def __init__(
self,
parent,
gravity=-9.81,
gamma=0.7,
initial_velocity=None,
initial_position=None,
):
Block.__init__(self, parent)
self.position = State(
self,
shape=2,
derivative_function=self.position_derivative,
initial_condition=initial_position,
)
self.velocity = State(
self,
shape=2,
derivative_function=self.velocity_derivative,
initial_condition=initial_velocity,
)
self.ground = ZeroCrossEventSource(self,
event_function=self.ground_event,
direction=-1)
self.ground.register_listener(self.on_ground_event)
self.gravity = gravity
self.gamma = gamma
def __init__(
self,
parent,
motor_constant,
resistance,
inductance,
moment_of_inertia,
initial_omega=0,
initial_current=0,
):
Block.__init__(self, parent)
self.motor_constant = motor_constant
self.resistance = resistance
self.inductance = inductance
self.moment_of_inertia = moment_of_inertia
self.voltage = Port()
self.external_torque = Port()
self.omega = State(
self,
derivative_function=self.omega_dot,
initial_condition=initial_omega,
)
self.current = State(
self,
derivative_function=self.current_dot,
initial_condition=initial_current,
)
def test_multi_time_system_state():
"""Test the system state with multiple time instances"""
system = System()
state_1 = State(owner=system)
state_2 = State(owner=system, shape=2)
input_1 = InputSignal(owner=system)
input_2 = InputSignal(owner=system, shape=2)
times = np.r_[0.0, 1.0, 2.0]
states = np.empty(shape=(system.num_states, times.shape[0]))
inputs = np.empty(shape=(system.num_inputs, times.shape[0]))
states[state_1.state_slice] = (1.0, 2.0, 3.0)
states[state_2.state_slice] = ((1.0, 2.0, 3.0), (4.0, 5.0, 6.0))
inputs[input_1.input_slice] = (1.0, 2.0, 3.0)
inputs[input_2.input_slice] = ((1.0, 2.0, 3.0), (4.0, 5.0, 6.0))
system_state = SystemState(system=system,
time=times,
state=states,
inputs=inputs)
npt.assert_equal(system_state[state_1], (1.0, 2.0, 3.0))
npt.assert_equal(system_state[state_2], ((1.0, 2.0, 3.0), (4.0, 5.0, 6.0)))
npt.assert_equal(system_state[input_1], (1.0, 2.0, 3.0))
npt.assert_equal(system_state[input_2], ((1.0, 2.0, 3.0), (4.0, 5.0, 6.0)))
def pendulum(length=1):
"""Create a steady-state model for a pendulum"""
system = System()
g = 9.81 # Gravity
def omega_dt(data):
"""Calculate the acceleration of the pendulum"""
return np.sin(phi(data)) * g / length
def phi_dt(data):
"""Calculate the velocity of the pendulum"""
return omega(data)
omega = State(system, derivative_function=omega_dt)
phi = State(system, derivative_function=phi_dt)
# Set up a steady-state configuration
config = SteadyStateConfiguration(system)
# Minimize the total energy
config.objective = lambda data: (g * length * (1 - np.cos(phi(data))) +
(length * omega(data))**2)
# Constrain the angular velocity (no steady state)
config.states[omega].steady_state = False
# Constrain the angle
config.states[phi].steady_state = False
config.states[phi].lower_bounds = -np.pi
config.states[phi].upper_bounds = np.pi
return config
def __init__(
self,
parent,
motor_constant,
resistance,
inductance,
moment_of_inertia,
initial_speed=None,
initial_current=None,
):
Block.__init__(self, parent)
self.motor_constant = motor_constant
self.resistance = resistance
self.inductance = inductance
self.moment_of_inertia = moment_of_inertia
# Create the velocity and current state
# These can also be used as signals which export the exact value of
# the respective state.
self.omega = State(
self,
derivative_function=self.omega_dt,
initial_condition=initial_speed,
)
self.current = State(
self,
derivative_function=self.current_dt,
initial_condition=initial_current,
)
# Create (input) ports for voltage and external torque load
self.voltage = Port()
self.external_torque = Port()
def test_system():
"""Test the ``System`` class"""
system = System()
state_a = State(
system,
shape=(3, 3),
initial_condition=[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
derivative_function=None,
)
state_b = State(
system,
shape=3,
initial_condition=[10, 11, 12],
derivative_function=None,
)
input_c = InputSignal(system, value=1)
input_d = InputSignal(system, shape=2, value=[2, 3])
event_a = ZeroCrossEventSource(system, event_function=None)
event_b = ZeroCrossEventSource(system, event_function=None)
# Check the counts
assert system.num_inputs == input_c.size + input_d.size
assert system.num_states == state_a.size + state_b.size
assert system.num_events == 2
# Check the initial condition
# This also checks that state indices are disjoint.
initial_condition = system.initial_condition
npt.assert_almost_equal(
initial_condition[state_a.state_slice],
state_a.initial_condition.ravel(),
)
npt.assert_almost_equal(
initial_condition[state_b.state_slice],
state_b.initial_condition.ravel(),
)
# Check the initial inputs
# This also checks that input indices are disjoint.
initial_input = system.initial_input
npt.assert_almost_equal(initial_input[input_c.input_slice],
np.atleast_1d(input_c.value).ravel())
npt.assert_almost_equal(initial_input[input_d.input_slice],
np.atleast_1d(input_d.value).ravel())
# Check that event indices are disjoint
assert event_a.event_index != event_b.event_index
def test_state_access():
"""Test whether calling a ``State`` object calls the ``get_state_value`` and
``set_state_value`` methods of the provider object"""
system = System()
state = State(system)
provider = Mock()
# Check read access
state(provider)
provider.get_state_value.assert_called_with(state)
# Check write access
provider.reset_mock()
state.set_value(provider, 10)
provider.set_state_value.assert_called_with(state, 10)
def test_system_state_dictionary_access():
"""Test the deprecated dictionary access for system states"""
system = System()
state_a = State(system, initial_condition=10)
state_b = State(system, shape=2, initial_condition=[11, 12])
state_c = State(system,
shape=(2, 2),
initial_condition=[[13, 14], [15, 16]])
system_state = SystemState(time=0, system=system)
npt.assert_equal(system_state[state_a], state_a(system_state))
npt.assert_equal(system_state[state_b], state_b(system_state))
npt.assert_equal(system_state[state_b, 0], state_b(system_state)[0])
npt.assert_equal(system_state[state_b, 1], state_b(system_state)[1])
npt.assert_equal(system_state[state_c, 0, 0], state_c(system_state)[0, 0])
def __init__(
self,
owner,
mass,
moment_of_inertia,
initial_velocity_earth=None,
initial_position_earth=None,
initial_transformation=None,
initial_angular_rates_earth=None,
):
Block.__init__(self, owner)
self.mass = mass
self.moment_of_inertia = moment_of_inertia
self.forces_body = Port(shape=3)
self.moments_body = Port(shape=3)
if initial_transformation is None:
initial_transformation = np.eye(3)
self.velocity_earth = State(
self,
shape=3,
derivative_function=self.velocity_earth_dot,
initial_condition=initial_velocity_earth,
)
self.position_earth = State(
self,
shape=3,
derivative_function=self.position_earth_dot,
initial_condition=initial_position_earth,
)
self.omega_earth = State(
self,
shape=3,
derivative_function=self.omega_earth_dot,
initial_condition=initial_angular_rates_earth,
)
self.dcm = State(
self,
shape=(3, 3),
derivative_function=self.dcm_dot,
initial_condition=initial_transformation,
)
def test_state_constraint_access():
"""Test access to state constraint properties"""
system = System()
state_1 = State(system)
state_2 = State(system)
config = SteadyStateConfiguration(system)
config.states[state_1].lower_bounds = 10
config.states[state_2].lower_bounds = 20
config.states[state_1].upper_bounds = 15
config.states[state_2].upper_bounds = 25
config.states[state_2].steady_state = False
config.states[state_1].initial_condition = 100
npt.assert_equal(config.states[state_1].lower_bounds, 10)
npt.assert_equal(config.states[state_2].lower_bounds, 20)
npt.assert_equal(config.states[state_1].upper_bounds, 15)
npt.assert_equal(config.states[state_2].upper_bounds, 25)
assert not config.states[state_2].steady_state
npt.assert_equal(config.states[state_1].initial_condition, 100)
def test_simulation_result_dictionary_access():
"""Test the deprecated dictionary access for simulation results"""
system = System()
state_a = State(system, initial_condition=10)
state_b = State(system, shape=2, initial_condition=[11, 12])
state_c = State(system,
shape=(2, 2),
initial_condition=[[13, 14], [15, 16]])
system_state = SystemState(time=0, system=system)
result = SimulationResult(system)
result.append(system_state)
npt.assert_equal(result[state_a], state_a(result))
npt.assert_equal(result[state_b], state_b(result))
npt.assert_equal(result[state_b, 0], state_b(result)[0])
npt.assert_equal(result[state_b, 1], state_b(result)[1])
npt.assert_equal(result[state_c, 0, 0], state_c(result)[0, 0])
def __init__(self, owner, shape=1, initial_condition=None):
"""
Constructor for ``ZeroOrderHold``
Args:
owner: The owner of the block (system or block)
shape: The shape of the input and output signal
initial_condition: The initial state of the sampling output
(before the first tick of the block)
"""
Block.__init__(self, owner)
self.event_input = EventPort(self)
self.event_input.register_listener(self.update_state)
self.input = Port(shape=shape)
self.output = State(
self,
shape=shape,
initial_condition=initial_condition,
derivative_function=None,
)
class ZeroOrderHold(Block):
"""A zero-order-hold block which samples an input signal when the connected
event occurs.
The block provides an event port ``event_input`` that should be connected
to the event source that shall trigger the sampling.
"""
def __init__(self, owner, shape=1, initial_condition=None):
"""
Constructor for ``ZeroOrderHold``
Args:
owner: The owner of the block (system or block)
shape: The shape of the input and output signal
initial_condition: The initial state of the sampling output
(before the first tick of the block)
"""
Block.__init__(self, owner)
self.event_input = EventPort(self)
self.event_input.register_listener(self.update_state)
self.input = Port(shape=shape)
self.output = State(
self,
shape=shape,
initial_condition=initial_condition,
derivative_function=None,
)
def update_state(self, data):
"""Update the state on a clock event
Args:
data: The time, states and signals of the system
"""
self.output.set_value(data, self.input(data))
def test_state():
"""Test the ``State`` class"""
system = System()
state_a = State(system, derivative_function=(lambda data: 0))
state_b = State(system,
shape=3,
derivative_function=(lambda data: np.zeros(3)))
state_c = State(system,
shape=(3, 3),
derivative_function=(lambda data: np.zeros(3, 3)))
state_d = State(system,
derivative_function=(lambda data: 0),
initial_condition=1)
# Check the sizes
assert state_a.size == 1
assert state_b.size == 3
assert state_c.size == 9
assert state_d.size == 1
# Test the slice property
assert state_c.state_slice == slice(state_c.state_index,
state_c.state_index + state_c.size)
def water_tank_model(
inflow_area=0.01,
outflow_area=0.02,
tank_area=0.2,
target_height=5,
initial_condition=None,
initial_guess=None,
max_inflow_velocity=None,
):
"""Create a steady-state configuration for a water tank"""
g = 9.81 # Gravity
# Create a new system
system = System()
# Model the inflow
inflow_velocity = InputSignal(system)
# Model the height state
def height_derivative(data):
"""Calculate the time derivative of the height"""
return (inflow_area * inflow_velocity(data) -
outflow_area * np.sqrt(2 * g * height_state(data))) / tank_area
height_state = State(system, derivative_function=height_derivative)
# Set up the steady-state configuration
config = SteadyStateConfiguration(system)
# Enforce the inflow to be non-negative
config.inputs[inflow_velocity].lower_bounds = 0
if max_inflow_velocity is not None:
config.inputs[inflow_velocity].upper_bounds = max_inflow_velocity
# Define the target height
config.states[height_state].lower_bounds = target_height
config.states[height_state].upper_bounds = target_height
if initial_condition is not None:
config.states[height_state].initial_condition = initial_condition
if initial_guess is not None:
config.inputs[inflow_velocity].initial_guess = initial_guess
return config
def test_system_state_updater_dictionary_access():
"""Test the deprecated dictionary access for simulation results"""
system = System()
counter = State(system, shape=(2, 2))
clock = Clock(system, 1.0)
def _update_counter(system_state):
old_val = counter(system_state).copy()
system_state[counter] += 1
system_state[counter, 0] += 1
system_state[counter, 0, 0] += 1
new_val = counter(system_state)
npt.assert_almost_equal(old_val + [[3, 2], [1, 1]], new_val)
clock.register_listener(_update_counter)
simulator = Simulator(system, start_time=0)
for _ in simulator.run_until(time_boundary=10):
pass
def test_excessive_events_second_level():
"""Test the detection of excessive events when it is introduced by
toggling the same event over and over."""
system = System()
state = State(system,
derivative_function=(lambda data: -1),
initial_condition=5)
event = ZeroCrossEventSource(system, event_function=state)
def event_handler(data):
"""Event handler for the zero-crossing event"""
state.set_value(data, -state(data))
event.register_listener(event_handler)
simulator = Simulator(system, start_time=0)
with pytest.raises(ExcessiveEventError):
for _ in simulator.run_until(6):
pass
def test_discrete_only():
"""Test a system with only discrete-time states."""
system = System()
clock = Clock(system, period=1.0)
counter = State(system)
def increase_counter(data):
"""Increase the counter whenever a clock event occurs"""
counter.set_value(data, counter(data) + 1)
clock.register_listener(increase_counter)
simulator = Simulator(system, start_time=0.0)
result = SimulationResult(system)
result.collect_from(simulator.run_until(5.5, include_last=False))
result.collect_from(simulator.run_until(10))
npt.assert_almost_equal(result.time,
[0, 1, 2, 3, 4, 5, 5.5, 6, 7, 8, 9, 10])
npt.assert_almost_equal(counter(result),
[1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11])
def integrator(owner, input_signal, initial_condition=None):
"""
Create a state that provides the integrated value of the input
callable.
The resulting signal will have the same shape as the input callable.
Args:
owner: The owner of the integrator
input_signal: A callable accepting an object implementing the system
object access protocol and providing the value of the derivative
initial_condition: The initial condition of the integrator
(default: ``None``)
Returns:
A state that provides the integrated value of the input signal
"""
return State(
owner,
shape=input_signal.shape,
derivative_function=input_signal,
initial_condition=initial_condition,
)
# Create the system
system = System()
# Define the derivatives
def velocity_dt(system_state):
"""Calculate the derivative of the velocity"""
pos = position(system_state)
distance = linalg.norm(pos, axis=0)
return -G * SUN_MASS / (distance**3) * pos
# Create the states
velocity = State(
owner=system,
shape=2,
derivative_function=velocity_dt,
initial_condition=V_0,
)
position = State(owner=system,
shape=2,
derivative_function=velocity,
initial_condition=X_0)
# Run a simulation
simulator = Simulator(system, start_time=0.0, max_step=24 * 60 * 60)
result = SimulationResult(system,
simulator.run_until(time_boundary=ROTATION_TIME))
# Plot the result
trajectory = position(result)
plt.plot(trajectory[0], trajectory[1])
def test_system_state():
"""Test the ``SystemState`` class"""
system = System()
input_a = InputSignal(system, shape=(3, 3), value=np.eye(3))
input_c = InputSignal(system, value=1)
input_d = InputSignal(system, shape=2, value=[2, 3])
state_a = State(
system,
shape=(3, 3),
initial_condition=[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
derivative_function=input_a,
)
state_a_dep = State(
system,
shape=(3, 3),
initial_condition=[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
derivative_function=input_a,
)
state_b = State(
system,
shape=3,
initial_condition=[10, 11, 12],
derivative_function=(lambda data: np.r_[13, 14, 15]),
)
state_b1 = State(system, shape=3, derivative_function=state_b)
state_b2 = State(system, shape=3, derivative_function=None)
signal_c = constant(value=16)
event_a = ZeroCrossEventSource(system, event_function=(lambda data: 23))
system_state = SystemState(time=0, system=system)
# Check the initial state
npt.assert_almost_equal(
system_state.state[state_a.state_slice],
state_a.initial_condition.ravel(),
)
npt.assert_almost_equal(
system_state.state[state_a_dep.state_slice],
state_a_dep.initial_condition.ravel(),
)
npt.assert_almost_equal(
system_state.state[state_b.state_slice],
state_b.initial_condition.ravel(),
)
npt.assert_almost_equal(
system_state.state[state_b1.state_slice],
state_b1.initial_condition.ravel(),
)
npt.assert_almost_equal(system_state.state[state_b2.state_slice],
np.zeros(state_b2.size))
# Check the inputs property
npt.assert_almost_equal(system_state.inputs[input_a.input_slice],
np.ravel(input_a.value))
npt.assert_almost_equal(system_state.inputs[input_c.input_slice],
np.ravel(input_c.value))
npt.assert_almost_equal(system_state.inputs[input_d.input_slice],
np.ravel(input_d.value))
# Check the get_state_value function
npt.assert_almost_equal(system_state.get_state_value(state_a),
state_a.initial_condition)
npt.assert_almost_equal(system_state.get_state_value(state_a_dep),
state_a_dep.initial_condition)
npt.assert_almost_equal(system_state.get_state_value(state_b),
state_b.initial_condition)
# Check the function access
npt.assert_equal(event_a(system_state),
event_a.event_function(system_state))
npt.assert_equal(state_a(system_state), state_a.initial_condition)
npt.assert_equal(input_a(system_state), input_a.value)
npt.assert_equal(signal_c(system_state), signal_c.value)
moment_of_inertia=MOMENT_OF_INERTIA,
thrust_coefficient=THRUST_COEFFICIENT,
power_coefficient=POWER_COEFFICIENT,
diameter=DIAMETER,
)
# Provide constant signals for the voltage and the air density
voltage = constant(value=3.5)
density = constant(value=1.29)
# Connect them to the corresponding inputs of the engine
engine.voltage.connect(voltage)
engine.density.connect(density)
# Set up the state for keeping the sampled value.
sample_state = State(system)
# Create a clock for sampling at 100Hz
sample_clock = Clock(system, period=0.01)
# Define the function for updating the state
def update_sample(system_state):
"""Update the state of the sampler"""
sample_state.set_value(system_state, engine.thrust(system_state))
# Register it as event handler on the clock
sample_clock.register_listener(update_sample)
# Create the simulator and run it
from matplotlib import pyplot as plt
from modypy.model import State, System, signal_function
from modypy.simulation import SimulationResult, Simulator
# Create a new system
system = System()
# Define the cosine signal
@signal_function
def cosine_input(system_state):
"""Calculate the value of the input signal"""
return np.cos(system_state.time)
integrator_state = State(system, derivative_function=cosine_input)
# Set up a simulation
simulator = Simulator(system, start_time=0.0, max_step=0.1)
# Run the simulation for 10s and capture the result
result = SimulationResult(system, simulator.run_until(time_boundary=10.0))
# Plot the result
input_line, integrator_line = plt.plot(
result.time,
cosine_input(result),
"r",
result.time,
integrator_state(result),
"g",
# Create a new system
system = System()
# Model the inflow
inflow_velocity = InputSignal(system)
# Model the height state
def height_derivative(data):
"""Calculate the time derivative of the height"""
return (A1 * inflow_velocity(data) -
A2 * np.sqrt(2 * G * height_state(data))) / At
height_state = State(system, derivative_function=height_derivative)
# Configure for steady-state determination
steady_state_config = SteadyStateConfiguration(system)
# Enforce the height to equal the target height
steady_state_config.states[height_state].lower_bounds = TARGET_HEIGHT
steady_state_config.states[height_state].upper_bounds = TARGET_HEIGHT
# Enforce the inflow to be non-negative
steady_state_config.inputs[inflow_velocity].lower_bounds = 0
# Find the steady state
result = find_steady_state(steady_state_config)
print("Target height: %f" % TARGET_HEIGHT)
print("Steady state height: %f" % height_state(result.system_state))
print("Steady state inflow: %f" % inflow_velocity(result.system_state))
print("Steady state height derivative: %f" %
def __init__(
self,
parent,
system_matrix,
input_matrix,
output_matrix,
feed_through_matrix,
initial_condition=None,
):
Block.__init__(self, parent)
# Determine the number of states and the shape of the state
if np.isscalar(system_matrix):
self.state_shape = ()
num_states = 1
else:
system_matrix = np.asarray(system_matrix)
if (system_matrix.ndim == 2 and system_matrix.shape[0] > 0
and system_matrix.shape[0] == system_matrix.shape[1]):
self.state_shape = system_matrix.shape[0]
num_states = self.state_shape
else:
raise InvalidLTIException("The system matrix must be a scalar "
"or a non-empty square matrix")
# Determine the number of inputs and the shape of the input signal
if np.isscalar(input_matrix):
if num_states > 1:
raise InvalidLTIException("There is more than one state, but "
"the input matrix is neither empty, "
"nor a vector or a matrix")
num_inputs = 1
self.input_shape = ()
else:
input_matrix = np.asarray(input_matrix)
if input_matrix.ndim == 1:
# The input matrix is a column vector => one input
if num_states != input_matrix.shape[0]:
raise InvalidLTIException(
"The height of the input matrix "
"must match the number of states")
num_inputs = 1
elif input_matrix.ndim == 2:
# The input matrix is a matrix
if num_states != input_matrix.shape[0]:
raise InvalidLTIException("The height of the input matrix "
"does not match the number of "
"states")
num_inputs = input_matrix.shape[1]
else:
raise InvalidLTIException("The input matrix must be empty,"
"a scalar, a vector or a matrix")
self.input_shape = num_inputs
# Determine the number of outputs and the shape of the output array
if np.isscalar(output_matrix):
if num_states > 1:
raise InvalidLTIException("There is more than one state, but "
"the output matrix is neither an "
"empty, a vector nor a matrix")
num_outputs = 1
self.output_shape = ()
else:
output_matrix = np.asarray(output_matrix)
if output_matrix.ndim == 1:
# The output matrix is a row vector => one output
if num_states != output_matrix.shape[0]:
raise InvalidLTIException("The width of the output matrix "
"does not match the number of "
"states")
num_outputs = 1
elif output_matrix.ndim == 2:
# The output matrix is a matrix
if num_states != output_matrix.shape[1]:
raise InvalidLTIException("The width of the output matrix "
"does not match the number of "
"states")
num_outputs = output_matrix.shape[0]
else:
raise InvalidLTIException("The output matrix must be empty, a"
"scalar, a vector or a matrix")
self.output_shape = num_outputs
if np.isscalar(feed_through_matrix):
if not (num_inputs == 1 and num_outputs == 1):
raise InvalidLTIException("A scalar feed-through matrix is "
"only allowed for systems with "
"exactly one input and one output")
else:
feed_through_matrix = np.asarray(feed_through_matrix)
if feed_through_matrix.ndim == 1:
# A vector feed_through_matrix is interpreted as row vector,
# so there must be exactly one output.
if num_outputs == 0:
raise InvalidLTIException("The feed-through matrix for a "
"system without outputs must be"
"empty")
elif num_outputs > 1:
raise InvalidLTIException("The feed-through matrix for a "
"system with more than one "
"output must be a matrix")
if feed_through_matrix.shape[0] != num_inputs:
raise InvalidLTIException(
"The width of the feed-through "
"matrix must match the number of "
"inputs")
elif feed_through_matrix.ndim == 2:
if feed_through_matrix.shape[0] != num_outputs:
raise InvalidLTIException(
"The height of the feed-through "
"matrix must match the number of "
"outputs")
if feed_through_matrix.shape[1] != num_inputs:
raise InvalidLTIException(
"The width of the feed-through "
"matrix must match the number of "
"inputs")
else:
raise InvalidLTIException("The feed-through matrix must be "
"empty, a scalar, a vector or a "
"matrix")
self.system_matrix = system_matrix
self.input_matrix = input_matrix
self.output_matrix = output_matrix
self.feed_through_matrix = feed_through_matrix
self.input = Port(shape=self.input_shape)
self.state = State(
self,
shape=self.state_shape,
derivative_function=self.state_derivative,
initial_condition=initial_condition,
)
self.output = Signal(shape=self.output_shape,
value=self.output_function)
# The initial conditions
INITIAL_HEIGHT = 10.0
INITIAL_VELOCITY = 0.0
# The system
system = System()
# The system states
def velocity_dt(_system_state):
"""Calculate the derivative of the vertical speed"""
return -G
velocity = State(system,
derivative_function=velocity_dt,
initial_condition=INITIAL_VELOCITY)
height = integrator(system,
input_signal=velocity,
initial_condition=INITIAL_HEIGHT)
# Run a simulation without event handler
simulator = Simulator(system=system, start_time=0, max_step=0.1)
result = SimulationResult(system=system)
result.collect_from(simulator.run_until(time_boundary=2))
# Plot the simulation result
plt.plot(result.time, height(result))
plt.xlabel("Time (s)")
plt.ylabel("Height (m)")
plt.title("Falling Ball")
def propeller_model(
thrust_coefficient=0.09,
power_coefficient=0.04,
density=1.29,
diameter=8 * 25.4e-3,
moment_of_inertia=5.284e-6,
target_thrust=1.5 * 9.81 / 4,
maximum_torque=None,
):
"""Create a steady-state configuration for two propellers"""
system = System()
torque_1 = InputSignal(system)
torque_2 = InputSignal(system)
density_signal = constant(density)
propeller_1 = Propeller(
system,
thrust_coefficient=thrust_coefficient,
power_coefficient=power_coefficient,
diameter=diameter,
)
propeller_2 = Propeller(
system,
thrust_coefficient=thrust_coefficient,
power_coefficient=power_coefficient,
diameter=diameter,
)
def speed_1_dt(data):
"""Derivative of the speed of the first propeller"""
tot_torque = torque_1(data) - propeller_1.torque(data)
return tot_torque / (2 * np.pi * moment_of_inertia)
def speed_2_dt(data):
"""Derivative of the speed of the second propeller"""
tot_torque = torque_2(data) - propeller_2.torque(data)
return tot_torque / (2 * np.pi * moment_of_inertia)
speed_1 = State(system, derivative_function=speed_1_dt)
speed_2 = State(system, derivative_function=speed_2_dt)
propeller_1.density.connect(density_signal)
propeller_2.density.connect(density_signal)
propeller_1.speed_rps.connect(speed_1)
propeller_2.speed_rps.connect(speed_2)
total_thrust = sum_signal((propeller_1.thrust, propeller_2.thrust))
total_power = sum_signal((propeller_1.power, propeller_2.power))
# Set up steady-state configuration
config = SteadyStateConfiguration(system)
# Minimize the total power
config.objective = total_power
# Constrain the speed to be positive
config.states[speed_1].lower_bounds = 0
config.states[speed_2].lower_bounds = 0
# Constrain the torques to be positive
config.inputs[torque_1].lower_bounds = 0
config.inputs[torque_2].lower_bounds = 0
npt.assert_equal(config.inputs[torque_1].lower_bounds, 0)
npt.assert_equal(config.inputs[torque_2].lower_bounds, 0)
if maximum_torque is not None:
config.inputs[torque_1].upper_bounds = maximum_torque
config.inputs[torque_2].upper_bounds = maximum_torque
# Constrain the total thrust
config.ports[total_thrust].lower_bounds = target_thrust
config.ports[total_thrust].upper_bounds = target_thrust
return config