murrayrm · Jun 16, 2021 · Jun 12, 2021 · Jun 12, 2021 · Jun 12, 2021 · Jun 12, 2021
diff --git a/control/flatsys/basis.py b/control/flatsys/basis.py
@@ -47,6 +47,11 @@ class BasisFamily:
 
       :math:`z_i^{(q)}(t)` = basis.eval_deriv(self, i, j, t)
 
+    Parameters
+    ----------
+    N : int
+        Order of the basis set.
+
     """
     def __init__(self, N):
         """Create a basis family of order N."""

diff --git a/control/flatsys/linflat.py b/control/flatsys/linflat.py
@@ -42,46 +42,53 @@
 
 
 class LinearFlatSystem(FlatSystem, LinearIOSystem):
+    """Base class for a linear, differentially flat system.
+
+    This class is used to create a differentially flat system representation
+    from a linear system.
+
+    Parameters
+    ----------
+    linsys : StateSpace
+        LTI StateSpace system to be converted
+    inputs : int, list of str or None, optional
+        Description of the system inputs.  This can be given as an integer
+        count or as a list of strings that name the individual signals.
+        If an integer count is specified, the names of the signal will be
+        of the form `s[i]` (where `s` is one of `u`, `y`, or `x`).  If
+        this parameter is not given or given as `None`, the relevant
+        quantity will be determined when possible based on other
+        information provided to functions using the system.
+    outputs : int, list of str or None, optional
+        Description of the system outputs.  Same format as `inputs`.
+    states : int, list of str, or None, optional
+        Description of the system states.  Same format as `inputs`.
+    dt : None, True or float, optional
+        System timebase.  None (default) indicates continuous
+        time, True indicates discrete time with undefined sampling
+        time, positive number is discrete time with specified
+        sampling time.
+    params : dict, optional
+        Parameter values for the systems.  Passed to the evaluation
+        functions for the system as default values, overriding internal
+        defaults.
+    name : string, optional
+        System name (used for specifying signals)
+
+    Returns
+    -------
+    iosys : LinearFlatSystem
+        Linear system represented as an flat input/output system
+
+    """
+
     def __init__(self, linsys, inputs=None, outputs=None, states=None,
                  name=None):
         """Define a flat system from a SISO LTI system.
 
         Given a reachable, single-input/single-output, linear time-invariant
         system, create a differentially flat system representation.
 
-        Parameters
-        ----------
-        linsys : StateSpace
-            LTI StateSpace system to be converted
-        inputs : int, list of str or None, optional
-            Description of the system inputs.  This can be given as an integer
-            count or as a list of strings that name the individual signals.
-            If an integer count is specified, the names of the signal will be
-            of the form `s[i]` (where `s` is one of `u`, `y`, or `x`).  If
-            this parameter is not given or given as `None`, the relevant
-            quantity will be determined when possible based on other
-            information provided to functions using the system.
-        outputs : int, list of str or None, optional
-            Description of the system outputs.  Same format as `inputs`.
-        states : int, list of str, or None, optional
-            Description of the system states.  Same format as `inputs`.
-        dt : None, True or float, optional
-            System timebase.  None (default) indicates continuous
-            time, True indicates discrete time with undefined sampling
-            time, positive number is discrete time with specified
-            sampling time.
-        params : dict, optional
-            Parameter values for the systems.  Passed to the evaluation
-            functions for the system as default values, overriding internal
-            defaults.
-        name : string, optional
-            System name (used for specifying signals)
-
-        Returns
-        -------
-        iosys : LinearFlatSystem
-            Linear system represented as an flat input/output system
-
         """
         # Make sure we can handle the system
         if (not control.isctime(linsys)):

diff --git a/control/frdata.py b/control/frdata.py
@@ -64,6 +64,29 @@ class FrequencyResponseData(LTI):
     The FrequencyResponseData (FRD) class is used to represent systems in
     frequency response data form.
 
+    Parameters
+    ----------
+    d : 1D or 3D complex array_like
+        The frequency response at each frequency point.  If 1D, the system is
+        assumed to be SISO.  If 3D, the system is MIMO, with the first
+        dimension corresponding to the output index of the FRD, the second
+        dimension corresponding to the input index, and the 3rd dimension
+        corresponding to the frequency points in omega
+    w : iterable of real frequencies
+        List of frequency points for which data are available.
+    smooth : bool, optional
+        If ``True``, create an interpolation function that allows the
+        frequency response to be computed at any frequency within the range of
+        frequencies give in ``w``.  If ``False`` (default), frequency response
+        can only be obtained at the frequencies specified in ``w``.
+
+    Attributes
+    ----------
+    ninputs, noutputs : int
+        Number of input and output variables.
+
+    Notes
+    -----
     The main data members are 'omega' and 'fresp', where `omega` is a 1D array
     with the frequency points of the response, and `fresp` is a 3D array, with
     the first dimension corresponding to the output index of the FRD, the
@@ -77,13 +100,35 @@ class FrequencyResponseData(LTI):
     above, i.e. the rows represent the outputs and the columns
     represent the inputs.
 
+    A frequency response data object is callable and returns the value of the
+    transfer function evaluated at a point in the complex plane (must be on
+    the imaginary access).  See :meth:`~control.FrequencyResponseData.__call__`
+    for a more detailed description.
+
     """
 
     # Allow NDarray * StateSpace to give StateSpace._rmul_() priority
     # https://docs.scipy.org/doc/numpy/reference/arrays.classes.html
     __array_priority__ = 11     # override ndarray and matrix types
 
-    epsw = 1e-8
+    #
+    # Class attributes
+    #
+    # These attributes are defined as class attributes so that they are
+    # documented properly.  They are "overwritten" in __init__.
+    #
+
+    #: Number of system inputs.
+    #:
+    #: :meta hide-value:
+    ninputs = 1
+
+    #: Number of system outputs.
+    #:
+    #: :meta hide-value:
+    noutputs = 1
+
+    _epsw = 1e-8                #: Bound for exact frequency match
 
     def __init__(self, *args, **kwargs):
         """Construct an FRD object.
@@ -141,7 +186,8 @@ def __init__(self, *args, **kwargs):
             self.omega = args[0].omega
             self.fresp = args[0].fresp
         else:
-            raise ValueError("Needs 1 or 2 arguments; received %i." % len(args))
+            raise ValueError(
+                "Needs 1 or 2 arguments; received %i." % len(args))
 
         # create interpolation functions
         if smooth:
@@ -378,7 +424,7 @@ def eval(self, omega, squeeze=None):
             then single-dimensional axes are removed.
 
         """
-        omega_array = np.array(omega, ndmin=1) # array-like version of omega
+        omega_array = np.array(omega, ndmin=1)  # array-like version of omega
 
         # Make sure that we are operating on a simple list
         if len(omega_array.shape) > 1:
@@ -389,7 +435,7 @@ def eval(self, omega, squeeze=None):
             raise ValueError("FRD.eval can only accept real-valued omega")
 
         if self.ifunc is None:
-            elements = np.isin(self.omega, omega) # binary array
+            elements = np.isin(self.omega, omega)  # binary array
             if sum(elements) < len(omega_array):
                 raise ValueError(
                     "not all frequencies omega are in frequency list of FRD "
@@ -398,7 +444,7 @@ def eval(self, omega, squeeze=None):
                 out = self.fresp[:, :, elements]
         else:
             out = empty((self.noutputs, self.ninputs, len(omega_array)),
-                         dtype=complex)
+                        dtype=complex)
             for i in range(self.noutputs):
                 for j in range(self.ninputs):
                     for k, w in enumerate(omega_array):
@@ -417,6 +463,9 @@ def __call__(self, s, squeeze=None):
         To evaluate at a frequency omega in radians per second, enter
         ``s = omega * 1j`` or use ``sys.eval(omega)``
 
+        For a frequency response data object, the argument must be an
+        imaginary number (since only the frequency response is defined).
+
         Parameters
         ----------
         s : complex scalar or 1D array_like
@@ -444,14 +493,15 @@ def __call__(self, s, squeeze=None):
             If `s` is not purely imaginary, because
             :class:`FrequencyDomainData` systems are only defined at imaginary
             frequency values.
+
         """
         # Make sure that we are operating on a simple list
         if len(np.atleast_1d(s).shape) > 1:
             raise ValueError("input list must be 1D")
 
         if any(abs(np.atleast_1d(s).real) > 0):
             raise ValueError("__call__: FRD systems can only accept "
-                            "purely imaginary frequencies")
+                             "purely imaginary frequencies")
 
         # need to preserve array or scalar status
         if hasattr(s, '__len__'):
@@ -510,6 +560,7 @@ def feedback(self, other=1, sign=-1):
 # fixes this problem.
 #
 
+
 FRD = FrequencyResponseData
 
 
@@ -534,7 +585,7 @@ def _convert_to_FRD(sys, omega, inputs=1, outputs=1):
     if isinstance(sys, FRD):
         omega.sort()
         if len(omega) == len(sys.omega) and \
-           (abs(omega - sys.omega) < FRD.epsw).all():
+           (abs(omega - sys.omega) < FRD._epsw).all():
             # frequencies match, and system was already frd; simply use
             return sys