def state_space(self, speed, nominal=False):
"""
Returns the A and B matrices for the Whipple model linearized about
the upright constant velocity configuration.
Parameters
----------
speed : float
The speed of the bicycle.
nominal : boolean, optional
The default is false and uarrays are returned with the calculated
uncertainties. If true ndarrays are returned without uncertainties.
Returns
-------
A : ndarray, shape(4,4)
The state matrix.
B : ndarray, shape(4,2)
The input matrix.
Notes
-----
``A`` and ``B`` describe the Whipple model in state space form:
x' = A * x + B * u
where
The states are [roll angle,
steer angle,
roll rate,
steer rate]
The inputs are [roll torque,
steer torque]
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
"""
M, C1, K0, K2 = self.canonical()
g = self.parameters['Benchmark']['g']
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, g)
if nominal is True:
return (unumpy.nominal_values(A), unumpy.nominal_values(B))
elif nominal is False:
return A, B
else:
raise ValueError('nominal must be True or False')
def state_space(self, speed, nominal=False):
"""
Returns the A and B matrices for the Whipple model linearized about
the upright constant velocity configuration.
Parameters
----------
speed : float
The speed of the bicycle.
nominal : boolean, optional
The default is false and uarrays are returned with the calculated
uncertainties. If true ndarrays are returned without uncertainties.
Returns
-------
A : ndarray, shape(4,4)
The state matrix.
B : ndarray, shape(4,2)
The input matrix.
Notes
-----
``A`` and ``B`` describe the Whipple model in state space form:
x' = A * x + B * u
where
The states are [roll angle,
steer angle,
roll rate,
steer rate]
The inputs are [roll torque,
steer torque]
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
"""
M, C1, K0, K2 = self.canonical()
g = self.parameters['Benchmark']['g']
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, g)
if nominal is True:
return (unumpy.nominal_values(A), unumpy.nominal_values(B))
elif nominal is False:
return A, B
else:
raise ValueError('nominal must be True or False')
def eig(self, speeds):
'''Returns the eigenvalues and eigenvectors of the Whipple bicycle
model linearized about the nominal configuration.
Parameters
----------
speeds : ndarray, shape (n,) or float
The speed at which to calculate the eigenvalues.
Returns
-------
evals : ndarray, shape (n, 4)
eigenvalues
evecs : ndarray, shape (n, 4, 4)
eigenvectors
Notes
-----
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
'''
# this allows you to enter a float
try:
speeds.shape
except AttributeError:
speeds = np.array([speeds])
par = io.remove_uncertainties(self.parameters['Benchmark'])
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
m, n = 4, speeds.shape[0]
evals = np.zeros((n, m), dtype='complex128')
evecs = np.zeros((n, m, m), dtype='complex128')
for i, speed in enumerate(speeds):
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, par['g'])
w, v = np.linalg.eig(A)
evals[i] = w
evecs[i] = v
return evals, evecs
def eig(self, speeds):
'''Returns the eigenvalues and eigenvectors of the Whipple bicycle
model linearized about the nominal configuration.
Parameters
----------
speeds : ndarray, shape (n,) or float
The speed at which to calculate the eigenvalues.
Returns
-------
evals : ndarray, shape (n, 4)
eigenvalues
evecs : ndarray, shape (n, 4, 4)
eigenvectors
Notes
-----
If you have a flywheel defined, body D, it will completely be ignored
in these results. These results are strictly for the Whipple bicycle
model.
'''
# this allows you to enter a float
try:
speeds.shape
except AttributeError:
speeds = np.array([speeds])
par = io.remove_uncertainties(self.parameters['Benchmark'])
M, C1, K0, K2 = bicycle.benchmark_par_to_canonical(par)
m, n = 4, speeds.shape[0]
evals = np.zeros((n, m), dtype='complex128')
evecs = np.zeros((n, m, m), dtype='complex128')
for i, speed in enumerate(speeds):
A, B = bicycle.ab_matrix(M, C1, K0, K2, speed, par['g'])
w, v = np.linalg.eig(A)
evals[i] = w
evecs[i] = v
return evals, evecs