From 85faffa27d30bf4cef06ff8a31d3c662aa498f05 Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Fri, 5 Feb 2021 21:27:06 -0800 Subject: [PATCH 1/8] add mirror_style keyword for nyquist --- control/config.py | 8 +++++++- control/freqplot.py | 44 ++++++++++++++++++++++++++++++++++++-------- 2 files changed, 43 insertions(+), 9 deletions(-) diff --git a/control/config.py b/control/config.py index a713e33d2..9bb2dfcf4 100644 --- a/control/config.py +++ b/control/config.py @@ -43,9 +43,10 @@ def reset_defaults(): # System level defaults defaults.update(_control_defaults) - from .freqplot import _bode_defaults, _freqplot_defaults + from .freqplot import _bode_defaults, _freqplot_defaults, _nyquist_defaults defaults.update(_bode_defaults) defaults.update(_freqplot_defaults) + defaults.update(_nyquist_defaults) from .nichols import _nichols_defaults defaults.update(_nichols_defaults) @@ -138,9 +139,11 @@ def use_fbs_defaults(): The following conventions are used: * Bode plots plot gain in powers of ten, phase in degrees, frequency in rad/sec, no grid + * Nyquist plots use dashed lines for mirror image of Nyquist curve """ set_defaults('bode', dB=False, deg=True, Hz=False, grid=False) + set_defaults('nyquist', mirror_style='--') # Decide whether to use numpy.matrix for state space operations @@ -239,4 +242,7 @@ def use_legacy_defaults(version): # time responses are only squeezed if SISO set_defaults('control', squeeze_time_response=True) + # switched mirror_style of nyquist from '-' to '--' + set_defaults('nyqist', mirror_style='-') + return (major, minor, patch) diff --git a/control/freqplot.py b/control/freqplot.py index 0876f1dde..2118abb83 100644 --- a/control/freqplot.py +++ b/control/freqplot.py @@ -520,11 +520,16 @@ def gen_zero_centered_series(val_min, val_max, period): # Nyquist plot # -def nyquist_plot( - syslist, omega=None, plot=True, omega_limits=None, omega_num=None, - label_freq=0, color=None, mirror='--', arrowhead_length=0.1, - arrowhead_width=0.1, *args, **kwargs): - """Nyquist plot for a system +# Default values for module parameter variables +_nyquist_defaults = { + 'nyquist.mirror_style': '--', +} + +def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, + omega_num=None, label_freq=0, arrowhead_length=0.1, + arrowhead_width=0.1, color=None, *args, **kwargs): + """ + Nyquist plot for a system Plots a Nyquist plot for the system over a (optional) frequency range. @@ -532,26 +537,41 @@ def nyquist_plot( ---------- syslist : list of LTI List of linear input/output systems (single system is OK) + plot : boolean If True, plot magnitude + omega : array_like Set of frequencies to be evaluated in rad/sec. + omega_limits : array_like of two values Limits to the range of frequencies. Ignored if omega is provided, and auto-generated if omitted. + omega_num : int Number of samples to plot. Defaults to config.defaults['freqplot.number_of_samples']. + color : string Used to specify the color of the line and arrowhead + + mirror_style : string or False + Linestyle for mirror image of the Nyquist curve. If `False` then + omit completely. Default linestyle ('--') is determined by + config.defaults['nyquist.mirror_style']. + label_freq : int Label every nth frequency on the plot + arrowhead_width : float Arrow head width + arrowhead_length : float Arrow head length + *args : :func:`matplotlib.pyplot.plot` positional properties, optional Additional arguments for `matplotlib` plots (color, linestyle, etc) + **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional Additional keywords (passed to `matplotlib`) @@ -559,8 +579,10 @@ def nyquist_plot( ------- real : ndarray (or list of ndarray if len(syslist) > 1)) real part of the frequency response array + imag : ndarray (or list of ndarray if len(syslist) > 1)) imaginary part of the frequency response array + omega : ndarray (or list of ndarray if len(syslist) > 1)) frequencies in rad/s @@ -586,6 +608,10 @@ def nyquist_plot( # Map 'labelFreq' keyword to 'label_freq' keyword label_freq = kwargs.pop('labelFreq') + # Get values for params (and pop from list to allow keyword use in plot) + mirror_style = config._get_param( + 'nyquist', 'mirror_style', kwargs, _nyquist_defaults, pop=True) + # If argument was a singleton, turn it into a list if not hasattr(syslist, '__iter__'): syslist = (syslist,) @@ -634,17 +660,19 @@ def nyquist_plot( raise ControlMIMONotImplemented( "Nyquist plot currently supports SISO systems.") - # Plot the primary curve and mirror image + # Plot the primary curve p = plt.plot(x, y, '-', color=color, *args, **kwargs) c = p[0].get_color() ax = plt.gca() + # Plot arrow to indicate Nyquist encirclement orientation ax.arrow(x[0], y[0], (x[1]-x[0])/2, (y[1]-y[0])/2, fc=c, ec=c, head_width=arrowhead_width, head_length=arrowhead_length) - if mirror is not False: - plt.plot(x, -y, mirror, color=c, *args, **kwargs) + # Plot the mirror image + if mirror_style is not False: + plt.plot(x, -y, mirror_style, color=c, *args, **kwargs) ax.arrow( x[-1], -y[-1], (x[-1]-x[-2])/2, (y[-1]-y[-2])/2, fc=c, ec=c, head_width=arrowhead_width, From 18888548f9b31bed53faed23ab214dddc20ea948 Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Fri, 5 Feb 2021 22:39:58 -0800 Subject: [PATCH 2/8] update arrow styles for nyquist --- control/freqplot.py | 202 ++++++++++++++++++++++++++-------- control/tests/nyquist_test.py | 85 ++++++++++++++ 2 files changed, 243 insertions(+), 44 deletions(-) create mode 100644 control/tests/nyquist_test.py diff --git a/control/freqplot.py b/control/freqplot.py index 2118abb83..95197ab83 100644 --- a/control/freqplot.py +++ b/control/freqplot.py @@ -157,9 +157,10 @@ def bode_plot(syslist, omega=None, generate the frequency response for a single system. 2. If a discrete time model is given, the frequency response is plotted - along the upper branch of the unit circle, using the mapping ``z = exp(1j - * omega * dt)`` where `omega` ranges from 0 to `pi/dt` and `dt` is the discrete - timebase. If timebase not specified (``dt=True``), `dt` is set to 1. + along the upper branch of the unit circle, using the mapping ``z = + exp(1j * omega * dt)`` where `omega` ranges from 0 to `pi/dt` and `dt` + is the discrete timebase. If timebase not specified (``dt=True``), + `dt` is set to 1. Examples -------- @@ -198,7 +199,8 @@ def bode_plot(syslist, omega=None, omega_range_given = True if omega is not None else False if omega is None: - omega_num = config._get_param('freqplot','number_of_samples', omega_num) + omega_num = config._get_param( + 'freqplot', 'number_of_samples', omega_num) if omega_limits is None: # Select a default range if none is provided omega = _default_frequency_range(syslist, @@ -246,11 +248,9 @@ def bode_plot(syslist, omega=None, # If no axes present, create them from scratch if ax_mag is None or ax_phase is None: plt.clf() - ax_mag = plt.subplot(211, - label='control-bode-magnitude') - ax_phase = plt.subplot(212, - label='control-bode-phase', - sharex=ax_mag) + ax_mag = plt.subplot(211, label='control-bode-magnitude') + ax_phase = plt.subplot( + 212, label='control-bode-phase', sharex=ax_mag) mags, phases, omegas, nyquistfrqs = [], [], [], [] for sys in syslist: @@ -340,9 +340,10 @@ def bode_plot(syslist, omega=None, np.nan, 0.7*min(mag_plot), 1.3*max(mag_plot))) mag_plot = np.hstack((mag_plot, mag_nyq_line)) phase_range = max(phase_plot) - min(phase_plot) - phase_nyq_line = np.array((np.nan, - min(phase_plot) - 0.2 * phase_range, - max(phase_plot) + 0.2 * phase_range)) + phase_nyq_line = np.array( + (np.nan, + min(phase_plot) - 0.2 * phase_range, + max(phase_plot) + 0.2 * phase_range)) phase_plot = np.hstack((phase_plot, phase_nyq_line)) # @@ -351,7 +352,7 @@ def bode_plot(syslist, omega=None, if dB: ax_mag.semilogx(omega_plot, 20 * np.log10(mag_plot), - *args, **kwargs) + *args, **kwargs) else: ax_mag.loglog(omega_plot, mag_plot, *args, **kwargs) @@ -523,11 +524,13 @@ def gen_zero_centered_series(val_min, val_max, period): # Default values for module parameter variables _nyquist_defaults = { 'nyquist.mirror_style': '--', + 'nyquist.arrows': 2, + 'nyquist.arrow_size': 8, } + def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, - omega_num=None, label_freq=0, arrowhead_length=0.1, - arrowhead_width=0.1, color=None, *args, **kwargs): + omega_num=None, label_freq=0, color=None, *args, **kwargs): """ Nyquist plot for a system @@ -542,18 +545,18 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, If True, plot magnitude omega : array_like - Set of frequencies to be evaluated in rad/sec. + Set of frequencies to be evaluated, in rad/sec. omega_limits : array_like of two values Limits to the range of frequencies. Ignored if omega is provided, and auto-generated if omitted. omega_num : int - Number of samples to plot. Defaults to + Number of frequency samples to plot. Defaults to config.defaults['freqplot.number_of_samples']. color : string - Used to specify the color of the line and arrowhead + Used to specify the color of the line and arrowhead. mirror_style : string or False Linestyle for mirror image of the Nyquist curve. If `False` then @@ -561,13 +564,25 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, config.defaults['nyquist.mirror_style']. label_freq : int - Label every nth frequency on the plot - - arrowhead_width : float - Arrow head width - - arrowhead_length : float - Arrow head length + Label every nth frequency on the plot. If not specified, no labels + are generated. + + arrows : int or 1D/2D array of floats + Specify the number of arrows to plot on the Nyquist curve. If an + integer is passed. that number of equally spaced arrows will be + plotted on each of the primary segment and the mirror image. If a 1D + array is passed, it should consist of a sorted list of floats between + 0 and 1, indicating the location along the curve to plot an arrow. If + a 2D array is passed, the first row will be used to specify arrow + locations for the primary curve and the second row will be used for + the mirror image. + + arrow_size : float + Arrowhead width and length (in display coordinates). Default value is + 8 and can be set using config.defaults['nyquist.arrow_size']. + + arrow_style : matplotlib.patches.ArrowStyle + Define style used for Nyquist curve arrows (overrides `arrow_size`). *args : :func:`matplotlib.pyplot.plot` positional properties, optional Additional arguments for `matplotlib` plots (color, linestyle, etc) @@ -588,7 +603,7 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, Examples -------- - >>> sys = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.") + >>> sys = ss([[1, -2], [3, -4]], [[5], [7]], [[6, 8]], [[9]]) >>> real, imag, freq = nyquist_plot(sys) """ @@ -608,9 +623,21 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, # Map 'labelFreq' keyword to 'label_freq' keyword label_freq = kwargs.pop('labelFreq') + # Check to see if legacy 'arrow_width' or 'arrow_length' were used + if 'arrow_width' in kwargs or 'arrow_length' in kwargs: + warn("'arrow_width' and 'arrow_length' keywords are deprecated in " + "nyquist_plot; use `arrow_size` instead", FutureWarning) + kwargs['arrow_size'] = \ + (kwargs.get('arrow_width', 0) + kwargs.get('arrow_width', 0)) / 2 + # Get values for params (and pop from list to allow keyword use in plot) mirror_style = config._get_param( 'nyquist', 'mirror_style', kwargs, _nyquist_defaults, pop=True) + arrows = config._get_param( + 'nyquist', 'arrows', kwargs, _nyquist_defaults, pop=True) + arrow_size = config._get_param( + 'nyquist', 'arrow_size', kwargs, _nyquist_defaults, pop=True) + arrow_style = config._get_param('nyquist', 'arrow_style', kwargs, None) # If argument was a singleton, turn it into a list if not hasattr(syslist, '__iter__'): @@ -620,7 +647,8 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, omega_range_given = True if omega is not None else False if omega is None: - omega_num = config._get_param('freqplot','number_of_samples',omega_num) + omega_num = config._get_param( + 'freqplot', 'number_of_samples', omega_num) if omega_limits is None: # Select a default range if none is provided omega = _default_frequency_range(syslist, @@ -636,6 +664,11 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, xs, ys, omegas = [], [], [] for sys in syslist: + if not sys.issiso(): + # TODO: Add MIMO nyquist plots. + raise ControlMIMONotImplemented( + "Nyquist plot currently only supports SISO systems.") + omega_sys = np.asarray(omega) if sys.isdtime(strict=True): nyquistfrq = math.pi / sys.dt @@ -655,28 +688,35 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, omegas.append(omega_sys) if plot: - if not sys.issiso(): - # TODO: Add MIMO nyquist plots. - raise ControlMIMONotImplemented( - "Nyquist plot currently supports SISO systems.") + # Parse the arrows keyword + if isinstance(arrows, int): + N = arrows + # Space arrows out, starting midway along each "region" + arrow_pos = np.linspace(0.5/N, 1 + 0.5/N, N, endpoint=False) + elif isinstance(arrows, (list, np.ndarray)): + arrow_pos = np.sort(np.atleast_1d(arrows)) + elif not arrows: + arrow_pos = [] + else: + raise ValueError("unknown or unsupported arrow location") + + # Set the arrow style + if arrow_style is None: + arrow_style = mpl.patches.ArrowStyle( + 'simple', head_width=arrow_size, head_length=arrow_size) # Plot the primary curve p = plt.plot(x, y, '-', color=color, *args, **kwargs) c = p[0].get_color() ax = plt.gca() - - # Plot arrow to indicate Nyquist encirclement orientation - ax.arrow(x[0], y[0], (x[1]-x[0])/2, (y[1]-y[0])/2, fc=c, ec=c, - head_width=arrowhead_width, - head_length=arrowhead_length) + _add_arrows_to_line2D( + ax, p[0], arrow_pos, arrowstyle=arrow_style, dir=1) # Plot the mirror image if mirror_style is not False: - plt.plot(x, -y, mirror_style, color=c, *args, **kwargs) - ax.arrow( - x[-1], -y[-1], (x[-1]-x[-2])/2, (y[-1]-y[-2])/2, - fc=c, ec=c, head_width=arrowhead_width, - head_length=arrowhead_length) + p = plt.plot(x, -y, mirror_style, color=c, *args, **kwargs) + _add_arrows_to_line2D( + ax, p[0], arrow_pos, arrowstyle=arrow_style, dir=-1) # Mark the -1 point plt.plot([-1], [0], 'r+') @@ -702,8 +742,8 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, # instead of 1.0, and this would otherwise be # truncated to 0. plt.text(xpt, ypt, ' ' + - str(int(np.round(f / 1000 ** pow1000, 0))) + ' ' + - prefix + 'Hz') + str(int(np.round(f / 1000 ** pow1000, 0))) + ' ' + + prefix + 'Hz') if plot: ax = plt.gca() @@ -716,6 +756,80 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, else: return xs, ys, omegas + +# Internal function to add arrows to a curve +def _add_arrows_to_line2D( + axes, line, arrow_locs=[0.2, 0.4, 0.6, 0.8], + arrowstyle='-|>', arrowsize=1, dir=1, transform=None): + """ + Add arrows to a matplotlib.lines.Line2D at selected locations. + + Parameters: + ----------- + axes: Axes object as returned by axes command (or gca) + line: Line2D object as returned by plot command + arrow_locs: list of locations where to insert arrows, % of total length + arrowstyle: style of the arrow + arrowsize: size of the arrow + transform: a matplotlib transform instance, default to data coordinates + + Returns: + -------- + arrows: list of arrows + + Based on https://stackoverflow.com/questions/26911898/ + + """ + if not isinstance(line, mpl.lines.Line2D): + raise ValueError("expected a matplotlib.lines.Line2D object") + x, y = line.get_xdata(), line.get_ydata() + + arrow_kw = { + "arrowstyle": arrowstyle, + } + + color = line.get_color() + use_multicolor_lines = isinstance(color, np.ndarray) + if use_multicolor_lines: + raise NotImplementedError("multicolor lines not supported") + else: + arrow_kw['color'] = color + + linewidth = line.get_linewidth() + if isinstance(linewidth, np.ndarray): + raise NotImplementedError("multiwidth lines not supported") + else: + arrow_kw['linewidth'] = linewidth + + if transform is None: + transform = axes.transData + + # Compute the arc length along the curve + s = np.cumsum(np.sqrt(np.diff(x) ** 2 + np.diff(y) ** 2)) + + arrows = [] + for loc in arrow_locs: + n = np.searchsorted(s, s[-1] * loc) + + # Figure out what direction to paint the arrow + if dir == 1: + arrow_tail = (x[n], y[n]) + arrow_head = (np.mean(x[n:n + 2]), np.mean(y[n:n + 2])) + elif dir == -1: + # Orient the arrow in the other direction on the segment + arrow_tail = (x[n + 1], y[n + 1]) + arrow_head = (np.mean(x[n:n + 2]), np.mean(y[n:n + 2])) + else: + raise ValueError("unknown value for keyword 'dir'") + + p = mpl.patches.FancyArrowPatch( + arrow_tail, arrow_head, transform=transform, lw=0, + **arrow_kw) + axes.add_patch(p) + arrows.append(p) + return arrows + + # # Gang of Four plot # @@ -840,7 +954,7 @@ def gangof4_plot(P, C, omega=None, **kwargs): # Compute reasonable defaults for axes def _default_frequency_range(syslist, Hz=None, number_of_samples=None, - feature_periphery_decades=None): + feature_periphery_decades=None): """Compute a reasonable default frequency range for frequency domain plots. diff --git a/control/tests/nyquist_test.py b/control/tests/nyquist_test.py new file mode 100644 index 000000000..0e85eb2e7 --- /dev/null +++ b/control/tests/nyquist_test.py @@ -0,0 +1,85 @@ +"""nyquist_test.py - test Nyquist plots + +RMM, 30 Jan 2021 + +This set of unit tests covers various Nyquist plot configurations. Because +much of the output from these tests are graphical, this file can also be run +from ipython to generate plots interactively. + +""" + +import pytest +import numpy as np +import scipy as sp +import matplotlib.pyplot as plt +import control as ct + +# In interactive mode, turn on ipython interactive graphics +plt.ion() + + +# Some FBS examples, for comparison +def test_nyquist_fbs_examples(): + s = ct.tf('s') + + """Run through various examples from FBS2e to compare plots""" + plt.figure() + plt.title("Figure 10.4: L(s) = 1.4 e^{-s}/(s+1)^2") + sys = ct.tf([1.4], [1, 2, 1]) * ct.tf(*ct.pade(1, 4)) + ct.nyquist_plot(sys) + + plt.figure() + plt.title("Figure 10.4: L(s) = 1/(s + a)^2 with a = 0.6") + sys = 1/(s + 0.6)**3 + ct.nyquist_plot(sys) + + plt.figure() + plt.title("Figure 10.6: L(s) = 1/(s (s+1)^2) - pole at the origin") + sys = 1/(s * (s+1)**2) + ct.nyquist_plot(sys) + + plt.figure() + plt.title("Figure 10.10: L(s) = 3 (s+6)^2 / (s (s+1)^2)") + sys = 3 * (s+6)**2 / (s * (s+1)**2) + ct.nyquist_plot(sys) + + plt.figure() + plt.title("Figure 10.10: L(s) = 3 (s+6)^2 / (s (s+1)^2) [zoom]") + ct.nyquist_plot(sys, omega_limits=[1.5, 1e3]) + + +@pytest.mark.parametrize("arrows", [ + None, # default argument + 1, 2, 3, 4, # specified number of arrows + [0.1, 0.5, 0.9], # specify arc lengths +]) +def test_nyquist_arrows(arrows): + sys = ct.tf([1.4], [1, 2, 1]) * ct.tf(*ct.pade(1, 4)) + plt.figure(); + plt.title("L(s) = 1.4 e^{-s}/(s+1)^2 / arrows = %s" % arrows) + ct.nyquist_plot(sys, arrows=arrows) + + +def test_nyquist_exceptions(): + # MIMO not implemented + sys = ct.rss(2, 2, 2) + with pytest.raises( + ct.exception.ControlMIMONotImplemented, + match="only supports SISO"): + ct.nyquist_plot(sys) + + +# +# Interactive mode: generate plots for manual viewing +# + +print("Nyquist examples from FBS") +test_nyquist_fbs_examples() + +print("Arrow test") +test_nyquist_arrows(None) +test_nyquist_arrows(1) +test_nyquist_arrows(2) +test_nyquist_arrows(3) +test_nyquist_arrows(4) +test_nyquist_arrows([0.1, 0.5, 0.9]) From 6de5e91b4fd87b8a085e1c5e91f03dd191224387 Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Sat, 6 Feb 2021 05:38:45 -0800 Subject: [PATCH 3/8] update MATLAB interface to bode, nyquist * regularize argument parsing by using _parse_freqplot_args * fix bug in exception handling (ControlArgument not defined) * change printed warning to use warnings.warn * add unit tests for exceptions, warnings --- control/matlab/__init__.py | 2 +- control/matlab/wrappers.py | 94 ++++++++++++++++++++++++++++++------ control/tests/matlab_test.py | 24 ++++++++- 3 files changed, 102 insertions(+), 18 deletions(-) diff --git a/control/matlab/__init__.py b/control/matlab/__init__.py index 6b88214c6..196a4a6c8 100644 --- a/control/matlab/__init__.py +++ b/control/matlab/__init__.py @@ -70,7 +70,7 @@ # Import MATLAB-like functions that can be used as-is from ..ctrlutil import * -from ..freqplot import nyquist, gangof4 +from ..freqplot import gangof4 from ..nichols import nichols from ..bdalg import * from ..pzmap import * diff --git a/control/matlab/wrappers.py b/control/matlab/wrappers.py index b0fda30a3..a120e151b 100644 --- a/control/matlab/wrappers.py +++ b/control/matlab/wrappers.py @@ -1,15 +1,18 @@ """ -Wrappers for the Matlab compatibility module +Wrappers for the MATLAB compatibility module """ import numpy as np from ..statesp import ss from ..xferfcn import tf +from ..ctrlutil import issys +from ..exception import ControlArgument from scipy.signal import zpk2tf +from warnings import warn -__all__ = ['bode', 'ngrid', 'dcgain'] +__all__ = ['bode', 'nyquist', 'ngrid', 'dcgain'] -def bode(*args, **keywords): +def bode(*args, **kwargs): """bode(syslist[, omega, dB, Hz, deg, ...]) Bode plot of the frequency response @@ -36,7 +39,7 @@ def bode(*args, **keywords): If True, plot frequency in Hz (omega must be provided in rad/sec) deg : boolean If True, return phase in degrees (else radians) - Plot : boolean + plot : boolean If True, plot magnitude and phase Examples @@ -53,19 +56,65 @@ def bode(*args, **keywords): * >>> bode(sys1, sys2, ..., sysN, w) * >>> bode(sys1, 'plotstyle1', ..., sysN, 'plotstyleN') """ + from ..freqplot import bode_plot - # If the first argument is a list, then assume python-control calling format - from ..freqplot import bode as bode_orig + # If first argument is a list, assume python-control calling format if (getattr(args[0], '__iter__', False)): - return bode_orig(*args, **keywords) + return bode_plot(*args, **kwargs) - # Otherwise, run through the arguments and collect up arguments - syslist = []; plotstyle=[]; omega=None; + # Parse input arguments + syslist, omega, args, other = _parse_freqplot_args(*args) + kwargs.update(other) + + # Call the bode command + return bode_plot(syslist, omega, *args, **kwargs) + + +def nyquist(*args, **kwargs): + """nyquist(syslist[, omega]) + + Nyquist plot of the frequency response + + Plots a Nyquist plot for the system over a (optional) frequency range. + + Parameters + ---------- + sys1, ..., sysn : list of LTI + List of linear input/output systems (single system is OK). + omega : array_like + Set of frequencies to be evaluated, in rad/sec. + + Returns + ------- + real : ndarray (or list of ndarray if len(syslist) > 1)) + real part of the frequency response array + imag : ndarray (or list of ndarray if len(syslist) > 1)) + imaginary part of the frequency response array + omega : ndarray (or list of ndarray if len(syslist) > 1)) + frequencies in rad/s + + """ + from ..freqplot import nyquist_plot + + # If first argument is a list, assume python-control calling format + if (getattr(args[0], '__iter__', False)): + return nyquist_plot(*args, **kwargs) + + # Parse arguments + syslist, omega, args, other = _parse_freqplot_args(*args) + kwargs.update(other) + + # Call the nyquist command + return nyquist_plot(syslist, omega, *args, **kwargs) + + +def _parse_freqplot_args(*args): + """Parse arguments to frequency plot routines (bode, nyquist)""" + syslist, plotstyle, omega, other = [], [], None, {} i = 0; while i < len(args): # Check to see if this is a system of some sort - from ..ctrlutil import issys - if (issys(args[i])): + if issys(args[i]): # Append the system to our list of systems syslist.append(args[i]) i += 1 @@ -79,11 +128,16 @@ def bode(*args, **keywords): continue # See if this is a frequency list - elif (isinstance(args[i], (list, np.ndarray))): + elif isinstance(args[i], (list, np.ndarray)): omega = args[i] i += 1 break + # See if this is a frequency range + elif isinstance(args[i], tuple) and len(args[i]) == 2: + other['omega_limits'] = args[i] + i += 1 + else: raise ControlArgument("unrecognized argument type") @@ -93,22 +147,30 @@ def bode(*args, **keywords): # Check to make sure we got the same number of plotstyles as systems if (len(plotstyle) != 0 and len(syslist) != len(plotstyle)): - raise ControlArgument("number of systems and plotstyles should be equal") + raise ControlArgument( + "number of systems and plotstyles should be equal") # Warn about unimplemented plotstyles #! TODO: remove this when plot styles are implemented in bode() #! TODO: uncomment unit test code that tests this out if (len(plotstyle) != 0): - print("Warning (matlab.bode): plot styles not implemented"); + warn("Warning (matlab.bode): plot styles not implemented"); + + if len(syslist) == 0: + raise ControlArgument("no systems specified") + elif len(syslist) == 1: + # If only one system given, retun just that system (not a list) + syslist = syslist[0] + + return syslist, omega, plotstyle, other - # Call the bode command - return bode_orig(syslist, omega, **keywords) from ..nichols import nichols_grid def ngrid(): return nichols_grid() ngrid.__doc__ = nichols_grid.__doc__ + def dcgain(*args): ''' Compute the gain of the system in steady state. diff --git a/control/tests/matlab_test.py b/control/tests/matlab_test.py index dd595be0f..4fa03257c 100644 --- a/control/tests/matlab_test.py +++ b/control/tests/matlab_test.py @@ -27,7 +27,7 @@ from control.matlab import pade from control.matlab import unwrap, c2d, isctime, isdtime from control.matlab import connect, append - +from control.exception import ControlArgument from control.frdata import FRD from control.tests.conftest import slycotonly @@ -802,6 +802,28 @@ def test_tf_string_args(self): np.testing.assert_array_almost_equal(G.den, [[[1, 2, 1]]]) assert isdtime(G, strict=True) + def test_matlab_wrapper_exceptions(self): + """Test out exceptions in matlab/wrappers.py""" + sys = tf([1], [1, 2, 1]) + + # Extra arguments in bode + with pytest.raises(ControlArgument, match="not all arguments"): + bode(sys, 'r-', [1e-2, 1e2], 5.0) + + # Multiple plot styles + with pytest.warns(UserWarning, match="plot styles not implemented"): + bode(sys, 'r-', sys, 'b--', [1e-2, 1e2]) + + # Incorrect number of arguments to dcgain + with pytest.raises(ValueError, match="needs either 1, 2, 3 or 4"): + dcgain(1, 2, 3, 4, 5) + + def test_matlab_freqplot_passthru(self): + """Test nyquist and bode to make sure the pass arguments through""" + sys = tf([1], [1, 2, 1]) + bode((sys,)) # Passing tuple will call bode_plot + nyquist((sys,)) # Passing tuple will call nyquist_plot + #! TODO: not yet implemented # def testMIMOtfdata(self): From 2021a7526e1d48855137e3c24c59704fc9cc33ec Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Sat, 6 Feb 2021 11:06:40 -0800 Subject: [PATCH 4/8] improvements to Nyquist contour tracing * start tracing from omega = 0 * add support for indenting around imaginary poles * change return value to number of encirclements (+ contour, if desired) * update MATLAB interface to retain legacy format * new unit tests --- control/freqplot.py | 164 +++++++++++++++----- control/matlab/wrappers.py | 8 +- control/tests/freqresp_test.py | 17 ++- control/tests/nyquist_test.py | 209 ++++++++++++++++++++++++-- examples/bode-and-nyquist-plots.ipynb | 2 +- examples/pvtol-nested.py | 1 - 6 files changed, 349 insertions(+), 52 deletions(-) diff --git a/control/freqplot.py b/control/freqplot.py index 95197ab83..e3063d708 100644 --- a/control/freqplot.py +++ b/control/freqplot.py @@ -46,11 +46,14 @@ import matplotlib as mpl import matplotlib.pyplot as plt import numpy as np +import warnings from .ctrlutil import unwrap from .bdalg import feedback from .margins import stability_margins from .exception import ControlMIMONotImplemented +from .statesp import StateSpace +from .xferfcn import TransferFunction from . import config __all__ = ['bode_plot', 'nyquist_plot', 'gangof4_plot', @@ -195,7 +198,7 @@ def bode_plot(syslist, omega=None, if not hasattr(syslist, '__iter__'): syslist = (syslist,) - # decide whether to go above nyquist. freq + # Decide whether to go above Nyquist frequency omega_range_given = True if omega is not None else False if omega is None: @@ -526,20 +529,29 @@ def gen_zero_centered_series(val_min, val_max, period): 'nyquist.mirror_style': '--', 'nyquist.arrows': 2, 'nyquist.arrow_size': 8, + 'nyquist.indent_radius': 1e-1, + 'nyquist.indent_direction': 'right', } def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, - omega_num=None, label_freq=0, color=None, *args, **kwargs): - """ - Nyquist plot for a system + omega_num=None, label_freq=0, color=None, + return_contour=False, warn_nyquist=True, *args, **kwargs): + """Nyquist plot for a system Plots a Nyquist plot for the system over a (optional) frequency range. + The curve is computed by evaluating the Nyqist segment along the positive + imaginary axis, with a mirror image generated to reflect the negative + imaginary axis. Poles on or near the imaginary axis are avoided using a + small indentation. The portion of the Nyquist contour at infinity is not + explicitly computed (since it maps to a constant value for any system with + a proper transfer function). Parameters ---------- syslist : list of LTI - List of linear input/output systems (single system is OK) + List of linear input/output systems (single system is OK). Nyquist + curves for each system are plotted on the same graph. plot : boolean If True, plot magnitude @@ -548,8 +560,8 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, Set of frequencies to be evaluated, in rad/sec. omega_limits : array_like of two values - Limits to the range of frequencies. Ignored if omega - is provided, and auto-generated if omitted. + Limits to the range of frequencies. Ignored if omega is provided, and + auto-generated if omitted. omega_num : int Number of frequency samples to plot. Defaults to @@ -563,6 +575,9 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, omit completely. Default linestyle ('--') is determined by config.defaults['nyquist.mirror_style']. + return_contour : bool + If 'True', return the contour used to evaluate the Nyquist plot. + label_freq : int Label every nth frequency on the plot. If not specified, no labels are generated. @@ -584,6 +599,17 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, arrow_style : matplotlib.patches.ArrowStyle Define style used for Nyquist curve arrows (overrides `arrow_size`). + indent_radius : float + Amount to indent the Nyquist contour around poles that are at or near + the imaginary axis. + + indent_direction : str + For poles on the imaginary axis, set the direction of indentation to + be 'right' (default), 'left', or 'none'. + + warn_nyquist : bool, optional + If set to `False', turn off warnings about frequencies above Nyquist. + *args : :func:`matplotlib.pyplot.plot` positional properties, optional Additional arguments for `matplotlib` plots (color, linestyle, etc) @@ -592,24 +618,39 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, Returns ------- - real : ndarray (or list of ndarray if len(syslist) > 1)) - real part of the frequency response array + count : int (or list of int if len(syslist) > 1) + Number of encirclements of the point -1 by the Nyquist curve. If + multiple systems are given, an array of counts is returned. - imag : ndarray (or list of ndarray if len(syslist) > 1)) - imaginary part of the frequency response array + contour : ndarray (or list of ndarray if len(syslist) > 1)), optional + The contour used to create the primary Nyquist curve segment. To + obtain the Nyquist curve values, evaluate system(s) along contour. - omega : ndarray (or list of ndarray if len(syslist) > 1)) - frequencies in rad/s + Notes + ----- + 1. If a discrete time model is given, the frequency response is computed + along the upper branch of the unit circle, using the mapping ``z = + exp(1j * omega * dt)`` where `omega` ranges from 0 to `pi/dt` and `dt` + is the discrete timebase. If timebase not specified (``dt=True``), + `dt` is set to 1. + + 2. If a continuous-time system contains poles on or near the imaginary + axis, a small indentation will be used to avoid the pole. The radius + of the indentation is given by `indent_radius` and it is taken the the + right of stable poles and the left of unstable poles. If a pole is + exactly on the imaginary axis, the `indent_direction` parameter can be + used to set the direction of indentation. Setting `indent_direction` + to `none` will turn off indentation. If `return_contour` is True, the + exact contour used for evaluation is returned. Examples -------- >>> sys = ss([[1, -2], [3, -4]], [[5], [7]], [[6, 8]], [[9]]) - >>> real, imag, freq = nyquist_plot(sys) + >>> count = nyquist_plot(sys) """ # Check to see if legacy 'Plot' keyword was used if 'Plot' in kwargs: - import warnings warnings.warn("'Plot' keyword is deprecated in nyquist_plot; " "use 'plot'", FutureWarning) # Map 'Plot' keyword to 'plot' keyword @@ -617,7 +658,6 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, # Check to see if legacy 'labelFreq' keyword was used if 'labelFreq' in kwargs: - import warnings warnings.warn("'labelFreq' keyword is deprecated in nyquist_plot; " "use 'label_freq'", FutureWarning) # Map 'labelFreq' keyword to 'label_freq' keyword @@ -625,12 +665,16 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, # Check to see if legacy 'arrow_width' or 'arrow_length' were used if 'arrow_width' in kwargs or 'arrow_length' in kwargs: - warn("'arrow_width' and 'arrow_length' keywords are deprecated in " - "nyquist_plot; use `arrow_size` instead", FutureWarning) + warnings.warn( + "'arrow_width' and 'arrow_length' keywords are deprecated in " + "nyquist_plot; use `arrow_size` instead", FutureWarning) kwargs['arrow_size'] = \ - (kwargs.get('arrow_width', 0) + kwargs.get('arrow_width', 0)) / 2 + (kwargs.get('arrow_width', 0) + kwargs.get('arrow_length', 0)) / 2 + kwargs.pop('arrow_width', False) + kwargs.pop('arrow_length', False) # Get values for params (and pop from list to allow keyword use in plot) + omega_num = config._get_param('freqplot', 'number_of_samples', omega_num) mirror_style = config._get_param( 'nyquist', 'mirror_style', kwargs, _nyquist_defaults, pop=True) arrows = config._get_param( @@ -638,21 +682,28 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, arrow_size = config._get_param( 'nyquist', 'arrow_size', kwargs, _nyquist_defaults, pop=True) arrow_style = config._get_param('nyquist', 'arrow_style', kwargs, None) + indent_radius = config._get_param( + 'nyquist', 'indent_radius', kwargs, _nyquist_defaults, pop=True) + indent_direction = config._get_param( + 'nyquist', 'indent_direction', kwargs, _nyquist_defaults, pop=True) # If argument was a singleton, turn it into a list - if not hasattr(syslist, '__iter__'): + isscalar = not hasattr(syslist, '__iter__') + if isscalar: syslist = (syslist,) - # decide whether to go above nyquist. freq + # Decide whether to go above Nyquist frequency omega_range_given = True if omega is not None else False + # Figure out the frequency limits if omega is None: - omega_num = config._get_param( - 'freqplot', 'number_of_samples', omega_num) if omega_limits is None: # Select a default range if none is provided - omega = _default_frequency_range(syslist, - number_of_samples=omega_num) + omega = _default_frequency_range( + syslist, number_of_samples=omega_num) + + # Replace first point with the origin + omega[0] = 0 else: omega_range_given = True omega_limits = np.asarray(omega_limits) @@ -662,30 +713,69 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, np.log10(omega_limits[1]), num=omega_num, endpoint=True) - xs, ys, omegas = [], [], [] + # Go through each system and keep track of the results + counts, contours = [], [] for sys in syslist: if not sys.issiso(): # TODO: Add MIMO nyquist plots. raise ControlMIMONotImplemented( "Nyquist plot currently only supports SISO systems.") + # Figure out the frequency range omega_sys = np.asarray(omega) + + # Determine the contour used to evaluate the Nyquist curve if sys.isdtime(strict=True): + # Transform frequencies in for discrete-time systems nyquistfrq = math.pi / sys.dt if not omega_range_given: # limit up to and including nyquist frequency omega_sys = np.hstack(( omega_sys[omega_sys < nyquistfrq], nyquistfrq)) - mag, phase, omega_sys = sys.frequency_response(omega_sys) + # Issue a warning if we are sampling above Nyquist + if np.any(omega_sys * sys.dt > np.pi) and warn_nyquist: + warnings.warn("evaluation above Nyquist frequency") + + # Transform frequencies to continuous domain + contour = np.exp(1j * omega * sys.dt) + else: + contour = 1j * omega_sys + + # Bend the contour around any poles on/near the imaginary access + if isinstance(sys, (StateSpace, TransferFunction)) and \ + sys.isctime() and indent_direction != 'none': + poles = sys.pole() + for i, s in enumerate(contour): + # Find the nearest pole + p = poles[(np.abs(poles - s)).argmin()] + + # See if we need to indent around it + if abs(s - p) < indent_radius: + if p.real < 0 or \ + (p.real == 0 and indent_direction == 'right'): + # Indent to the right + contour[i] += \ + np.sqrt(indent_radius ** 2 - (s-p).imag ** 2) + elif p.real > 0 or \ + (p.real == 0 and indent_direction == 'left'): + # Indent to the left + contour[i] -= \ + np.sqrt(indent_radius ** 2 - (s-p).imag ** 2) + else: + ValueError("unknown value for indent_direction") + + # TODO: add code to indent around discrete poles on unit circle # Compute the primary curve - x = mag * np.cos(phase) - y = mag * np.sin(phase) + resp = sys(contour) - xs.append(x) - ys.append(y) - omegas.append(omega_sys) + # Compute CW encirclements of -1 by integrating the (unwrapped) angle + phase = -unwrap(np.angle(resp + 1)) + count = int(np.round(np.sum(np.diff(phase)) / np.pi, 0)) + + counts.append(count) + contours.append(contour) if plot: # Parse the arrows keyword @@ -705,6 +795,9 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, arrow_style = mpl.patches.ArrowStyle( 'simple', head_width=arrow_size, head_length=arrow_size) + # Save the components of the response + x, y = resp.real, resp.imag + # Plot the primary curve p = plt.plot(x, y, '-', color=color, *args, **kwargs) c = p[0].get_color() @@ -751,10 +844,11 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, ax.set_ylabel("Imaginary axis") ax.grid(color="lightgray") - if len(syslist) == 1: - return xs[0], ys[0], omegas[0] + # Return counts and (optionally) the contour we used + if return_contour: + return (counts[0], contours[0]) if isscalar else (counts, contours) else: - return xs, ys, omegas + return counts[0] if isscalar else counts # Internal function to add arrows to a curve diff --git a/control/matlab/wrappers.py b/control/matlab/wrappers.py index a120e151b..941fb3ffb 100644 --- a/control/matlab/wrappers.py +++ b/control/matlab/wrappers.py @@ -105,7 +105,13 @@ def nyquist(*args, **kwargs): kwargs.update(other) # Call the nyquist command - return nyquist_plot(syslist, omega, *args, **kwargs) + kwargs['return_contour'] = True + _, contour = nyquist_plot(syslist, omega, *args, **kwargs) + + # Create the MATLAB output arguments + freqresp = syslist(contour) + real, imag = freqresp.real, freqresp.imag + return real, imag, contour.imag def _parse_freqplot_args(*args): diff --git a/control/tests/freqresp_test.py b/control/tests/freqresp_test.py index 86de0e77a..5599e4491 100644 --- a/control/tests/freqresp_test.py +++ b/control/tests/freqresp_test.py @@ -75,11 +75,18 @@ def test_nyquist_basic(ss_siso): tf_siso = tf(ss_siso) nyquist_plot(ss_siso) nyquist_plot(tf_siso) - assert len(nyquist_plot(tf_siso, plot=False, omega_num=20)[0] == 20) - omega = nyquist_plot(tf_siso, plot=False, omega_limits=(1, 100))[2] - assert_allclose(omega[0], 1) - assert_allclose(omega[-1], 100) - assert len(nyquist_plot(tf_siso, plot=False, omega=np.logspace(-1, 1, 10))[0])==10 + count, contour = nyquist_plot( + tf_siso, plot=False, return_contour=True, omega_num=20) + assert len(contour) == 20 + + count, contour = nyquist_plot( + tf_siso, plot=False, omega_limits=(1, 100), return_contour=True) + assert_allclose(contour[0], 1j) + assert_allclose(contour[-1], 100j) + + count, contour = nyquist_plot( + tf_siso, plot=False, omega=np.logspace(-1, 1, 10), return_contour=True) + assert len(contour) == 10 @pytest.mark.filterwarnings("ignore:.*non-positive left xlim:UserWarning") diff --git a/control/tests/nyquist_test.py b/control/tests/nyquist_test.py index 0e85eb2e7..bfedd6749 100644 --- a/control/tests/nyquist_test.py +++ b/control/tests/nyquist_test.py @@ -17,35 +17,140 @@ # In interactive mode, turn on ipython interactive graphics plt.ion() +# Utility function for counting unstable poles of open loop (P in FBS) +def _P(sys, indent='right'): + if indent == 'right': + return (sys.pole().real > 0).sum() + elif indent == 'left': + return (sys.pole().real < 0).sum() + elif indent == 'none': + if any(sys.pole().real == 0): + raise ValueError("indent must be left or right for imaginary pole") + else: + raise TypeError("unknown indent value") + +# Utility function for counting unstable poles of closed loop (Z in FBS) +def _Z(sys): + return (sys.feedback().pole().real >= 0).sum() + +# Decorator to close figures when done with test (to avoid matplotlib warning) +@pytest.fixture(scope="function") +def figure_cleanup(): + plt.close('all') + yield + plt.close('all') + +# Basic tests +@pytest.mark.usefixtures("figure_cleanup") +def test_nyquist_basic(): + # Simple Nyquist plot + sys = ct.rss(5, 1, 1) + N_sys = ct.nyquist_plot(sys) + assert _Z(sys) == N_sys + _P(sys) + + # Unstable system + sys = ct.tf([10], [1, 2, 2, 1]) + N_sys = ct.nyquist_plot(sys) + assert _Z(sys) > 0 + assert _Z(sys) == N_sys + _P(sys) + + # Multiple systems - return value is final system + sys1 = ct.rss(3, 1, 1) + sys2 = ct.rss(4, 1, 1) + sys3 = ct.rss(5, 1, 1) + counts = ct.nyquist_plot([sys1, sys2, sys3]) + for N_sys, sys in zip(counts, [sys1, sys2, sys3]): + assert _Z(sys) == N_sys + _P(sys) + + # Nyquist plot with poles at the origin, omega specified + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0]) + omega = np.linspace(0, 1e2, 100) + count, contour = ct.nyquist_plot(sys, omega, return_contour=True) + np.testing.assert_array_equal( + contour[contour.real < 0], omega[contour.real < 0]) + + # Make sure things match at unmodified frequencies + np.testing.assert_almost_equal( + contour[contour.real == 0], + 1j*np.linspace(0, 1e2, 100)[contour.real == 0]) + + # Make sure that we can turn off frequency modification + count, contour_indented = ct.nyquist_plot( + sys, np.linspace(1e-4, 1e2, 100), return_contour=True) + assert not all(contour_indented.real == 0) + count, contour = ct.nyquist_plot( + sys, np.linspace(1e-4, 1e2, 100), return_contour=True, + indent_direction='none') + np.testing.assert_almost_equal(contour, 1j*np.linspace(1e-4, 1e2, 100)) + + # Nyquist plot with poles at the origin, omega unspecified + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0]) + count, contour = ct.nyquist_plot(sys, return_contour=True) + assert _Z(sys) == count + _P(sys) + + # Nyquist plot with poles at the origin, return contour + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0]) + count, contour = ct.nyquist_plot(sys, return_contour=True) + assert _Z(sys) == count + _P(sys) + + # Nyquist plot with poles on imaginary axis, omega specified + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) + count = ct.nyquist_plot(sys, np.linspace(1e-3, 1e1, 1000)) + assert _Z(sys) == count + _P(sys) + + # Nyquist plot with poles on imaginary axis, omega specified, with contour + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) + count, contour = ct.nyquist_plot( + sys, np.linspace(1e-3, 1e1, 1000), return_contour=True) + assert _Z(sys) == count + _P(sys) + + # Nyquist plot with poles on imaginary axis, return contour + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) + count, contour = ct.nyquist_plot(sys, return_contour=True) + assert _Z(sys) == count + _P(sys) + + # Nyquist plot with poles at the origin and on imaginary axis + sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) * ct.tf([1], [1, 0]) + count, contour = ct.nyquist_plot(sys, return_contour=True) + assert _Z(sys) == count + _P(sys) + # Some FBS examples, for comparison +@pytest.mark.usefixtures("figure_cleanup") def test_nyquist_fbs_examples(): s = ct.tf('s') - + """Run through various examples from FBS2e to compare plots""" plt.figure() plt.title("Figure 10.4: L(s) = 1.4 e^{-s}/(s+1)^2") sys = ct.tf([1.4], [1, 2, 1]) * ct.tf(*ct.pade(1, 4)) - ct.nyquist_plot(sys) + count = ct.nyquist_plot(sys) + assert _Z(sys) == count + _P(sys) plt.figure() plt.title("Figure 10.4: L(s) = 1/(s + a)^2 with a = 0.6") sys = 1/(s + 0.6)**3 - ct.nyquist_plot(sys) + count = ct.nyquist_plot(sys) + assert _Z(sys) == count + _P(sys) plt.figure() plt.title("Figure 10.6: L(s) = 1/(s (s+1)^2) - pole at the origin") sys = 1/(s * (s+1)**2) - ct.nyquist_plot(sys) + count = ct.nyquist_plot(sys) + assert _Z(sys) == count + _P(sys) plt.figure() plt.title("Figure 10.10: L(s) = 3 (s+6)^2 / (s (s+1)^2)") sys = 3 * (s+6)**2 / (s * (s+1)**2) - ct.nyquist_plot(sys) + count = ct.nyquist_plot(sys) + assert _Z(sys) == count + _P(sys) plt.figure() plt.title("Figure 10.10: L(s) = 3 (s+6)^2 / (s (s+1)^2) [zoom]") - ct.nyquist_plot(sys, omega_limits=[1.5, 1e3]) + count = ct.nyquist_plot(sys, omega_limits=[1.5, 1e3]) + # Frequency limits for zoom give incorrect encirclement count + # assert _Z(sys) == count + _P(sys) + assert count == -1 @pytest.mark.parametrize("arrows", [ @@ -53,11 +158,68 @@ def test_nyquist_fbs_examples(): 1, 2, 3, 4, # specified number of arrows [0.1, 0.5, 0.9], # specify arc lengths ]) +@pytest.mark.usefixtures("figure_cleanup") def test_nyquist_arrows(arrows): sys = ct.tf([1.4], [1, 2, 1]) * ct.tf(*ct.pade(1, 4)) plt.figure(); plt.title("L(s) = 1.4 e^{-s}/(s+1)^2 / arrows = %s" % arrows) - ct.nyquist_plot(sys, arrows=arrows) + count = ct.nyquist_plot(sys, arrows=arrows) + assert _Z(sys) == count + _P(sys) + + +@pytest.mark.usefixtures("figure_cleanup") +def test_nyquist_encirclements(): + # Example 14.14: effect of friction in a cart-pendulum system + s = ct.tf('s') + sys = (0.02 * s**3 - 0.1 * s) / (s**4 + s**3 + s**2 + 0.25 * s + 0.04) + + plt.figure(); + count = ct.nyquist_plot(sys) + plt.title("Stable system; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys) + + plt.figure(); + count = ct.nyquist_plot(sys * 3) + plt.title("Unstable system; encirclements = %d" % count) + assert _Z(sys * 3) == count + _P(sys * 3) + + # System with pole at the origin + sys = ct.tf([3], [1, 2, 2, 1, 0]) + + plt.figure(); + count = ct.nyquist_plot(sys) + plt.title("Pole at the origin; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys) + + +@pytest.mark.usefixtures("figure_cleanup") +def test_nyquist_indent(): + # FBS Figure 10.10 + s = ct.tf('s') + sys = 3 * (s+6)**2 / (s * (s+1)**2) + + plt.figure(); + count = ct.nyquist_plot(sys) + plt.title("Pole at origin; indent_radius=default") + assert _Z(sys) == count + _P(sys) + + plt.figure(); + count = ct.nyquist_plot(sys, indent_radius=0.01) + plt.title("Pole at origin; indent_radius=0.01; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys) + + plt.figure(); + count = ct.nyquist_plot(sys, indent_direction='right') + plt.title( + "Pole at origin; indent_direction='right'; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys) + + plt.figure(); + count = ct.nyquist_plot( + sys, omega_limits=[1e-2, 1e-3], indent_direction='none') + plt.title( + "Pole at origin; indent_direction='none'; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys) def test_nyquist_exceptions(): @@ -68,10 +230,27 @@ def test_nyquist_exceptions(): match="only supports SISO"): ct.nyquist_plot(sys) + # Legacy keywords for arrow size + sys = ct.rss(2, 1, 1) + with pytest.warns(FutureWarning, match="use `arrow_size` instead"): + ct.nyquist_plot(sys, arrow_width=8, arrow_length=6) + + # Discrete time system sampled above Nyquist frequency + sys = ct.drss(2, 1, 1) + sys.dt = 0.01 + with pytest.warns(UserWarning, match="above Nyquist"): + ct.nyquist_plot(sys, np.logspace(-2, 3)) + # # 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. +# + +# Start by clearing existing figures +plt.close('all') print("Nyquist examples from FBS") test_nyquist_fbs_examples() @@ -79,7 +258,19 @@ def test_nyquist_exceptions(): print("Arrow test") test_nyquist_arrows(None) test_nyquist_arrows(1) -test_nyquist_arrows(2) test_nyquist_arrows(3) -test_nyquist_arrows(4) test_nyquist_arrows([0.1, 0.5, 0.9]) + +print("Stability checks") +test_nyquist_encirclements() + +print("Indentation checks") +test_nyquist_indent() + +print("Unusual Nyquist plot") +sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) +print(sys) +print("Poles:", sys.pole()) +plt.figure() +count = ct.nyquist_plot(sys) +assert _Z(sys) == count + _P(sys) diff --git a/examples/bode-and-nyquist-plots.ipynb b/examples/bode-and-nyquist-plots.ipynb index e66ec98dc..4568f8cd0 100644 --- a/examples/bode-and-nyquist-plots.ipynb +++ b/examples/bode-and-nyquist-plots.ipynb @@ -10011,7 +10011,7 @@ ], "source": [ "fig = plt.figure()\n", - "mag, phase, omega = ct.nyquist_plot([pt1_w001hzis, pt2_w001hz])" + "ct.nyquist_plot([pt1_w001hzis, pt2_w001hz])" ] }, { diff --git a/examples/pvtol-nested.py b/examples/pvtol-nested.py index 7efce9ccd..7388ce361 100644 --- a/examples/pvtol-nested.py +++ b/examples/pvtol-nested.py @@ -133,7 +133,6 @@ plt.figure(7) plt.clf() nyquist(L, (0.0001, 1000)) -plt.axis([-700, 5300, -3000, 3000]) # Add a box in the region we are going to expand plt.plot([-400, -400, 200, 200, -400], [-100, 100, 100, -100, -100], 'r-') From b859aece3e8a561e24bbfda711193a4fa18c5c5f Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Sat, 6 Feb 2021 11:08:41 -0800 Subject: [PATCH 5/8] updated examples and small tweaks to docs --- control/freqplot.py | 2 +- control/tests/nyquist_test.py | 30 ++++++++++++++++++++++------- examples/pvtol-lqr-nested.ipynb | 34 ++++++++++++++++----------------- examples/pvtol-nested.py | 5 ++--- examples/secord-matlab.py | 2 +- examples/tfvis.py | 6 +++--- 6 files changed, 47 insertions(+), 32 deletions(-) diff --git a/control/freqplot.py b/control/freqplot.py index e3063d708..23b5571ce 100644 --- a/control/freqplot.py +++ b/control/freqplot.py @@ -742,7 +742,7 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, else: contour = 1j * omega_sys - # Bend the contour around any poles on/near the imaginary access + # Bend the contour around any poles on/near the imaginary axis if isinstance(sys, (StateSpace, TransferFunction)) and \ sys.isctime() and indent_direction != 'none': poles = sys.pole() diff --git a/control/tests/nyquist_test.py b/control/tests/nyquist_test.py index bfedd6749..debda6030 100644 --- a/control/tests/nyquist_test.py +++ b/control/tests/nyquist_test.py @@ -22,7 +22,7 @@ def _P(sys, indent='right'): if indent == 'right': return (sys.pole().real > 0).sum() elif indent == 'left': - return (sys.pole().real < 0).sum() + return (sys.pole().real >= 0).sum() elif indent == 'none': if any(sys.pole().real == 0): raise ValueError("indent must be left or right for imaginary pole") @@ -209,16 +209,33 @@ def test_nyquist_indent(): assert _Z(sys) == count + _P(sys) plt.figure(); - count = ct.nyquist_plot(sys, indent_direction='right') + count = ct.nyquist_plot(sys, indent_direction='left') plt.title( - "Pole at origin; indent_direction='right'; encirclements = %d" % count) + "Pole at origin; indent_direction='left'; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys, indent='left') + + # System with poles on the imaginary axis + sys = ct.tf([1, 1], [1, 0, 1]) + + # Imaginary poles with standard indentation + plt.figure(); + count = ct.nyquist_plot(sys) + plt.title("Imaginary poles; encirclements = %d" % count) assert _Z(sys) == count + _P(sys) + # Imaginary poles with indentation to the left + plt.figure(); + count = ct.nyquist_plot(sys, indent_direction='left', label_freq=300) + plt.title( + "Imaginary poles; indent_direction='left'; encirclements = %d" % count) + assert _Z(sys) == count + _P(sys, indent='left') + + # Imaginary poles with no indentation plt.figure(); count = ct.nyquist_plot( - sys, omega_limits=[1e-2, 1e-3], indent_direction='none') + sys, np.linspace(0, 1e3, 1000), indent_direction='none') plt.title( - "Pole at origin; indent_direction='none'; encirclements = %d" % count) + "Imaginary poles; indent_direction='none'; encirclements = %d" % count) assert _Z(sys) == count + _P(sys) @@ -269,8 +286,7 @@ def test_nyquist_exceptions(): print("Unusual Nyquist plot") sys = ct.tf([1], [1, 3, 2]) * ct.tf([1], [1, 0, 1]) -print(sys) -print("Poles:", sys.pole()) plt.figure() +plt.title("Poles: %s" % np.array2string(sys.pole(), precision=2, separator=',')) count = ct.nyquist_plot(sys) assert _Z(sys) == count + _P(sys) diff --git a/examples/pvtol-lqr-nested.ipynb b/examples/pvtol-lqr-nested.ipynb index 9fff756ff..ceb6424c0 100644 --- a/examples/pvtol-lqr-nested.ipynb +++ b/examples/pvtol-lqr-nested.ipynb @@ -217,7 +217,7 @@ "outputs": [ { "data": { - "image/png": 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eAKBzXzj81/7GaHxjicC0WRtyi/h45XY+WrmNxRt3EVBIToxl/MBUxg9I5YgBKfRNSUQa688lklWUOP3riMD7N0FpPoy5wnnip8eoxvvCMRHBEoFpUzbkFvHesmzeW7aVH7YVADC8R0emTxzIMUO6clDvZKvXb4wqrP8CFj4Bm+bD9cshNgEunOHc+cd481KSCV2WCIzv8ovLmbk0m9cXZ7Esy+myd0zfzvzh1OGcMLwbvbsk+hxhiKgogWUznIFOdqyEdl1g9MXOgCqxCZA2uPFjmIhkicD4QlWZv24nL3yzkY9XbKe8KsDQ7kncevJQTj2wJz2Tvet7PWxtXQrvXut0xTz1X85AJrEJfkdlQoAlAhNURWWVvPFtFs99vZHMHYV0ahfLhYf24Zwx6Yzo2cnv8ELLro0w7+9OG8CJ/+t073DVp9DrYKv7N81iicAExY6CUp79agMvzN/E7pIKRvVO5i9nH8hpo3qSEBuGb+Z6KTfTGQd36SvO+LZj3HcxRfYO5mJMM1giMJ7atruUf3+eycsLN1NRFeDE4d355dH9OaRvZ79DC02LnnLGyI2Oh3HTnLFxO/XyOyoT4iwRGE/kFJTxyGeZvLRgE4GAcvYh6Vx9zAAyUtv7HVro2bURApWQMgD6HQOHT4cjroUOaX5HZsKEJQLTqkrKq3jiy3U8OmctZZUBzj4knd9MHGhP/rREYQ58+aDT/cOQk+C8551kcMK9fkdmwowlAtMqVJV3l23lvvdXsW1PKSeO6MbNk4fSP62D36GFnvJi+PoRmPeQ80jo6IuDMlyjiVyWCMx+W5dTyB3vrGBuZi4H9OrEPy4czdiMLn6HFbq++gd8fh8MOw2Ou9MZy9cYD1kiMC1WWRXgP1+s4+///ZH42CjunTqCCw/ta2/+tkTWYtAA9B4Lh10NGUdCxni/ozIRwhKBaZG1OYXcOGMpSzbnc8oBPbhzynC6JtnLS81WuAP+ezcsecFpCL50JiR0siRggsoSgWkWVeWlBZu4592VtIuL5h8XjOa0UT39Div0BAKw+Gn45G6nTeCIa+GY//E7KhOhLBGYJisqq+TWt5bzzpJsjh6cxoNnH0jXjlYKaJHvX3cGgsk4Ck75P0gb4ndEJoJZIjBNkrmjgF89v5j1uUXcdMJgfj1hIFHWFtA8FSWQu8bp/nnkWRDXHoacbN1BGN9ZIjCNmvtjLv/vxcXEx0TxwlWHcsSAVL9DCj0b5sHMa5zxAK5bBvEdnKEgjWkDLBGYBr28YBO3v/09g7p24MnLxtLLegVtnvJi+OQe+ObfkNwXznrSSQLGtCGWCEydVJUHP1rNI5+tZcKQNP5xwWiSEmL9Diu0FO+EJ46DneucfoEm3eVUBxnTxlgiMD+jqtz97kqe+WoDF4zrzb1TR9rg7y2R2AUGnwRDJkO/o/2Oxph62f/dZh+BgHLrW8t55qsNXDG+H/edcYAlgebIWQNPneR8A0y+z5KAafPs/3Dzk0BAufmNZby8YDPTJw7kD6cOs4Hhm0oVvn0OHjsGcn6Agmy/IzKmyaxqyABOddD9H6zitcVZXHvcIG443sa3bbKSfHjvt7DiTefu/4zHoGMPv6MypsksERgAHp2zjse/XM+lh/flt5Osk7Nm+foRWPkOHHcHjL8eomzENRNaLBEYXl24iQdm/8CUUT2587QRVh3UFKpQnAftU+Hom5zxAnod7HdUxrSItRFEuG/W5XHbW987XUacM8reFm6K8iJ44yp4/Fgo3QMx8ZYETEizEkEE25Jfwq9f/JY+KYn888LRxMXYfUGj8tbCqxc7DcITb4M4eznMhD5P/88XkckislpEMkXkZ0MsiUgfEflMRL4TkWUicrKX8Zi9SsqrmPbcIsorAzx+yRg62stijVvzITw2EQq2wsVvOFVCUZY8TejzrEQgItHAI8DxQBawUERmqurKGpvdDsxQ1X+LyHBgFpDhVUzGoar8/s1lrNy6hycvHcMAG06ycaow72HokgHnPg+d+/odkTGtxsuqoXFApqquAxCRV4CpQM1EoEBHd7oTYA9fB8Gb327h7SXZ3HD8YI4d2s3vcNq28mKoKoN2nZ3B42PbOR9jwoiX5dpewOYa81nuspruAi4WkSyc0sA1dR1IRKaJyCIRWZSTk+NFrBFjY14Rd7zzPeMyuvCbiQP9Dqdt25MNT58Er13mlAgSu1gSMGHJy0RQ1+MnWmv+AuAZVU0HTgaeF5GfxaSqj6nqGFUdk5aW5kGokaGiKsD1ry4hKkr42/kH2djCDdm6FB4/DvIy4dCrbcwAE9a8TARZQO8a8+n8vOrnSmAGgKp+DSQA1tm9R/7xaSbfbcrnvjMOsO6kG/LDLHhqsnPxv2K2846AMWHMy0SwEBgkIv1EJA44H5hZa5tNwHEAIjIMJxFY3Y8HVmbv4ZHPMjlzdC8bY7ghFaUw+2Zn6MhffgrdD/A7ImM851ljsapWish04EMgGnhKVVeIyD3AIlWdCdwIPC4iv8WpNrpMVWtXH5n9VBVQfv/WcpLbxXLHacP9DqdtCgQAhdgEuOQd6NAd4hL9jsqYoPD0hTJVnYXTCFxz2R01plcC472MwcCL32xk6eZ8HjrvIJIT4/wOp+2pLIO3/x8kJDsDyXfp73dExgSVvQ0T5rbvKeXPs1dz1KBUph5kVUI/U1YAL54D378Byb0b396YMGRdTIS5u99dQUVVgD+ePtI6k6utMAdePAu2fQ+nPwoHXeB3RMb4whJBGPt6bR6zlm/jphMG0zfFxsrdR6AKnj/d6Tvogldg8Al+R2SMbywRhKlAQLlv1ip6dkrgqqOszvtnoqKdweQTOkHvcX5HY4yvrI0gTL27LJvlW3Zz4wlDSIi1gVJ+snUpLH3VmR50vCUBY7ASQVgqrajiz7NXM7xHR84YXbtXjwi2eQG8cDa06wTDp1h3Eca4rEQQhp77egNb8ku47ZRhNtBMtQ3z4PkzoH0KXDbLkoAxNVgiCDO7Syr456eZTBiSxviB1lsHAOs+hxfPho49nSRgj4kasw+rGgozz361gT2llfzuxCF+h9J2bFkMnTPcN4a7+h2NMW2OJYIwUlhWyVPz1jNpWFdG9Ozkdzj+qyh1uow46kanB9E4e4TWmLpY1VAYeWH+RvKLK5h+7CC/Q/Hf2s/g4dHOy2JgScCYBlgiCBMl5VU88eU6jhqUykG9k/0Ox1/rPoeXz3cGkknq4Xc0xrR5lgjCxMsLNpFbWM61x0V4aWDjV/DS+U7HcZfMdJ4SMsY0yBJBGCirrOI/X6zl0H5dGJvRxe9w/LN9hdOBXHJvp2HYkoAxTWKJIAy8t3Qr2/eU2RjEXQbAqPOdkoA9HWRMk9lTQyFOVXn6q/UM6tqBowZF6HsDeWud9oB2nZ3xBIwxzWIlghC3eOMuvt+yh8vGZ0RmN9O7NsIzp8LrV/odiTEhyxJBiHt63gY6JsREZp9CBdvgualQUQTH3+N3NMaELEsEISw7v4TZK7Zxwbg+JMZFWC1fST68cBYU7oCL3oDuI/2OyJiQFWFXj/Dy/PyNqCq/OLyv36EE36ybIGc1XDQDeo/1OxpjQpolghBVWlHFyws2ceKI7qR3TvQ7nOCbdDeMPBsGHOt3JMaEPKsaClHvL9tKfnEFlxye4XcowaMKy2Y4w0x26gVDJvsdkTFhwRJBiHp10Wb6pbbnsP4R9ALZ5/fDm7+EFW/5HYkxYcUSQQhan1vEgvU7OWdMeuQ8MrroaZjzAIy+GEae5Xc0xoQVSwQhaMaizURHCWcfnO53KMGxeja8fwMMPB5OfQgiJfkZEySWCEJMZVWANxZnMWFwGl07JvgdjvfKCuGdX0OPUXDOMxAd63dExoQde2ooxHy+OocdBWWcOzZChluM7wAXvQadejvTxphWZyWCEPPqos2kdojn2KFh3qlaST58/4Yz3esQ60TOGA9ZIgghOwpK+fSHHZx1cC9io8P4T1dZDjN+AW/+yulLyBjjKU+vJiIyWURWi0imiNxSzzbnishKEVkhIi95GU+oe3fpVqoCyjljwriRWNVpGF7/BUz9J3SOwLemjQkyz9oIRCQaeAQ4HsgCForITFVdWWObQcDvgfGquktErPzfgJlLsxneoyMDuyb5HYp3vnoYvnsejv6dM7aAMcZzXpYIxgGZqrpOVcuBV4Cptbb5JfCIqu4CUNUdHsYT0jbmFbF0cz5TD+rpdyjeyVkDH98JI86ACbf6HY0xEcPLp4Z6AZtrzGcBh9baZjCAiMwDooG7VHW2hzGFrJlLsgE4dVQYJ4K0wXDBK9D/GIgK4zYQY9qYJicCETkCyKi5j6o+19AudSzTOs4/CJgApANfishIVc2vde5pwDSAPn36NDXksKGqzFyazdiMzvRKbud3OK2vcIfTKNx7rPUfZIwPmnTbJSLPAw8CRwJj3c+YRnbLAmo+7J4OZNexzTuqWqGq64HVOIlhH6r6mKqOUdUxaWlpTQk5rPywrYAfdxQy5aAwHHymsgxeuQhePBtK9/gdjTERqaklgjHAcFWtfUffkIXAIBHpB2wBzgcurLXN28AFwDMikopTVbSuGeeICDOXZhMdJZw8srvfobQuVXj3eshaAOc8Cwkd/Y7ImIjU1IrY74FmXYVUtRKYDnwIrAJmqOoKEblHRKa4m30I5InISuAz4Heqmtec84Q7VWXmkmyOHJhKSod4v8NpXfP/BUtfggm/hxGn+x2NMRGrqSWCVGCliCwAyqoXquqU+ncBVZ0FzKq17I4a0wrc4H5MHb7dlM+W/BJuOH6w36G0ri3fwke3w7DT4Oj/8TsaYyJaUxPBXV4GYer3wfKtxEVHccKIbn6H0rp6jIIT/ggHX2pPCBnjsyYlAlWdIyLdcBqJARbYM//eU1Vmr9jG+IEpJCWESa+bZQXOp2NPOPw3fkdjjKHpTw2dCywAzgHOBb4RkbO9DMzAyq17yNpVwuRwaSRWhbf/Hzx+HJQX+R2NMcbV1Kqh24Cx1aUAEUkD/gu87lVgBj78fhtRApOGhUm10Ny/wqp34YT/hbj2fkdjjHE1tXI2qlZVUF4z9jUtNHvFNsZmdAmPp4V+/C98ci+MPNuqhIxpY5p6MZ8tIh+KyGUichnwPrWeBjKta11OIWu2F4ZHtdDO9fDGldBtBEz5hw01aUwb09TG4t+JyFnAeJyuIx5T1bc8jSzCfbhiOwAnjgiDRJDYBQZPhgm3QFyi39EYY2ppcl9DqvoG8IaHsZgaZq/YxoHpnegZyn0LqUJVBSR0gjP/43c0xph6NFg1JCJz3e8CEdlT41MgItYxjEe27i5h6eb80C8NLHoSnjweinf6HYkxpgENlghU9Uj3O4xHQml7Pl4ZBtVCWYvhg1ug/wRISPY7GmNMA5rT+2ijy0zr+GTVDvqltmdg1w5+h9IyRXkw4xLo2APOfMzeHDamjWvq/6Ejas6ISAxwSOuHY4rLK/l6XR7HDg3RUTsDVfDmL6Foh9OjaGIXvyMyxjSisTaC34tIAXBgzfYBYDvwTlAijDDzMvMorwxwXKgmguI82LMFTnoAeh3sdzTGmCZorI3gfuB+EblfVX8fpJgi2qc/bKdDfAxjMkL0TrpDV5g2B2LC4CU4YyJEYyWCoe7kayJycO1PEOKLKKrKpz/s4OjBqcTFhFi9+p5seP8mpw+h2AR7acyYENLYewQ34IwV/H91rFPg2FaPKIKtyN7D9j1lHDs0xPoWqqqE16+Arcvg0F9B6s9GGzXGtGGNVQ1Nc78nBiecyPbpDzsQgQlDQmxc5k/vhU1fw5lPWBIwJgQ19fHRc0QkyZ2+XUTeFJHR3oYWeT75YQej0pNJDaVO5tZ8CPMegkMuhwPP8TsaY0wLNLUi+g+qWiAiRwInAs8Cj3oXVuTJKShjWVZ+aD0tVFUJH9wM3Q6AyX/yOxpjTAs1ta+hKvf7FODfqvqOiNzlTUiR6fPVO1CFiaGUCKJj4JJ3QKucBmJjTEhqaolgi4j8B2d0slkiEt+MfU0TfL4mh65J8Yzo2dHvUJpm41dOp3Kd+0KX/n5HY4zZD029mJ8LfAhMVtV8oAvwO8+iijBVAWXuj7kcPTgNCYXHLn/8GJ4+CRY+4XckxphW0KREoKrFwMH8B2AAABaOSURBVFrgRBGZDnRV1Y88jSyCLM3KZ3dJBUcPDoGnhfZkw1u/gm4jYfTFfkdjjGkFTX1q6DrgRaCr+3lBRK7xMrBI8sWaHETgqIGpfofSsEAVvDkNKkrg7KchNoTHSjDG/KSpjcVXAoeqahGAiDwAfA38w6vAIskXa3I4MD2Zzu3j/A6lYV/8BTZ8Caf/G9IG+x2NMaaVNLWNQNj75BDudAhUZrd9u4srWLI5n2MGtfHSAECfw+Hw6XDQhX5HYoxpRU0tETwNfCMi1eMUnw486U1IkWVuZi4BpW23DwQCzpgC/Y9xPsaYsNLUxuK/ApcDO4FdwOWq+pCXgUWKOWt2kJQQw0G92+goXqrw6kUw5y9+R2KM8UiDJQIRSQCuBgYCy4F/qWplMAKLBKrKF2tyOXJgKjHRbfS1jG8ehdWznCEnjTFhqbGrz7PAGJwkcBLwoOcRRZAfdxSybU9p260W2roUPr4DhpwM46b5HY0xxiONJYLhqnqxqv4HOBs4ujkHF5HJIrJaRDJF5JYGtjtbRFRExjTn+KFuzuocoI22D5QVwmuXQ2IqTH3ExhcwJow1lggqqieaWyUkItHAIzglieHABSIyvI7tkoBrgW+ac/xw8GVmLgPS2tMruQ0+j795vjPk5FmP27jDxoS5xhLBqFpjFVePXVwgInsa2XcckKmq61S1HHgFmFrHdvcCfwZKmx19CCutqGLB+jyOGtQGSwMAAyfB9csh40i/IzHGeKzBRKCq0ara0f0kqWpMjenGekfrBWyuMZ/lLvuJO6ZBb1V9r6EDicg0EVkkIotycnIaOW1o+HbjLkorAhzZ1t4m3rkeVr3rTHcIoZ5QjTEt5uWjKnVVKutPK0WigL8BNzZ2IFV9TFXHqOqYtLQ2egfdTF9m5hITJRw2IMXvUPaqqoA3roK3fwPFO/2OxhgTJF4mgiygd435dCC7xnwSMBL4XEQ2AIcBMyOlwXheZi6j+yTTIb6p7/QFwef3w5ZFcNpD1i5gTATxMhEsBAaJSD8RiQPOB2ZWr1TV3aqaqqoZqpoBzAemqOoiD2NqE3YVlbN8y27Gt6VqofVfwJd/dXoUHXmm39EYY4LIs0TgPmU0HWccg1XADFVdISL3iMgUr84bCr5am4cqHNVW+hcqK3B6FU0ZACf92e9ojDFB5mm9hKrOAmbVWnZHPdtO8DKWtmRuZi5J8TGMSm8j3UrEJ8GkuyBtKMS19zsaY0yQtaEK6sgxNzOHwwaktI1uJcoKIb4DjDrf70iMMT5pA1eiyLIxr4jNO0vaxmOjO36Ah0bCGhtszphIZokgyL78MReAI/1uH6gohdevAImGHqP8jcUY4yurGgqyeZm59OyUQP9Un+vi/3sn7FgBF74GSd38jcUY4ysrEQRRVUD5am0e4wemIn524rbmQ6d76UOvhsEn+BeHMaZNsEQQRCuyd7O7pML/aqHsJdDtAJh0t79xGGPaBEsEQTQvMw+AIwb4nAgm3AxXfQyxCf7GYYxpEywRBNG8zFyGdk8iLSnenwC+exE2L3CmY9tg19fGGF9YIgiS0ooqFmzY6V+3EluXwrvXwVf/8Of8xpg2yxJBkCzeuIvySp+6nS4vgtevhPapcOpDwT+/MaZNs8dHg2Su2+30uH4+9Oo5+xbIy4RLZ0L7NtTttTGmTbASQZBUdzvdPtjdTq/7HL59Do78LfRr1pDTxpgIYYkgCPKLfex2OuMoOO1hmHhr8M9tjAkJlgiCYP46p9vpoLYPVFVCYQ5ERcMhl0J0bPDObYwJKZYIgmBuZi7t46IZ1TuI3U5/+SD86zAo2Ba8cxpjQpIlgiCY+2Muh/VPITZY3U5vmg9zHoCBkyCpe3DOaYwJWZYIPLZ5ZzEb8oqD161EST688UtI7gunPBiccxpjQpo9PuqxuZlOt9NBGZZSFd69Fgqy4YqPnJHHjDGmEVYi8NjcH3Pp3jGBAWkdvD9ZZRloAI67A9IP8f58xpiwYCUCD1UFlHlrc5k0rFtwup2OTYBzn3dKBsYY00RWIvDQiuzd5BdXeF8tVFECb/4K8taCCETZn9UY03R2xfBQ9bCUnr9INvv3sOwV2LXe2/MYY8KSJQIPzf0xl2E9OpLawcNup1e8BYufhvHXOY+LGmNMM1ki8EhxeSWLN+7ytlpo53qYeS2kj4Vj/+DdeYwxYc0SgUe+Wb+T8iqPu53+/E9Om8BZT1oXEsaYFrOnhjwy98dc4mKivO12+tS/Qc406NzXu3MYY8KelQg8MvfHXMZmdCYhNrr1D77lWygrhLhE6GXvCxhj9o8lAg9k55ewensBxwxOa/2D52+G58+Amde0/rGNMRHJEoEH5qzJAWDCkK6te+CqCnj9cghUwbG3t+6xjTERy9NEICKTRWS1iGSKyC11rL9BRFaKyDIR+UREwqKye87qHHp2SmBQ11buVuK/d0HWQpjyMKQMaN1jG2MilmeJQESigUeAk4DhwAUiMrzWZt8BY1T1QOB14M9exRMsFVUB5mXmcsyQtNbtVmLVe/D1P2HcNBh5Zusd1xgT8bwsEYwDMlV1naqWA68AU2tuoKqfqWqxOzsfSPcwnqBYvHEXBWWVHDO4lauFehwIh1wGJ/yxdY9rjIl4XiaCXsDmGvNZ7rL6XAl8UNcKEZkmIotEZFFOTk4rhtj6Pl+dQ0yUMH5gSuscsLIcAgFI7gOn/R1iPHxL2RgTkbxMBHXVi9TZLaaIXAyMAf5S13pVfUxVx6jqmLQ0D57EaUVz1uQwJqMzSQmt9ILXrBvhlQudBmJjjPGAl4kgC+hdYz4dyK69kYhMAm4DpqhqmYfxeG77nlJWbd3TetVCi5+Fb5+DbsOdQeiNMcYDXiaChcAgEeknInHA+cDMmhuIyGjgPzhJYIeHsQTFnNXVj422Qqkl+zuY9TvoPwEm3rb/xzPGmHp4lghUtRKYDnwIrAJmqOoKEblHRKa4m/0F6AC8JiJLRGRmPYcLCZ+v2UG3jvEM7b6fQ0QW74RXL4EOXeGsp6w0YIzxlKd9DanqLGBWrWV31JgOm36TyysDfLkml5MP6LH/j43uznK+z30W2rdSo7MxxtTDOp1rJfPX5VFQVskJI7rt/8F6HAjXLIaYuP0/ljHGNMK6mGglH67YRmJc9P6NRrb8dfjv3c4TQpYEjDFBYiWCVhAIKB+v3M4xg9Na3tvo1mXwznToOdpJBNYuYIwJEisRtIKlWfnsKChrebVQ4Q54+QJI7OK0C1hpwBgTRFYiaAUfrdxOTJRw7JAWJIKKUnjlIijOgytmO08KGWNMEFkiaAUfrtjGYf1T6JTYgreJtyyGrUvhzMeg50GtH5wxptkqKirIysqitLTU71CaLSEhgfT0dGJjm349skSwnzJ3FLIup4jLjsho2QEyxsN1S6Bjz1aNyxjTcllZWSQlJZGRkdG6vQh7TFXJy8sjKyuLfv36NXk/ayPYTx+t3AbApGHNrBb6/k1Y9pozbUnAmDaltLSUlJSUkEoCACJCSkpKs0sylgj200crtnNgeid6Jrdr+k6b5sNbV8OiJ52eRY0xbU6oJYFqLYnbEsF+2JRXzJLN+Zw4onvTd8pb6zwh1KkXnPciRNmfwBjjL7sK7Ye3vtuCCJw+uqFhFmoo3AEvnOVMX/S6dR9hjKmTqnLkkUfywQd7h2iZMWMGkydP9uR81ljcQqrKm99lcVi/FHo1tVpo1Uwo3A6XzLQxh40x9RIRHn30Uc455xwmTpxIVVUVt912G7Nnz/bkfJYIWujbTbvYmFfM9IkDm77T2Ktg0AnOaGPGmJBw97srWJm9p1WPObxnR+48bUSD24wcOZLTTjuNBx54gKKiIi655BJ27tzJGWecwYIFC6iqqmLcuHG8+uqrjBw5cr/isUTQQm9+u4WE2ChOOqBHwxtWVcKsm+CQS53uIywJGGOa6M477+Tggw8mLi6ORYsWER8fz5QpU7j99tspKSnh4osv3u8kAJYIWqSssor3lm3lxBHd6RDfwD9hoAre+TUsexW6DnMSgTEmpDR25+6l9u3bc95559GhQwfi453xyu+44w7Gjh1LQkICDz/8cKucxxqLW+CzH3awu6SCMw9Or38jVXjveicJHHs7HPqr4AVojAkbUVFRRNV4unDnzp0UFhZSUFDQam8+WyJogTe+3ULXpHjGD6jnqR9V+OB/nPGGj7oJjv5dcAM0xoStadOmce+993LRRRdx8803t8oxrWqombbtLuWzH3Zw+fgMYqLryaOBSsjfBIdPd0oDxhjTCp577jliYmK48MILqaqq4ogjjuDTTz/l2GOP3a/jiqq2UojBMWbMGF20aJFv579v1iqe+HIdc343kd5dEvddGaiCsgJolwxVFRAVAyH6dqIxkWzVqlUMGzbM7zBarK74RWSxqo6pa3urGmqG3SUVvPTNJk45sOfPk0BlGbxxFTx7qtO1dHSsJQFjTEiwRNAML32zicKySn51dP99V5TuhhfPhhVvwgHnQmyCPwEaY0wLWBtBE5VWVPHUvPUcNSiVkb067V2xJxtePAdyfoAz/gOjzvcvSGOMaQErETTR299tIaegjKuPqdU1xLvXwa4NcNFrlgSMMSHJSgRNUBVQHvtiHSN7deSI6kdGqweYP+nPTgNxjwP9DdIYY1rISgRN8NTc9azLLWL6xIFIVTl8cAu8foXzvkCXfpYEjDEhzRJBI9bnFvHgR6uZNKwbJ3bdDU8cB9/8G5J6OKUCY4xpZdYNdRsSCCg3v7GM+Bj4a78FyGN3Q1x7OP9lGHqy3+EZY8KUdUPdhry4YBML1u/kb1P60nHubyDjKJj6CCQ1c3xiY0xoe/qUny8bcTqM+yWUFztPDtZ20IUw+iIoyoMZl+y77vL3Gz1lXd1QP/PMM6SmpnLdddcBcNttt9GtWzeuvfbalvyqn1giqMfK1avZNetBjh54OacfPgKGfgKdM+wlMWNM0NTuhnrr1q2ceeaZXHfddQQCAV555RUWLFiw3+exRFBb/may37+fAWtmMDiqil2HXeAMBt2ln9+RGWP80tAdfFxiw+vbpzSpBFDnrrW6oc7IyCAlJYXvvvuO7du3M3r0aFJS9n/IW08TgYhMBv4ORANPqOqfaq2PB54DDgHygPNUdYOXMdWrJB/euprAjx+TGlA+iZ/E2IvvIa3PUF/CMcYY+Hk31FdddRXPPPMM27Zt44orrmiVc3iWCEQkGngEOB7IAhaKyExVXVljsyuBXao6UETOBx4AzvMiHlVFVKE0H4p3wu7NkLUQomLYM/Ya3l+2mwPXb+bLisks73ku919xMh0TYr0IxRhjWuyMM87gjjvuoKKigpdeeqlVjulliWAckKmq6wBE5BVgKlAzEUwF7nKnXwf+KSKiHnSJ+uTc9Qz9+BKOjFq+z/KvOZBffDCUyoAyqOt9nHNUOv93eAYJsdGtHYIxxuy3uLg4Jk6cSHJyMtHRrXOd8jIR9AI215jPAg6tbxtVrRSR3UAKkFtzIxGZBkwD6NOnZWP+HtCrE1sHncv7JRPJJ4md0pltHYYh7Trxq3axnDiiOwf06uS0BxhjTBtx11137TMfCASYP38+r732Wqudw8tEUNcVtfadflO2QVUfAx4DZzyClgRzaP8U6L9/j1gZY4yfVq5cyamnnsoZZ5zBoEGDWu24XiaCLKB3jfl0ILuebbJEJAboBOz0MCZjjAlZw4cPZ926da1+XC+7mFgIDBKRfiISB5wPzKy1zUzgUnf6bOBTL9oHjDGmuUL1UtSSuD1LBKpaCUwHPgRWATNUdYWI3CMiU9zNngRSRCQTuAG4xat4jDGmqRISEsjLywu5ZKCq5OXlkZDQvMGxbMxiY4yppaKigqysLEpLS/0OpdkSEhJIT08nNnbfx98bGrPY3iw2xphaYmNj6dcvcnoTsG6ojTEmwlkiMMaYCGeJwBhjIlzINRaLSA6wsYW7p1LrreUIYL85Mthvjgz785v7qmpaXStCLhHsDxFZVF+rebiy3xwZ7DdHBq9+s1UNGWNMhLNEYIwxES7SEsFjfgfgA/vNkcF+c2Tw5DdHVBuBMcaYn4u0EoExxphaLBEYY0yEi5hEICKTRWS1iGSKSNj3cioivUXkMxFZJSIrROQ6v2MKBhGJFpHvROQ9v2MJBhFJFpHXReQH9299uN8xeU1Efuv+N/29iLwsIs3rajMEiMhTIrJDRL6vsayLiHwsIj+6351b63wRkQhEJBp4BDgJGA5cICLD/Y3Kc5XAjao6DDgM+E0E/GaA63C6PY8Ufwdmq+pQYBRh/ttFpBdwLTBGVUcC0ThjnYSbZ4DJtZbdAnyiqoOAT2jFbvsjIhEA44BMVV2nquXAK8BUn2PylKpuVdVv3ekCnAtEL3+j8paIpAOnAE/4HUswiEhH4GiccT1Q1XJVzfc3qqCIAdq5oxom8vORD0Oeqn7Bz0drnAo8604/C5zeWueLlETQC9hcYz6LML8o1iQiGcBo4Bt/I/HcQ8D/AAG/AwmS/kAO8LRbHfaEiLT3OygvqeoW4EFgE7AV2K2qH/kbVdB0U9Wt4NzoAV1b68CRkgikjmUR8dysiHQA3gCuV9U9fsfjFRE5Fdihqov9jiWIYoCDgX+r6migiDAf5c+tF58K9AN6Au1F5GJ/owp9kZIIsoDeNebTCcPiZG0iEouTBF5U1Tf9jsdj44EpIrIBp+rvWBF5wd+QPJcFZKlqdUnvdZzEEM4mAetVNUdVK4A3gSN8jilYtotIDwD3e0drHThSEsFCYJCI9BOROJzGpZk+x+QpERGcuuNVqvpXv+Pxmqr+XlXTVTUD5+/7qaqG9Z2iqm4DNovIEHfRccBKH0MKhk3AYSKS6P43fhxh3kBew0zgUnf6UuCd1jpwRAxVqaqVIjId+BDnKYOnVHWFz2F5bTzwC2C5iCxxl92qqrN8jMm0vmuAF90bnHXA5T7H4ylV/UZEXge+xXky7jvCsKsJEXkZmACkikgWcCfwJ2CGiFyJkxDPabXzWRcTxhgT2SKlasgYY0w9LBEYY0yEs0RgjDERzhKBMcZEOEsExhgT4SwRmIglIikissT9bBORLTXmv/LonKNFpN6+kEQkTURme3FuY+oTEe8RGFMXVc0DDgIQkbuAQlV90OPT3gr8sYGYckRkq4iMV9V5HsdiDGAlAmPqJCKF7vcEEZkjIjNEZI2I/ElELhKRBSKyXEQGuNulicgbIrLQ/Yyv45hJwIGqutSdP6ZGCeQ7dz3A28BFQfqpxlgiMKYJRuGMc3AAztvag1V1HE5319e42/wd+JuqjgXOou6usMcA39eYvwn4jaoeBBwFlLjLF7nzxgSFVQ0Z07iF1d3/ishaoLrb4+XARHd6EjDc6f4GgI4ikuSOBVGtB0630dXmAX8VkReBN1U1y12+A6dnTWOCwhKBMY0rqzEdqDEfYO//Q1HA4apaQv1KgJ+GVVTVP4nI+8DJwHwRmaSqP7jbNHQcY1qVVQ0Z0zo+AqZXz4jIQXVsswoYWGObAaq6XFUfwKkOGuquGsy+VUjGeMoSgTGt41pgjIgsE5GVwNW1N3Dv9jvVaBS+3h2AfSlOCeADd/lE4P1gBG0MWO+jxgSViPwWKFDVht4l+AKYqqq7gheZiWRWIjAmuP7Nvm0O+xCRNOCvlgRMMFmJwBhjIpyVCIwxJsJZIjDGmAhnicAYYyKcJQJjjIlwlgiMMSbC/X+tzNd7cgkkBQAAAABJRU5ErkJggg==\n", 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\n", 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" ] @@ -276,7 +276,7 @@ "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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CcZtn8eHvn5CjOTSr1Yzujbtz7enXckLFE4r94zTFI7f6qv5x9cMnQQCISF3ggyMkiP8Bc1V1sv/xCqCVqm7K75zJycnarFmzUIRrTNH4fO6LeOtW2LnTfWGD++UeWO1TvryrEooKk4kLVF0p5MCB4FvmATiQCQcOkCk+NibDpiTIioa4HKixD2pkxFJO4tHYWDQ2zm0xsQdvfTGxaEwcGh2L+t937ldN4FdOUe8f6bn8vsaOtK8wX32F/Xos7q/RIp1PFVEfor6g93Nvl6T+HFFtELWBDQGPU/3P/SVBiEh/oD9AfHzpGIBiIpTP5xLCli3ul7iqSwiVKkFKirstH7xHjuqhmqLA27z38265rwu8n99tsO3wfYJqHKpxB+PK3Q6K3wVVUqHcVgBi0itQYU9FktLjiCaLPRwggwPEcYA49hFHFkLwbzUfQhaxZBNLFjFkE0M2sf7baP9tDDlEk+N/LodofESTQ5T/fhQQjtVWShQ+/6bIwfslsbnrhfJT8TJBBHtfQf/CVHUUMApcFdPcuXNDGJYxh8s6oOyZ+QXRr48l6eOpRO/fy74qdVjdsidLG3Rk6XEXs2NfHLt3H6rp2bv38G3fvkO1TUcjOhri4137dHy8a56Ii3O3uY9zn4uJcfdzbwPvx8QcauvO3XKbOSQ6h9+ip/Fd9L9JZRGJVKZFzCDOi7uV6rH1Dh4XFXWozTz3vqAkHNhN4p4tJOxNI3HfVhL3pBG/O434vduI27ed+D3biN27ndh9O4ndu4PYvTuIydhX6M/AFx2DLz4RjU/AFxvvSitx8a7kEhMLMbFoTAxIFBodDVH+AEUOL70J7le1zwfqQ3w+xJcDvhwkx3+bnYVkZ0N2lv++f8s6gBw4AFkH3P1iKDpofDwan+DeS4J7f3k3AvfFxaMJ/udyt/j4g4+JP/TZHLwfE0v16y4pcmxeJohUoE7A4xRgo0exmDLE53NV85s3u45Emze7qvktW9yWluYKCfu27OPSzRO5OfNlzmAJu6jAa1zHBG7gy20XoXOjYK774q1Y0dUmVajgbqtWhbp1XWEiKcnd5jYv5N7mdkIK3BISDt/i3f9xokM4DVC2L5vJiyfz9FdP8+vWX2lQuQEvn/syvc/qXYTxCQJU9G8nF+Hi2S6r7tp1KLPmtqnk9ujatw/S04nKyCAqPd1V5WVmHtpyG+6zstx9nw9ysiAnwxWLcvzFr7wN57kZLkb8WTPur9kzMMvmZuO4uENb4OPAf7DERHeb+1zuP27gff9jiYoqmbLRdUV/iZcJYjowUETexDVS7yqo/cGYwtizB9auhd9/P7Rt2OA6D6WmwsaNwTsCJSS4jj31K+/gjr0v0mXTcJIO7GBzzbP4vM1o0i7tQUrNcgyt5GqSKlVyiSEhIeS9SUMi25fNhJ8n8OSXT7Jmxxqa1GjCW13f4ppG15TcxHQxMYe65ZqwE7IEISKTgVZAVRFJBR4HYgFUdSTwIa4H0ypcN9c+oYrFlD7797ueoytWwMqV8NtvbluzxpUAAsXHu05DKSlw0UWu89Dxxx/eWadGDUg6sB3593MwYoTLMp06wf33U/P886kZiRngCHzqY8qyKTz6+aOs2LaCZrWa8X739+l4SkfrnmoOE7IEoao9CtivwIBQXd+UDllZbvjA4sXwyy/udtkyVyoIrP6tUwdOPhk6d4b69V2P0nr14MQTXU/SfDsQZWbCyy/Dk0+6qo5rr4WHHoImTUL99krc3HVz+fucv7Nw00JOr3Y6U6+dSueGnS0xmKBsJLUJG9nZsHQpfP89LFgAP/3kkkJmptsfGwsNG8K550KfPtCokXvcoIGr0y8yVZg6Fe6/39VJtWsHzz4LZ5xRrO8rHKzctpIHPn6A91e8T50KdRjfeTzXn3F9mVzjwBSeJQjjmZ07Yf58+Oorty1Y4KqOwFVJN20Kd9zhbps0gVNOcW2BxWLdOhgwAD780J18zhy47LJiOnn42JO5hyfmPcGw74aREJPA05c8zd3n3k1ibOFGTZuyzRKEKTF798KXX8Jnn7ntp5/cj/iYGJcEbr4ZzjkHWrRwpYKQ1HpkZ8MLL8Djj7t6pxdegIED8x+5HIFUlbeWvsV9c+5j456N9Gvaj6cueYoaSTW8Ds1EkNL1v8KEFVU3FdFHH8GsWa6UkJXlSgHnn+++oy+6yCWEI4wtK16rV8MNN7hiS6dO8NJLrvGilFm1fRW3fXAbn679lLNrnc2Ua6dwbsq5XodlIpAlCFOssrPdVETvvee2devc82ecAffcA5df7pJDIeeFKx6qMHq0CyA2FiZNgh759qGISFk5WTw//3kGzxtMXHQcIzqM4NZmt1o7gzlqliDMMfP5XOngrbfgnXdcN9P4eLj0UtcZqH1718XUE7t3Q9++MGUKtGkDr71WKksNP2/+md7v92bR5kV0adiFl9q/RO0Ktb0Oy0Q4SxDmqP32G4wbB+PHuwFoiYnQsSN06+Y6BCV5vQzA4sVwzTVucMRzz8G994bPhHnFJCsni3999S+e+OIJqiRWYeq1U+nSqIvXYZlSwhKEKZLMTHj7bRg1ypUaoqKgbVsYOhSuuioMkkKuCRPg1lvdcOfPP3eNHaXM8rTl3DDtBhZuWkiPxj14qf1LVClXxeuwTCliCcIUyoYN8N//uqr8tDQ3KO2ZZ1ybb+1wqsnw+Vy91tCh0KoVTJ7shkqXIqrKfxf8l/vm3EdSXBLvdnuXa067xuuwTClkCcLka8kSN3Zs8mT33duxoxs+0KZNGNbW7NvnMta0aa708NJLrlG6FNmybwv9pvfjg5Uf0LZBW8Z1HkfNpNKVAE34sARhglq4EIYMgRkz3CjlAQPg7rvdDKVhadMmuPJKWLQIhg2DO++MzBn08vH52s+5fur17EjfwfB2wxl4zkCiJNyytClNLEGYwyxbBo895jr9HHecSxIDBrgVMcPW6tWu/+yff8L06XDFFV5HVKxyfDk8+cWTPPHFE5xS5RTm9JrDGTVK33QgJvxYgjCAWwfhoYdcL9Dy5d0gtnvvdesbhLWff3at5NnZbnj2Oed4HVGx+nPvn1w/9Xo+W/sZNzS5gVeueIWkuHDpCWBKO0sQZVxWlpvIdPBgNw/SXXe5RFG1qteRFcJXX7lqpeRk11OpUSOvIypW36Z+S9e3u7ItfRtjrhpDn7P62KyrpkRZgijD5s+Hfv1g+XI3bmHYMDj1VK+jKqR586BDBzfobc4cOOEEryMqNrm9lO6edTd1KtZhfr/5nFXzLK/DMmWQtXCVQfv3w333wQUXuI4/06e7SU0jJjnMneuSw4knukRRipJDZnYm/ab3Y8CHA7iswWUsuGWBJQfjGStBlDHffQe9esGqVfB//+eGCyQnex1VEcyd6xqh69Z1bQ41Ss/spJv3bubqt65mfup8Hr34UQa3Gmy9lIynLEGUEarw/PPw4INuYNtnn0Hr1l5HVUTffFNqk8OCjQvo/GZndmTs4J1u79D1tK5eh2SMJYiyYNs26N0bPvgAunSBsWPdDBQR5eefXbVSSkqpSw7vLnuXG6bdQPXy1fm679dWpWTChpVfS7mlS6F5c9eO++KLbnxDxCWHlSvdOIcKFeDjj0tNclBVhn41lG7vdKNpzab8cMsPlhxMWAlpghCRdiKyQkRWiciDQfZXFJEZIvKziCwVkT6hjKesmT3brb2QkeFWcrvjjggcXLxhg5s3XNUlh1LSIJ2Vk8UtM27hwU8fpHvj7nx202dUL1/d67CMOUzIEoSIRAMjgPbAaUAPETktz2EDgGWqeibQCviPiBTXqsNl2iuvuOr6evXg++8jdPzYzp1uMYldu1y2i5huVvnbnbmbKyZdwZifxvDoxY/yxtVvkBCT4HVYxvxFKNsgzgFWqeoaABF5E+gELAs4RoFkcaN/koDtQHYIYyr1VN30GEOGuDFkkyeH0RTcRXHggFvLYeVKt2Zp06ZeR1QsNu7ZyBWTrmDxn4sZe9VY+jS1QrMJX6FMELWBDQGPU4EWeY55GZgObASSgetU1Zf3RCLSH+gPcEIpqWIIBVUYNMitjdOnD7z6KkRH4mqTqnDzza4xevx4N3VsKbA8bTnt3mjH9vTtzLx+Jm1Paut1SMbkK5RtEMFquzXP47bAIuB44CzgZRH5y+w/qjpKVZuravNq1aoVd5ylgs/n2hiee85Nrjd6dIQmB3ATQU2YAP/8p5u+uxT4NvVbLhh7AZnZmczrPc+Sg4kIoUwQqUDg4r8puJJCoD7AVHVWAWuBhiGMqVRSdbNbjxgBf/+7WwYh7NZqKKxJk1xi6NcPHn7Y62iKxaxVs2gzvg3HJR7H/H7zObvW2V6HZEyhhPJr5AfgZBGp52947o6rTgq0HmgDICI1gFOBNSGMqVR64gmXHO6/3y3uE3E9lXL98INLDBdf7FrZI/aNHDJp8SQ6Tu7IKVVO4eu+X1Ovcj2vQzKm0ELWBqGq2SIyEJgNRANjVXWpiNzm3z8S+CcwTkQW46qkBqnq1lDFVBq98oqbibVPHzdtRsR+p/7xB3Tq5JYHffddiIv8zmz//eG/3P7h7bQ8sSXvd3+figkVvQ7JmCIJ6UhqVf0Q+DDPcyMD7m8ELg9lDKXZ22/DwIFuGdBRoyI4OaSnQ+fOsGeP685aCtqZnv36WQZ9MogrT7mSt7u+TWJsotchGVNkhapiEpGrReQ3EdklIrtFZI+I7A51cObIvv8ebrzRDYR7802IidRJU1Rdq/qCBTBxIpwR2SulqSqPfPYIgz4ZRPfG3Zl67VRLDiZiFfZr5Vmgo6ouD2UwpnA2b4arr4ZateC999ya0RFr1Ci3jN2jj7oqpgimqtw35z5e+PYFbm56MyOvHEl0VKR2JTOm8AniT0sO4eHAAejaFbZvdwv+RMTKb0fy3Xeub267dq5rawTzqY+BHw7kvwv+y10t7uKFti/Y6m8m4hU2QSwQkbeA94DM3CdVdWoogjJHdtdd8PXXboT0mWd6Hc0x2LLFZbrateGNNyJ40Abk+HK49YNbGfPTGB44/wH+dem/LDmYUqGwCaICsJ/DG5QVsARRgiZMgJEj4YEHoHt3r6M5Bjk50LMnbN3q1ng47jivIzpqOb4c+k7vy/ifx/PoxY8ypNUQSw6m1ChUglBVmzDGY2vXurbcCy+Ep5/2Oppj9Mwz8Mknbi6QCJ5jKceXQ+/3ezPxl4k80eoJHm35qNchGVOsCtuLKUVEponIFhH5U0SmiEhKqIMzTna2WyZUxHX0ieDaGLeG9OOPw/XXu0FxESowOfyz9T8tOZhSqbAjqV/DjYI+HjcJ3wz/c6YEPP20q4kZORJOPNHraI7Bli3QowecdJJ7MxFaFROYHJ5s/SSPXPyI1yEZExKFTRDVVPU1Vc32b+OAyB/NFAG+/dZNpdGrl/tujVg+n5t4b/t2N8IvOdnriI6KT330nd73YHJ4+OLSMV+UMcEUNkFsFZFeIhLt33oB20IZmIHMTLeWdEoKvPyy19EcoxdecOueDhsWsd2vfOqj/4z+jP95PE+0esKSgyn1CtuLqS9u7YYXcL2XvvE/Z0LomWdgxQo3+0TFSJ7G58cf4R//gC5d4NZbvY7mqKgqA2YOYMxPY3jkokeszcGUCYXtxbQeuCrEsZgAy5e7toeePeHySJ6tat8+VzdWrZrrtRSB7Q6qyj2z72HkwpE8cP4DPNH6Ca9DMqZE5JsgROQBVX1WRF7ir4v9oKp3hiyyMszncz+0k5Ph+ee9juYY3XMP/Pab69ZapYrX0RyVhz97mOHfDeeuFnfZIDhTphRUgsidXmNBqAMxh4wZA19+6W6rV/c6mmMwbZorNTz4IFxyidfRHJWnvniKZ756hv5n97fpM0yZI6p/KRj89SCRbqr6TkHPlYTmzZvrggWlN19t3Qonn+zacT//PCJrZJzNm6FxY9cvd/78iFzf4YX5L3DvnHvp1aQXr3d+nSiJ1GX6jAERWaiqzYvymsL+xf+jkM+ZYzR4sFsWIaIXVFOFm2927Q8TJkRkchj942junXMv1zS6htc6vWbJwZRJBbVBtAc6ALVF5MWAXRWA7FAGVhYtX+7Gj916K5x2mtfRHINXX4WZM12X1gh8I28teYv+M/rT7qR2TLpmEjFRkbrYhjHHpqC//I249oergIUBz+8B7glVUGXV/fdDUpIrRUSs1avh3nuhTRs3lXeEmblyJr2m9eLCEy5kyrVTiIuOvNKPMcUl3wShqj8DP4vIG6pqJYYQ+vhj96P7uecieMXNnBy46Sa3vN1rr0FUZFXLzFs3j67vdOXMGmcyo8cMysVG8kpMxhy7gqqY3lbVa4GfRCSwNVsAVdUmIY2ujMjJgfvug3r1IvJH9yHDhrnFKsaPhzp1vI6mSH7c9CMdJ3ekXqV6zOo1i4oJkTwy0ZjiUVAV013+2yuP5uQi0g4YDkQDo1X1X0GOaQUMA2KBrara8miuFcnGjYPFi+GddyA+3utojtKvv8LDD7tlQ3v18jqaIlm5bSXtJrajcmJl5twwh6rlInmZPmOKT2G7uZYH0lXVJyKnAA2Bj1Q1K5/XRAMrgcuAVOAHoIeqLgs4phJu2o52qrpeRKqr6pb8Yilt3VwPHHDdWmvWdBPzRWTPpexsuOAC1/6wdCnUqOF1RIW2YdcGLnztQtKz0vmq71ecUuUUr0MyJiRC2c31CyBBRGoDnwJ9gHEFvOYcYJWqrlHVA8CbQN5V6a8Hpvqn8qCg5FAajR0L69fDP/8ZockB4N//hu+/hxEjIio5bNu/jbYT27IzYyeze8225GBMHoVNEKKq+4GrgZdUtQtQUP/F2sCGgMep/ucCnQJUFpG5IrJQRG4MenGR/iKyQEQWpKWlFTLk8JeRAU895X58X3aZ19EcpaVL3QJA3brBddd5HU2h7T2wlw6TOrB251pm9JhB01qRu7KdMaFS2A7eIiLnAT2B3GXACnptsN/DeeuzYoBmQBsgEZgvIt+q6srDXqQ6ChgFroqpkDGHvdGjITUVXn89QksP2dnQty9UqOBKDxHiQM4Brnn7GhZuXMjU66Zy8YkXex2SMWGpsAnibtzI6WmqulRE6gOfF/CaVCCwK0sKblxF3mO2quo+YJ+IfAGciWu7KNXS091srS1bQuvWXkdzlIYNc1VLb74ZMX1zferjpvduYs7qOYy9aixXnWqTFBtzJIWd7nseME9EkkUkSVXXAAXN5PoDcLKI1AP+ALrj2hwCvQ+8LCIxQBzQArfmRKk3ciRs2gSTJ0do6WHlSnj0UejcGa691utoCkVVueuju3hzyZsMvXQofZr28TokY8JaoRKEiJwBjAeOcw8lDbhRVZce6TWqmi0iA4HZuG6uY/2lj9v8+0eq6nIRmQX8AvhwXWGXHNtbCn8ZGfDss26C05aR2KnX53NVSwkJETVp1NNfPs3LP7zMfefdxwMXPOB1OMaEvcJWMf0PuFdVP4eDYxdeBc7P70Wq+iHwYZ7nRuZ5/BzwXCHjKBXGj3eTnb7xhteRHKURI9yAuHHjoFYtr6MplNE/juaRzx+hV5NePHvZs16HY0xEKOw4iJ9V9cyCnisJkT4OIicHGjaESpVc9X2E/Pg+5Pff4fTT4cIL4aOPIuINvP/r+1z99tVc3uBypnefTmx0rNchGVPijmYcRGFLEGtE5FFggv9xL2BtUS5knGnTYNUqN2o6Ar5bD6d6aE3p//0vIt7AV+u/ovuU7jQ/vjnvdHvHkoMxRVDYcRB9gWrAVP9WFTdYzhSBKgwd6kZOd+nidTRHYcIEmD0b/vUvtxBQmFu6ZSkdJ3fkhIonMPP6mSTFJXkdkjERpaDJ+hKA24CTgMXAfflNr2Hy9/nnsGCB+/EdHe11NEW0ZYtbX/r88+H2272OpkAbdm2g3RvtSIxJZHav2Ta/kjFHoaAqpteBLOBLoD3QCDcmwhyFoUPdTBQ3Bh0vHubuvBP27nWj+8J8Gu/t6dtp90Y7dmfu5ss+X1K3Ul2vQzImIhWUIE5T1TMARGQM8H3oQyqdfv4Z5syBZ55xvUMjyowZ8NZbbsKoRo28jiZf6VnpXDX5KlZtX8XsXrNpUsNmpDfmaBWUIA5WJ/nHNYQ4nNJr+HAoV+5QG2/E2L3bVSmdcQY8EN5jB7J92fSY0oNvNnzDW13folXdVl6HZExEKyhBnCkiu/33BUj0P85dMKhCSKMrJdLSYNIk6NMHKlf2Opoieugh+OMPePddiAvf5TdVlQEzB/D+ivd5sd2LdDu9m9chGRPxClpyNNKaUsPSq69CZmYErhb39ddupPSdd0KLFl5Hk68n5j3BqB9H8Y8L/8EdLSLtgzYmPBVqoFw4ibSBcllZbinR005zbRARIzMTmjaFffvclN5J4dtF9NWFr9L/g/7cdOZNvNbpNawq1Ji/CuVAOXOUpk1zNTQjRxZ8bFh55hlYvhw+/DCsk8P0FdO5beZttD+pPa92fNWSgzHFKLz7K5YCw4dDgwbQoYPXkRTBsmVuLvLrr4f27b2O5oi+2fAN1717Hc1qNbNR0saEgCWIEFqwAL75xrU9hPnQgUN8PrjlFkhOhhfCd+b15WnLuXLSldSpUIeZ18+kfFx5r0MyptSxKqYQevllVzvTu7fXkRTB//7nstq4cVC9utfRBJW6O5W2E9sSHxPP7F6zqVY+MhYrMibSWIIIke3b3diy3r2hYkWvoymkP/6AQYPg0kvDdrj3jvQdtH+jPTszdjKv9zzqVa7ndUjGlFqWIEJk/Hi3MNBtt3kdSREMHOjWmR45Mixnak3PSqfTm51YsXUFH/X8iKa1mnodkjGlmiWIEFB137HnngtnlviKGUdp6lR47z03YVSDBl5H8xc5vhx6Tu3Jl+u/ZPI1k2lTv43XIRlT6lmCCIF582DFCnj9da8jKaSdO13poWlTuPder6P5C1Xl9pm3M+3XaQxvN5zujbt7HZIxZYIliBAYOdJNqdEtUmZ7GDQI/vzTTcoXE35/EkPmDTk4SvrOFnd6HY4xZUakdL6MGH/+6WpreveGxESvoymEL76AUaPcWg/NmnkdzV+MXDCSIfOG0OesPjx1yVNeh2NMmRLSBCEi7URkhYisEpEH8znubyKSIyJdQxlPSXjtNTe9RkTM2pqRAf37u7lAhgzxOpq/eHfZu9w+83auPOVKRnUcZaOkjSlhIatPEJFoYARwGZAK/CAi01V1WZDjhgKzQxVLSfH53I/x1q3h1FO9jqYQnnzSNZbMng3lw2ug2WdrP6Pn1J6cX+d83ur6FjFR4Vf1ZUxpF8oSxDnAKlVdo6oHgDeBTkGOuwOYAmwJYSwl4tNPYe1a96M87P3yi+uxdNNNcPnlXkdzmIUbF9LpzU6cUuUUZvSYQbnYcl6HZEyZFMoEURvYEPA41f/cQSJSG+gC5DuVnYj0F5EFIrIgLS2t2AMtLqNHw3HHQZcuXkdSgOxs6NfPBfuf/3gdzWFWbltJ+zfaUyWxCrN6zqJyYqQtoGFM6RHKBBGswjjv3OLDgEGqmpPfiVR1lKo2V9Xm1aqF57QKW7e6mVtvvBHi472OpgAvvugminrxRahSxetoDkrdncplEy4DYM4Nc6hdoXYBrzDGhFIoK3ZTgToBj1OAjXmOaQ686W98rAp0EJFsVX0vhHGFxPjxrnG6Xz+vIynAmjXwyCPQsSNce63X0Ry0bf822k5sy470HcztPZdTqpzidUjGlHmhTBA/ACeLSD3gD6A7cH3gAap6cCIdERkHfBCJyUHVVS+dey40bux1NPlQdTO1xsS4leLCpFfQ3gN76TCpA6u3r2Z2r9mcXetsr0MyxhDCBKGq2SIyENc7KRoYq6pLReQ2//5IW0LniObPd2vrjB7tdSQFGD0aPvvMzdiakuJ1NABkZGfQ+c3OLNy4kCnXTqFl3ZZeh2SM8bMlR4tBnz7w7ruwaVMYL76WmurWPW3e3HW3CoPSQ1ZOFt3e6cb7K95nQpcJ9GrSy+uQjCm1jmbJURtJfYx27YK334YePcI4Oai6aWVzcuDVV8MiOfjUR9/pfXl/xfu81P4lSw7GhCEbfXSM3nwT9u8P88bpSZNg5ky3QlwYzNSqqtzx4R1M/GUiT7Z+koHnDPQ6JGNMEFaCOEZjxriG6XPO8TqSI9i8Ge68E847z6196jFVZdAng3hlwSvcf/79PHTRQ16HZIw5AksQx2DxYvjhB1d6CINam7/KrVrav99NEhUd7XVEPPnFkzz3zXPc3vx2hl461OZXMiaMWRXTMRg7FmJjoVe4Vp+/8Qa8/z78+99hMTnU8/Of57G5j3HTmTfxUoeXLDkYE+asBHGUMjNhwgTo3BmqVvU6miA2bXJVS+efD3ff7XU0jPh+BPfNuY9up3Vj9FWjiRL70zMm3Nn/0qM0fTps2wZ9+3odSRCqbr7x9PSwqFp6deGrDPxoIJ1O7cQbV79hM7MaEyHsf+pRGjMG6tSByy7zOpIgXn/drQ73/PNwirdTVoxbNI5bP7iVDid34K2ubxEbHetpPMaYwrMSxFFYvx7mzHGrxoVBu+/h1q1zVUstW8Jdd3kaysRfJtL3/b5cWv9Splw7hfiYcJ/F0BgTyBLEUXj9dVeL06eP15Hk4fO5rAUuyCjv/nkn/jKRG6fdSOt6rXmv+3skxCR4Fosx5uhYFVMR+Xyu91KbNm6lzrDywgswb55rdzjxRM/CCEwOtuCPMZHLShBF9Mknrhbn5pu9jiSPJUvgoYegUye3SpxHJvw8wZKDMaWEJYgiGj3arbETVqvGZWTA9ddDxYpuUWyPxheM/nE0N713E5fUu8SSgzGlgCWIIkhLg/feC8NV4wYNcsO6x42D6tU9CWHE9yO4ZcYttD2prSUHY0oJa4Mogtdfd6vGhVX10syZbunQO++EDh08CeH5+c9z35z7uOrUq3i769vWW8lEvKysLFJTU8nIyPA6lCJLSEggJSWF2Nhj71Ju60EUkio0auSql77+usQvH9zmzdCkCdSsCd9/Dwkl21NIVXli3hMMnjeYbqd1442r37BxDqZUWLt2LcnJyVSpUiWipoRRVbZt28aePXuol6cXzdGsB2EliEL66itYscJ1EAoLuV1a9+yBzz8v8eTgUx/3zb6PYd8No/dZvXm146s2QtqUGhkZGdStWzeikgOAiFClShXS0tKK5Xz2P7qQRo+GChWgWzevI/EbOhRmz3ZrS59+eoleOtuXTf8Z/Xlt0Wvc1eIunm/7vM2tZEqdSEsOuYozbksQhbBzJ7zzjus9Wr6819EAX3wBjzwC113npvMuQelZ6Vw/9Xre+/U9BrcczGMtH4vY/0jGmPzZz75CeP11N+9d//5eRwJs2QLdu7uV4Uq4S+uO9B20ndiW9399n+HthvN4q8ctORgTAqrKhRdeyEcffXTwubfffpt27drRt29fqlevTuPGjUMeR0gThIi0E5EVIrJKRB4Msr+niPzi374RkTNDGc/RUHW1OOedB02behxMTo5bfGLHDlekqVChxC79x+4/uHjcxXyb+i2Tr5nMnS3uLLFrG1PWiAgjR47k3nvvJSMjg3379vHwww8zYsQIevfuzaxZs0okjpBVMYlINDACuAxIBX4QkemquizgsLVAS1XdISLtgVFAi1DFdDQ++wxWrnRrP3huyBD4+GN49VU4s+Ry6eI/F3PFpCvYmbGTWb1mcUm9S0rs2sZ47e67YdGi4j3nWWfBsGH5H9O4cWM6duzI0KFD2bdvHzfeeCMNGjSgQYMGrFu3rngDOoJQtkGcA6xS1TUAIvIm0Ak4mCBU9ZuA478FUkIYz1F55RW3IFDXrh4HMm0a/POfbgGKfv1K7LJzVs+h69tdSY5PZl7veTSt5XUxypiy4/HHH+fss88mLi4OL7r3hzJB1AY2BDxOJf/SQT/go2A7RKQ/0B/ghBNOKK74CpSa6lbs/PvfS7wX6eGWLXPDt885B0aMKLF2h9E/jua2D27j9OqnM/P6maRUCLv8bUzIFfRLP5TKly/PddddR1JSEvEeTN8QyjaIYN9iQUfliUhrXIIYFGy/qo5S1eaq2rxatWrFGGL+Xn3VDTe49dYSu+Rf7drl1jUtVw6mTCmRTJXjy+H+Ofdzy4xbuKzBZXzZ50tLDsZ4JCoqiiiPpu4PZQkiFagT8DgF2Jj3IBFpAowG2qvqthDGUyRZWa6TUIcOHk7rnZ0NPXrA2rWuMSQl9F/SuzJ20WNKDz5a9RED/jaAYe2G2QA4Y8qoUKalH4CTRaSeiMQB3YHpgQeIyAnAVOAGVV0ZwliKbNo0N5PF7bd7FICqax376CNXrXTRRSG/5Krtqzh3zLl8vOZjRl4xkpc7vGzJwZgw06NHD8477zxWrFhBSkoKY8aMCdm1Qva/X1WzRWQgMBuIBsaq6lIRuc2/fyTwGFAFeMXfnz67qHOFhIKqW865QQNo29ajIF580SWGv/+9RAZgzFgxgxum3UBMVAwf3/Axreq2Cvk1jTEFGzx48GGPJ0+eXGLXDunPQ1X9EPgwz3MjA+7fDITT3KiAm3fpu+/c97Mna05Pnw733OMWnRg6NKSXyvHlMHjuYJ788knOrnU2U66dQt1KdUN6TWNMZLD6gyCee851bc1d3rlEffuta3do3hwmTgzputJp+9K4YdoNzF49m75n9WXEFSNs7WhjzEGWIPJYvhxmzIDHH3cdh0rUkiWuVbxWLVeKCGEAc9fNpefUnmzbv41RV47ilma3hOxaxpjIZHMx5fGf/7iepAMGlPCF16yByy+HxEQ3WrpmzZBcJrdKqc34NiTFJfHdzd9ZcjDGBGUliACbNrkpNfr2hRIcbuEufNllkJnpZmoNUb/a1dtXc+N7N/LNhm+48cwbGdFhBElxSSG5ljEm8lmCCPDSS278w733luBF//gDLrkE/vwTPv00JGs7qCqjfxzNPbPvISYqholdJtKzSc9iv44xpnSxKia/7dvdvEtdusDJJ5fQRTdsgJYtYeNGmDULWhT/PIWpu1PpOLkj/T/oT4uUFiz+v8WWHIwJc0ea7rtNmza0bt2aRo0acfrppzN8+PCQxmElCL9nnoHduyFPl+PQ+f13aN0atm1zbQ7nnlusp/epj1ELR/HAxw+QozkMazuMO1rcYSu/GRMBcqf77tatG61btyYnJ4eHH36YcePGkZiYyNlnn82ePXto1qwZl112GaeddlpI4rAEgZuU76WX4IYb4IwzSuCCS5dC+/ZuPelPPoG//a1YT78sbRn/N/P/+OL3L2hTrw2jOo6ifuX6xXoNY8oMj+b7Djbd9wUXXHBwf3JyMo0aNeKPP/6wBBFKgwe70dNDhpTAxebOPTT53ty5xbquw57MPTwx7wmGfTeM5Lhkxlw1hj5n9bFV34yJUPlN971u3Tp++uknWoSgajpXmU8Qv/4Kr70Gd9wBdeuG+GKTJ7vRdyed5OZYKqapy33qY9LiSQz6ZBAb92zk5qY388ylz1C1XNViOb8xZZqH830fabrvvXv3cs011zBs2DAqhHBlyTKfIB5+GMqXd7chk5MDjz0GTz/tGqWnTYPKlYvl1J+t/Yz7P76fHzf9SLNazZhy7RTOTSne9gxjjHfyTvedlZXFNddcQ8+ePbn66qtDeu0ynSC+/BKmTnVVSyEb97B1q5s645NP4Oab4eWXoRgW/liwcQGPff4YH636iBMqnsDELhPpcUYPa4Q2phRTVfr160ejRo24twT645fZBLFvnxsQV7duCMc9zJ8P110HW7bA6NHFslTowo0LGTxvMB+s/IDjEo9j6KVDubPFnTaHkjFlwNdff82ECRM444wzOOusswB4+umn6dChQ0iuV2YTxD/+AatWweefQ1JxDybOzHSTOT33HNSpA19/Dc2aHfXpVJVP137Kc988x5zVc6icUJknWz/JHS3uoEJ86OofjTHeC5zu+8ILL0Q16MKcIVEmE8Tcua5b6513QqtWxXzyH3+Em25yE+/16+cWljjKRqT0rHTeXvo2w74bxqLNi6iZVJOnL3maAecMsMRgjAm5Mpcg9uyBPn1cR6Knny7GE6eluYboUaOgRg2YOdPNzHoUVm5byf8W/I9xP49je/p2GlVtxOiOo+nVpBfxMSW/cLkxpmwqUwnC54Nbb3WDmL/80vVeOmaZmW6OjiFDYO9eNw3skCFF7qW0bf823lr6FhN+mcC3qd8SExVDl4ZduK35bbSu29rGMhhjSlyZSRCq7rt78mR46ikIGJB4dPbudaWF//zHzaXUtq2rTirCiMY/9/7J9BXTmfbrND5Z8wlZviwaV2/Mv9r8ixvPvJFaybWOMUhjjDl6ZSJBqML998PIkTBokGugPmqrV7uRdSNHunmUWreG11+HNm2ggF/52b5sFmxcwJzVc5i9ejbzN8xHUepXrs9dLe6iZ5OenFnjTCstGGPCQqlPED6fm0rjP/+BgQPdpHxF/v7dvt0tMzdunGvhjoqCK6+EBx+E88474svSs9JZuGkhX63/iq/Wf8XXG75mZ8ZOBKHZ8c149OJHubrR1TSp0cSSgjEm7IQ0QYhIO2A4EA2MVtV/5dkv/v0dgP1Ab1X9sbiuv2QJ3Hab62Xapw8MH17I5HDgAPz8s+sD+8EH7gQ+HzRo4OqnbrwRUlIOHq6qbNi9geVpy1m+dTk/bf6JHzf9yPK05eRoDgANqzbkmkbXcGn9S7m0/qU2DYYx5ohUlYsuuoiHH36Y9u3bA26677Fjx7J9+3YyMzPJzs6ma9euDAnhJHIhSxAiEg2MAC4DUoEfRGS6qi4LOKw9cLJ/awH81397TFJT3YDl//wHKlZ0NUI33RQkOeTkwObNsHIlrFjhJmZasAAWLoSMDAB8Z53JzofuYWvrFmyuX52NezexccPbrF+ynrU717J2x1rW7FjDvqx9B09bo3wNmh3fjM6ndqb58c05v875VCtfkkvUGWMi2ZGm+541axY1atQgKSmJrKwsLrzwQtq3b8+5xbxcQK5QliDOAVap6hoAEXkT6AQEJohOwHh1Iz++FZFKIlJLVTcd6aTrf1/FHbd1IjrKfeEr7se9z6fs2a1s3ars36dEiY+enbNpUC+Lzb9m8/S9GWQfSCcnM4PsjP0c2L+HAxn7OBAN6TGwPxbSE6LZ26w8uy+pwO6EiuyMOsCOA4vx6c/wJW7zKxdbjvqV61OvUj0uqXcJDas2pFHVRjSq1ojq5asX/6dpjPHE3bPuZtHmRcV6zrNqnsWwdsPyPSbYdN8NGjQ4uD8rK4usrKyQVk+HMkHUBjYEPE7lr6WDYMfUBg5LECLSH+gPQC14udb04Fc8Pp9oEg/djfEJ8UQTKwnERcVSLq48iYnJJCYmkxyXTO34ZBrFV6BifEWqJFahSrkqVEmsQq3kWtRKqsXxycdTKaGStRsYY0Iq2HTfOTk5NGvWjFWrVjFgwICIne472Ldn3jHihTkGVR0FjAJockYTnXbth2RkwIFMJToG4uMgLhYqHRdNTFwUSBRERREVn4BERSEIMVExREdF22R2xpgiKeiXfigFm+47OjqaRYsWsXPnTrp06cKSJUto3LhxSK4fygSRCtQJeJwCbDyKYw4TFx9Hg0Yp+R1ijDGlRt7pvnNVqlSJVq1aMWvWrJAliFD+nP4BOFlE6olIHNAdyFs3NB24UZxzgV35tT8YY0xZlpaWxs6dOwFIT0/nk08+oWHDhiG7XshKEKqaLSIDgdm4bq5jVXWpiNzm3z8S+BDXxXUVrptrn1DFY4wxkW7Tpk3cdNNN5OTk4PP5uPbaa7nyyitDdj0pyalji0Pz5s0179qsxhhTnJYvX06jRo28DuOoBYtfRBaqavOinMdabI0xxgRlCcIYY0xQliCMMSaISKt+z1WccVuCMMaYPBISEti2bVvEJQlVZdu2bSQkFM8a9aV+NldjjCmqlJQUUlNTSUtL8zqUIktISCAlpXjGilmCMMaYPGJjY6lXr57XYXjOqpiMMcYEZQnCGGNMUJYgjDHGBBVxI6lFZA+wwus4wkRVYKvXQYQJ+ywOsc/iEPssDjlVVZOL8oJIbKReUdTh4qWViCywz8Kxz+IQ+ywOsc/iEBEp8hxFVsVkjDEmKEsQxhhjgorEBDHK6wDCiH0Wh9hncYh9FofYZ3FIkT+LiGukNsYYUzIisQRhjDGmBFiCMMYYE1REJQgRaSciK0RklYg86HU8XhGROiLyuYgsF5GlInKX1zF5SUSiReQnEfnA61i8JiKVRORdEfnV//dxntcxeUFE7vH/31giIpNFpHimN40QIjJWRLaIyJKA544TkY9F5Df/beWCzhMxCUJEooERQHvgNKCHiJzmbVSeyQbuU9VGwLnAgDL8WQDcBSz3OogwMRyYpaoNgTMpg5+LiNQG7gSaq2pjIBro7m1UJW4c0C7Pcw8Cn6rqycCn/sf5ipgEAZwDrFLVNap6AHgT6ORxTJ5Q1U2q+qP//h7cl0Btb6PyhoikAFcAo72OxWsiUgG4GBgDoKoHVHWnp0F5JwZIFJEYoByw0eN4SpSqfgFsz/N0J+B1//3Xgc4FnSeSEkRtYEPA41TK6JdiIBGpCzQFvvM4FK8MAx4AfB7HEQ7qA2nAa/4qt9EiUt7roEqaqv4B/BtYD2wCdqnqHG+jCgs1VHUTuB+ZQPWCXhBJCUKCPFem++iKSBIwBbhbVXd7HU9JE5ErgS2qutDrWMJEDHA28F9VbQrsoxDVCKWNv269E1APOB4oLyK9vI0qMkVSgkgF6gQ8TqGMFRsDiUgsLjm8oapTvY7HIxcAV4nIOlyV4yUiMtHbkDyVCqSqam5p8l1cwihrLgXWqmqaqmYBU4HzPY4pHPwpIrUA/LdbCnpBJCWIH4CTRaSeiMThGp2mexyTJ0REcPXMy1X1ea/j8Yqq/kNVU1S1Lu7v4TNVLbO/FFV1M7BBRE71P9UGWOZhSF5ZD5wrIuX8/1faUAYb64OYDtzkv38T8H5BL4iY2VxVNVtEBgKzcb0SxqrqUo/D8soFwA3AYhFZ5H/uIVX90LuQTJi4A3jD/yNqDdDH43hKnKp+JyLvAj/ievz9RBmbckNEJgOtgKoikgo8DvwLeFtE+uGSaLcCz2NTbRhjjAkmkqqYjDHGlCBLEMYYY4KyBGGMMSYoSxDGGGOCsgRhjDEmKEsQpswSkSoissi/bRaRP/z394rIKyG65t0icmM++68UkSGhuLYxRWXdXI0BRGQwsFdV/x3Ca8Tg+uafrarZRzhG/MdcoKr7QxWLMYVhJQhj8hCRVrlrS4jIYBF5XUTmiMg6EblaRJ4VkcUiMss/5Qki0kxE5onIQhGZnTulQR6XAD/mJgcRuVNElonILyLyJoC6X2xzgStL5M0akw9LEMYUrAFuSvFOwETgc1U9A0gHrvAniZeArqraDBgLPBXkPBcAgRMLPgg0VdUmwG0Bzy8ALir2d2FMEUXMVBvGeOgjVc0SkcW4aV5m+Z9fDNQFTgUaAx+7GiKicdNM51WLw+cE+gU3LcZ7wHsBz2/BzUJqjKcsQRhTsEwAVfWJSJYearjz4f4PCbBUVQta3jMdCFz68grcAj9XAY+KyOn+6qcE/7HGeMqqmIw5diuAarnrP4tIrIicHuS45cBJ/mOigDqq+jluwaNKQJL/uFOAJUFeb0yJsgRhzDHyL4HbFRgqIj8Diwi+/sBHuBIDuGqoif5qq5+AFwKWB20NzAxlzMYUhnVzNaYEicg04AFV/e0I+2sAk1S1TclGZsxfWYIwpgT5F/Op4V9UPtj+vwFZqrqoRAMzJghLEMYYY4KyNghjjDFBWYIwxhgTlCUIY4wxQVmCMMYYE5QlCGOMMUH9P7053yDpNCoUAAAAAElFTkSuQmCC\n", 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" ] @@ -329,7 +329,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -343,7 +343,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ @@ -361,7 +361,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -397,7 +397,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ @@ -418,7 +418,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -429,12 +429,12 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 17, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -464,12 +464,12 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 18, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -487,12 +487,12 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", 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" ] @@ -510,12 +510,12 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -547,7 +547,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.7" + "version": "3.7.9" } }, "nbformat": 4, diff --git a/examples/pvtol-nested.py b/examples/pvtol-nested.py index 7388ce361..7b48d2bb5 100644 --- a/examples/pvtol-nested.py +++ b/examples/pvtol-nested.py @@ -135,14 +135,13 @@ nyquist(L, (0.0001, 1000)) # Add a box in the region we are going to expand -plt.plot([-400, -400, 200, 200, -400], [-100, 100, 100, -100, -100], 'r-') +plt.plot([-2, -2, 1, 1, -2], [-4, 4, 4, -4, -4], 'r-') # Expanded region plt.figure(8) plt.clf() -plt.subplot(231) nyquist(L) -plt.axis([-10, 5, -20, 20]) +plt.axis([-2, 1, -4, 4]) # set up the color color = 'b' diff --git a/examples/secord-matlab.py b/examples/secord-matlab.py index 5473adb0a..6cef881c1 100644 --- a/examples/secord-matlab.py +++ b/examples/secord-matlab.py @@ -29,7 +29,7 @@ # Nyquist plot for the system plt.figure(3) -nyquist(sys, logspace(-2, 2)) +nyquist(sys) plt.show(block=False) # Root lcous plot for the system diff --git a/examples/tfvis.py b/examples/tfvis.py index 60b837d99..f05a45780 100644 --- a/examples/tfvis.py +++ b/examples/tfvis.py @@ -341,12 +341,12 @@ def redraw(self): self.f_bode.clf() plt.figure(self.f_bode.number) - control.matlab.bode(self.sys, logspace(-2, 2)) + control.matlab.bode(self.sys, logspace(-2, 2, 1000)) plt.suptitle('Bode Diagram') self.f_nyquist.clf() plt.figure(self.f_nyquist.number) - control.matlab.nyquist(self.sys, logspace(-2, 2)) + control.matlab.nyquist(self.sys, logspace(-2, 2, 1000)) plt.suptitle('Nyquist Diagram') self.f_step.clf() @@ -354,7 +354,7 @@ def redraw(self): try: # Step seems to get intro trouble # with purely imaginary poles - tvec, yvec = control.matlab.step(self.sys) + yvec, tvec = control.matlab.step(self.sys) plt.plot(tvec.T, yvec) except: print("Error plotting step response") From 1d9fc80c883007dc29ee88d237047299e94c84ff Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Sun, 7 Feb 2021 16:36:00 -0800 Subject: [PATCH 6/8] update descfcn module for compatibility --- control/descfcn.py | 5 +++-- examples/describing_functions.ipynb | 2 +- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/control/descfcn.py b/control/descfcn.py index 236125b2e..14a345495 100644 --- a/control/descfcn.py +++ b/control/descfcn.py @@ -241,8 +241,9 @@ def describing_function_plot( """ # Start by drawing a Nyquist curve - H_real, H_imag, H_omega = nyquist_plot(H, omega, plot=True, **kwargs) - H_vals = H_real + 1j * H_imag + count, contour = nyquist_plot( + H, omega, plot=True, return_contour=True, **kwargs) + H_omega, H_vals = contour.imag, H(contour) # Compute the describing function df = describing_function(F, A) diff --git a/examples/describing_functions.ipynb b/examples/describing_functions.ipynb index 7d090bf17..766feb2e2 100644 --- a/examples/describing_functions.ipynb +++ b/examples/describing_functions.ipynb @@ -369,7 +369,7 @@ "amp = np.linspace(0.6, 5, 50)\n", "\n", "# Describing function plot\n", - "ct.describing_function_plot(H_multiple, F_backlash, amp, omega, mirror=False)" + "ct.describing_function_plot(H_multiple, F_backlash, amp, omega, mirror_style=False)" ] }, { From 078e02856d15d3518097dc31120d954f109c92a9 Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Sun, 7 Feb 2021 17:55:35 -0800 Subject: [PATCH 7/8] small fixes based on @sawyerbfuller, @bnavigator comments --- control/freqplot.py | 14 +++++++------- control/matlab/wrappers.py | 4 ++-- control/tests/nyquist_test.py | 18 +++++++----------- 3 files changed, 16 insertions(+), 20 deletions(-) diff --git a/control/freqplot.py b/control/freqplot.py index 23b5571ce..452928236 100644 --- a/control/freqplot.py +++ b/control/freqplot.py @@ -688,8 +688,7 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, 'nyquist', 'indent_direction', kwargs, _nyquist_defaults, pop=True) # If argument was a singleton, turn it into a list - isscalar = not hasattr(syslist, '__iter__') - if isscalar: + if not hasattr(syslist, '__iter__'): syslist = (syslist,) # Decide whether to go above Nyquist frequency @@ -844,11 +843,12 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None, ax.set_ylabel("Imaginary axis") ax.grid(color="lightgray") + # "Squeeze" the results + if len(syslist) == 1: + counts, contours = counts[0], contours[0] + # Return counts and (optionally) the contour we used - if return_contour: - return (counts[0], contours[0]) if isscalar else (counts, contours) - else: - return counts[0] if isscalar else counts + return (counts, contours) if return_contour else counts # Internal function to add arrows to a curve @@ -1101,7 +1101,7 @@ def _default_frequency_range(syslist, Hz=None, number_of_samples=None, freq_interesting = [] # detect if single sys passed by checking if it is sequence-like - if not getattr(syslist, '__iter__', False): + if not hasattr(syslist, '__iter__'): syslist = (syslist,) for sys in syslist: diff --git a/control/matlab/wrappers.py b/control/matlab/wrappers.py index 941fb3ffb..f7cbaea41 100644 --- a/control/matlab/wrappers.py +++ b/control/matlab/wrappers.py @@ -59,7 +59,7 @@ def bode(*args, **kwargs): from ..freqplot import bode_plot # If first argument is a list, assume python-control calling format - if (getattr(args[0], '__iter__', False)): + if hasattr(args[0], '__iter__'): return bode_plot(*args, **kwargs) # Parse input arguments @@ -97,7 +97,7 @@ def nyquist(*args, **kwargs): from ..freqplot import nyquist_plot # If first argument is a list, assume python-control calling format - if (getattr(args[0], '__iter__', False)): + if hasattr(args[0], '__iter__'): return nyquist_plot(*args, **kwargs) # Parse arguments diff --git a/control/tests/nyquist_test.py b/control/tests/nyquist_test.py index debda6030..84898cc74 100644 --- a/control/tests/nyquist_test.py +++ b/control/tests/nyquist_test.py @@ -17,6 +17,7 @@ # In interactive mode, turn on ipython interactive graphics plt.ion() + # Utility function for counting unstable poles of open loop (P in FBS) def _P(sys, indent='right'): if indent == 'right': @@ -29,19 +30,14 @@ def _P(sys, indent='right'): else: raise TypeError("unknown indent value") + # Utility function for counting unstable poles of closed loop (Z in FBS) def _Z(sys): return (sys.feedback().pole().real >= 0).sum() -# Decorator to close figures when done with test (to avoid matplotlib warning) -@pytest.fixture(scope="function") -def figure_cleanup(): - plt.close('all') - yield - plt.close('all') # Basic tests -@pytest.mark.usefixtures("figure_cleanup") +@pytest.mark.usefixtures("mplcleanup") def test_nyquist_basic(): # Simple Nyquist plot sys = ct.rss(5, 1, 1) @@ -116,7 +112,7 @@ def test_nyquist_basic(): # Some FBS examples, for comparison -@pytest.mark.usefixtures("figure_cleanup") +@pytest.mark.usefixtures("mplcleanup") def test_nyquist_fbs_examples(): s = ct.tf('s') @@ -158,7 +154,7 @@ def test_nyquist_fbs_examples(): 1, 2, 3, 4, # specified number of arrows [0.1, 0.5, 0.9], # specify arc lengths ]) -@pytest.mark.usefixtures("figure_cleanup") +@pytest.mark.usefixtures("mplcleanup") def test_nyquist_arrows(arrows): sys = ct.tf([1.4], [1, 2, 1]) * ct.tf(*ct.pade(1, 4)) plt.figure(); @@ -167,7 +163,7 @@ def test_nyquist_arrows(arrows): assert _Z(sys) == count + _P(sys) -@pytest.mark.usefixtures("figure_cleanup") +@pytest.mark.usefixtures("mplcleanup") def test_nyquist_encirclements(): # Example 14.14: effect of friction in a cart-pendulum system s = ct.tf('s') @@ -192,7 +188,7 @@ def test_nyquist_encirclements(): assert _Z(sys) == count + _P(sys) -@pytest.mark.usefixtures("figure_cleanup") +@pytest.mark.usefixtures("mplcleanup") def test_nyquist_indent(): # FBS Figure 10.10 s = ct.tf('s') From e0521b987418071bf760b5731a5c2a24faadca92 Mon Sep 17 00:00:00 2001 From: Richard Murray Date: Wed, 10 Feb 2021 22:09:45 -0800 Subject: [PATCH 8/8] add mplcleanup to fix nichols error --- control/tests/matlab_test.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/control/tests/matlab_test.py b/control/tests/matlab_test.py index 4fa03257c..61bc3bdcb 100644 --- a/control/tests/matlab_test.py +++ b/control/tests/matlab_test.py @@ -818,7 +818,7 @@ def test_matlab_wrapper_exceptions(self): with pytest.raises(ValueError, match="needs either 1, 2, 3 or 4"): dcgain(1, 2, 3, 4, 5) - def test_matlab_freqplot_passthru(self): + def test_matlab_freqplot_passthru(self, mplcleanup): """Test nyquist and bode to make sure the pass arguments through""" sys = tf([1], [1, 2, 1]) bode((sys,)) # Passing tuple will call bode_plot