def test_brachistochrone_backward_shooting(self):
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, RungeKutta
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=RungeKutta(num_segments=20))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(-2.0, -0.5))
phase.set_state_options('x', fix_initial=True)
phase.set_state_options('y', fix_initial=True)
phase.set_state_options('v', fix_initial=False)
phase.add_control('theta', units='deg', lower=0.01, upper=179.9, ref0=0, ref=180.0,
rate_continuity=True, rate2_continuity=True)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Final state values can't be controlled with simple bounds in ExplicitPhase,
# so use nonlinear boundary constraints instead.
phase.add_boundary_constraint('x', loc='final', equals=0)
phase.add_boundary_constraint('y', loc='final', equals=10)
phase.add_boundary_constraint('v', loc='final', equals=0)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=-1)
p.model.linear_solver = DirectSolver()
p.setup(check=True)
p['phase0.t_initial'] = 1.8016
p['phase0.t_duration'] = -1.8016
p['phase0.states:x'] = 10
p['phase0.states:y'] = 5
p['phase0.states:v'] = 10
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, p['phase0.time'][-1], -1.8016, tolerance=1.0E-3)
# Generate the explicitly simulated trajectory
exp_out = phase.simulate()
assert_rel_error(self, exp_out.get_val('phase0.timeseries.states:x')[-1, 0], 0,
tolerance=1.0E-3)
assert_rel_error(self, exp_out.get_val('phase0.timeseries.states:y')[-1, 0], 10,
tolerance=1.0E-3)
def test_initial_val_and_final_val_stick(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8, order=3))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=False, fix_duration=False,
initial_val=0.01, duration_val=1.9)
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, fix_final=False)
phase.add_control('theta', continuity=True, rate_continuity=True,
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_boundary_constraint('time', loc='initial', equals=0)
p.model.linear_solver = DirectSolver()
p.setup(check=True)
assert_rel_error(self, p['phase0.t_initial'], 0.01)
assert_rel_error(self, p['phase0.t_duration'], 1.9)
def test_control_rate_path_constraint_gl(self):
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, GaussLobatto
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(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)
phase.add_path_constraint('theta_rate',
lower=0,
upper=100,
units='deg/s')
p.model.linear_solver = DirectSolver()
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,
p.get_val('phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-3)
def ssto_moon(transcription='gauss-lobatto',
num_seg=10,
optimizer='SLSQP',
top_level_jacobian='csc',
transcription_order=5,
compressed=False):
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['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
else:
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(transcription,
ode_class=LaunchVehicleODE,
ode_init_kwargs={'central_body': 'moon'},
num_segments=num_seg,
compressed=compressed,
transcription_order=3)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(10, 1000))
phase.set_state_options('x', fix_initial=True, scaler=1.0E-5, lower=0)
phase.set_state_options('y', fix_initial=True, scaler=1.0E-5, lower=0)
phase.set_state_options('vx', fix_initial=True, scaler=1.0E-3, lower=0)
phase.set_state_options('vy', fix_initial=True, scaler=1.0E-3)
phase.set_state_options('m', fix_initial=True, scaler=1.0E-3)
phase.add_boundary_constraint('y', loc='final', equals=1.85E5, linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=1627.0)
phase.add_boundary_constraint('vy', loc='final', equals=0)
if transcription == 'radau-ps':
# This constraint is necessary using the Radau-Pseudospectral method since the
# last value of the control does not impact the collocation defects.
phase.add_boundary_constraint('theta_rate2', loc='final', equals=0)
phase.add_control('theta', units='rad', lower=-1.57, upper=1.57)
phase.add_design_parameter('thrust',
units='N',
opt=False,
val=3.0 * 50000.0 * 1.61544)
phase.add_design_parameter('Isp', units='s', opt=False, val=1.0E6)
phase.add_objective('time', index=-1, scaler=0.01)
p.model.options['assembled_jac_type'] = top_level_jacobian.lower()
p.model.linear_solver = DirectSolver(assemble_jac=True)
return p
def test_ex_brachistochrone_vs_rungekutta_compressed(self):
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from dymos import Phase, RungeKutta
from dymos.examples.brachistochrone.brachistochrone_vector_states_ode import \
BrachistochroneVectorStatesODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=RungeKutta(num_segments=20,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
phase.set_state_options('pos', fix_initial=True, fix_final=False)
phase.set_state_options('v', fix_initial=True, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
phase.add_boundary_constraint('pos', loc='final', lower=[10, 5])
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = DirectSolver()
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 1.80162174
pos0 = [0, 10]
posf = [10, 5]
p['phase0.states:pos'] = phase.interpolate(ys=[pos0, posf],
nodes='state_input')
p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9],
nodes='state_input')
p['phase0.controls:theta'] = phase.interpolate(ys=[0.46, 100.22900215],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
self.assert_results(p)
self.tearDown()
def setUpClass(cls):
import matplotlib
matplotlib.use('Agg')
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from dymos import Phase, load_simulation_results
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='rad',
rate_continuity=False,
lower=0.001,
upper=3.14)
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()
cls.exp_out = phase.simulate(
times=100, record_file='phase_simulation_test_sim.db')
cls.exp_out_loaded = load_simulation_results(
'phase_simulation_test_sim.db')
def test_unbounded_time(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=8,
transcription_order=3)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=False, fix_duration=False)
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, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
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_boundary_constraint('time', loc='initial', equals=0)
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'] = 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],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
self.assertTrue(p.driver.result.success,
msg='Brachistochrone with outbounded times has failed')
def setUpClass(cls):
p = cls.p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SNOPT'
p.driver.options['dynamic_simul_derivs'] = True
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['iSumm'] = 6
phase = Phase('radau-ps',
ode_class=CadreOrbitODE,
num_segments=10,
transcription_order=7,
compressed=False)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(duration, duration))
phase.set_state_options('r_e2b_I', defect_scaler=1000, fix_initial=True, units='km')
phase.set_state_options('v_e2b_I', defect_scaler=1000, fix_initial=True, units='km/s')
# phase.set_state_options('SOC', defect_scaler=1, fix_initial=True, units=None)
# phase.add_design_parameter('P_bat', opt=False, units='W')
phase.add_design_parameter('Gamma', opt=False, units='rad')
phase.add_objective('time', loc='final', scaler=10)
# p.model.options['assembled_jac_type'] = 'csc'
# p.model.linear_solver = DirectSolver(assemble_jac=True)
p.setup(check=True, force_alloc_complex=True)
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = duration
# print(phase.grid_data.num_nodes)
#
p['phase0.states:r_e2b_I'][:, 0] = rmag
p['phase0.states:r_e2b_I'][:, 1] = 0.0
p['phase0.states:r_e2b_I'][:, 2] = 0.0
p['phase0.states:v_e2b_I'][:, 0] = 0.0
p['phase0.states:v_e2b_I'][:, 1] = vcirc
p['phase0.states:v_e2b_I'][:, 2] = 0.0
# p['phase0.design_parameters:P_bat'] = 2.0
p['phase0.design_parameters:Gamma'] = 0.0
p.run_model()
p.run_driver()
def test_add_existing_control_as_design_parameter(self):
p = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8, order=3))
p.add_control('theta')
with self.assertRaises(ValueError) as e:
p.add_design_parameter('theta')
expected = 'theta has already been added as a control.'
self.assertEqual(str(e.exception), expected)
def test_objective_design_parameter_radau(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=Radau(num_segments=20,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(4, 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, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=True, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('g')
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver()
p.setup(check=True)
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],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
assert_rel_error(self, p['phase0.t_duration'], 10, tolerance=1.0E-3)
def test_add_existing_design_parameter_as_input_parameter(self):
p = Phase(ode_class=_A,
transcription=GaussLobatto(num_segments=14,
order=3,
compressed=True))
p.add_design_parameter('theta')
with self.assertRaises(ValueError) as e:
p.add_input_parameter('theta')
expected = 'theta has already been added as a design parameter.'
self.assertEqual(str(e.exception), expected)
def test_invalid_design_parameter_name(self):
p = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=8,
transcription_order=3)
with self.assertRaises(ValueError) as e:
p.add_design_parameter('foo')
expected = 'foo is not a controllable parameter in the ODE system.'
self.assertEqual(str(e.exception), expected)
def test_add_existing_design_parameter_as_input_parameter(self):
p = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=8,
transcription_order=3)
p.add_design_parameter('theta')
with self.assertRaises(ValueError) as e:
p.add_input_parameter('theta')
expected = 'theta has already been added as a design parameter.'
self.assertEqual(str(e.exception), expected)
def test_invalid_options_nonoptimal_design_param(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=16,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(4, 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, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
opt=False)
phase.add_design_parameter('g',
units='m/s**2',
opt=False,
lower=5,
upper=10,
ref0=5,
ref=10,
scaler=1,
adder=0)
# Minimize time at the end of the phase
phase.add_objective('g')
p.model.linear_solver = DirectSolver()
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
p.setup(check=False)
print('\n'.join([str(ww.message) for ww in w]))
expected = 'Invalid options for non-optimal design_parameter \'g\' in phase \'phase0\': ' \
'lower, upper, scaler, adder, ref, ref0'
self.assertIn(expected, [str(ww.message) for ww in w])
def test_fixed_time_invalid_options(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8, order=3))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, fix_duration=True,
initial_bounds=(1.0, 5.0), initial_adder=0.0,
initial_scaler=1.0, initial_ref0=0.0,
initial_ref=1.0, duration_bounds=(1.0, 5.0),
duration_adder=0.0, duration_scaler=1.0,
duration_ref0=0.0, duration_ref=1.0)
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, fix_final=False)
phase.add_control('theta', continuity=True, rate_continuity=True,
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_boundary_constraint('time', loc='initial', equals=0)
p.model.linear_solver = DirectSolver()
expected_msg0 = 'Phase time options have no effect because fix_initial=True for ' \
'phase \'phase0\': initial_bounds, initial_scaler, initial_adder, ' \
'initial_ref, initial_ref0'
expected_msg1 = 'Phase time options have no effect because fix_duration=True for' \
' phase \'phase0\': duration_bounds, duration_scaler, ' \
'duration_adder, duration_ref, duration_ref0'
with warnings.catch_warnings(record=True) as ctx:
warnings.simplefilter('always')
p.setup(check=True)
self.assertIn(expected_msg0, [str(w.message) for w in ctx])
self.assertIn(expected_msg1, [str(w.message) for w in ctx])
def test_ex_double_integrator_input_and_fixed_times_warns(self):
"""
Tests that time optimization options cause a ValueError to be raised when t_initial and
t_duration are connected to external sources.
"""
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8, order=3))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(input_initial=True, fix_initial=True,
input_duration=True, fix_duration=True)
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, fix_final=False)
phase.add_control('theta', continuity=True, rate_continuity=True,
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_boundary_constraint('time', loc='initial', equals=0)
p.model.linear_solver = DirectSolver()
with warnings.catch_warnings(record=True) as ctx:
warnings.simplefilter('always')
p.setup(check=True)
expected_msg0 = 'Phase \'phase0\' initial time is an externally-connected input, therefore ' \
'fix_initial has no effect.'
expected_msg1 = 'Phase \'phase0\' time duration is an externally-connected input, ' \
'therefore fix_duration has no effect.'
self.assertIn(expected_msg0, [str(w.message) for w in ctx])
self.assertIn(expected_msg1, [str(w.message) for w in ctx])
def test_invalid_options_nonoptimal_design_param(self):
p = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=8,
transcription_order=3)
with warnings.catch_warnings(record=True) as w:
warnings.simplefilter('always')
p.add_design_parameter('g', opt=False, lower=5, upper=10, ref0=5, ref=10,
scaler=1, adder=0)
expected = 'Invalid options for non-optimal design parameter "g":' \
'lower, upper, scaler, adder, ref, ref0'
self.assertEqual(len(w), 1)
self.assertEqual(str(w[0].message), expected)
def _make_problem(self, transcription, num_seg, transcription_order=3):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
# Compute sparsity/coloring when run_driver is called
p.driver.options['dynamic_simul_derivs'] = True
t = {'gauss-lobatto': GaussLobatto(num_segments=num_seg, order=transcription_order),
'radau-ps': Radau(num_segments=num_seg, order=transcription_order),
'runge-kutta': RungeKutta(num_segments=num_seg)}
phase = Phase(ode_class=_BrachistochroneTestODE, transcription=t[transcription])
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(1, 1), duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True)
phase.set_state_options('y', fix_initial=True)
phase.set_state_options('v', fix_initial=True)
phase.add_control('theta', units='deg', rate_continuity=True, lower=0.01, upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
phase.add_boundary_constraint('x', loc='final', equals=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
p.model.linear_solver = DirectSolver()
p.setup()
p['phase0.t_initial'] = 1.0
p['phase0.t_duration'] = 3.0
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')
return p
def ssto_earth(transcription='gauss-lobatto', num_seg=10, transcription_order=5,
top_level_jacobian='csc', optimizer='SLSQP', compressed=False):
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['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
else:
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(transcription,
ode_class=LaunchVehicleODE,
ode_init_kwargs={'central_body': 'earth'},
num_segments=num_seg,
transcription_order=transcription_order,
compressed=compressed)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(10, 500))
phase.set_state_options('x', fix_initial=True, scaler=1.0E-5)
phase.set_state_options('y', fix_initial=True, scaler=1.0E-5)
phase.set_state_options('vx', fix_initial=True, scaler=1.0E-3)
phase.set_state_options('vy', fix_initial=True, scaler=1.0E-3)
phase.set_state_options('m', fix_initial=True, scaler=1.0E-3)
phase.add_boundary_constraint('y', loc='final', equals=1.85E5, linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=7796.6961)
phase.add_boundary_constraint('vy', loc='final', equals=0)
phase.add_control('theta', units='rad', lower=-1.57, upper=1.57)
phase.add_design_parameter('thrust', units='N', opt=False, val=2100000.0)
phase.add_objective('time', loc='final', scaler=0.01)
p.model.options['assembled_jac_type'] = top_level_jacobian.lower()
p.model.linear_solver = DirectSolver(assemble_jac=True)
return p
def test_invalid_ode_wrong_class(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=_A,
transcription=GaussLobatto(num_segments=20,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(4, 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, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
opt=False)
phase.add_design_parameter('g', units='m/s**2', opt=True, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('g')
p.model.linear_solver = DirectSolver()
with self.assertRaises(ValueError) as e:
p.setup(check=True)
self.assertEqual(
str(e.exception),
'ode_class must be derived from openmdao.core.System.')
def test_brachistochrone_for_docs_gauss_lobatto_without_simul_derivs(self):
from openmdao.api import Problem, Group, pyOptSparseDriver, 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 = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
phase = Phase('gauss-lobatto',
ode_class=BrachistochroneODE,
num_segments=100,
transcription_order=3,
compressed=True)
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)
def test_two_burn_orbit_raise_gl_rk_gl_constrained(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, GaussLobatto, RungeKutta, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=Group())
p.model.add_subsystem('traj', traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=True)
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5, units='DU/TU')
# First Phase (burn)
burn1 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr', fix_initial=True, fix_final=False)
burn1.set_state_options('vt', fix_initial=True, fix_final=False)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
# Second Phase (Coast)
coast = Phase(ode_class=FiniteBurnODE,
transcription=RungeKutta(num_segments=20, compressed=True))
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), duration_ref=10)
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=False)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_design_parameter('u1', opt=False, val=0.0)
# Third Phase (burn)
burn2 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), initial_ref=10)
burn2.set_state_options('r', fix_initial=False, fix_final=True)
burn2.set_state_options('theta', fix_initial=False, fix_final=False)
burn2.set_state_options('vr', fix_initial=False, fix_final=True)
burn2.set_state_options('vt', fix_initial=False, fix_final=True)
burn2.set_state_options('accel', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.set_state_options('deltav', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
burn1.add_timeseries_output('pos_x', units='DU')
coast.add_timeseries_output('pos_x', units='DU')
burn2.add_timeseries_output('pos_x', units='DU')
burn1.add_timeseries_output('pos_y', units='DU')
coast.add_timeseries_output('pos_y', units='DU')
burn2.add_timeseries_output('pos_y', units='DU')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.linear_solver = DirectSolver()
p.setup(check=True, force_alloc_complex=True)
# Set Initial Guesses
p.set_val('traj.design_parameters:c', value=1.5)
p.set_val('traj.burn1.t_initial', value=0.0)
p.set_val('traj.burn1.t_duration', value=2.25)
p.set_val('traj.burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('traj.burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('traj.burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('traj.burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('traj.burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'), )
p.set_val('traj.burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
p.set_val('traj.coast.t_initial', value=2.25)
p.set_val('traj.coast.t_duration', value=3.0)
p.set_val('traj.coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('traj.coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('traj.coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('traj.coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('traj.coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
# p.set_val('traj.coast.controls:u1',
# value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('traj.burn2.t_initial', value=5.25)
p.set_val('traj.burn2.t_duration', value=1.75)
p.set_val('traj.burn2.states:r',
value=burn2.interpolate(ys=[1.8, 3], nodes='state_input'))
p.set_val('traj.burn2.states:theta',
value=burn2.interpolate(ys=[3.2, 4.0], nodes='state_input'))
p.set_val('traj.burn2.states:vr',
value=burn2.interpolate(ys=[.5, 0], nodes='state_input'))
p.set_val('traj.burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)], nodes='state_input'))
p.set_val('traj.burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('traj.burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
p.get_val('traj.burn2.timeseries.states:deltav')[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate()
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = dict((phs, p.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_sol = dict((phs, p.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_sol = dict((phs, p.get_val('traj.{0}.timeseries.controls:u1'.format(phs), units='deg'))
for phs in ['burn1', 'burn2'])
t_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.controls:u1'.format(phs),
units='deg'))
for phs in ['burn1', 'burn2'])
for phs in ['burn1', 'coast', 'burn2']:
try:
ax_u1.plot(t_sol[phs], u1_sol[phs], 'ro', ms=3)
ax_u1.plot(t_exp[phs], u1_exp[phs], 'b-')
except KeyError:
pass
ax_deltav.plot(t_sol[phs], dv_sol[phs], 'ro', ms=3)
ax_deltav.plot(t_exp[phs], dv_exp[phs], 'b-')
ax_xy.plot(x_sol[phs], y_sol[phs], 'ro', ms=3, label='implicit')
ax_xy.plot(x_exp[phs], y_exp[phs], 'b-', label='explicit')
plt.show()
def test_timeseries_gl(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, 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, fix_final=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
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_phase', loc='final', scaler=10)
p.model.linear_solver = DirectSolver()
p.setup(check=True)
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],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
gd = phase.options['transcription'].grid_data
state_input_idxs = gd.subset_node_indices['state_input']
control_input_idxs = gd.subset_node_indices['control_input']
col_idxs = gd.subset_node_indices['col']
assert_rel_error(self, p.get_val('phase0.time'),
p.get_val('phase0.timeseries.time')[:, 0])
assert_rel_error(self, p.get_val('phase0.time_phase'),
p.get_val('phase0.timeseries.time_phase')[:, 0])
for state in ('x', 'y', 'v'):
assert_rel_error(
self, p.get_val('phase0.states:{0}'.format(state)),
p.get_val('phase0.timeseries.states:'
'{0}'.format(state))[state_input_idxs])
assert_rel_error(
self,
p.get_val('phase0.state_interp.state_col:{0}'.format(state)),
p.get_val('phase0.timeseries.states:'
'{0}'.format(state))[col_idxs])
for control in ('theta', ):
assert_rel_error(
self, p.get_val('phase0.controls:{0}'.format(control)),
p.get_val('phase0.timeseries.controls:'
'{0}'.format(control))[control_input_idxs])
for dp in ('g', ):
for i in range(gd.subset_num_nodes['all']):
assert_rel_error(
self,
p.get_val('phase0.design_parameters:{0}'.format(dp))[0, :],
p.get_val('phase0.timeseries.design_parameters:{0}'.format(
dp))[i])
def setUpClass(cls):
cls.traj = Trajectory()
p = Problem(model=cls.traj)
# Since we're only testing features like get_values that don't rely on a converged
# solution, no driver is attached. We'll just invoke run_model.
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=4,
transcription_order=3,
compressed=True)
cls.traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg')
burn1.add_design_parameter('c', opt=False, val=1.5)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
cls.traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
coast.add_design_parameter('c', opt=False, val=1.5)
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=3,
transcription_order=3,
compressed=True)
cls.traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=1.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
ref0=0,
ref=10)
burn2.add_design_parameter('c', opt=False, val=1.5)
burn2.add_objective('deltav', loc='final')
# Link Phases
cls.traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
cls.traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.add_recorder(SqliteRecorder('test_trajectory_rec.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'))
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('burn1.design_parameters:c', value=1.5)
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('coast.design_parameters:c', value=1.5)
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.set_val('burn2.design_parameters:c', value=1.5)
p.run_model()
def test_brachistochrone_recording(self):
import matplotlib
matplotlib.use('Agg')
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver, \
SqliteRecorder, CaseReader
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, GaussLobatto
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(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()
# 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,
p.get_val('phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-3)
cr = CaseReader('brachistochrone_solution.db')
system_cases = cr.list_cases('root')
case = cr.get_case(system_cases[-1])
outputs = dict([
(o[0], o[1])
for o in case.list_outputs(units=True, shape=True, out_stream=None)
])
assert_rel_error(
self, p['phase0.controls:theta'],
outputs['phase0.control_group.indep_controls.controls:theta']
['value'])
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 setUpClass(cls):
p = cls.p = Problem(model=Group())
# p.driver = pyOptSparseDriver()
# p.driver.options['optimizer'] = 'SNOPT'
# p.driver.options['dynamic_simul_derivs'] = True
# p.driver.opt_settings['Major iterations limit'] = 1000
# p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-4
# p.driver.opt_settings['Major optimality tolerance'] = 1.0E-4
# p.driver.opt_settings['iSumm'] = 6
NUM_SEG = 10
TRANSCRIPTION_ORDER = 7
orbit_phase = Phase('radau-ps',
ode_class=CadreOrbitODE,
num_segments=NUM_SEG,
transcription_order=TRANSCRIPTION_ORDER,
compressed=False)
p.model.add_subsystem('orbit_phase', orbit_phase)
orbit_phase.set_time_options(fix_initial=True, fix_duration=True)
orbit_phase.set_state_options('r_e2b_I',
defect_scaler=1000,
fix_initial=True,
units='km')
orbit_phase.set_state_options('v_e2b_I',
defect_scaler=1000,
fix_initial=True,
units='km/s')
# orbit_phase.set_state_options('SOC', defect_scaler=1, fix_initial=True, units=None)
# orbit_phase.add_design_parameter('P_bat', opt=False, units='W')
orbit_phase.add_design_parameter('Gamma', opt=False, units='rad')
orbit_phase.add_objective('time', loc='final', scaler=10)
# Add a control interp comp to interpolate the rates of O_BI from the orbit phase.
faux_control_options = {'O_BI': {'units': None, 'shape': (3, 3)}}
p.model.add_subsystem(
'obi_rate_interp_comp',
ControlInterpComp(control_options=faux_control_options,
time_units='s',
grid_data=orbit_phase.grid_data),
promotes_outputs=[('control_rates:O_BI_rate', 'Odot_BI')])
control_input_nodes_idxs = orbit_phase.grid_data.subset_node_indices[
'control_input']
src_idxs = get_src_indices_by_row(control_input_nodes_idxs,
shape=(3, 3))
p.model.connect('orbit_phase.rhs_all.O_BI',
'obi_rate_interp_comp.controls:O_BI',
src_indices=src_idxs,
flat_src_indices=True)
p.model.connect(
'orbit_phase.time.dt_dstau',
('obi_rate_interp_comp.dt_dstau', 'w_B_rate_interp_comp.dt_dstau'))
# Use O_BI and Odot_BI to compute the angular velocity vector
p.model.add_subsystem(
'angular_velocity_comp',
AngularVelocityComp(num_nodes=orbit_phase.grid_data.num_nodes))
p.model.connect('orbit_phase.rhs_all.O_BI',
'angular_velocity_comp.O_BI')
p.model.connect('Odot_BI', 'angular_velocity_comp.Odot_BI')
# Add another interpolation comp to compute the rate of w_B
faux_control_options = {'w_B': {'units': '1/s', 'shape': (3, )}}
p.model.add_subsystem(
'w_B_rate_interp_comp',
ControlInterpComp(control_options=faux_control_options,
time_units='s',
grid_data=orbit_phase.grid_data),
promotes_outputs=[('control_rates:w_B_rate', 'wdot_B')])
src_idxs = get_src_indices_by_row(control_input_nodes_idxs,
shape=(3, ))
p.model.connect('angular_velocity_comp.w_B',
'w_B_rate_interp_comp.controls:w_B',
src_indices=src_idxs,
flat_src_indices=True)
# Now add the systems phase
systems_phase = Phase('radau-ps',
ode_class=CadreSystemsODE,
num_segments=NUM_SEG,
transcription_order=TRANSCRIPTION_ORDER,
compressed=False)
p.model.add_subsystem('systems_phase', systems_phase)
systems_phase.set_time_options(fix_initial=True, fix_duration=True)
systems_phase.set_state_options('SOC',
defect_ref=1,
fix_initial=True,
units=None)
systems_phase.set_state_options('w_RW',
defect_ref=100,
fix_initial=True,
units='1/s')
systems_phase.set_state_options('data',
defect_ref=10,
fix_initial=True,
units='Gibyte')
systems_phase.set_state_options('temperature',
ref0=273,
ref=373,
defect_ref=100,
fix_initial=True,
units='degK')
systems_phase.add_design_parameter('LD', opt=False, units='d')
systems_phase.add_design_parameter('fin_angle',
opt=False,
lower=0.,
upper=np.pi / 2.)
systems_phase.add_design_parameter('antAngle',
opt=False,
lower=-np.pi / 4,
upper=np.pi / 4)
systems_phase.add_design_parameter('cellInstd',
opt=False,
lower=0.0,
upper=1.0,
ref=1.0)
# Add r_e2b_I and O_BI as non-optimized controls, allowing them to be connected to external sources
systems_phase.add_control('r_e2b_I', opt=False, units='km')
systems_phase.add_control('O_BI', opt=False)
systems_phase.add_control('w_B', opt=False)
systems_phase.add_control('wdot_B', opt=False)
systems_phase.add_control('P_comm',
opt=False,
lower=0.0,
upper=30.0,
units='W')
systems_phase.add_control('Isetpt',
opt=False,
lower=0.0,
upper=0.4,
units='A')
# Connect r_e2b_I and O_BI values from all nodes in the orbit phase to the input values
# in the attitude phase.
src_idxs = get_src_indices_by_row(control_input_nodes_idxs,
shape=(3, ))
p.model.connect('orbit_phase.states:r_e2b_I',
'systems_phase.controls:r_e2b_I',
src_indices=src_idxs,
flat_src_indices=True)
p.model.connect('angular_velocity_comp.w_B',
'systems_phase.controls:w_B',
src_indices=src_idxs,
flat_src_indices=True)
p.model.connect('wdot_B',
'systems_phase.controls:wdot_B',
src_indices=src_idxs,
flat_src_indices=True)
src_idxs = get_src_indices_by_row(control_input_nodes_idxs,
shape=(3, 3))
p.model.connect('orbit_phase.rhs_all.O_BI',
'systems_phase.controls:O_BI',
src_indices=src_idxs,
flat_src_indices=True)
p.setup(check=True)
# from openmdao.api import view_model
# view_model(p.model)
# Initialize values in the orbit phase
p['orbit_phase.t_initial'] = 0.0
p['orbit_phase.t_duration'] = duration
# p['systems_phase.states:w_RW'][:, 0] = 0.0
# p['systems_phase.states:w_RW'][:, 1] = 0.0
# p['systems_phase.states:w_RW'][:, 2] = 0.0
# Default starting orbit
# [ 2.89078958e+03 5.69493134e+03 -2.55340189e+03 2.56640460e-01
# 3.00387409e+00 6.99018448e+00]
p['orbit_phase.states:r_e2b_I'][:, 0] = 2.89078958e+03
p['orbit_phase.states:r_e2b_I'][:, 1] = 5.69493134e+03
p['orbit_phase.states:r_e2b_I'][:, 2] = -2.55340189e+03
p['orbit_phase.states:v_e2b_I'][:, 0] = 2.56640460e-01
p['orbit_phase.states:v_e2b_I'][:, 1] = 3.00387409e+00
p['orbit_phase.states:v_e2b_I'][:, 2] = 6.99018448e+00
# Initialize values in the systems phase
p['systems_phase.t_initial'] = 0.0
p['systems_phase.t_duration'] = duration
# p['systems_phase.states:w_RW'][:, 0] = 0.0
# p['systems_phase.states:w_RW'][:, 1] = 0.0
# p['systems_phase.states:w_RW'][:, 2] = 0.0
p['systems_phase.states:SOC'] = 1.0
p['systems_phase.states:w_RW'] = 100.0
p['systems_phase.states:data'] = 0.0
p['systems_phase.states:temperature'] = 273.0
# p['systems_phase.states:v_e2b_I'][:, 0] = 0.0
# p['systems_phase.states:v_e2b_I'][:, 1] = vcirc
# p['systems_phase.states:v_e2b_I'][:, 2] = 0.0
p['systems_phase.design_parameters:LD'] = 5233.5
p['systems_phase.design_parameters:fin_angle'] = 70.0
p.run_model()
def test_brachistochrone_integrated_control_radau_ps(self):
import numpy as np
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, Radau
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase(ode_class=BrachistochroneODE,
transcription=Radau(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.set_state_options('theta', targets='theta', fix_initial=False)
phase.add_control('theta_dot',
units='deg/s',
rate_continuity=True,
lower=0,
upper=60)
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()
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.states:theta'] = np.radians(
phase.interpolate(ys=[0.05, 100.0], nodes='state_input'))
p['phase0.controls:theta_dot'] = phase.interpolate(
ys=[50, 50], nodes='control_input')
# Solve for the optimal trajectory
p.run_driver()
# Test the results
assert_rel_error(self,
p.get_val('phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-3)
sim_out = phase.simulate(times_per_seg=20)
x_sol = p.get_val('phase0.timeseries.states:x')
y_sol = p.get_val('phase0.timeseries.states:y')
v_sol = p.get_val('phase0.timeseries.states:v')
theta_sol = p.get_val('phase0.timeseries.states:theta')
theta_dot_sol = p.get_val('phase0.timeseries.controls:theta_dot')
time_sol = p.get_val('phase0.timeseries.time')
x_sim = sim_out.get_val('phase0.timeseries.states:x')
y_sim = sim_out.get_val('phase0.timeseries.states:y')
v_sim = sim_out.get_val('phase0.timeseries.states:v')
theta_sim = sim_out.get_val('phase0.timeseries.states:theta')
theta_dot_sim = sim_out.get_val('phase0.timeseries.controls:theta_dot')
time_sim = sim_out.get_val('phase0.timeseries.time')
x_interp = interp1d(time_sim[:, 0], x_sim[:, 0])
y_interp = interp1d(time_sim[:, 0], y_sim[:, 0])
v_interp = interp1d(time_sim[:, 0], v_sim[:, 0])
theta_interp = interp1d(time_sim[:, 0], theta_sim[:, 0])
theta_dot_interp = interp1d(time_sim[:, 0], theta_dot_sim[:, 0])
assert_rel_error(self, x_interp(time_sol), x_sol, tolerance=1.0E-5)
assert_rel_error(self, y_interp(time_sol), y_sol, tolerance=1.0E-5)
assert_rel_error(self, v_interp(time_sol), v_sol, tolerance=1.0E-5)
assert_rel_error(self,
theta_interp(time_sol),
theta_sol,
tolerance=1.0E-5)
assert_rel_error(self,
theta_dot_interp(time_sol),
theta_dot_sol,
tolerance=1.0E-5)
fix_initial=True,
fix_final=False)
# phase.set_state_options('p%dmass' % i,
# scaler=0.01, defect_scaler=0.1, fix_initial=True,
# lower=0.0)
# phase.set_state_options('p%dimpulse' % i,
# scaler=0.01, defect_scaler=0.1, fix_initial=True)
phase.add_boundary_constraint('space%d.err_space_dist' % i,
constraint_name='space%d_err_space_dist' % i,
loc='final',
lower=0.0)
phase.add_design_parameter('speed%d' % i,
opt=True,
val=1.0,
upper=20,
lower=1e-9,
units='m/s')
phase.add_design_parameter('heading%d' % i,
opt=False,
val=heading,
units='rad')
phase.add_objective('time', loc='final', scaler=1.0)
p.model.add_constraint('phase0.rhs_disc.pairwise.dist', lower=20.0)
p.setup()
phase = p.model.phase0
def thermal_mission_problem(num_seg=5, transcription_order=3, meeting_altitude=20000., Q_env=0., Q_sink=0., Q_out=0., m_recirculated=0., opt_m_recirculated=False, opt_m_burn=False, opt_throttle=True, engine_heat_coeff=0., pump_heat_coeff=0., T=None, T_o=None, opt_m=False, m_initial=20.e3, transcription='gauss-lobatto'):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SNOPT'
p.driver.opt_settings['Major iterations limit'] = 5000
p.driver.opt_settings['Iterations limit'] = 5000000000000000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-8
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-8
p.driver.opt_settings['Verify level'] = -1
p.driver.opt_settings['Linesearch tolerance'] = .1
p.driver.opt_settings['Major step limit'] = .1
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(transcription, ode_class=ThermalMissionODE,
ode_init_kwargs={'engine_heat_coeff':engine_heat_coeff, 'pump_heat_coeff':pump_heat_coeff}, num_segments=num_seg,
transcription_order=transcription_order)
p.model.add_subsystem('phase', phase)
phase.set_time_options(opt_initial=False, 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=5.0E-0, 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=not opt_m, lower=15.e3, upper=80e3,
scaler=1.0E-3, defect_scaler=1.0E-3, units='kg')
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
rate_continuity=True)
phase.add_design_parameter('S', val=1., units='m**2', opt=False)
if opt_throttle:
phase.add_control('throttle', val=1.0, lower=0.0, upper=1.0, opt=True, rate_continuity=True)
else:
phase.add_design_parameter('throttle', val=1.0, opt=False)
phase.add_design_parameter('W0', val=10.5e3, opt=False, units='kg')
phase.add_boundary_constraint('h', loc='final', equals=meeting_altitude, scaler=1.0E-3, units='m')
phase.add_boundary_constraint('aero.mach', loc='final', equals=1., 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='time', upper=110.)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=100.0)
# phase.add_objective('energy', loc='final', ref=100.0)
# phase.add_objective('m', loc='final', ref=-10000.0)
# Set the state options for mass, temperature, and energy.
phase.set_state_options('T', fix_initial=True, ref=300, defect_scaler=1e-2)
phase.set_state_options('energy', fix_initial=True, ref=10e3, defect_scaler=1e-4)
# Allow the optimizer to vary the fuel flow
if opt_m_recirculated:
phase.add_control('m_recirculated', val=m_recirculated, lower=0., opt=True, rate_continuity=True, ref=20.)
else:
phase.add_control('m_recirculated', val=m_recirculated, opt=False)
phase.add_design_parameter('Q_env', val=Q_env, opt=False)
phase.add_design_parameter('Q_sink', val=Q_sink, opt=False)
phase.add_design_parameter('Q_out', val=Q_out, opt=False)
# Constrain the temperature, 2nd derivative of fuel mass in the tank, and make
# sure that the amount recirculated is at least 0, otherwise we'd burn
# more fuel than we pumped.
if opt_m_recirculated:
phase.add_path_constraint('m_flow', lower=0., upper=50., units='kg/s', ref=10.)
if T is not None:
phase.add_path_constraint('T', upper=T, units='K')
if T_o is not None:
phase.add_path_constraint('T_o', upper=T_o, units='K', ref=300.)
# phase.add_path_constraint('m_flow', lower=0., upper=20., units='kg/s', ref=10.)
p.setup(mode='fwd', check=True)
p['phase.t_initial'] = 0.0
p['phase.t_duration'] = 200.
p['phase.states:r'] = phase.interpolate(ys=[0.0, 111319.54], nodes='state_input')
p['phase.states:h'] = phase.interpolate(ys=[100.0, meeting_altitude], nodes='state_input')
# p['phase.states:h'][:] = 10000.
p['phase.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
# p['phase.states:v'][:] = 200.
p['phase.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['phase.states:m'] = phase.interpolate(ys=[m_initial, 12.e3], nodes='state_input')
p['phase.controls:alpha'] = phase.interpolate(ys=[1., 1.], nodes='control_input')
# Give initial values for the phase states, controls, and time
p['phase.states:T'] = 310.
return p
