Jun 30, 2024 · Apr 24, 2024 · Apr 29, 2024 · Apr 29, 2024 · Jun 30, 2024
diff --git a/control/freqplot.py b/control/freqplot.py
    'nyquist.max_curve_magnitude': 20,          # clip large values
    'nyquist.max_curve_offset': 0.02,           # offset of primary/mirror
    'nyquist.start_marker': 'o',                # marker at start of curve
    'nyquist.start_marker_size': 4,             # size of the maker
    'nyquist.start_marker_size': 4,             # size of the marker
    'nyquist.circle_style':                     # style for unit circles
      {'color': 'black', 'linestyle': 'dashed', 'linewidth': 1}
 }



 def nyquist_plot(
        data, omega=None, plot=None, label_freq=0, color=None, label=None,
        return_contour=None, title=None, legend_loc='upper right',
 ax=None, **kwargs):
        return_contour=None, title=None, legend_loc='upper right', ax=None,
 unit_circle=False, mt_circles=None, ms_circles=None, **kwargs):
    """Nyquist plot for a system.

    Generates a Nyquist plot for the system over a (optional) frequency
        ``omega_limits``.
    color : string, optional
        Used to specify the color of the line and arrowhead.

    unit_circle : bool, optional
        If ``True``, display the unit circle, to read gain crossover frequency.
    mt_circles : array_like, optional
        Draw circles corresponding to the given magnitudes of sensitivity.
    ms_circles : array_like, optional
        Draw circles corresponding to the given magnitudes of complementary
        sensitivity.
    **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
        Additional keywords (passed to `matplotlib`)

        # Mark the -1 point
        plt.plot([-1], [0], 'r+')

        # Label the frequencies of the points
        #
        # Draw circles for gain crossover and sensitivity functions
        #
        theta = np.linspace(0, 2*np.pi, 100)
        cos = np.cos(theta)
        sin = np.sin(theta)
        label_pos = 15

        # Display the unit circle, to read gain crossover frequency
        if unit_circle:
            plt.plot(cos, sin, **config.defaults['nyquist.circle_style'])

        # Draw circles for given magnitudes of sensitivity
        if ms_circles is not None:
            for ms in ms_circles:
                pos_x = -1 + (1/ms)*cos
                pos_y = (1/ms)*sin
                plt.plot(
                    pos_x, pos_y, **config.defaults['nyquist.circle_style'])
                plt.text(pos_x[label_pos], pos_y[label_pos], ms)

        # Draw circles for given magnitudes of complementary sensitivity
        if mt_circles is not None:
            for mt in mt_circles:
                if mt != 1:
                    ct = -mt**2/(mt**2-1)  # Mt center
                    rt = mt/(mt**2-1)  # Mt radius
                    pos_x = ct+rt*cos
                    pos_y = rt*sin
                    plt.plot(
                        pos_x, pos_y,
                        **config.defaults['nyquist.circle_style'])
                    plt.text(pos_x[label_pos], pos_y[label_pos], mt)
                else:
                    _, _, ymin, ymax = plt.axis()
                    pos_y = np.linspace(ymin, ymax, 100)
                    plt.vlines(
                        -0.5, ymin=ymin, ymax=ymax,
                        **config.defaults['nyquist.circle_style'])
                    plt.text(-0.5, pos_y[label_pos], 1)

        # Label the frequencies of the points on the Nyquist curve
        if label_freq:
            ind = slice(None, None, label_freq)
            omega_sys = np.imag(splane_contour[np.real(splane_contour) == 0])
diff --git a/control/tests/nyquist_test.py b/control/tests/nyquist_test.py
    assert _Z(sys) == response.count + _P(sys)


 def test_sensitivity_circles():
    A = np.array([
        [-3.56355873, -1.22980795, -1.5626527 , -0.4626829],
        [-8.52361371, -3.60331459, -3.71574266, -0.43839201],
        [-2.50458726, -0.72361335, -1.77795489, -0.4038419],
        [-0.281183  ,  0.23391825,  0.19096003, -0.9771515]])
    B = np.array([[-0.], [-1.42827213], [ 0.76806551], [-1.07987454]])
    C = np.array([[-0.,  0.35557249,  0.35941791, -0.]])
    D = np.array([[0]])
    sys1 = ct.ss(A, B, C, D)
    sys2 = ct.ss(A, B, C, D, dt=0.1)
    plt.figure()
    ct.nyquist_plot(sys1, unit_circle=True, mt_circles=[0.9,1,1.1,1.2], ms_circles=[0.9,1,1.1,1.2])
    ct.nyquist_plot(sys2, unit_circle=True, mt_circles=[0.9,1,1.1,1.2], ms_circles=[0.9,1,1.1,1.2])


 def test_nyquist_encirclements():
    # Example 14.14: effect of friction in a cart-pendulum system
    s = ct.tf('s')
    test_nyquist_arrows(3)
    test_nyquist_arrows([0.1, 0.5, 0.9])

    print("Test sensitivity circles")
    test_sensitivity_circles()

    print("Stability checks")
    test_nyquist_encirclements()
Original file line number	Diff line number	Diff line change
Expand Up		@@ -1060,7 +1060,9 @@ def gen_zero_centered_series(val_min, val_max, period):
		'nyquist.max_curve_magnitude': 20, # clip large values
		'nyquist.max_curve_offset': 0.02, # offset of primary/mirror
		'nyquist.start_marker': 'o', # marker at start of curve
		'nyquist.start_marker_size': 4, # size of the maker
		'nyquist.start_marker_size': 4, # size of the marker
		'nyquist.circle_style': # style for unit circles
		{'color': 'black', 'linestyle': 'dashed', 'linewidth': 1}
		}


Expand DownExpand Up		@@ -1477,8 +1479,8 @@ def nyquist_response(

		def nyquist_plot(
		data, omega=None, plot=None, label_freq=0, color=None, label=None,
		return_contour=None, title=None, legend_loc='upper right',
		ax=None, **kwargs):
		return_contour=None, title=None, legend_loc='upper right', ax=None,
		unit_circle=False, mt_circles=None, ms_circles=None, **kwargs):
		"""Nyquist plot for a system.

		Generates a Nyquist plot for the system over a (optional) frequency
Expand All		@@ -1501,7 +1503,13 @@ def nyquist_plot(
		``omega_limits``.
		color : string, optional
		Used to specify the color of the line and arrowhead.

		unit_circle : bool, optional
		If ``True``, display the unit circle, to read gain crossover frequency.
		mt_circles : array_like, optional
		Draw circles corresponding to the given magnitudes of sensitivity.
		ms_circles : array_like, optional
		Draw circles corresponding to the given magnitudes of complementary
		sensitivity.
		**kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
		Additional keywords (passed to `matplotlib`)

Expand DownExpand Up		@@ -1856,7 +1864,48 @@ def _parse_linestyle(style_name, allow_false=False):
		# Mark the -1 point
		plt.plot([-1], [0], 'r+')

		# Label the frequencies of the points
		#
		# Draw circles for gain crossover and sensitivity functions
		#
		theta = np.linspace(0, 2*np.pi, 100)
		cos = np.cos(theta)
		sin = np.sin(theta)
		label_pos = 15

		# Display the unit circle, to read gain crossover frequency
		if unit_circle:
		plt.plot(cos, sin, **config.defaults['nyquist.circle_style'])

		# Draw circles for given magnitudes of sensitivity
		if ms_circles is not None:
		for ms in ms_circles:
		pos_x = -1 + (1/ms)*cos
		pos_y = (1/ms)*sin
		plt.plot(
		pos_x, pos_y, **config.defaults['nyquist.circle_style'])
		plt.text(pos_x[label_pos], pos_y[label_pos], ms)

		# Draw circles for given magnitudes of complementary sensitivity
		if mt_circles is not None:
		for mt in mt_circles:
		if mt != 1:
		ct = -mt2/(mt2-1) # Mt center
		rt = mt/(mt**2-1) # Mt radius
		pos_x = ct+rt*cos
		pos_y = rt*sin
		plt.plot(
		pos_x, pos_y,
		**config.defaults['nyquist.circle_style'])
		plt.text(pos_x[label_pos], pos_y[label_pos], mt)
		else:
		_, _, ymin, ymax = plt.axis()
		pos_y = np.linspace(ymin, ymax, 100)
		plt.vlines(
		-0.5, ymin=ymin, ymax=ymax,
		**config.defaults['nyquist.circle_style'])
		plt.text(-0.5, pos_y[label_pos], 1)

		# Label the frequencies of the points on the Nyquist curve
		if label_freq:
		ind = slice(None, None, label_freq)
		omega_sys = np.imag(splane_contour[np.real(splane_contour) == 0])
Expand Down
Original file line number	Diff line number	Diff line change
Expand Up		@@ -214,6 +214,22 @@ def test_nyquist_arrows(arrows):
		assert _Z(sys) == response.count + _P(sys)


		def test_sensitivity_circles():
		A = np.array([
		[-3.56355873, -1.22980795, -1.5626527 , -0.4626829],
		[-8.52361371, -3.60331459, -3.71574266, -0.43839201],
		[-2.50458726, -0.72361335, -1.77795489, -0.4038419],
		[-0.281183 , 0.23391825, 0.19096003, -0.9771515]])
		B = np.array([[-0.], [-1.42827213], [ 0.76806551], [-1.07987454]])
		C = np.array([[-0., 0.35557249, 0.35941791, -0.]])
		D = np.array([[0]])
		sys1 = ct.ss(A, B, C, D)
		sys2 = ct.ss(A, B, C, D, dt=0.1)
		plt.figure()
		ct.nyquist_plot(sys1, unit_circle=True, mt_circles=[0.9,1,1.1,1.2], ms_circles=[0.9,1,1.1,1.2])
		ct.nyquist_plot(sys2, unit_circle=True, mt_circles=[0.9,1,1.1,1.2], ms_circles=[0.9,1,1.1,1.2])


		def test_nyquist_encirclements():
		# Example 14.14: effect of friction in a cart-pendulum system
		s = ct.tf('s')
Expand DownExpand Up		@@ -518,6 +534,9 @@ def test_nyquist_frd():
		test_nyquist_arrows(3)
		test_nyquist_arrows([0.1, 0.5, 0.9])

		print("Test sensitivity circles")
		test_sensitivity_circles()

		print("Stability checks")
		test_nyquist_encirclements()

Expand Down