def test_1dof_nonlinear_system(self):
s = System()
j = PrismaticJoint('joint', [0, 0, 1])
k = 0.45 # quadratic stiffness coefficient
j.internal_force = lambda el, t: -k * el.xstrain[0]**2
b = RigidBody('body', 10)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
# Linearise around z0 = 0: stiffness should be zero
linsys = LinearisedSystem.from_system(s, z0=0)
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[0.0]])
# Linearise about z0 = 2: stiffness should be 2kx
linsys = LinearisedSystem.from_system(s, z0=[2])
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[2 * k * 2]])
# Test setting z0 in another way
linsys = LinearisedSystem.from_system(s, z0={'joint': [4.2]})
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[2 * k * 4.2]])
def test_1dof_nonlinear_system(self):
s = System()
j = PrismaticJoint('joint', [0, 0, 1])
k = 0.45 # quadratic stiffness coefficient
j.internal_force = lambda el, t: -k * el.xstrain[0]**2
b = RigidBody('body', 10)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
# Linearise around z0 = 0: stiffness should be zero
linsys = LinearisedSystem.from_system(s, z0=0)
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[0.0]])
# Linearise about z0 = 2: stiffness should be 2kx
linsys = LinearisedSystem.from_system(s, z0=[2])
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[2 * k * 2]])
# Test setting z0 in another way
linsys = LinearisedSystem.from_system(s, z0={'joint': [4.2]})
assert_aae(linsys.M, [[10.0]])
assert_aae(linsys.C, [[0.0]])
assert_aae(linsys.K, [[2 * k * 4.2]])
def test_1dof_linear_system(self):
s = System()
j = PrismaticJoint('joint', [0, 0, 1])
j.stiffness = 5.0
j.damping = 2.3
b = RigidBody('body', 10)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
linsys = LinearisedSystem.from_system(s)
assert_array_equal(linsys.M, [[10.0]])
assert_array_equal(linsys.C, [[2.3]])
assert_array_equal(linsys.K, [[5.0]])
def test_1dof_linear_system(self):
s = System()
j = PrismaticJoint('joint', [0, 0, 1])
j.stiffness = 5.0
j.damping = 2.3
b = RigidBody('body', 10)
s.add_leaf(j)
j.add_leaf(b)
s.setup()
linsys = LinearisedSystem.from_system(s)
assert_array_equal(linsys.M, [[10.0]])
assert_array_equal(linsys.C, [[2.3]])
assert_array_equal(linsys.K, [[5.0]])
def linearised_system(self, z0=None, zd0=None, mbc=False, perturbation=None):
# Linearise the system about the given operating point
self.system.update_kinematics()
linsys = LinearisedSystem.from_system(self.system, z0=z0, zd0=zd0, perturbation=perturbation)
# Apply multi-blade coordinate transform if needed
if mbc:
iazimuth = self.system.free_dof_indices("shaft")[0]
iblades = [self.system.free_dof_indices("blade{}".format(i + 1)) for i in range(3)]
if mbc == 2:
linsys = linsys.multiblade_transform2(iazimuth, iblades)
else:
linsys = linsys.multiblade_transform(iazimuth, iblades)
return linsys
def linearised_system(self, z0=None, zd0=None, mbc=False,
perturbation=None):
# Linearise the system about the given operating point
self.system.update_kinematics()
linsys = LinearisedSystem.from_system(self.system, z0=z0, zd0=zd0,
perturbation=perturbation)
# Apply multi-blade coordinate transform if needed
if mbc:
iazimuth = self.system.free_dof_indices('shaft')[0]
iblades = [self.system.free_dof_indices('blade{}'.format(i+1))
for i in range(3)]
if mbc == 2:
linsys = linsys.multiblade_transform2(iazimuth, iblades)
else:
linsys = linsys.multiblade_transform(iazimuth, iblades)
return linsys
def structure(rigid_body_configs):
system = build_structure(rigid_body_configs)
system.update_kinematics()
linsys = LinearisedSystem.from_system(system)
return LinearSystem(linsys.M, linsys.C, linsys.K)
def structure(rigid_body_configs):
system = build_structure(rigid_body_configs)
system.update_kinematics()
linsys = LinearisedSystem.from_system(system)
return LinearSystem(linsys.M, linsys.C, linsys.K)
