def test_control_rate2_path_constraint_radau(self):
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase('radau-ps',
ode_class=BrachistochroneODE,
num_segments=10,
transcription_order=5)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True, fix_final=True)
phase.set_state_options('y', fix_initial=True, fix_final=True)
phase.set_state_options('v', fix_initial=True)
phase.add_control('theta', units='deg', lower=0.01, upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
phase.add_path_constraint('theta_rate2',
lower=-200,
upper=200,
units='rad/s**2')
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_rel_error(self,
phase.get_values('time')[-1],
1.8016,
tolerance=1.0E-3)
from openmdao.api import Problem, Group
from dymos import Phase
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
phase = Phase('radau-ps', ode_class=BrachistochroneODE, num_segments=4,
transcription_order=[3, 5, 3, 5])
p.model.add_subsystem('phase0', phase)
p.setup()
p['phase0.t_initial'] = 1.0
p['phase0.t_duration'] = 9.0
p.run_model()
t_disc = phase.get_values('time', nodes='state_disc')
t_col = phase.get_values('time', nodes='col')
t_all = phase.get_values('time', nodes='all')
def f(x):
return np.sin(x) / x + 1
def fu(x):
return (np.cos(x) * x - np.sin(x))/x**2
def plot_01():
fig, axes = plt.subplots(1, 1)
def test_min_time_climb_for_docs_gauss_lobatto(self):
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase
from dymos.examples.min_time_climb.min_time_climb_ode import MinTimeClimbODE
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
# Compute sparsity/coloring when run_driver is called
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase('gauss-lobatto',
ode_class=MinTimeClimbODE,
num_segments=12,
compressed=True,
transcription_order=3)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True,
duration_bounds=(50, 400),
duration_ref=100.0)
phase.set_state_options('r',
fix_initial=True,
lower=0,
upper=1.0E6,
ref=1.0E3,
defect_ref=1000.0,
units='m')
phase.set_state_options('h',
fix_initial=True,
lower=0,
upper=20000.0,
ref=1.0E2,
defect_ref=100.0,
units='m')
phase.set_state_options('v',
fix_initial=True,
lower=10.0,
ref=1.0E2,
defect_ref=0.1,
units='m/s')
phase.set_state_options('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
ref=1.0,
defect_scaler=1.0,
units='rad')
phase.set_state_options('m',
fix_initial=True,
lower=10.0,
upper=1.0E5,
ref=1.0E3,
defect_ref=0.1)
rate_continuity = True
phase.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=rate_continuity,
rate_continuity_scaler=100.0,
rate2_continuity=False)
phase.add_design_parameter('S', val=49.2386, units='m**2', opt=False)
phase.add_design_parameter('Isp', val=1600.0, units='s', opt=False)
phase.add_design_parameter('throttle', val=1.0, opt=False)
phase.add_boundary_constraint('h',
loc='final',
equals=20000,
scaler=1.0E-3,
units='m')
phase.add_boundary_constraint('aero.mach',
loc='final',
equals=1.0,
units=None)
phase.add_boundary_constraint('gam',
loc='final',
equals=0.0,
units='rad')
phase.add_path_constraint(name='h',
lower=100.0,
upper=20000,
ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
phase.add_path_constraint(name='alpha', lower=-8, upper=8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final')
p.driver.options['dynamic_simul_derivs'] = True
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 500
p['phase0.states:r'] = phase.interpolate(ys=[0.0, 50000.0],
nodes='state_input')
p['phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159],
nodes='state_input')
p['phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0],
nodes='state_input')
p['phase0.states:m'] = phase.interpolate(ys=[19030.468, 10000.],
nodes='state_input')
p['phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_rel_error(self,
p.model.phase0.get_values('time')[-1],
321.0,
tolerance=2)
exp_out = phase.simulate(times=50)
fig, axes = plt.subplots(2, 1, sharex=True)
axes[0].plot(phase.get_values('time'), phase.get_values('h'), 'ro')
axes[0].plot(exp_out.get_values('time'), exp_out.get_values('h'), 'b-')
axes[0].set_xlabel('time (s)')
axes[0].set_ylabel('altitude (m)')
axes[1].plot(phase.get_values('time'),
phase.get_values('alpha', units='deg'), 'ro')
axes[1].plot(exp_out.get_values('time'),
exp_out.get_values('alpha', units='deg'), 'b-')
axes[1].set_xlabel('time (s)')
axes[1].set_ylabel('alpha (deg)')
plt.show()
def ex_aircraft_steady_flight(optimizer='SLSQP',
transcription='gauss-lobatto'):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings["Linesearch tolerance"] = 0.10
p.driver.opt_settings['iSumm'] = 6
num_seg = 15
seg_ends, _ = lgl(num_seg + 1)
phase = Phase(transcription,
ode_class=AircraftODE,
num_segments=num_seg,
segment_ends=seg_ends,
transcription_order=5,
compressed=False)
# Pass Reference Area from an external source
assumptions = p.model.add_subsystem('assumptions', IndepVarComp())
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(300, 10000),
duration_ref=3600)
phase.set_state_options('range',
units='NM',
fix_initial=True,
fix_final=False,
scaler=0.001,
defect_scaler=1.0E-2)
phase.set_state_options('mass_fuel',
units='lbm',
fix_initial=True,
fix_final=True,
upper=1.5E5,
lower=0.0,
scaler=1.0E-5,
defect_scaler=1.0E-1)
phase.add_control('alt',
units='kft',
opt=True,
lower=0.0,
upper=50.0,
rate_param='climb_rate',
rate_continuity=True,
rate_continuity_scaler=1.0,
rate2_continuity=True,
rate2_continuity_scaler=1.0,
ref=1.0,
fix_initial=True,
fix_final=True)
phase.add_control('mach', units=None, opt=False)
phase.add_input_parameter('S', units='m**2')
phase.add_input_parameter('mass_empty', units='kg')
phase.add_input_parameter('mass_payload', units='kg')
phase.add_path_constraint('propulsion.tau', lower=0.01, upper=1.0)
phase.add_path_constraint('alt_rate',
units='ft/min',
lower=-3000,
upper=3000,
ref=3000)
p.model.connect('assumptions.S', 'phase0.input_parameters:S')
p.model.connect('assumptions.mass_empty',
'phase0.input_parameters:mass_empty')
p.model.connect('assumptions.mass_payload',
'phase0.input_parameters:mass_payload')
phase.add_objective('range', loc='final', ref=-1.0)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 3600.0
p['phase0.states:range'] = phase.interpolate(ys=(0, 1000.0),
nodes='state_input')
p['phase0.states:mass_fuel'] = phase.interpolate(ys=(30000, 0),
nodes='state_input')
p['phase0.controls:mach'][:] = 0.8
p['phase0.controls:alt'][:] = 10.0
p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400
p.run_driver()
exp_out = phase.simulate(
times=np.linspace(0, p['phase0.t_duration'], 500),
record=True,
record_file='test_ex_aircraft_steady_flight_rec.db')
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('alt', nodes='all'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('alt'), 'b-')
plt.suptitle('altitude vs time')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('alt_rate', nodes='all', units='ft/min'), 'ro')
plt.plot(exp_out.get_values('time'),
exp_out.get_values('alt_rate', units='ft/min'), 'b-')
plt.suptitle('altitude rate vs time')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('mass_fuel', nodes='all'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('mass_fuel'), 'b-')
plt.suptitle('fuel mass vs time')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('propulsion.dXdt:mass_fuel', nodes='all'), 'ro')
plt.plot(exp_out.get_values('time'),
exp_out.get_values('propulsion.dXdt:mass_fuel'), 'b-')
plt.suptitle('fuel mass flow rate vs time')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('mach', nodes='all'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('mach'), 'b-')
plt.suptitle('mach vs time')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('mach_rate', nodes='all'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('mach_rate'), 'b-')
plt.suptitle('mach rate vs time')
print('time')
print(phase.get_values('time', nodes='all').T)
print('alt')
print(phase.get_values('alt', nodes='all').T)
print('alt_rate')
print(phase.get_values('alt_rate', nodes='all').T)
print('alt_rate2')
print(phase.get_values('alt_rate2', nodes='all').T)
print('range')
print(phase.get_values('range', nodes='all').T)
print('flight path angle')
print(phase.get_values('gam_comp.gam').T)
print('true airspeed')
print(phase.get_values('tas_comp.TAS', units='m/s').T)
print('coef of lift')
print(phase.get_values('aero.CL').T)
print('coef of drag')
print(phase.get_values('aero.CD').T)
print('atmos density')
print(phase.get_values('atmos.rho').T)
print('alpha')
print(phase.get_values('flight_equilibrium.alpha', units='rad').T)
print('coef of thrust')
print(phase.get_values('flight_equilibrium.CT').T)
print('fuel flow rate')
print(phase.get_values('propulsion.dXdt:mass_fuel').T)
print('max_thrust')
print(phase.get_values('propulsion.max_thrust', units='N').T)
print('tau')
print(phase.get_values('propulsion.tau').T)
print('dynamic pressure')
print(phase.get_values('q_comp.q', units='Pa').T)
print('S')
print(phase.get_values('S', units='m**2').T)
plt.show()
return p
def test_double_integrator_for_docs(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from dymos import Phase
from dymos.examples.double_integrator.double_integrator_ode import DoubleIntegratorODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase('gauss-lobatto',
ode_class=DoubleIntegratorODE,
num_segments=20,
transcription_order=3,
compressed=True)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(1.0, 1.0))
phase.set_state_options('x', fix_initial=True)
phase.set_state_options('v', fix_initial=True, fix_final=True)
phase.add_control('u',
units='m/s**2',
scaler=0.01,
continuity=False,
rate_continuity=False,
rate2_continuity=False,
lower=-1.0,
upper=1.0)
# Maximize distance travelled in one second.
phase.add_objective('x', loc='final', scaler=-1)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup(check=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 1.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 0.25],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 0],
nodes='state_input')
p['phase0.controls:u'] = phase.interpolate(ys=[1, -1],
nodes='control_input')
p.run_driver()
exp_out = phase.simulate(times=np.linspace(p['phase0.t_initial'],
p['phase0.t_duration'],
100),
record=False)
# Plot results
fig, axes = plt.subplots(3, 1)
fig.suptitle('Double Integrator Direct Collocation Solution')
t_imp = phase.get_values('time', nodes='all')
x_imp = phase.get_values('x', nodes='all')
v_imp = phase.get_values('v', nodes='all')
u_imp = phase.get_values('u', nodes='all')
t_exp = exp_out.get_values('time')
x_exp = exp_out.get_values('x')
v_exp = exp_out.get_values('v')
u_exp = exp_out.get_values('u')
axes[0].plot(t_imp, x_imp, 'ro', label='implicit')
axes[0].plot(t_exp, x_exp, 'b-', label='explicit')
axes[0].set_xlabel('time (s)')
axes[0].set_ylabel('x (m)')
axes[0].grid(True)
axes[0].legend(loc='best')
axes[1].plot(t_imp, v_imp, 'ro', label='implicit')
axes[1].plot(t_exp, v_exp, 'b-', label='explicit')
axes[1].set_xlabel('time (s)')
axes[1].set_ylabel('v (m/s)')
axes[1].grid(True)
axes[1].legend(loc='best')
axes[2].plot(t_imp, u_imp, 'ro', label='implicit')
axes[2].plot(t_exp, u_exp, 'b-', label='explicit')
axes[2].set_xlabel('time (s)')
axes[2].set_ylabel('u (m/s**2)')
axes[2].grid(True)
axes[2].legend(loc='best')
plt.show()
def test_cruise_results(self):
p = Problem(model=Group())
if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major step limit'] = 0.05
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings["Linesearch tolerance"] = 0.10
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
else:
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase('gauss-lobatto',
ode_class=AircraftODE,
num_segments=1,
transcription_order=13)
# Pass Reference Area from an external source
assumptions = p.model.add_subsystem('assumptions', IndepVarComp())
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0),
duration_bounds=(3600, 3600),
duration_ref=3600)
phase.set_state_options('range',
units='km',
fix_initial=True,
fix_final=False,
scaler=0.01,
defect_scaler=0.01)
phase.set_state_options('mass_fuel',
fix_final=True,
upper=20000.0,
lower=0.0,
scaler=1.0E-4,
defect_scaler=1.0E-2)
phase.add_control('alt',
units='km',
opt=False,
rate_param='climb_rate')
phase.add_control('mach', units=None, opt=False)
phase.add_input_parameter('S', units='m**2')
phase.add_input_parameter('mass_empty', units='kg')
phase.add_input_parameter('mass_payload', units='kg')
phase.add_path_constraint('propulsion.tau', lower=0.01, upper=1.0)
p.model.connect('assumptions.S', 'phase0.input_parameters:S')
p.model.connect('assumptions.mass_empty',
'phase0.input_parameters:mass_empty')
p.model.connect('assumptions.mass_payload',
'phase0.input_parameters:mass_payload')
phase.add_objective('time', loc='final', ref=3600)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 1.515132 * 3600.0
p['phase0.states:range'] = phase.interpolate(ys=(0, 1296.4),
nodes='state_input')
p['phase0.states:mass_fuel'] = phase.interpolate(ys=(12236.594555, 0),
nodes='state_input')
p['phase0.controls:mach'] = 0.8
p['phase0.controls:alt'] = 5.0
p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400
p.run_driver()
tas = phase.get_values('tas_comp.TAS', units='m/s')
time = phase.get_values('time', units='s')
range = phase.get_values('range', units='m')
assert_rel_error(self, range, tas * time, tolerance=1.0E-9)
def test_brachistochrone_recording_for_docs(self):
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver, \
SqliteRecorder, CaseReader
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=10)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True, fix_final=True)
phase.set_state_options('y', fix_initial=True, fix_final=True)
phase.set_state_options('v', fix_initial=True)
phase.add_control('theta',
units='deg',
rate_continuity=False,
lower=0.01,
upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
# Recording
rec = SqliteRecorder('brachistochrone_solution.db')
p.driver.recording_options['record_desvars'] = True
p.driver.recording_options['record_responses'] = True
p.driver.recording_options['record_objectives'] = True
p.driver.recording_options['record_constraints'] = True
p.model.recording_options['record_metadata'] = True
p.driver.add_recorder(rec)
p.model.add_recorder(rec)
phase.add_recorder(rec)
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_rel_error(self,
phase.get_values('time')[-1],
1.8016,
tolerance=1.0E-3)
cr = CaseReader('brachistochrone_solution.db')
outputs = dict([
(o[0], o[1])
for o in cr.list_outputs(units=True, shape=True, out_stream=None)
])
assert_rel_error(
self, p['phase0.controls:theta'],
outputs['phase0.indep_controls.controls:theta']['value'])
phase0_options = cr.system_metadata['phase0']['component_options']
num_segments = phase0_options['num_segments']
transcription_order = phase0_options['transcription_order']
segment_ends = phase0_options['segment_ends']
ode_class = phase0_options['ode_class']
print(num_segments)
print(transcription_order)
print(ode_class)
print(segment_ends)
def min_time_climb(optimizer='SLSQP', num_seg=3, transcription='gauss-lobatto',
transcription_order=3, top_level_jacobian='csc', simul_derivs=True,
force_alloc_complex=False):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
if simul_derivs:
p.driver.options['dynamic_simul_derivs'] = True
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['Function precision'] = 1.0E-6
p.driver.opt_settings['Linesearch tolerance'] = 0.10
p.driver.opt_settings['Major step limit'] = 0.5
# p.driver.opt_settings['Verify level'] = 3
phase = Phase(transcription,
ode_class=MinTimeClimbODE,
num_segments=num_seg,
compressed=True,
transcription_order=transcription_order)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)
phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E6,
scaler=1.0E-3, defect_scaler=1.0E-2, units='m')
phase.set_state_options('h', fix_initial=True, lower=0, upper=20000.0,
scaler=1.0E-3, defect_scaler=1.0E-3, units='m')
phase.set_state_options('v', fix_initial=True, lower=10.0,
scaler=1.0E-2, defect_scaler=1.0E-2, units='m/s')
phase.set_state_options('gam', fix_initial=True, lower=-1.5, upper=1.5,
ref=1.0, defect_scaler=1.0, units='rad')
phase.set_state_options('m', fix_initial=True, lower=10.0, upper=1.0E5,
scaler=1.0E-3, defect_scaler=1.0E-3)
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
continuity=True, rate_continuity=True, rate2_continuity=False)
phase.add_design_parameter('S', val=49.2386, units='m**2', opt=False)
phase.add_design_parameter('Isp', val=1600.0, units='s', opt=False)
phase.add_design_parameter('throttle', val=1.0, opt=False)
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m')
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None)
phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
phase.add_path_constraint(name='alpha', lower=-8, upper=8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final')
p.model.options['assembled_jac_type'] = top_level_jacobian.lower()
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup(check=True, force_alloc_complex=force_alloc_complex)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 298.46902
p['phase0.states:r'] = phase.interpolate(ys=[0.0, 111319.54], nodes='state_input')
p['phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0], nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
p['phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['phase0.states:m'] = phase.interpolate(ys=[19030.468, 16841.431], nodes='state_input')
p['phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0], nodes='control_input')
p.run_driver()
if SHOW_PLOTS:
exp_out = phase.simulate(times=np.linspace(0, p['phase0.t_duration'], 100))
import matplotlib.pyplot as plt
plt.plot(phase.get_values('time'), phase.get_values('h'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('h'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('altitude (m)')
plt.figure()
plt.plot(phase.get_values('v'), phase.get_values('h'), 'ro')
plt.plot(exp_out.get_values('v'), exp_out.get_values('h'), 'b-')
plt.xlabel('airspeed (m/s)')
plt.ylabel('altitude (m)')
plt.figure()
plt.plot(phase.get_values('time'), phase.get_values('alpha'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('alpha'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('alpha (rad)')
plt.figure()
plt.plot(phase.get_values('time'), phase.get_values('prop.thrust', units='lbf'), 'ro')
plt.plot(exp_out.get_values('time'), exp_out.get_values('prop.thrust', units='lbf'), 'b-')
plt.xlabel('time (s)')
plt.ylabel('thrust (lbf)')
plt.show()
return p
def test_brachistochrone_for_docs_gauss_lobatto(self):
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=10)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True, fix_final=True)
phase.set_state_options('y', fix_initial=True, fix_final=True)
phase.set_state_options('v', fix_initial=True)
phase.add_control('theta',
units='deg',
rate_continuity=False,
lower=0.01,
upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 2.0
p['phase0.states:x'] = phase.interpolate(ys=[0, 10],
nodes='state_input')
p['phase0.states:y'] = phase.interpolate(ys=[10, 5],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5],
nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_rel_error(self,
phase.get_values('time')[-1],
1.8016,
tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
t0 = p['phase0.t_initial']
tf = t0 + p['phase0.t_duration']
exp_out = phase.simulate(times=np.linspace(t0, tf, 50))
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = phase.get_values('x', nodes='all')
y_imp = phase.get_values('y', nodes='all')
x_exp = exp_out.get_values('x')
y_exp = exp_out.get_values('y')
ax.plot(x_imp, y_imp, 'ro', label='solution')
ax.plot(x_exp, y_exp, 'b-', label='simulated')
ax.set_xlabel('x (m)')
ax.set_ylabel('y (m)')
ax.grid(True)
ax.legend(loc='upper right')
plt.show()
def test_steady_aircraft_for_docs(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver, IndepVarComp
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase
from dymos.examples.aircraft_steady_flight.aircraft_ode import AircraftODE
from dymos.utils.lgl import lgl
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.options['dynamic_simul_derivs'] = True
num_seg = 15
seg_ends, _ = lgl(num_seg + 1)
phase = Phase('gauss-lobatto',
ode_class=AircraftODE,
num_segments=num_seg,
segment_ends=seg_ends,
transcription_order=5,
compressed=False)
# Pass design parameters in externally from an external source
assumptions = p.model.add_subsystem('assumptions', IndepVarComp())
assumptions.add_output('mach', val=0.8, units=None)
assumptions.add_output('S', val=427.8, units='m**2')
assumptions.add_output('mass_empty', val=1.0, units='kg')
assumptions.add_output('mass_payload', val=1.0, units='kg')
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True,
duration_bounds=(300, 10000),
duration_ref=3600)
phase.set_state_options('range', units='NM', fix_initial=True, fix_final=False,
scaler=0.001,
defect_scaler=1.0E-2)
phase.set_state_options('mass_fuel', units='lbm', fix_initial=True, fix_final=True,
upper=1.5E5, lower=0.0, scaler=1.0E-5, defect_scaler=1.0E-1)
phase.add_control('alt', units='kft', opt=True, lower=0.0, upper=50.0,
rate_param='climb_rate',
rate_continuity=True, rate_continuity_scaler=1.0,
rate2_continuity=True, rate2_continuity_scaler=1.0, ref=1.0,
fix_initial=True, fix_final=True)
phase.add_input_parameter('mach', units=None)
phase.add_input_parameter('S', units='m**2')
phase.add_input_parameter('mass_empty', units='kg')
phase.add_input_parameter('mass_payload', units='kg')
phase.add_path_constraint('propulsion.tau', lower=0.01, upper=1.0)
phase.add_path_constraint('alt_rate', units='ft/min', lower=-3000, upper=3000, ref=3000)
p.model.connect('assumptions.mach', 'phase0.input_parameters:mach')
p.model.connect('assumptions.S', 'phase0.input_parameters:S')
p.model.connect('assumptions.mass_empty', 'phase0.input_parameters:mass_empty')
p.model.connect('assumptions.mass_payload', 'phase0.input_parameters:mass_payload')
phase.add_objective('range', loc='final', ref=-1.0)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup()
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 3600.0
p['phase0.states:range'] = phase.interpolate(ys=(0, 1000.0), nodes='state_input')
p['phase0.states:mass_fuel'] = phase.interpolate(ys=(30000, 0), nodes='state_input')
p['phase0.controls:alt'][:] = 10.0
p['assumptions.mach'][:] = 0.8
p['assumptions.S'] = 427.8
p['assumptions.mass_empty'] = 0.15E6
p['assumptions.mass_payload'] = 84.02869 * 400
p.run_driver()
exp_out = phase.simulate(times=np.linspace(0, p['phase0.t_duration'], 500), record=True,
record_file='test_doc_aircraft_steady_flight_rec.db')
assert_rel_error(self, phase.get_values('range', units='NM')[-1], 726.7, tolerance=1.0E-2)
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('alt', nodes='all', units='ft'),
'ro')
plt.plot(exp_out.get_values('time'),
exp_out.get_values('alt', units='ft'),
'b-')
plt.suptitle('Altitude vs Time')
plt.xlabel('Time (s)')
plt.ylabel('Altitude (ft)')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('alt_rate', nodes='all', units='ft/min'),
'ro')
plt.plot(exp_out.get_values('time'),
exp_out.get_values('alt_rate', units='ft/min'),
'b-')
plt.suptitle('Climb Rate vs Time')
plt.xlabel('Time (s)')
plt.ylabel('Climb Rate (ft/min)')
plt.figure()
plt.plot(phase.get_values('time', nodes='all'),
phase.get_values('mass_fuel', nodes='all', units='lbm'),
'ro')
plt.plot(exp_out.get_values('time'),
exp_out.get_values('mass_fuel', units='lbm'),
'b-')
plt.suptitle('Fuel Mass vs Time')
plt.xlabel('Time (s)')
plt.ylabel('Fuel Mass (lbm)')
plt.show()
