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

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Merged
murrayrm merged 2 commits into from
Jul 11, 2020
Merged

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

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8584f40
fix #406
bnavigator Jul 4, 2020
786ce2d
more precise docstrings for *.freqresp()
bnavigator Jul 4, 2020
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33 changes: 23 additions & 10 deletions control/frdata.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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))
Expand Down
26 changes: 17 additions & 9 deletions control/lti.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand All @@ -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:
Expand Down Expand Up @@ -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.
Expand All @@ -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
--------
Expand Down Expand Up @@ -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

Expand Down
17 changes: 5 additions & 12 deletions control/statesp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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,

Expand All @@ -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)

Expand Down
33 changes: 25 additions & 8 deletions control/xferfcn.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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))
Expand Down
2 changes: 1 addition & 1 deletion examples/robust_mimo.py
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Original file line number Diff line number Diff line change
Expand Up @@ -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

Expand Down