Fix phase for triv_sigma in examples/robust_mimo.py (#428)

bnavigator · web-flow · commit 2777de3e0709 · 2020-07-10T19:32:38.000-07:00
* fix issue #406 * more precise docstrings for *.freqresp()
diff --git a/control/frdata.py b/control/frdata.py
@@ -400,17 +400,30 @@ def _evalfr(self, omega):
 
     # Method for generating the frequency response of the system
     def freqresp(self, omega):
-        """Evaluate a transfer function at a list of angular frequencies.
-
-        mag, phase, omega = self.freqresp(omega)
-
-        reports the value of the magnitude, phase, and angular frequency of
-        the transfer function matrix evaluated at s = i * omega, where omega
-        is a list of angular frequencies, and is a sorted version of the input
-        omega.
-
+        """Evaluate the frequency response at a list of angular frequencies.
+
+        Reports the value of the magnitude, phase, and angular frequency of
+        the requency response evaluated at omega, where omega is a list of
+        angular frequencies, and is a sorted version of the input omega.
+
+        Parameters
+        ----------
+        omega : array_like
+            A list of frequencies in radians/sec at which the system should be
+            evaluated. The list can be either a python list or a numpy array
+            and will be sorted before evaluation.
+
+        Returns
+        -------
+        mag : (self.outputs, self.inputs, len(omega)) ndarray
+            The magnitude (absolute value, not dB or log10) of the system
+            frequency response.
+        phase : (self.outputs, self.inputs, len(omega)) ndarray
+            The wrapped phase in radians of the system frequency response.
+        omega : ndarray or list or tuple
+            The list of sorted frequencies at which the response was
+            evaluated.
         """
-
         # Preallocate outputs.
         numfreq = len(omega)
         mag = empty((self.outputs, self.inputs, numfreq))
diff --git a/control/lti.py b/control/lti.py
@@ -55,8 +55,8 @@ def isdtime(self, strict=False):
         Parameters
         ----------
         strict: bool, optional
-            If strict is True, make sure that timebase is not None.  Default 
-            is False. 
+            If strict is True, make sure that timebase is not None.  Default
+            is False.
         """
 
         # If no timebase is given, answer depends on strict flag
@@ -75,8 +75,8 @@ def isctime(self, strict=False):
         sys : LTI system
             System to be checked
         strict: bool, optional
-            If strict is True, make sure that timebase is not None.  Default 
-            is False. 
+            If strict is True, make sure that timebase is not None.  Default
+            is False.
         """
         # If no timebase is given, answer depends on strict flag
         if self.dt is None:
@@ -421,6 +421,7 @@ def evalfr(sys, x):
         return sys.horner(x)[0][0]
     return sys.horner(x)
 
+
 def freqresp(sys, omega):
     """
     Frequency response of an LTI system at multiple angular frequencies.
@@ -430,13 +431,20 @@ def freqresp(sys, omega):
     sys: StateSpace or TransferFunction
         Linear system
     omega: array_like
-        List of frequencies
+        A list of frequencies in radians/sec at which the system should be
+        evaluated. The list can be either a python list or a numpy array
+        and will be sorted before evaluation.
 
     Returns
     -------
-    mag: ndarray
-    phase: ndarray
-    omega: list, tuple, or ndarray
+    mag : (self.outputs, self.inputs, len(omega)) ndarray
+        The magnitude (absolute value, not dB or log10) of the system
+        frequency response.
+    phase : (self.outputs, self.inputs, len(omega)) ndarray
+        The wrapped phase in radians of the system frequency response.
+    omega : ndarray or list or tuple
+        The list of sorted frequencies at which the response was
+        evaluated.
 
     See Also
     --------
@@ -472,9 +480,9 @@ def freqresp(sys, omega):
         #>>> # frequency response from the 1st input to the 2nd output, for
         #>>> # s = 0.1i, i, 10i.
     """
-
     return sys.freqresp(omega)
 
+
 def dcgain(sys):
     """Return the zero-frequency (or DC) gain of the given system
 
diff --git a/control/statesp.py b/control/statesp.py
@@ -462,11 +462,8 @@ def horner(self, s):
                                     self.B)) + self.D
         return array(resp)
 
-    # Method for generating the frequency response of the system
     def freqresp(self, omega):
-        """Evaluate the system's transfer func. at a list of freqs, omega.
-
-        mag, phase, omega = self.freqresp(omega)
+        """Evaluate the system's transfer function at a list of frequencies
 
         Reports the frequency response of the system,
 
@@ -479,26 +476,22 @@ def freqresp(self, omega):
 
         Parameters
         ----------
-        omega : array
+        omega : array_like
             A list of frequencies in radians/sec at which the system should be
             evaluated. The list can be either a python list or a numpy array
             and will be sorted before evaluation.
 
         Returns
         -------
-        mag : float
+        mag : (self.outputs, self.inputs, len(omega)) ndarray
             The magnitude (absolute value, not dB or log10) of the system
             frequency response.
-
-        phase : float
+        phase : (self.outputs, self.inputs, len(omega)) ndarray
             The wrapped phase in radians of the system frequency response.
-
-        omega : array
+        omega : ndarray
             The list of sorted frequencies at which the response was
             evaluated.
-
         """
-
         # In case omega is passed in as a list, rather than a proper array.
         omega = np.asarray(omega)
 
diff --git a/control/xferfcn.py b/control/xferfcn.py
@@ -639,19 +639,36 @@ def horner(self, s):
 
         return out
 
-    # Method for generating the frequency response of the system
     def freqresp(self, omega):
-        """Evaluate a transfer function at a list of angular frequencies.
+        """Evaluate the transfer function at a list of angular frequencies.
 
-        mag, phase, omega = self.freqresp(omega)
+        Reports the frequency response of the system,
 
-        reports the value of the magnitude, phase, and angular frequency of
-        the transfer function matrix evaluated at s = i * omega, where omega
-        is a list of angular frequencies, and is a sorted version of the input
-        omega.
+             G(j*omega) = mag*exp(j*phase)
 
-        """
+        for continuous time. For discrete time systems, the response is
+        evaluated around the unit circle such that
+
+             G(exp(j*omega*dt)) = mag*exp(j*phase).
+
+        Parameters
+        ----------
+        omega : array_like
+            A list of frequencies in radians/sec at which the system should be
+            evaluated. The list can be either a python list or a numpy array
+            and will be sorted before evaluation.
 
+        Returns
+        -------
+        mag : (self.outputs, self.inputs, len(omega)) ndarray
+            The magnitude (absolute value, not dB or log10) of the system
+            frequency response.
+        phase : (self.outputs, self.inputs, len(omega)) ndarray
+            The wrapped phase in radians of the system frequency response.
+        omega : ndarray or list or tuple
+            The list of sorted frequencies at which the response was
+            evaluated.
+        """
         # Preallocate outputs.
         numfreq = len(omega)
         mag = empty((self.outputs, self.inputs, numfreq))
diff --git a/examples/robust_mimo.py b/examples/robust_mimo.py
@@ -44,7 +44,7 @@ def triv_sigma(g, w):
     w - frequencies, length m
     s - (m,n) array of singular values of g(1j*w)"""
     m, p, _ = g.freqresp(w)
-    sjw = (m*np.exp(1j*p*np.pi/180)).transpose(2, 0, 1)
+    sjw = (m*np.exp(1j*p)).transpose(2, 0, 1)
     sv = np.linalg.svd(sjw, compute_uv=False)
     return sv
 
