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# -*- coding: utf-8 -*-
Import python libreries needed.
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%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
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import plotly.offline as offline
import plotly.graph_objs as go
import plotly.tools as tls
# notebook mode - inline
offline.init_notebook_mode()
Import PyFME classes
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from pyfme.aircrafts import Cessna172
from pyfme.environment.environment import Environment
from pyfme.environment.atmosphere import ISA1976
from pyfme.environment.gravity import VerticalConstant
from pyfme.environment.wind import NoWind
from pyfme.models.systems import EulerFlatEarth
from pyfme.simulator import BatchSimulation
from pyfme.utils.trimmer import steady_state_flight_trimmer
from pyfme.utils.input_generator import doublet
Initialize variables
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aircraft = Cessna172()
atmosphere = ISA1976()
gravity = VerticalConstant()
wind = NoWind()
environment = Environment(atmosphere, gravity, wind)
Initial conditions
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TAS = 45 # m/s
h0 = 2000 # m
psi0 = 1 # rad
x0, y0 = 0, 0 # m
turn_rate = 0.0 # rad/s
gamma0 = 0.00 # rad
Define system
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system = EulerFlatEarth(lat=0, lon=0, h=h0, psi=psi0, x_earth=x0, y_earth=y0)
not_trimmed_controls = {'delta_elevator': 0.05,
'delta_aileron': 0.01 * np.sign(turn_rate),
'delta_rudder': 0.01 * np.sign(turn_rate),
'delta_t': 0.5}
controls2trim = ['delta_elevator', 'delta_aileron', 'delta_rudder', 'delta_t']
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trimmed_ac, trimmed_sys, trimmed_env, results = steady_state_flight_trimmer(
aircraft, system, environment, TAS=TAS, controls_0=not_trimmed_controls,
controls2trim=controls2trim, gamma=gamma0, turn_rate=turn_rate, verbose=1)
Steady state flight trimmer results
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print('delta_elevator = ',"%8.4f" % np.rad2deg(results['delta_elevator']), 'deg')
print('delta_aileron = ', "%8.4f" % np.rad2deg(results['delta_aileron']), 'deg')
print('delta_rudder = ', "%8.4f" % np.rad2deg(results['delta_rudder']), 'deg')
print('delta_t = ', "%8.4f" % results['delta_t'], '%')
print()
print('alpha = ', "%8.4f" % np.rad2deg(results['alpha']), 'deg')
print('beta = ', "%8.4f" % np.rad2deg(results['beta']), 'deg')
print()
print('u = ', "%8.4f" % results['u'], 'm/s')
print('v = ', "%8.4f" % results['v'], 'm/s')
print('w = ', "%8.4f" % results['w'], 'm/s')
print()
print('psi = ', "%8.4f" % np.rad2deg(psi0), 'deg')
print('theta = ', "%8.4f" % np.rad2deg(results['theta']), 'deg')
print('phi = ', "%8.4f" % np.rad2deg(results['phi']), 'deg')
print()
print('p =', "%8.4f" % results['p'], 'rad/s')
print('q =', "%8.4f" % results['q'], 'rad/s')
print('r =', "%8.4f" % results['r'], 'rad/s')
Initialise simulation
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my_simulation = BatchSimulation(trimmed_ac, trimmed_sys, trimmed_env)
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tfin = 20 # seconds
N = tfin * 100 + 1
time = np.linspace(0, tfin, N)
initial_controls = trimmed_ac.controls
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controls = {}
for control_name, control_value in initial_controls.items():
controls[control_name] = np.ones_like(time) * control_value
Rudder doublet; Rudder travel: +16º/-16º
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amplitude = np.deg2rad(20)
controls['delta_rudder'] = doublet(t_init=2,
T=2,
A=amplitude,
time=time,
offset=np.deg2rad(0))
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my_simulation.set_controls(time, controls)
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par_list = ['x_earth', 'y_earth', 'height',
'psi', 'theta', 'phi',
'u', 'v', 'w',
'v_north', 'v_east', 'v_down',
'p', 'q', 'r',
'alpha', 'beta', 'TAS',
'F_xb', 'F_yb', 'F_zb',
'M_xb', 'M_yb', 'M_zb']
Run Simulation
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my_simulation.set_par_dict(par_list)
my_simulation.run_simulation()
Plot results
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plt.style.use('ggplot')
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# for ii in range(len(par_list) // 3):
# three_params = par_list[3 * ii:3 * ii + 3]
# fig, ax = plt.subplots(3, 1, sharex=True)
# for jj, par in enumerate(three_params):
# ax[jj].plot(time, my_simulation.par_dict[par])
# ax[jj].set_ylabel(par)
# ax[jj].set_xlabel('time (s)')
# fig = plt.figure()
# ax = Axes3D(fig)
# ax.plot(my_simulation.par_dict['x_earth'],
# my_simulation.par_dict['y_earth'],
# my_simulation.par_dict['height'])
# ax.plot(my_simulation.par_dict['x_earth'],
# my_simulation.par_dict['y_earth'],
# my_simulation.par_dict['height'] * 0)
# ax.set_xlabel('x_earth')
# ax.set_ylabel('y_earth')
# ax.set_zlabel('z_earth')
# plt.show()
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camera = dict(
up=dict(x=2, y=1, z=1),
center=dict(x=0, y=0, z=0),
eye=dict(x=2, y=1, z=0.7)
)
layout = {
'autosize': False,
'width': 900,
'height': 500,
'xaxis': {
'range': [-2, 4.5],
'zeroline': False,
},
'yaxis': {
'range': [-2, 4.5]
},
'width': 800,
'height': 800,
'scene':{
'camera': camera
}
}
trace_with_height = go.Scatter3d(
x=my_simulation.par_dict['x_earth'],
y=my_simulation.par_dict['y_earth'],
z=my_simulation.par_dict['height'],
mode='lines')
trace_without_height = go.Scatter3d(
x=my_simulation.par_dict['x_earth'],
y=my_simulation.par_dict['y_earth'],
z=my_simulation.par_dict['height'] * 0,
mode='lines')
data = [trace_with_height, trace_without_height]
fig = {
'data': data,
'layout': layout,
}
offline.iplot(fig)
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for ii in range(len(par_list) // 3):
three_params = par_list[3 * ii:3 * ii + 3]
trace1 = go.Scatter(
x=time,
y=my_simulation.par_dict[three_params[0]]
)
trace2 = go.Scatter(
x=time,
y=my_simulation.par_dict[three_params[1]]
)
trace3 = go.Scatter(
x=time,
y=my_simulation.par_dict[three_params[2]]
)
fig = tls.make_subplots(rows=3, cols=1, subplot_titles=('Plot 1', 'Plot 2', 'Plot 3'))
# add subplots
fig.append_trace(trace1, 1, 1)
fig.append_trace(trace2, 2, 1)
fig.append_trace(trace3, 3, 1)
# Edit the layout
# All of the axes properties here: https://plot.ly/python/reference/#XAxis
fig['layout']['xaxis3'].update(title='time (s)', showgrid=True)
# All of the axes properties here: https://plot.ly/python/reference/#YAxis
fig['layout']['yaxis1'].update(title=three_params[0], showgrid=True)
fig['layout']['yaxis2'].update(title=three_params[1], showgrid=True)
fig['layout']['yaxis3'].update(title=three_params[2], showgrid=True)
fig['layout'].update(title='Output subplots')
offline.iplot(fig)