from .iosys import isctime, isdtime
+from .timeplot import time_response_plot
__all__ = ['forced_response', 'step_response', 'step_info',
@@ -169,10 +170,24 @@ class TimeResponseData:
input_labels, output_labels, state_labels : array of str
Names for the input, output, and state variables.
- ntraces : int
+ sysname : str, optional
+ Name of the system that created the data.
+
+ plot_inputs : bool, optional
+ Whether or not to plot the inputs by default (can be overridden in
+ the plot() method)
+
+ ntraces : int, optional
Number of independent traces represented in the input/output
- response. If ntraces is 0 then the data represents a single trace
- with the trace index surpressed in the data.
+ response. If ntraces is 0 (default) then the data represents a
+ single trace with the trace index surpressed in the data.
+
+ trace_labels : array of string, optional
+ Labels to use for traces (set to sysname it ntraces is 0)
+
+ trace_types : array of string, optional
+ Type of trace. Currently only 'step' is supported, which controls
+ the way in which the signal is plotted.
Notes
-----
@@ -210,7 +225,9 @@ class TimeResponseData:
def __init__(
self, time, outputs, states=None, inputs=None, issiso=None,
output_labels=None, state_labels=None, input_labels=None,
- transpose=False, return_x=False, squeeze=None, multi_trace=False
+ title=None, transpose=False, return_x=False, squeeze=None,
+ multi_trace=False, trace_labels=None, trace_types=None,
+ plot_inputs=True, sysname=None
):
"""Create an input/output time response object.
@@ -241,9 +258,8 @@ def __init__(
single-input, multi-trace response), or a 3D array indexed by
input, trace, and time.
- sys : LTI or InputOutputSystem, optional
- System that generated the data. If desired, the system used to
- generate the data can be stored along with the data.
+ title : str, optonal
+ Title of the data set (used as figure title in plotting).
squeeze : bool, optional
By default, if a system is single-input, single-output (SISO)
@@ -267,6 +283,9 @@ def __init__(
Optional labels for the inputs, outputs, and states, given as a
list of strings matching the appropriate signal dimension.
+ sysname : str, optional
+ Name of the system that created the data.
+
transpose : bool, optional
If True, transpose all input and output arrays (for backward
compatibility with MATLAB and :func:`scipy.signal.lsim`).
@@ -276,6 +295,10 @@ def __init__(
If True, return the state vector when enumerating result by
assigning to a tuple (default = False).
+ plot_inputs : bool, optional
+ Whether or not to plot the inputs by default (can be overridden
+ in the plot() method)
+
multi_trace : bool, optional
If ``True``, then 2D input array represents multiple traces. For
a MIMO system, the ``input`` attribute should then be set to
@@ -290,6 +313,8 @@ def __init__(
self.t = np.atleast_1d(time)
if self.t.ndim != 1:
raise ValueError("Time vector must be 1D array")
+ self.title = title
+ self.sysname = sysname
#
# Output vector (and number of traces)
@@ -363,9 +388,11 @@ def __init__(
if inputs is None:
self.u = None
self.ninputs = 0
+ self.plot_inputs = False
else:
self.u = np.array(inputs)
+ self.plot_inputs = plot_inputs
# Make sure the shape is OK and figure out the nuumber of inputs
if multi_trace and self.u.ndim == 3 and \
@@ -397,6 +424,11 @@ def __init__(
self.input_labels = _process_labels(
input_labels, "input", self.ninputs)
+ # Check and store trace labels, if present
+ self.trace_labels = _process_labels(
+ trace_labels, "trace", self.ntraces)
+ self.trace_types = trace_types
+
# Figure out if the system is SISO
if issiso is None:
# Figure out based on the data
@@ -655,6 +687,10 @@ def to_pandas(self):
return pandas.DataFrame(data)
+ # Plot data
+ def plot(self, *args, **kwargs):
+ return time_response_plot(self, *args, **kwargs)
+
# Process signal labels
def _process_labels(labels, signal, length):
@@ -1132,7 +1168,8 @@ def forced_response(sys, T=None, U=0., X0=0., transpose=False,
return TimeResponseData(
tout, yout, xout, U, issiso=sys.issiso(),
output_labels=sys.output_labels, input_labels=sys.input_labels,
- state_labels=sys.state_labels,
+ state_labels=sys.state_labels, sysname=sys.name, plot_inputs=True,
+ title="Forced response for " + sys.name, trace_types=['forced'],
transpose=transpose, return_x=return_x, squeeze=squeeze)
@@ -1324,7 +1361,7 @@ def step_response(sys, T=None, X0=0, input=None, output=None, T_num=None,
from .statesp import _convert_to_statespace
# Create the time and input vectors
- if T is None or np.asarray(T).size == 1 and isinstance(sys, LTI):
+ if T is None or np.asarray(T).size == 1:
T = _default_time_vector(sys, N=T_num, tfinal=T, is_step=True)
T = np.atleast_1d(T).reshape(-1)
if T.ndim != 1 and len(T) < 2:
@@ -1338,7 +1375,7 @@ def step_response(sys, T=None, X0=0, input=None, output=None, T_num=None,
"with given X0.")
# Convert to state space so that we can simulate
- if sys.nstates is None:
+ if isinstance(sys, LTI) and sys.nstates is None:
sys = _convert_to_statespace(sys)
# Set up arrays to handle the output
@@ -1349,11 +1386,16 @@ def step_response(sys, T=None, X0=0, input=None, output=None, T_num=None,
uout = np.empty((ninputs, ninputs, T.size))
# Simulate the response for each input
+ trace_labels, trace_types = [], []
for i in range(sys.ninputs):
# If input keyword was specified, only simulate for that input
if isinstance(input, int) and i != input:
continue
+ # Save a label and type for this plot
+ trace_labels.append(f"From {sys.input_labels[i]}")
+ trace_types.append('step')
+
# Create a set of single inputs system for simulation
U = np.zeros((sys.ninputs, T.size))
U[i, :] = np.ones_like(T)
@@ -1377,8 +1419,10 @@ def step_response(sys, T=None, X0=0, input=None, output=None, T_num=None,
return TimeResponseData(
response.time, yout, xout, uout, issiso=issiso,
output_labels=output_labels, input_labels=input_labels,
- state_labels=sys.state_labels,
- transpose=transpose, return_x=return_x, squeeze=squeeze)
+ state_labels=sys.state_labels, title="Step response for " + sys.name,
+ transpose=transpose, return_x=return_x, squeeze=squeeze,
+ sysname=sys.name, trace_labels=trace_labels,
+ trace_types=trace_types, plot_inputs=False)
def step_info(sysdata, T=None, T_num=None, yfinal=None,
@@ -1695,10 +1739,7 @@ def initial_response(sys, T=None, X0=0, output=None, T_num=None,
# Create the time and input vectors
if T is None or np.asarray(T).size == 1:
- if isinstance(sys, LTI):
- T = _default_time_vector(sys, N=T_num, tfinal=T, is_step=False)
- elif T_num is not None:
- T = np.linspace(0, T, T_num)
+ T = _default_time_vector(sys, N=T_num, tfinal=T, is_step=False)
T = np.atleast_1d(T).reshape(-1)
if T.ndim != 1 and len(T) < 2:
raise ValueError("invalid value of T for this type of system")
@@ -1718,7 +1759,8 @@ def initial_response(sys, T=None, X0=0, output=None, T_num=None,
return TimeResponseData(
response.t, yout, response.x, None, issiso=issiso,
output_labels=output_labels, input_labels=None,
- state_labels=sys.state_labels,
+ state_labels=sys.state_labels, sysname=sys.name,
+ title="Initial response for " + sys.name, trace_types=['initial'],
transpose=transpose, return_x=return_x, squeeze=squeeze)
@@ -1819,7 +1861,7 @@ def impulse_response(sys, T=None, input=None, output=None, T_num=None,
from .lti import LTI
# Create the time and input vectors
- if T is None or np.asarray(T).size == 1 and isinstance(sys, LTI):
+ if T is None or np.asarray(T).size == 1:
T = _default_time_vector(sys, N=T_num, tfinal=T, is_step=False)
T = np.atleast_1d(T).reshape(-1)
if T.ndim != 1 and len(T) < 2:
@@ -1845,11 +1887,16 @@ def impulse_response(sys, T=None, input=None, output=None, T_num=None,
uout = np.full((ninputs, ninputs, np.asarray(T).size), None)
# Simulate the response for each input
+ trace_labels, trace_types = [], []
for i in range(sys.ninputs):
# If input keyword was specified, only handle that case
if isinstance(input, int) and i != input:
continue
+ # Save a label for this plot
+ trace_labels.append(f"From {sys.input_labels[i]}")
+ trace_types.append('impulse')
+
#
# Compute new X0 that contains the impulse
#
@@ -1887,8 +1934,10 @@ def impulse_response(sys, T=None, input=None, output=None, T_num=None,
return TimeResponseData(
response.time, yout, xout, uout, issiso=issiso,
output_labels=output_labels, input_labels=input_labels,
- state_labels=sys.state_labels,
- transpose=transpose, return_x=return_x, squeeze=squeeze)
+ state_labels=sys.state_labels, trace_labels=trace_labels,
+ trace_types=trace_types, title="Impulse response for " + sys.name,
+ sysname=sys.name, plot_inputs=False, transpose=transpose,
+ return_x=return_x, squeeze=squeeze)
# utility function to find time period and time increment using pole locations
@@ -2062,6 +2111,20 @@ def _ideal_tfinal_and_dt(sys, is_step=True):
def _default_time_vector(sys, N=None, tfinal=None, is_step=True):
"""Returns a time vector that has a reasonable number of points.
if system is discrete-time, N is ignored """
+ from .lti import LTI
+
+ # For non-LTI system, need tfinal
+ if not isinstance(sys, LTI):
+ if tfinal is None:
+ raise ValueError(
+ "can't automatically compute T for non-LTI system")
+ elif isinstance(tfinal, (int, float, np.number)):
+ if N is None:
+ return np.linspace(0, tfinal)
+ else:
+ return np.linspace(0, tfinal, N)
+ else:
+ return tfinal # Assume we got passed something appropriate
N_max = 5000
N_min_ct = 100 # min points for cont time systems
diff --git a/doc/Makefile b/doc/Makefile
index 6e1012343..88a1b7bad 100644
--- a/doc/Makefile
+++ b/doc/Makefile
@@ -15,10 +15,13 @@ help:
.PHONY: help Makefile
# Rules to create figures
-FIGS = classes.pdf
+FIGS = classes.pdf timeplot-mimo_step-pi_cs.png
classes.pdf: classes.fig
fig2dev -Lpdf $< $@
+timeplot-mimo_step-pi_cs.png: ../control/tests/timeplot_test.py
+ PYTHONPATH=.. python $<
+
# Catch-all target: route all unknown targets to Sphinx using the new
# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS).
html pdf clean doctest: Makefile $(FIGS)
diff --git a/doc/index.rst b/doc/index.rst
index 98b184286..ec556e7ce 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -26,6 +26,7 @@ implements basic operations for analysis and design of feedback control systems.
conventions
control
classes
+ plotting
matlab
flatsys
iosys
diff --git a/doc/plotting.rst b/doc/plotting.rst
new file mode 100644
index 000000000..d762a6755
--- /dev/null
+++ b/doc/plotting.rst
@@ -0,0 +1,142 @@
+.. _plotting-module:
+
+*************
+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: :func:`~control.forced_response`,
+:func:`~control.impulse_response`, :func:`~control.initial_response`,
+:func:`~control.input_output_response`, :func:`~control.step_response`.
+Each of these return a :class:`~control.TimeResponseData` object, which
+contains the time, input, state, and output vectors associated with the
+simulation. Time response data can be plotted with the
+:func:`~control.time_response_plot` function, which is also available as
+the :func:`~control.TimeResponseData.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:
+
+.. image:: timeplot-mimo_step-default.png
+
+The :class:`~control.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
+:func:`~control.impulse_response` and :func:`~control.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]")
+
+.. image:: timeplot-mimo_step-pi_cs.png
+
+Input/output response plots created with either the
+:func:`~control.forced_response` or the
+:func:`~control.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]")
+
+.. image:: timeplot-mimo_ioresp-ov_lm.png
+
+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]")
+
+.. image:: timeplot-mimo_ioresp-mt_tr.png
+
+This figure also illustrates the ability to create "multi-trace" plots
+using the :func:`~control.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
+:func:`~control.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 ['-', '--']])
+
+.. image:: timeplot-mimo_step-linestyle.png
+
+Plotting functions
+==================
+
+.. autosummary::
+ :toctree: generated/
+
+ ~control.time_response_plot
+ ~control.combine_time_responses
+ ~control.get_plot_axes
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