EXAMPLE 004

Cessna 172, ISA1976 integrated with Flat Earth (Euler angles).

Example with trimmed aircraft: stationary, horizontal turn.

The main purpose of this example is to check if the aircraft trimmed in a given state maintains the trimmed flight condition.


In [1]:
# -*- coding: utf-8 -*-

Import python libreries needed.


In [2]:
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

In [3]:
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


In [4]:
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

Initialize variables


In [5]:
aircraft = Cessna172()
atmosphere = ISA1976()
gravity = VerticalConstant()
wind = NoWind()
environment = Environment(atmosphere, gravity, wind)

Initial conditions


In [6]:
TAS = 45  # m/s
h0 = 3000  # m
psi0 = 1.0  # rad
x0, y0 = 0, 0  # m
turn_rate = 0.005  # rad/s
gamma0 = 0.0  # rad

Define system


In [7]:
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']

In [8]:
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)


`gtol` termination condition is satisfied.
Function evaluations: 22, initial cost: 6.1292e+00, final cost 2.5366e-05, first-order optimality 1.90e-11.
c:\python35-32\lib\site-packages\pyfme\utils\trimmer.py:138: RuntimeWarning:

Trim process did not converge

Steady state flight trimmer results


In [9]:
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')


delta_elevator =   -4.0230 deg
delta_aileron =   -0.6914 deg
delta_rudder =    9.7531 deg
delta_t =    0.6209 %

alpha =    5.5924 deg
beta =  -14.3239 deg

u =   43.3935 m/s
v =  -11.1332 m/s
w =    4.2490 m/s

psi =   57.2958 deg
theta =    5.2659 deg
phi =    1.2789 deg

p =  -0.0005 rad/s
q =   0.0001 rad/s
r =   0.0001 rad/s

Initialise simulation


In [10]:
my_simulation = BatchSimulation(trimmed_ac, trimmed_sys, trimmed_env)

In [11]:
tfin = 100  # seconds
N = tfin * 100 + 1
time = np.linspace(0, tfin, N)
initial_controls = trimmed_ac.controls

In [12]:
controls = {}
for control_name, control_value in initial_controls.items():
    controls[control_name] = np.ones_like(time) * control_value

my_simulation.set_controls(time, controls)

In [13]:
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


In [14]:
my_simulation.set_par_dict(par_list)
my_simulation.run_simulation()

Plot results


In [15]:
plt.style.use('ggplot')

In [16]:
# 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()

In [17]:
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)



In [18]:
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)


This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]

This is the format of your plot grid:
[ (1,1) x1,y1 ]
[ (2,1) x2,y2 ]
[ (3,1) x3,y3 ]