python-control · bnavigator · Aug 18, 2020 · Aug 14, 2020 · Aug 14, 2020 · Aug 14, 2020
diff --git a/control/freqplot.py b/control/freqplot.py
@@ -110,9 +110,9 @@ def bode_plot(syslist, omega=None,
         config.defaults['freqplot.number_of_samples'].
     margins : bool
         If True, plot gain and phase margin.
-    *args : `matplotlib` plot positional properties, optional
+    *args : :func:`matplotlib.pyplot.plot` positional properties, optional
         Additional arguments for `matplotlib` plots (color, linestyle, etc)
-    **kwargs : `matplotlib` plot keyword properties, optional
+    **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
         Additional keywords (passed to `matplotlib`)
 
     Returns
@@ -128,21 +128,22 @@ def bode_plot(syslist, omega=None,
     ----------------
     grid : bool
         If True, plot grid lines on gain and phase plots.  Default is set by
-        config.defaults['bode.grid'].
+        `config.defaults['bode.grid']`.
+
 
     The default values for Bode plot configuration parameters can be reset
     using the `config.defaults` dictionary, with module name 'bode'.
 
     Notes
     -----
-    1. Alternatively, you may use the lower-level method (mag, phase, freq)
-    = sys.freqresp(freq) to generate the frequency response for a system,
-    but it returns a MIMO response.
+    1. Alternatively, you may use the lower-level method
+       ``(mag, phase, freq) = sys.freqresp(freq)`` to generate the frequency
+       response for a system, but it returns a MIMO response.
 
     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(j
-    \\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
-    timebase.  If not timebase is specified (dt = True), dt is set to 1.
+       along the upper branch of the unit circle, using the mapping z = exp(j
+       \\omega dt) where omega ranges from 0 to pi/dt and dt is the discrete
+       timebase.  If not timebase is specified (dt = True), dt is set to 1.
 
     Examples
     --------
@@ -464,9 +465,9 @@ def nyquist_plot(syslist, omega=None, plot=True, label_freq=0,
         Label every nth frequency on the plot
     arrowhead_width : arrow head width
     arrowhead_length : arrow head length
-    *args : `matplotlib` plot positional properties, optional
+    *args : :func:`matplotlib.pyplot.plot` positional properties, optional
         Additional arguments for `matplotlib` plots (color, linestyle, etc)
-    **kwargs : `matplotlib` plot keyword properties, optional
+    **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
         Additional keywords (passed to `matplotlib`)
 
     Returns
@@ -539,13 +540,13 @@ def nyquist_plot(syslist, omega=None, plot=True, label_freq=0,
                 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_width=arrowhead_width,
                          head_length=arrowhead_length)
 
                 plt.plot(x, -y, '-', 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, 
+                    fc=c, ec=c, head_width=arrowhead_width,
                     head_length=arrowhead_length)
 
                 # Mark the -1 point
@@ -601,7 +602,7 @@ def gangof4_plot(P, C, omega=None, **kwargs):
         Linear input/output systems (process and control)
     omega : array
         Range of frequencies (list or bounds) in rad/sec
-    **kwargs : `matplotlib` plot keyword properties, optional
+    **kwargs : :func:`matplotlib.pyplot.plot` keyword properties, optional
         Additional keywords (passed to `matplotlib`)
 
     Returns

diff --git a/control/iosys.py b/control/iosys.py
@@ -1514,8 +1514,9 @@ def find_eqpt(sys, x0, u0=[], y0=None, t=0, params={},
     return_y : bool, optional
         If True, return the value of output at the equilibrium point.
     return_result : bool, optional
-        If True, return the `result` option from the scipy root function used
-        to compute the equilibrium point.
+        If True, return the `result` option from the
+        :func:`scipy.optimize.root` function used to compute the equilibrium
+        point.
 
     Returns
     -------
@@ -1529,9 +1530,9 @@ def find_eqpt(sys, x0, u0=[], y0=None, t=0, params={},
         If `return_y` is True, returns the value of the outputs at the
         equilibrium point, or `None` if no equilibrium point was found and
         `return_result` was False.
-    result : scipy root() result object, optional
-        If `return_result` is True, returns the `result` from the scipy root
-        function.
+    result : :class:`scipy.optimize.OptimizeResult`, optional
+        If `return_result` is True, returns the `result` from the
+        :func:`scipy.optimize.root` function.
 
     """
     from scipy.optimize import root

diff --git a/control/nichols.py b/control/nichols.py
@@ -135,11 +135,9 @@ def nichols_grid(cl_mags=None, cl_phases=None, line_style='dotted'):
         Array of closed-loop phases defining the iso-phase lines on a custom
         Nichols chart. Must be in the range -360 < cl_phases < 0
     line_style : string, optional
-        .. seealso:: https://matplotlib.org/gallery/lines_bars_and_markers/linestyles.html
+        :doc:`Matplotlib linestyle \
+            <matplotlib:gallery/lines_bars_and_markers/linestyles>`
 
-    Returns
-    -------
-    None
     """
     # Default chart size
     ol_phase_min = -359.99

diff --git a/control/phaseplot.py b/control/phaseplot.py
@@ -73,7 +73,7 @@ def phase_plot(odefun, X=None, Y=None, scale=1, X0=None, T=None,
     func : callable(x, t, ...)
         Computes the time derivative of y (compatible with odeint).
         The function should be the same for as used for
-        scipy.integrate.  Namely, it should be a function of the form
+        :mod:`scipy.integrate`.  Namely, it should be a function of the form
         dxdt = F(x, t) that accepts a state x of dimension 2 and
         returns a derivative dx/dt of dimension 2.
 

diff --git a/control/pzmap.py b/control/pzmap.py
@@ -66,7 +66,7 @@ def pzmap(sys, plot=True, grid=False, title='Pole Zero Map', **kwargs):
     ----------
     sys: LTI (StateSpace or TransferFunction)
         Linear system for which poles and zeros are computed.
-    plot: bool
+    plot: bool, optional
         If ``True`` a graph is generated with Matplotlib,
         otherwise the poles and zeros are only computed and returned.
     grid: boolean (default = False)

diff --git a/control/rlocus.py b/control/rlocus.py
@@ -75,7 +75,7 @@
 
 # Main function: compute a root locus diagram
 def root_locus(sys, kvect=None, xlim=None, ylim=None,
-               plotstr=None, plot=True, print_gain=None, grid=None, ax=None, 
+               plotstr=None, plot=True, print_gain=None, grid=None, ax=None,
                **kwargs):
 
     """Root locus plot
@@ -91,18 +91,22 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
     kvect : list or ndarray, optional
         List of gains to use in computing diagram.
     xlim : tuple or list, optional
-        Set limits of x axis, normally with tuple (see matplotlib.axes).
+        Set limits of x axis, normally with tuple
+        (see :doc:`matplotlib:api/axes_api`).
     ylim : tuple or list, optional
-        Set limits of y axis, normally with tuple (see matplotlib.axes).
+        Set limits of y axis, normally with tuple
+        (see :doc:`matplotlib:api/axes_api`).
+    plotstr : :func:`matplotlib.pyplot.plot` format string, optional
+        plotting style specification
     plot : boolean, optional
         If True (default), plot root locus diagram.
     print_gain : bool
         If True (default), report mouse clicks when close to the root locus
         branches, calculate gain, damping and print.
     grid : bool
         If True plot omega-damping grid.  Default is False.
-    ax : Matplotlib axis
-        axis on which to create root locus plot 
+    ax : :class:`matplotlib.axes.Axes`
+        Axes on which to create root locus plot
 
     Returns
     -------
@@ -160,7 +164,7 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
             fig = kwargs['fig']
             ax = fig.axes[1]
         else:
-            if ax is None: 
+            if ax is None:
                 ax = plt.gca()
                 fig = ax.figure
                 ax.set_title('Root Locus')

diff --git a/control/robust.py b/control/robust.py
@@ -119,8 +119,8 @@ def hinfsyn(P, nmeas, ncon):
     rcond: 4-vector, reciprocal condition estimates of:
         1: control transformation matrix
         2: measurement transformation matrix
-        3: X-Ricatti equation
-        4: Y-Ricatti equation
+        3: X-Riccati equation
+        4: Y-Riccati equation
     TODO: document significance of rcond
 
     Raises

diff --git a/control/sisotool.py b/control/sisotool.py
@@ -26,10 +26,11 @@ def sisotool(sys, kvect = None, xlim_rlocus = None, ylim_rlocus = None,
     kvect : list or ndarray, optional
         List of gains to use for plotting root locus
     xlim_rlocus : tuple or list, optional
-        control of x-axis range, normally with tuple (see matplotlib.axes)
+        control of x-axis range, normally with tuple
+        (see :doc:`matplotlib:api/axes_api`).
     ylim_rlocus : tuple or list, optional
         control of y-axis range
-    plotstr_rlocus : Additional options to matplotlib
+    plotstr_rlocus : :func:`matplotlib.pyplot.plot` format string, optional
         plotting style for the root locus plot(color, linestyle, etc)
     rlocus_grid: boolean (default = False)
         If True plot s-plane grid.

diff --git a/control/statefbk.py b/control/statefbk.py
@@ -53,6 +53,7 @@
 # Pole placement
 def place(A, B, p):
     """Place closed loop eigenvalues
+
     K = place(A, B, p)
 
     Parameters
@@ -69,21 +70,24 @@ def place(A, B, p):
     K : 2-d array
         Gain such that A - B K has eigenvalues given in p
 
-    Algorithm
-    ---------
-    This is a wrapper function for scipy.signal.place_poles, which
-    implements the Tits and Yang algorithm [1]. It will handle SISO,
-    MISO, and MIMO systems. If you want more control over the algorithm,
-    use scipy.signal.place_poles directly.
 
-    [1] A.L. Tits and Y. Yang, "Globally convergent algorithms for robust
-    pole assignment by state feedback, IEEE Transactions on Automatic
-    Control, Vol. 41, pp. 1432-1452, 1996.
+    Notes
+    -----
+    Algorithm
+        This is a wrapper function for :func:`scipy.signal.place_poles`, which
+        implements the Tits and Yang algorithm [1]_. It will handle SISO,
+        MISO, and MIMO systems. If you want more control over the algorithm,
+        use :func:`scipy.signal.place_poles` directly.
 
     Limitations
-    -----------
-    The algorithm will not place poles at the same location more
-    than rank(B) times.
+        The algorithm will not place poles at the same location more
+        than rank(B) times.
+
+    References
+    ----------
+    .. [1] A.L. Tits and Y. Yang, "Globally convergent algorithms for robust
+       pole assignment by state feedback, IEEE Transactions on Automatic
+       Control, Vol. 41, pp. 1432-1452, 1996.
 
     Examples
     --------
@@ -227,11 +231,11 @@ def lqe(A, G, C, QN, RN, NN=None):
     Linear quadratic estimator design (Kalman filter) for continuous-time
     systems. Given the system
 
-    Given the system
     .. math::
-        x = Ax + Bu + Gw
-        y = Cx + Du + v
-
+
+        x &= Ax + Bu + Gw \\\\
+        y &= Cx + Du + v
+
     with unbiased process noise w and measurement noise v with covariances
 
     .. math::       E{ww'} = QN,    E{vv'} = RN,    E{wv'} = NN
@@ -260,11 +264,14 @@ def lqe(A, G, C, QN, RN, NN=None):
         Kalman estimator gain
     P: 2D array
         Solution to Riccati equation
+
         .. math::
-            A P + P A^T - (P C^T + G N) R^-1  (C P + N^T G^T) + G Q G^T = 0
+
+            A P + P A^T - (P C^T + G N) R^{-1}  (C P + N^T G^T) + G Q G^T = 0
+
     E: 1D array
         Eigenvalues of estimator poles eig(A - L C)
-        
+
 
     Examples
     --------
@@ -381,7 +388,7 @@ def lqr(*args, **keywords):
     See Also
     --------
     lqe
-    
+
     """
 
     # Make sure that SLICOT is installed

diff --git a/control/statesp.py b/control/statesp.py
@@ -72,7 +72,7 @@
 _statesp_defaults = {
     'statesp.use_numpy_matrix': True,
     'statesp.default_dt': None,
-    'statesp.remove_useless_states': True, 
+    'statesp.remove_useless_states': True,
     }
 
 
@@ -149,7 +149,7 @@ class StateSpace(LTI):
     Setting dt = 0 specifies a continuous system, while leaving dt = None
     means the system timebase is not specified.  If 'dt' is set to True, the
     system will be treated as a discrete time system with unspecified sampling
-    time. The default value of 'dt' is None and can be changed by changing the 
+    time. The default value of 'dt' is None and can be changed by changing the
     value of ``control.config.defaults['statesp.default_dt']``.
 
     """
@@ -788,15 +788,15 @@ def minreal(self, tol=0.0):
 
     # TODO: add discrete time check
     def returnScipySignalLTI(self):
-        """Return a list of a list of scipy.signal.lti objects.
+        """Return a list of a list of :class:`scipy.signal.lti` objects.
 
         For instance,
 
         >>> out = ssobject.returnScipySignalLTI()
         >>> out[3][5]
 
-        is a signal.scipy.lti object corresponding to the transfer function from
-        the 6th input to the 4th output."""
+        is a :class:`scipy.signal.lti` object corresponding to the transfer
+        function from the 6th input to the 4th output."""
 
         # Preallocate the output.
         out = [[[] for _ in range(self.inputs)] for _ in range(self.outputs)]
@@ -809,8 +809,9 @@ def returnScipySignalLTI(self):
         return out
 
     def append(self, other):
-        """Append a second model to the present model. The second
-        model is converted to state-space if necessary, inputs and
+        """Append a second model to the present model.
+
+        The second model is converted to state-space if necessary, inputs and
         outputs are appended and their order is preserved"""
         if not isinstance(other, StateSpace):
             other = _convertToStateSpace(other)
@@ -870,8 +871,8 @@ def sample(self, Ts, method='zoh', alpha=None, prewarp_frequency=None):
 
         prewarp_frequency : float within [0, infinity)
             The frequency [rad/s] at which to match with the input continuous-
-            time system's magnitude and phase (the gain=1 crossover frequency, 
-            for example). Should only be specified with method='bilinear' or 
+            time system's magnitude and phase (the gain=1 crossover frequency,
+            for example). Should only be specified with method='bilinear' or
             'gbt' with alpha=0.5 and ignored otherwise.
 
         Returns
@@ -881,7 +882,7 @@ def sample(self, Ts, method='zoh', alpha=None, prewarp_frequency=None):
 
         Notes
         -----
-        Uses the command 'cont2discrete' from scipy.signal
+        Uses :func:`scipy.signal.cont2discrete`
 
         Examples
         --------
@@ -896,7 +897,7 @@ def sample(self, Ts, method='zoh', alpha=None, prewarp_frequency=None):
         if (method=='bilinear' or (method=='gbt' and alpha==0.5)) and \
                 prewarp_frequency is not None:
             Twarp = 2*np.tan(prewarp_frequency*Ts/2)/prewarp_frequency
-        else: 
+        else:
             Twarp = Ts
         Ad, Bd, C, D, _ = cont2discrete(sys, Twarp, method, alpha)
         return StateSpace(Ad, Bd, C, D, Ts)