def side_force_coeff_test_cases():
constants = SkywalkerX8Constants()
b = constants.wing_span
state1 = State()
state1.vx = 20.0
state1.vy = 0.0
state1.vz = 0.0
state2 = State()
state2.vx = 28.6362532829
state2.vy = 1.0
state2.vz = 0.0
state2.ang_rate_x = 5 * np.pi / 180
state2.ang_rate_z = 5 * np.pi / 180
wind = np.zeros(6)
airspeed = np.sqrt(np.sum(calc_airspeed(state2, wind)**2))
zero_input = ControlInput()
aileron_input = ControlInput()
aileron_input.aileron_deflection = 2.0 * np.pi / 180.0
return [
(state1, wind, 0.0, zero_input, 2.99968641720902E-08),
(state1, wind, 1.0, zero_input, -7.94977329537982E-06),
(state2, wind, 0.0, aileron_input,
-0.008604744865183 + -0.085 * b / (2 * airspeed) * state2.ang_rate_x +
0.005 * b / (2 * airspeed) * state2.ang_rate_z +
0.0433 * aileron_input.aileron_deflection),
(state2, wind, 1.0, aileron_input,
-0.007089388672593 + -0.133 * b / (2 * airspeed) * state2.ang_rate_x +
0.002 * b / (2 * airspeed) * state2.ang_rate_z +
0.0433 * aileron_input.aileron_deflection)
]
def yaw_moment_coeff_test_cases():
constants = SkywalkerX8Constants()
b = constants.wing_span
state1 = State()
state1.vx = 20.0
state1.vy = 0.0
state1.vz = 0.0
state2 = State()
state2.vx = 28.6362532829
state2.vy = 1.0
state2.vz = 0.0
state2.ang_rate_x = 5 * np.pi / 180
state2.ang_rate_z = 5 * np.pi / 180
wind = np.zeros(6)
airspeed = np.sqrt(np.sum(calc_airspeed(state2, wind)**2))
zero_input = ControlInput()
aileron_input = ControlInput()
aileron_input.aileron_deflection = 2.0 * np.pi / 180.0
return [
(state1, wind, 0.0, zero_input, 4.9176697574439E-06),
(state1, wind, 1.0, zero_input, 1.96093394589053E-05),
(state2, wind, 0.0, aileron_input,
0.000825947539055 + 0.027 * b / (2 * airspeed) * state2.ang_rate_x +
-0.022 * b / (2 * airspeed) * state2.ang_rate_z -
0.00339 * aileron_input.aileron_deflection),
(state2, wind, 1.0, aileron_input,
0.001052911121301 + 0.017 * b / (2 * airspeed) * state2.ang_rate_x +
-0.049 * b / (2 * airspeed) * state2.ang_rate_z -
0.00339 * aileron_input.aileron_deflection)
]
def roll_moment_coeff_test_cases():
constants = SkywalkerX8Constants()
b = constants.wing_span
state1 = State()
state1.vx = 20.0
state1.vy = 0.0
state1.vz = 0.0
state2 = State()
state2.vx = 28.6362532829
state2.vy = 1.0
state2.vz = 0.0
state2.ang_rate_x = 5 * np.pi / 180
state2.ang_rate_z = 5 * np.pi / 180
wind = np.zeros(6)
airspeed = np.sqrt(np.sum(calc_airspeed(state2, wind)**2))
zero_input = ControlInput()
aileron_input = ControlInput()
aileron_input.aileron_deflection = 2.0 * np.pi / 180.0
return [
(state1, wind, 0.0, zero_input, -8.40821757613653E-05),
(state1, wind, 1.0, zero_input, -7.34515369827804E-05),
(state2, wind, 0.0, aileron_input,
-0.00380800071177 + -0.409 * b / (2 * airspeed) * state2.ang_rate_x +
0.039 * b / (2 * airspeed) * state2.ang_rate_z +
0.12 * aileron_input.aileron_deflection),
(state2, wind, 1.0, aileron_input,
-0.003067251004494 + -0.407 * b / (2 * airspeed) * state2.ang_rate_x +
0.158 * b / (2 * airspeed) * state2.ang_rate_z +
0.12 * aileron_input.aileron_deflection)
]
def body2wind_test_cases():
state1 = State()
vec1 = np.array([1.0, 0.0, 0.0])
wind1 = np.zeros(6)
expect1 = np.array([1.0, 0.0, 0.0])
state2 = State()
state2.vx = 10.0
vec2 = np.array([1.0, 0.0, 0.0])
wind2 = np.array([0.0, 10.0, 0.0])
expect2 = np.array([np.sqrt(2.0) / 2.0, -np.sqrt(2.0) / 2.0, 0.0])
state3 = State()
state3.vx = 10.0
vec3 = np.array([0.0, 1.0, 0.0])
wind3 = np.array([0.0, 10.0, 0.0])
expect3 = np.array([np.sqrt(2.0) / 2.0, np.sqrt(2.0) / 2.0, 0.0])
state4 = State()
state4.vx = 10.0
state4.vz = 10.0
vec4 = np.array([1.0, 0.0, 0.0])
wind4 = np.array([0.0, 0.0, 0.0])
expect4 = np.array([np.sqrt(2.0) / 2.0, 0.0, -np.sqrt(2.0) / 2.0])
return [(state1, vec1, wind1, expect1), (state2, vec2, wind2, expect2),
(state3, vec3, wind3, expect3), (state4, vec4, wind4, expect4)]
def test_skywalkerX8_force_x_dir():
control_input = ControlInput()
control_input.throttle = 0.0
t = 0
state = State()
state.vx = 20.0
for j in range(3):
state.pitch = state.pitch + 0.05
state.roll = state.roll + 0.05
state.yaw = state.yaw + 0.05
x_update = np.zeros(11)
constants = SkywalkerX8Constants()
for i in range(0, 11):
control_input.throttle = i * 0.1
prop = IcedSkywalkerX8Properties(control_input)
params = {"prop": prop, "wind": no_wind()}
update = dynamics_kinetmatics_update(t,
x=state.state,
u=control_input.control_input,
params=params)
x_update[i] = update[6]
S_p = constants.propeller_area
C_p = constants.motor_efficiency_fact
k_m = constants.motor_constant
m = constants.mass
K = 2 * m / (AIR_DENSITY * S_p * C_p * k_m**2)
for i in range(0, 10):
throttle_0 = i * 0.1
throttle_1 = (i + 1) * 0.1
assert np.allclose(K * (x_update[i + 1] - x_update[i]),
throttle_1**2 - throttle_0**2)
def test_interconnected_system():
control_input = ControlInput()
control_input.throttle = 0.5
wind_model = no_wind()
state = State()
state.vx = 20
prop = IcedSkywalkerX8Properties(control_input)
outputs = [
"x", "y", "z", "roll", "pitch", "yaw", "vx", "vy", "vz", "ang_rate_x",
"ang_rate_y", "ang_rate_z"
]
aircraft_model = build_nonlin_sys(prop, wind_model, outputs)
initial_control_input_state = ControlInput()
initial_control_input_state.throttle = 0.4
motor_time_constant = 0.001
elevon_time_constant = 0.001
actuator_model = build_flying_wing_actuator_system(elevon_time_constant,
motor_time_constant)
x0 = np.concatenate(
(initial_control_input_state.control_input, state.state))
connected_system = add_actuator(actuator_model, aircraft_model)
t = np.linspace(0.0, 0.5, 10, endpoint=True)
u = np.array([
control_input.control_input,
] * len(t)).transpose()
T, yout_without_actuator = input_output_response(aircraft_model,
t,
U=u,
X0=state.state)
T, yout_with_actuator = input_output_response(connected_system,
t,
U=u,
X0=x0)
assert np.allclose(yout_with_actuator[6, :],
yout_without_actuator[6, :],
atol=5.e-3)
assert np.allclose(yout_with_actuator[7, :],
yout_without_actuator[7, :],
atol=5.e-3)
assert np.allclose(yout_with_actuator[8, :],
yout_without_actuator[8, :],
atol=5.e-3)
assert np.allclose(yout_with_actuator[9, :],
yout_without_actuator[9, :],
atol=5.e-3)
assert np.allclose(yout_with_actuator[10, :],
yout_without_actuator[10, :],
atol=5.e-3)
assert np.allclose(yout_with_actuator[11, :],
yout_without_actuator[11, :],
atol=5.e-3)
def lift_coeff_test_cases():
constants = SkywalkerX8Constants()
c = constants.mean_chord
state1 = State()
state1.vx = 20.0
state1.vz = 0.0
state2 = State()
state2.vx = 20.0
state2.vz = 0.0
state2.ang_rate_y = 5 * np.pi / 180
wind1 = np.zeros(6)
wind2 = np.zeros(6)
wind3 = np.zeros(6)
wind2[0] = 1.0
wind2[2] = -19.0 * np.tan(8 * np.pi / 180.0)
wind3[0] = 1.0
wind3[2] = -19.0 * np.tan(8 * np.pi / 180.0)
wind3[4] = 3 * np.pi / 180
ang_rate_y2 = state2.ang_rate_y - wind3[4]
airspeed2 = np.sqrt(np.sum(calc_airspeed(state2, wind2)**2))
zero_input = ControlInput()
elevator_input = ControlInput()
elevator_input.elevator_deflection = 2.0 * np.pi / 180.0
return [(state1, wind1, 0.0, zero_input, 0.030075562375465),
(state1, wind1, 1.0, zero_input, 0.018798581619545),
(state1, wind2, 0.0, zero_input, 0.609296679062686),
(state1, wind2, 1.0, zero_input, 0.454153721254944),
(state1, wind1, 0.0, elevator_input,
0.030075562375465 + 0.278 * elevator_input.elevator_deflection),
(state1, wind1, 1.0, elevator_input,
0.018798581619545 + 0.278 * elevator_input.elevator_deflection),
(state2, wind3, 0.0, elevator_input,
0.609296679062686 + 4.60 * c / (2 * airspeed2) * ang_rate_y2 +
0.278 * elevator_input.elevator_deflection),
(state2, wind3, 1.0, elevator_input,
0.454153721254944 - 3.51 * c / (2 * airspeed2) * ang_rate_y2 +
0.278 * elevator_input.elevator_deflection)]
def main():
# Initialize gain scheduled controller
# Using two simple P-controllers, see also fcat.longitudinal_controller for more complicated examples
# Note that this is just an example on how to build and simulate an aircraft system
# The controllers are simple not tuned to get desired reference tracking
controllers = [
SaturatedStateSpaceMatricesGS(
A = -1*np.eye(1),
B = np.zeros((1,1)),
C = np.eye(1),
D = np.zeros((1,1)),
upper = 1,
lower = -1,
switch_signal = 0.3
),
SaturatedStateSpaceMatricesGS(
A = -1*np.eye(1),
B = np.zeros((1,1)),
C = np.eye(1),
D = np.zeros((1,1)),
upper = 1,
lower = -1,
switch_signal = 0.6
)
]
# Using similar controllers for simplicity
lat_gs_controller = init_gs_controller(controllers, Direction.LATERAL, 'icing')
lon_gs_controller = init_gs_controller(controllers, Direction.LONGITUDINAL, 'icing')
airspeed_pi_controller = init_airspeed_controller()
control_input = ControlInput()
control_input.throttle = 0.5
state = State()
state.vx = 20
prop = IcedSkywalkerX8Properties(control_input)
aircraft_model = build_nonlin_sys(prop, no_wind(), outputs=State.names+['icing', 'airspeed'])
motor_time_constant = 0.001
elevon_time_constant = 0.001
actuator_model = build_flying_wing_actuator_system(elevon_time_constant, motor_time_constant)
closed_loop = build_closed_loop(actuator_model, aircraft_model, lon_gs_controller, lat_gs_controller, airspeed_pi_controller)
X0 = get_init_vector(closed_loop, control_input, state)
constant_input = np.array([20, 0.04, -0.00033310605950459315])
sim_time = 15
t = np.linspace(0, sim_time, sim_time*5, endpoint=True)
u = np.array([constant_input, ]*(len(t))).transpose()
T, yout_non_lin, _ = input_output_response(
closed_loop, U=u, T=t, X0=X0, return_x=True, method='BDF')
def test_dynamics_forces():
control_input = ControlInput()
prop = SimpleTestAircraftNoMoments(control_input)
t = 0
for i in range(-50, 101, 50):
control_input.throttle = 0.8
control_input.elevator_deflection = i
control_input.aileron_deflection = i
control_input.rudder_deflection = i
state = State()
state.vx = 20.0
state.vy = 1
state.vz = 0
params = {"prop": prop, "wind": no_wind()}
update = dynamics_kinetmatics_update(t=t,
x=state.state,
u=control_input.control_input,
params=params)
V_a = np.sqrt(np.sum(calc_airspeed(state, params['wind'].get(0.0))**2))
forces_aero_wind_frame = np.array([
-np.abs(control_input.elevator_deflection),
control_input.aileron_deflection, -control_input.rudder_deflection
])
forces_aero_body_frame = wind2body(forces_aero_wind_frame, state,
params['wind'].get(0))
force_propulsion = np.array([(2 * control_input.throttle)**2 - V_a**2,
0, 0])
force_gravity = inertial2body(
np.array([0, 0, prop.mass() * GRAVITY_CONST]), state)
forces_body = forces_aero_body_frame + force_propulsion + force_gravity
vx_update_expect = (1 / prop.mass()) * forces_body[0]
vy_update_expect = (1 / prop.mass()) * forces_body[1]
vz_update_expect = (1 / prop.mass()) * forces_body[2]
# No moments
ang_rate_x_update_expect = 0
ang_rate_y_update_expect = 0
ang_rate_z_update_expect = 0
assert np.allclose(vx_update_expect, update[6])
assert np.allclose(vy_update_expect, update[7])
assert np.allclose(vz_update_expect, update[8])
assert np.allclose(ang_rate_x_update_expect, update[9])
assert np.allclose(ang_rate_y_update_expect, update[10])
assert np.allclose(ang_rate_z_update_expect, update[11])
def test_dynamics_moments():
control_input = ControlInput()
t = 0
for i in range(-50, 51, 50):
control_input.throttle = i
control_input.elevator_deflection = i
control_input.aileron_deflection = i
control_input.rudder_deflection = i
prop = SimpleTestAircraftNoForces(control_input)
state = State()
state.vx = 20.0
state.vy = 1
state.vz = 0
state.ang_rate_x = 0.157079633
state.ang_rate_y = 0.157079633
state.ang_rate_z = 0.157079633
params = {"prop": prop, "wind": no_wind()}
update = dynamics_kinetmatics_update(t=t,
x=state.state,
u=control_input.control_input,
params=params)
moments_aero = np.array([
control_input.elevator_deflection,
control_input.aileron_deflection, control_input.rudder_deflection
])
omega = np.array(
[state.ang_rate_x, state.ang_rate_y, state.ang_rate_z])
coreolis_term = prop.inv_inertia_matrix().dot(
np.cross(omega,
prop.inertia_matrix().dot(omega)))
ang_rate_x_update_expect = (2 / 3) * moments_aero[0] - (
1 / 3) * moments_aero[2] - coreolis_term[0]
ang_rate_y_update_expect = (1 / 2) * moments_aero[1] - coreolis_term[1]
ang_rate_z_update_expect = (2 / 3) * moments_aero[2] - (
1 / 3) * moments_aero[0] - coreolis_term[2]
assert np.allclose(ang_rate_x_update_expect, update[9])
assert np.allclose(ang_rate_y_update_expect, update[10])
assert np.allclose(ang_rate_z_update_expect, update[11])
def drag_coeff_test_cases():
state1 = State()
state1.vx = 20.0
state1.vz = 0.0
wind1 = np.zeros(6)
wind2 = np.zeros(6)
wind2[0] = 1.0
wind2[2] = -19.0 * np.tan(6 * np.pi / 180.0)
zero_input = ControlInput()
elevator_input = ControlInput()
elevator_input.elevator_deflection = 2.0 * np.pi / 180.0
return [(state1, wind1, 0.0, zero_input, 0.015039166436721),
(state1, wind1, 1.0, zero_input, 0.043224285541117),
(state1, wind2, 0.0, zero_input, 0.027939336576642),
(state1, wind2, 1.0, zero_input, 0.082879203470842),
(state1, wind1, 0.0, elevator_input,
0.015039166436721 + 0.0633 * elevator_input.elevator_deflection),
(state1, wind1, 1.0, elevator_input,
0.043224285541117 + 0.0633 * elevator_input.elevator_deflection)]
def pitch_moment_coeff_test_cases():
state1 = State()
state1.vx = 20.0
state1.vz = 0.0
wind1 = np.zeros(6)
wind2 = np.zeros(6)
wind2[0] = 1.0
wind2[2] = -19.0 * np.tan(6 * np.pi / 180.0)
zero_input = ControlInput()
elevator_input = ControlInput()
elevator_input.elevator_deflection = 2.0 * np.pi / 180.0
return [(state1, wind1, 0.0, zero_input, 0.001161535578433),
(state1, wind1, 1.0, zero_input, -0.004297270367523),
(state1, wind2, 0.0, zero_input, -0.064477317568596),
(state1, wind2, 1.0, zero_input, -0.01808304889307),
(state1, wind1, 0.0, elevator_input,
0.001161535578433 - 0.206 * elevator_input.elevator_deflection),
(state1, wind1, 1.0, elevator_input,
-0.004297270367523 - 0.206 * elevator_input.elevator_deflection)]
def test_kinematics():
control_input = ControlInput()
prop = FrictionlessBall(control_input)
outputs = [
"x", "y", "z", "roll", "pitch", "yaw", "vx", "vy", "vz", "ang_rate_x",
"ang_rate_y", "ang_rate_z"
]
system = build_nonlin_sys(prop, no_wind(), outputs)
t = np.linspace(0.0, 10, 500, endpoint=True)
state = State()
state.vx = 20.0
state.vy = 1
for i in range(3):
state.roll = 0
state.pitch = 0
state.yaw = 0
if i == 0:
state.ang_rate_x = 0.157079633
state.ang_rate_y = 0
state.ang_rate_z = 0
elif i == 1:
state.ang_rate_x = 0
state.ang_rate_y = 0.157079633
state.ang_rate_z = 0
elif i == 2:
state.ang_rate_x = 0
state.ang_rate_y = 0
state.ang_rate_z = 0.157079633
T, yout = input_output_response(system, t, U=0, X0=state.state)
pos = np.array(yout[:3])
eul_ang = np.array(yout[3:6])
vel_inertial = np.array(
[np.zeros(len(t)),
np.zeros(len(t)),
np.zeros(len(t))])
for j in range(len(vel_inertial[0])):
state.roll = yout[3, j]
state.pitch = yout[4, j]
state.yaw = yout[5, j]
vel = np.array([yout[6, j], yout[7, j], yout[8, j]])
vel_inertial_elem = body2inertial(vel, state)
vel_inertial[0, j] = vel_inertial_elem[0]
vel_inertial[1, j] = vel_inertial_elem[1]
vel_inertial[2, j] = vel_inertial_elem[2]
vx_inertial_expect = 20 * np.ones(len(t))
vy_inertial_expect = 1 * np.ones(len(t))
vz_inertial_expect = GRAVITY_CONST * t
x_expect = 20 * t
y_expect = 1 * t
z_expect = 0.5 * GRAVITY_CONST * t**2
roll_expect = state.ang_rate_x * t
pitch_expect = state.ang_rate_y * t
yaw_expect = state.ang_rate_z * t
assert np.allclose(vx_inertial_expect, vel_inertial[0], atol=7e-3)
assert np.allclose(vy_inertial_expect, vel_inertial[1], atol=5e-3)
assert np.allclose(vz_inertial_expect, vel_inertial[2], atol=8e-3)
assert np.allclose(x_expect, pos[0], atol=8e-2)
assert np.allclose(y_expect, pos[1], atol=5e-2)
assert np.allclose(z_expect, pos[2], atol=7e-2)
assert np.allclose(roll_expect, eul_ang[0], atol=1e-3)
assert np.allclose(pitch_expect, eul_ang[1], atol=1e-3)
assert np.allclose(yaw_expect, eul_ang[2], atol=1e-3)