[python-control-discuss] SF.net SVN: python-control:[144] branches/control-0.4b

[<mur...@us...>]

Revision: 144
          http://python-control.svn.sourceforge.net/python-control/?rev=144&view=rev
Author:   murrayrm
Date:     2011-04-02 15:52:38 +0000 (Sat, 02 Apr 2011)

Log Message:
-----------
* Moved nichols() code to separate file, added unit test; add'l updates pending
* Moved slycot imports inside functions that need them
* Updated pvtol-nested example to work with v0.4
* See ChangeLog for detailed listing of changes

Modified Paths:
--------------
    branches/control-0.4b/ChangeLog
    branches/control-0.4b/examples/pvtol-nested.py
    branches/control-0.4b/src/__init__.py
    branches/control-0.4b/src/freqplot.py
    branches/control-0.4b/src/matlab.py
    branches/control-0.4b/src/statesp.py
    branches/control-0.4b/src/xferfcn.py

Added Paths:
-----------
    branches/control-0.4b/src/nichols.py
    branches/control-0.4b/tests/nichols_test.py

Modified: branches/control-0.4b/ChangeLog
===================================================================
--- branches/control-0.4b/ChangeLog	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/ChangeLog	2011-04-02 15:52:38 UTC (rev 144)
@@ -1,3 +1,27 @@
+2011-03-31  Richard Murray  <murray@malabar.local>
+
+	* examples/pvtol-nested.py: updated stability margin plot to use
+	proper calling format for bode().
+
+	* src/statesp.py (_convertToStateSpace): moved slycot import
+	to the location where it is actually needed (allows running some
+	commands without slycot installed)
+
+	* src/xferfcn.py (_convertToTransferFunction): moved slycot import
+	to the location where it is actually needed (allows running some
+	commands without slycot installed)
+
+	* src/nichols.py: new file for Nichols plot routines; move
+	nichols(), nichols_grid(), closed_loop_contours(), m_circles(),
+	n_circles()
+
+	* src/__init__.py, src/freqresp.py, src/matlab.py: updated to match
+	new file structure for Nichols charts
+
+	* src/nichols.py (nichols): updated processing of freqresp to take
+	into account the fact that return arguments are now a matrix of
+	results (even for a SISO system)
+
 2011-03-30  Richard Murray  <murray@malabar.local>
 
 	* tests/: added top level subdirectory, to be used for unit tests.

Modified: branches/control-0.4b/examples/pvtol-nested.py
===================================================================
--- branches/control-0.4b/examples/pvtol-nested.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/examples/pvtol-nested.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -84,22 +84,22 @@
 # (gm, pm, wgc, wpc) = margin(L); 
 
 #! TODO: this figure has something wrong; axis limits mismatch
-figure(6); clf; subplot(221);
-(magh, phaseh) = bode(L);
+figure(6); clf; 
+bode(L);
 
 # Add crossover line
-subplot(magh); hold(True);
-loglog([10^-4, 10^3], [1, 1], 'k-')
+subplot(211); hold(True);
+loglog([1e-4, 1e3], [1, 1], 'k-')
 
 # Replot phase starting at -90 degrees
 bode(L, logspace(-4, 3));
 (mag, phase, w) = freqresp(L, logspace(-4, 3));
 phase = phase - 360;
-subplot(phaseh);
-semilogx([10^-4, 10^3], [-180, -180], 'k-')
+subplot(212);
+semilogx([1e-4, 1e3], [-180, -180], 'k-')
 hold(True);
 semilogx(w, np.squeeze(phase), 'b-')
-axis([10^-4, 10^3, -360, 0]);
+axis([1e-4, 1e3, -360, 0]);
 xlabel('Frequency [deg]'); ylabel('Phase [deg]');
 # set(gca, 'YTick', [-360, -270, -180, -90, 0]);
 # set(gca, 'XTick', [10^-4, 10^-2, 1, 100]);

Modified: branches/control-0.4b/src/__init__.py
===================================================================
--- branches/control-0.4b/src/__init__.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/src/__init__.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -59,6 +59,7 @@
 from xferfcn import *
 from statesp import *
 from freqplot import *
+from nichols import *
 from bdalg import *
 from statefbk import *
 from delay import *

Modified: branches/control-0.4b/src/freqplot.py
===================================================================
--- branches/control-0.4b/src/freqplot.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/src/freqplot.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -212,139 +212,7 @@
                 plt.plot([-1], [0], 'r+')
 
         return x, y, omega
-# Nichols plot
-# Contributed by Allan McInnes <All...@ca...>
-#! TODO: need unit test code
-def nichols(syslist, omega=None):
-    """Nichols plot for a system
 
-    Usage
-    =====
-    magh = nichols(sys, omega=None)
-
-    Plots a Nichols plot for the system over a (optional) frequency range.
-
-    Parameters
-    ----------
-    syslist : linsys
-        List of linear input/output systems (single system is OK)
-    omega : freq_range
-        Range of frequencies (list or bounds) in rad/sec
-
-    Return values
-    -------------
-    None
-    """
-
-    # If argument was a singleton, turn it into a list
-    if (not getattr(syslist, '__iter__', False)):
-        syslist = (syslist,)
-
-    # Select a default range if none is provided
-    if (omega == None):
-        omega = default_frequency_range(syslist)
-
-    for sys in syslist:
-        # Get the magnitude and phase of the system
-        mag, phase, omega = sys.freqresp(omega)
-    
-        # Convert to Nichols-plot format (phase in degrees, 
-        # and magnitude in dB)
-        x = unwrap(sp.degrees(phase), 360)
-        y = 20*sp.log10(mag)
-    
-        # Generate the plot
-        plt.plot(x, y)
-        
-    plt.xlabel('Phase (deg)')
-    plt.ylabel('Magnitude (dB)')
-    plt.title('Nichols Plot')
-
-    # Mark the -180 point
-    plt.plot([-180], [0], 'r+')
-    
-# Nichols grid
-def nichols_grid():
-    """Nichols chart grid
-    
-    Usage
-    =====
-    nichols_grid()
-
-    Plots a Nichols chart grid on the current axis.
-
-    Parameters
-    ----------
-    None
-
-    Return values
-    -------------
-    None    
-    """
-    mag_min_default = -40.0 # dB
-    mag_step = 20.0         # dB
-
-    # Chart defaults
-    phase_min, phase_max, mag_min, mag_max = -360.0, 0.0, mag_min_default, 40.0
-
-    # Set actual chart bounds based on current plot
-    if plt.gcf().gca().has_data():
-        phase_min, phase_max, mag_min, mag_max = plt.axis()
-        
-    # M-circle magnitudes.
-    # The "fixed" set are always generated, since this guarantees a recognizable
-    # Nichols chart grid.
-    mags_fixed = np.array([-40.0, -20.0, -12.0, -6.0, -3.0, -1.0, -0.5, 0.0,
-                                 0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
-
-    if mag_min < mag_min_default:
-        # Outside the "fixed" set of magnitudes, the generated M-circles
-        # are extended in steps of 'mag_step' dB to cover anything made
-        # visible by the range of the existing plot
-        mags_adjust = np.arange(mag_step*np.floor(mag_min/mag_step),
-                                mag_min_default, mag_step)
-        mags = np.concatenate((mags_adjust, mags_fixed))
-    else:
-        mags = mags_fixed
-                     
-    # N-circle phases (should be in the range -360 to 0)
-    phases = np.array([-0.25, -10.0, -20.0, -30.0, -45.0, -60.0, -90.0,
-                       -120.0, -150.0, -180.0, -210.0, -240.0, -270.0,
-                       -310.0, -325.0, -340.0, -350.0, -359.75])
-
-    # Find the M-contours
-    m = m_circles(mags, phase_min=np.min(phases), phase_max=np.max(phases))
-    m_mag = 20*sp.log10(np.abs(m))
-    m_phase = sp.mod(sp.degrees(sp.angle(m)), -360.0) # Unwrap
-
-    # Find the N-contours
-    n = n_circles(phases, mag_min=np.min(mags), mag_max=np.max(mags))
-    n_mag = 20*sp.log10(np.abs(n))
-    n_phase = sp.mod(sp.degrees(sp.angle(n)), -360.0) # Unwrap
-
-    # Plot the contours behind other plot elements.
-    # The "phase offset" is used to produce copies of the chart that cover
-    # the entire range of the plotted data, starting from a base chart computed
-    # over the range -360 < phase < 0 (see above). Given the range 
-    # the base chart is computed over, the phase offset should be 0
-    # for -360 < phase_min < 0.
-    phase_offset_min = 360.0*np.ceil(phase_min/360.0)
-    phase_offset_max = 360.0*np.ceil(phase_max/360.0) + 360.0
-    phase_offsets = np.arange(phase_offset_min, phase_offset_max, 360.0)
-    for phase_offset in phase_offsets:
-        plt.plot(m_phase + phase_offset, m_mag, color='gray',
-                 linestyle='dashed', zorder=0)
-        plt.plot(n_phase + phase_offset, n_mag, color='gray',
-                 linestyle='dashed', zorder=0)
-
-    # Add magnitude labels
-    for x, y, m in zip(m_phase[:][-1], m_mag[:][-1], mags):
-        align = 'right' if m < 0.0 else 'left'
-        plt.text(x, y, str(m) + ' dB', size='small', ha=align)
-
-    # Make sure axes conform to any pre-existing plot.
-    plt.axis([phase_min, phase_max, mag_min, mag_max])
-
 # Gang of Four
 #! TODO: think about how (and whether) to handle lists of systems
 def gangof4(P, C, omega=None):
@@ -462,84 +330,3 @@
                         
     return omega
 
-# Compute contours of a closed-loop transfer function
-def closed_loop_contours(Hmag, Hphase):
-    """Contours of the function H = G/(1+G).
-
-    Usage
-    =====
-    contours = closed_loop_contours(mags, phases)
-
-    Parameters
-    ----------
-    mags : array-like
-        Meshgrid array of magnitudes of the contours
-    phases : array-like
-        Meshgrid array of phases in radians of the contours
-
-    Return values
-    -------------
-    contours : complex array
-        Array of complex numbers corresponding to the contours.
-    """
-    # Compute the contours in H-space
-    H = Hmag*sp.exp(1.j*Hphase)
-
-    # Invert H = G/(1+G) to get an expression for the contours in G-space
-    return H/(1.0 - H)
-
-# M-circle
-def m_circles(mags, phase_min=-359.75, phase_max=-0.25):
-    """Constant-magnitude contours of the function H = G/(1+G).
-
-    Usage
-    =====
-    contours = m_circles(mags)
-
-    Parameters
-    ----------
-    mags : array-like
-        Array of magnitudes in dB of the M-circles
-    phase_min : degrees
-        Minimum phase in degrees of the N-circles
-    phase_max : degrees
-        Maximum phase in degrees of the N-circles
-
-    Return values
-    -------------
-    contours : complex array
-        Array of complex numbers corresponding to the contours.
-    """
-    # Convert magnitudes and phase range into a grid suitable for
-    # building contours
-    phases = sp.radians(sp.linspace(phase_min, phase_max, 500))
-    Hmag, Hphase = sp.meshgrid(10.0**(mags/20.0), phases)
-    return closed_loop_contours(Hmag, Hphase)
-
-# N-circle
-def n_circles(phases, mag_min=-40.0, mag_max=12.0):
-    """Constant-phase contours of the function H = G/(1+G).
-
-    Usage
-    ===== 
-    contour = n_circles(angles)
-
-    Parameters
-    ----------
-    phases : array-like
-        Array of phases in degrees of the N-circles
-    mag_min : dB
-        Minimum magnitude in dB of the N-circles
-    mag_max : dB
-        Maximum magnitude in dB of the N-circles
-
-    Return values
-    -------------
-    contours : complex array
-        Array of complex numbers corresponding to the contours.
-    """
-    # Convert phases and magnitude range into a grid suitable for
-    # building contours    
-    mags = sp.linspace(10**(mag_min/20.0), 10**(mag_max/20.0), 2000)
-    Hphase, Hmag = sp.meshgrid(sp.radians(phases), mags)
-    return closed_loop_contours(Hmag, Hphase)

Modified: branches/control-0.4b/src/matlab.py
===================================================================
--- branches/control-0.4b/src/matlab.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/src/matlab.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -74,7 +74,8 @@
 
 # Import MATLAB-like functions that can be used as-is
 from ctrlutil import unwrap
-from freqplot import nyquist, nichols, gangof4
+from freqplot import nyquist, gangof4
+from nichols import nichols, nichols_grid
 from bdalg import series, parallel, negate, feedback
 from pzmap import pzmap
 from statefbk import ctrb, obsv, gram, place, lqr
@@ -752,7 +753,7 @@
     =====
     ngrid()
     """
-    freqplot.nichols_grid()
+    nichols_grid()
 
 #
 # Modifications to scipy.signal functions

Added: branches/control-0.4b/src/nichols.py
===================================================================
--- branches/control-0.4b/src/nichols.py	                        (rev 0)
+++ branches/control-0.4b/src/nichols.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -0,0 +1,267 @@
+# nichols.py - Nichols plot
+#
+# Contributed by Allan McInnes <All...@ca...>
+# 
+# This file contains some standard control system plots: Bode plots,
+# Nyquist plots, Nichols plots and pole-zero diagrams
+#
+# Copyright (c) 2010 by California Institute of Technology
+# All rights reserved.
+#
+# Redistribution and use in source and binary forms, with or without
+# modification, are permitted provided that the following conditions
+# are met:
+#
+# 1. Redistributions of source code must retain the above copyright
+#    notice, this list of conditions and the following disclaimer.
+# 
+# 2. Redistributions in binary form must reproduce the above copyright
+#    notice, this list of conditions and the following disclaimer in the
+#    documentation and/or other materials provided with the distribution.
+# 
+# 3. Neither the name of the California Institute of Technology nor
+#    the names of its contributors may be used to endorse or promote
+#    products derived from this software without specific prior
+#    written permission.
+# 
+# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+# FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL CALTECH
+# OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
+# USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
+# OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
+# OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+# SUCH DAMAGE.
+# 
+# $Id: freqplot.py 139 2011-03-30 16:19:59Z murrayrm $
+
+import matplotlib.pyplot as plt
+import scipy as sp
+import numpy as np
+from ctrlutil import unwrap
+from freqplot import default_frequency_range
+
+def nichols(syslist, omega=None):
+    """Nichols plot for a system
+
+    Usage
+    =====
+    magh = nichols(sys, omega=None)
+
+    Plots a Nichols plot for the system over a (optional) frequency range.
+
+    Parameters
+    ----------
+    syslist : linsys
+        List of linear input/output systems (single system is OK)
+    omega : freq_range
+        Range of frequencies (list or bounds) in rad/sec
+
+    Return values
+    -------------
+    None
+    """
+
+    # If argument was a singleton, turn it into a list
+    if (not getattr(syslist, '__iter__', False)):
+        syslist = (syslist,)
+
+    # Select a default range if none is provided
+    if (omega == None):
+        omega = default_frequency_range(syslist)
+
+    for sys in syslist:
+        # Get the magnitude and phase of the system
+        mag_tmp, phase_tmp, omega = sys.freqresp(omega)
+        mag = np.squeeze(mag_tmp)
+        phase = np.squeeze(phase_tmp)
+    
+        # Convert to Nichols-plot format (phase in degrees, 
+        # and magnitude in dB)
+        x = unwrap(sp.degrees(phase), 360)
+        y = 20*sp.log10(mag)
+    
+        # Generate the plot
+        plt.plot(x, y)
+        
+    plt.xlabel('Phase (deg)')
+    plt.ylabel('Magnitude (dB)')
+    plt.title('Nichols Plot')
+
+    # Mark the -180 point
+    plt.plot([-180], [0], 'r+')
+    
+# Nichols grid
+def nichols_grid():
+    """Nichols chart grid
+    
+    Usage
+    =====
+    nichols_grid()
+
+    Plots a Nichols chart grid on the current axis.
+
+    Parameters
+    ----------
+    None
+
+    Return values
+    -------------
+    None    
+    """
+    mag_min_default = -40.0 # dB
+    mag_step = 20.0         # dB
+
+    # Chart defaults
+    phase_min, phase_max, mag_min, mag_max = -360.0, 0.0, mag_min_default, 40.0
+
+    # Set actual chart bounds based on current plot
+    if plt.gcf().gca().has_data():
+        phase_min, phase_max, mag_min, mag_max = plt.axis()
+        
+    # M-circle magnitudes.
+    # The "fixed" set are always generated, since this guarantees a recognizable
+    # Nichols chart grid.
+    mags_fixed = np.array([-40.0, -20.0, -12.0, -6.0, -3.0, -1.0, -0.5, 0.0,
+                                 0.25, 0.5, 1.0, 3.0, 6.0, 12.0])
+
+    if mag_min < mag_min_default:
+        # Outside the "fixed" set of magnitudes, the generated M-circles
+        # are extended in steps of 'mag_step' dB to cover anything made
+        # visible by the range of the existing plot
+        mags_adjust = np.arange(mag_step*np.floor(mag_min/mag_step),
+                                mag_min_default, mag_step)
+        mags = np.concatenate((mags_adjust, mags_fixed))
+    else:
+        mags = mags_fixed
+                     
+    # N-circle phases (should be in the range -360 to 0)
+    phases = np.array([-0.25, -10.0, -20.0, -30.0, -45.0, -60.0, -90.0,
+                       -120.0, -150.0, -180.0, -210.0, -240.0, -270.0,
+                       -310.0, -325.0, -340.0, -350.0, -359.75])
+
+    # Find the M-contours
+    m = m_circles(mags, phase_min=np.min(phases), phase_max=np.max(phases))
+    m_mag = 20*sp.log10(np.abs(m))
+    m_phase = sp.mod(sp.degrees(sp.angle(m)), -360.0) # Unwrap
+
+    # Find the N-contours
+    n = n_circles(phases, mag_min=np.min(mags), mag_max=np.max(mags))
+    n_mag = 20*sp.log10(np.abs(n))
+    n_phase = sp.mod(sp.degrees(sp.angle(n)), -360.0) # Unwrap
+
+    # Plot the contours behind other plot elements.
+    # The "phase offset" is used to produce copies of the chart that cover
+    # the entire range of the plotted data, starting from a base chart computed
+    # over the range -360 < phase < 0 (see above). Given the range 
+    # the base chart is computed over, the phase offset should be 0
+    # for -360 < phase_min < 0.
+    phase_offset_min = 360.0*np.ceil(phase_min/360.0)
+    phase_offset_max = 360.0*np.ceil(phase_max/360.0) + 360.0
+    phase_offsets = np.arange(phase_offset_min, phase_offset_max, 360.0)
+    for phase_offset in phase_offsets:
+        plt.plot(m_phase + phase_offset, m_mag, color='gray',
+                 linestyle='dashed', zorder=0)
+        plt.plot(n_phase + phase_offset, n_mag, color='gray',
+                 linestyle='dashed', zorder=0)
+
+    # Add magnitude labels
+    for x, y, m in zip(m_phase[:][-1], m_mag[:][-1], mags):
+        align = 'right' if m < 0.0 else 'left'
+        plt.text(x, y, str(m) + ' dB', size='small', ha=align)
+
+    # Make sure axes conform to any pre-existing plot.
+    plt.axis([phase_min, phase_max, mag_min, mag_max])
+
+#
+# Utility functions
+#
+# This section of the code contains some utility functions for
+# generating Nichols plots
+#
+   
+# Compute contours of a closed-loop transfer function
+def closed_loop_contours(Hmag, Hphase):
+    """Contours of the function H = G/(1+G).
+
+    Usage
+    =====
+    contours = closed_loop_contours(mags, phases)
+
+    Parameters
+    ----------
+    mags : array-like
+        Meshgrid array of magnitudes of the contours
+    phases : array-like
+        Meshgrid array of phases in radians of the contours
+
+    Return values
+    -------------
+    contours : complex array
+        Array of complex numbers corresponding to the contours.
+    """
+    # Compute the contours in H-space
+    H = Hmag*sp.exp(1.j*Hphase)
+
+    # Invert H = G/(1+G) to get an expression for the contours in G-space
+    return H/(1.0 - H)
+
+# M-circle
+def m_circles(mags, phase_min=-359.75, phase_max=-0.25):
+    """Constant-magnitude contours of the function H = G/(1+G).
+
+    Usage
+    =====
+    contours = m_circles(mags)
+
+    Parameters
+    ----------
+    mags : array-like
+        Array of magnitudes in dB of the M-circles
+    phase_min : degrees
+        Minimum phase in degrees of the N-circles
+    phase_max : degrees
+        Maximum phase in degrees of the N-circles
+
+    Return values
+    -------------
+    contours : complex array
+        Array of complex numbers corresponding to the contours.
+    """
+    # Convert magnitudes and phase range into a grid suitable for
+    # building contours
+    phases = sp.radians(sp.linspace(phase_min, phase_max, 500))
+    Hmag, Hphase = sp.meshgrid(10.0**(mags/20.0), phases)
+    return closed_loop_contours(Hmag, Hphase)
+
+# N-circle
+def n_circles(phases, mag_min=-40.0, mag_max=12.0):
+    """Constant-phase contours of the function H = G/(1+G).
+
+    Usage
+    ===== 
+    contour = n_circles(angles)
+
+    Parameters
+    ----------
+    phases : array-like
+        Array of phases in degrees of the N-circles
+    mag_min : dB
+        Minimum magnitude in dB of the N-circles
+    mag_max : dB
+        Maximum magnitude in dB of the N-circles
+
+    Return values
+    -------------
+    contours : complex array
+        Array of complex numbers corresponding to the contours.
+    """
+    # Convert phases and magnitude range into a grid suitable for
+    # building contours    
+    mags = sp.linspace(10**(mag_min/20.0), 10**(mag_max/20.0), 2000)
+    Hphase, Hmag = sp.meshgrid(sp.radians(phases), mags)
+    return closed_loop_contours(Hmag, Hphase)

Modified: branches/control-0.4b/src/statesp.py
===================================================================
--- branches/control-0.4b/src/statesp.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/src/statesp.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -78,7 +78,6 @@
 from numpy.linalg import inv, det, solve
 from numpy.linalg.linalg import LinAlgError
 from scipy.signal import lti
-from slycot import td04ad
 from lti import Lti
 import xferfcn
 
@@ -457,6 +456,7 @@
         # Already a state space system; just return it
         return sys
     elif isinstance(sys, xferfcn.TransferFunction):
+        from slycot import td04ad
         if len(kw):
             raise TypeError("If sys is a TransferFunction, _convertToStateSpace \
 cannot take keywords.")

Modified: branches/control-0.4b/src/xferfcn.py
===================================================================
--- branches/control-0.4b/src/xferfcn.py	2011-04-01 04:46:30 UTC (rev 143)
+++ branches/control-0.4b/src/xferfcn.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -79,7 +79,6 @@
     polyadd, polymul, polyval, roots, sort, sqrt, zeros
 from scipy.signal import lti
 from copy import deepcopy
-from slycot import tb04ad
 from lti import Lti
 import statesp
 
@@ -707,6 +706,7 @@
 
         return sys
     elif isinstance(sys, statesp.StateSpace):
+        from slycot import tb04ad
         if len(kw):
             raise TypeError("If sys is a StateSpace, _convertToTransferFunction \
 cannot take keywords.")

Added: branches/control-0.4b/tests/nichols_test.py
===================================================================
--- branches/control-0.4b/tests/nichols_test.py	                        (rev 0)
+++ branches/control-0.4b/tests/nichols_test.py	2011-04-02 15:52:38 UTC (rev 144)
@@ -0,0 +1,37 @@
+#!/usr/bin/env python
+#
+# nichols_test.py - test Nichols plot
+# RMM, 31 Mar 2011
+
+import unittest
+import numpy as np
+from control.matlab import *
+
+class TestStateSpace(unittest.TestCase):
+    """Tests for the Nichols plots."""
+
+    def setUp(self):
+        """Set up a system to test operations on."""
+
+        A = [[-3., 4., 2.], [-1., -3., 0.], [2., 5., 3.]]
+        B = [[1.], [-3.], [-2.]]
+        C = [[4., 2., -3.]]
+        D = [[0.]]
+        
+        self.sys = StateSpace(A, B, C, D) 
+
+    def testNichols(self):
+        """Generate a Nichols plot."""
+        nichols(self.sys)
+
+    def testNgrid(self):
+        """Generate a Nichols plot."""
+        nichols(self.sys)
+        ngrid()
+
+def suite():
+   return unittest.TestLoader().loadTestsFromTestCase(TestStateSpace)
+
+        
+if __name__ == "__main__":
+    unittest.main()


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