Merge pull request #547 from murrayrm/doc_updates

murrayrm · web-flow · commit 4788f6bafc51 · 2021-02-24T16:36:31.000-08:00
Small documentation updates
diff --git a/control/freqplot.py b/control/freqplot.py
@@ -608,7 +608,7 @@ def nyquist_plot(syslist, omega=None, plot=True, omega_limits=None,
         be 'right' (default), 'left', or 'none'.
 
     warn_nyquist : bool, optional
-        If set to `False', turn off warnings about frequencies above Nyquist.
+        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)
diff --git a/control/margins.py b/control/margins.py
@@ -211,36 +211,40 @@ def fun(wdt):
 # Sawyer B. Fuller <minster@uw.edu>, removed a lot of the innards
 # and replaced with analytical polynomial functions for LTI systems.
 #
-# idea for the frequency data solution copied/adapted from
+# The idea for the frequency data solution copied/adapted from
 # https://github.com/alchemyst/Skogestad-Python/blob/master/BODE.py
 # Rene van Paassen <rene.vanpaassen@gmail.com>
 #
 # RvP, July 8, 2014, corrected to exclude phase=0 crossing for the gain
 #                    margin polynomial
+#
 # RvP, July 8, 2015, augmented to calculate all phase/gain crossings with
 #                    frd data. Correct to return smallest phase
 #                    margin, smallest gain margin and their frequencies
-# RvP, Jun 10, 2017, modified the inclusion of roots found for phase
-#                    crossing to include all >= 0, made subsequent calc
-#                    insensitive to div by 0
-#                    also changed the selection of which crossings to
-#                    return on basis of "A note on the Gain and Phase
+#
+# RvP, Jun 10, 2017, modified the inclusion of roots found for phase crossing
+#                    to include all >= 0, made subsequent calc insensitive to
+#                    div by 0.  Also changed the selection of which crossings
+#                    to return on basis of "A note on the Gain and Phase
 #                    Margin Concepts" Journal of Control and Systems
-#                    Engineering, Yazdan Bavafi-Toosi, Dec 2015, vol 3
-#                    issue 1, pp 51-59, closer to Matlab behavior, but
-#                    not completely identical in edge cases, which don't
-#                    cross but touch gain=1
+#                    Engineering, Yazdan Bavafi-Toosi, Dec 2015, vol 3 issue
+#                    1, pp 51-59, closer to Matlab behavior, but not
+#                    completely identical in edge cases, which don't cross but
+#                    touch gain=1.
+#
 # BG, Nov 9, 2020,   removed duplicate implementations of the same code
 #                    for crossover frequencies and enhanced to handle discrete
 #                    systems
+
+
 def stability_margins(sysdata, returnall=False, epsw=0.0):
     """Calculate stability margins and associated crossover frequencies.
 
     Parameters
     ----------
     sysdata: LTI system or (mag, phase, omega) sequence
         sys : LTI system
-            Linear SISO system
+            Linear SISO system representing the loop transfer function
         mag, phase, omega : sequence of array_like
             Arrays of magnitudes (absolute values, not dB), phases (degrees),
             and corresponding frequencies. Crossover frequencies returned are
@@ -255,18 +259,25 @@ def stability_margins(sysdata, returnall=False, epsw=0.0):
 
     Returns
     -------
-    gm: float or array_like
+    gm : float or array_like
         Gain margin
-    pm: float or array_loke
+    pm : float or array_loke
         Phase margin
-    sm: float or array_like
+    sm : float or array_like
         Stability margin, the minimum distance from the Nyquist plot to -1
-    wg: float or array_like
-        Frequency for gain margin (at phase crossover, phase = -180 degrees)
-    wp: float or array_like
-        Frequency for phase margin (at gain crossover, gain = 1)
-    ws: float or array_like
-        Frequency for stability margin (complex gain closest to -1)
+    wpc : float or array_like
+        Phase crossover frequency (where phase crosses -180 degrees)
+    wgc : float or array_like
+        Gain crossover frequency (where gain crosses 1)
+    wms : float or array_like
+        Stability margin frequency (where Nyquist plot is closest to -1)
+
+    Note that the gain margin is determined by the gain of the loop
+    transfer function at the phase crossover frequency(s), the phase
+    margin is determined by the phase of the loop transfer function at
+    the gain crossover frequency(s), and the stability margin is
+    determined by the frequency of maximum sensitivity (given by the
+    magnitude of 1/(1+L)).
     """
     try:
         if isinstance(sysdata, frdata.FRD):
@@ -398,7 +409,8 @@ def _dstab(w):
             (not SM.shape[0] and float('inf')) or np.amin(SM),
             (not gmidx != -1 and float('nan')) or w_180[gmidx][0],
             (not wc.shape[0] and float('nan')) or wc[pmidx][0],
-            (not wstab.shape[0] and float('nan')) or wstab[SM==np.amin(SM)][0])
+            (not wstab.shape[0] and float('nan')) or
+            wstab[SM == np.amin(SM)][0])
 
 
 # Contributed by Steffen Waldherr <waldherr@ist.uni-stuttgart.de>
@@ -455,7 +467,7 @@ def margin(*args):
     ----------
     sysdata : LTI system or (mag, phase, omega) sequence
         sys : StateSpace or TransferFunction
-            Linear SISO system
+            Linear SISO system representing the loop transfer function
         mag, phase, omega : sequence of array_like
             Input magnitude, phase (in deg.), and frequencies (rad/sec) from
             bode frequency response data
@@ -466,17 +478,16 @@ def margin(*args):
         Gain margin
     pm : float
         Phase margin (in degrees)
-    wg: float
-        Frequency for gain margin (at phase crossover, phase = -180 degrees)
-    wp: float
-        Frequency for phase margin (at gain crossover, gain = 1)
+    wpc : float or array_like
+        Phase crossover frequency (where phase crosses -180 degrees)
+    wgc : float or array_like
+        Gain crossover frequency (where gain crosses 1)
 
     Margins are calculated for a SISO open-loop system.
 
-    If there is more than one gain crossover, the one at the smallest
-    margin (deviation from gain = 1), in absolute sense, is
-    returned. Likewise the smallest phase margin (in absolute sense)
-    is returned.
+    If there is more than one gain crossover, the one at the smallest margin
+    (deviation from gain = 1), in absolute sense, is returned. Likewise the
+    smallest phase margin (in absolute sense) is returned.
 
     Examples
     --------
@@ -491,6 +502,6 @@ def margin(*args):
         margin = stability_margins(args)
     else:
         raise ValueError("Margin needs 1 or 3 arguments; received %i."
-            % len(args))
+                         % len(args))
 
     return margin[0], margin[1], margin[3], margin[4]
diff --git a/doc/descfcn.rst b/doc/descfcn.rst
@@ -59,7 +59,7 @@ nonlinearity constructors are predefined:
 
 .. code:: python
 
-  backlash_nonlinearity(b)		# backlash nonlinearity with width b
+  friction_backlash_nonlinearity(b)	# backlash nonlinearity with width b
   relay_hysteresis_nonlinearity(b, c)   # relay output of amplitude b with
 					# hysteresis of half-width c
   saturation_nonlinearity(ub[, lb])	# saturation nonlinearity with upper
@@ -81,6 +81,6 @@ Module classes and functions
    :toctree: generated/
 
    ~control.DescribingFunctionNonlinearity
-   ~control.backlash_nonlinearity
+   ~control.friction_backlash_nonlinearity
    ~control.relay_hysteresis_nonlinearity
    ~control.saturation_nonlinearity
