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_brachistochrone_forward_shooting_path_constrained_ode_output(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=(0.5, 2.0))
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', 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=10)
phase.add_boundary_constraint('y', loc='final', equals=5)
phase.add_path_constraint('check', lower=-500, upper=500, shape=(1,), units='m/s')
# Minimize time at the end of the phase
phase.add_objective('time_phase', loc='final', scaler=1)
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'] = 0
p['phase0.states:y'] = 10
p['phase0.states:v'] = 0
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], 10,
tolerance=1.0E-3)
assert_rel_error(self, exp_out.get_val('phase0.timeseries.states:y')[-1, 0], 5,
tolerance=1.0E-3)
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 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 test_invalid_boundary_loc(self):
p = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=8,
order=3,
compressed=True))
with self.assertRaises(ValueError) as e:
p.add_boundary_constraint('x', loc='foo')
expected = 'Invalid boundary constraint location "foo". Must be "initial" or "final".'
self.assertEqual(str(e.exception), expected)
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_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 _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 min_time_climb_problem(num_seg=3, transcription_order=5,
transcription='gauss-lobatto',
top_level_densejacobian=True):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SNOPT'
p.driver.opt_settings['Major iterations limit'] = 500
p.driver.opt_settings['Iterations limit'] = 1000000000
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-10
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-10
p.driver.opt_settings['Verify level'] = 1
p.driver.opt_settings['Function precision'] = 1.0E-6
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=MinTimeClimbODE,
num_segments=num_seg,
transcription_order=transcription_order)
p.model.add_subsystem('phase', phase)
phase.set_time_options(opt_initial=False, duration_bounds=(50, 1e8),
duration_ref=100.0)
phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E8,
scaler=1.0E-4, defect_scaler=1.0E-3, 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, upper=500.,
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, 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=49.2386, units='m**2', opt=False)
# phase.add_design_parameter('throttle', val=1.0, opt=False)
phase.add_control('throttle', val=1.0, opt=True, lower=0., upper=1., rate_continuity=False)
phase.add_boundary_constraint('h', loc='final', equals=100., 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_boundary_constraint('r', loc='final', equals=1e6, units='m')
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='prop.m_dot', upper=0.)
# phase.add_path_constraint(name='flight_dynamics.r_dot', lower=0.)
# Minimize time at the end of the phase
# phase.add_objective('time', loc='final', ref=100.0)
phase.add_objective('m', loc='final', ref=-1000.0)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
p.setup(mode='fwd', check=True)
p['phase.t_initial'] = 0.0
p['phase.t_duration'] = 2000.
p['phase.states:r'] = phase.interpolate(ys=[0.0, 1e6], nodes='state_input')
p['phase.states:h'] = phase.interpolate(ys=[100.0, 1e4], nodes='state_input')
p['phase.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
p['phase.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['phase.states:m'] = phase.interpolate(ys=[30e3, 29e3], nodes='state_input')
# p['phase.controls:alpha'] = phase.interpolate(ys=[0.50, 0.50], nodes='all')
return p
def brachistochrone_min_time(transcription='gauss-lobatto',
num_segments=8,
transcription_order=3,
run_driver=True,
compressed=True,
optimizer='SLSQP'):
p = Problem(model=Group())
# if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
if transcription == 'gauss-lobatto':
t = GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
t = Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'runge-kutta':
t = RungeKutta(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
phase = Phase(ode_class=BrachistochroneODE, transcription=t)
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=False,
solve_segments=False)
phase.set_state_options('y',
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.set_state_options('v',
fix_initial=True,
fix_final=False,
solve_segments=False)
phase.add_control('theta',
continuity=True,
rate_continuity=True,
units='deg',
lower=0.01,
upper=179.9)
phase.add_input_parameter('g', units='m/s**2', 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_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.input_parameters:g'] = 9.80665
p.run_model()
if run_driver:
p.run_driver()
# Plot results
if SHOW_PLOTS:
exp_out = phase.simulate()
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.states:x')
y_imp = p.get_val('phase0.timeseries.states:y')
x_exp = exp_out.get_val('phase0.timeseries.states:x')
y_exp = exp_out.get_val('phase0.timeseries.states:y')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('x (m)')
ax.set_ylabel('y (m)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.time_phase')
y_imp = p.get_val('phase0.timeseries.controls:theta')
x_exp = exp_out.get_val('phase0.timeseries.time_phase')
y_exp = exp_out.get_val('phase0.timeseries.controls:theta')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('time (s)')
ax.set_ylabel('theta (rad)')
ax.grid(True)
ax.legend(loc='lower right')
plt.show()
return p
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 test_brachistochrone_undecorated_ode_rk(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, RungeKutta
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
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=(.5, 10),
units='s')
phase.set_state_options('x',
fix_initial=True,
rate_source='xdot',
units='m')
phase.set_state_options('y',
fix_initial=True,
rate_source='ydot',
units='m')
phase.set_state_options('v',
fix_initial=True,
rate_source='vdot',
targets=['v'],
units='m/s')
phase.add_control('theta',
units='deg',
rate_continuity=False,
lower=0.01,
upper=179.9,
targets=['theta'])
phase.add_design_parameter('g',
units='m/s**2',
opt=False,
val=9.80665,
targets=['g'])
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'] = 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)
defect_scaler=0.01,
fix_initial=True,
fix_final=False)
phase.set_state_options('p%dy' % i,
scaler=0.1,
defect_scaler=0.01,
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)
def test_two_phase_cannonball_for_docs(self):
from openmdao.api import Problem, Group, IndepVarComp, DirectSolver, SqliteRecorder, \
pyOptSparseDriver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, Trajectory, Radau, GaussLobatto
from dymos.examples.cannonball.cannonball_ode import CannonballODE
from dymos.examples.cannonball.size_comp import CannonballSizeComp
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.options['dynamic_simul_derivs'] = True
external_params = p.model.add_subsystem('external_params', IndepVarComp())
external_params.add_output('radius', val=0.10, units='m')
external_params.add_output('dens', val=7.87, units='g/cm**3')
external_params.add_design_var('radius', lower=0.01, upper=0.10, ref0=0.01, ref=0.10)
p.model.add_subsystem('size_comp', CannonballSizeComp())
traj = p.model.add_subsystem('traj', Trajectory())
transcription = Radau(num_segments=5, order=3, compressed=True)
ascent = Phase(ode_class=CannonballODE, transcription=transcription)
ascent = traj.add_phase('ascent', ascent)
# All initial states except flight path angle are fixed
# Final flight path angle is fixed (we will set it to zero so that the phase ends at apogee)
ascent.set_time_options(fix_initial=True, duration_bounds=(1, 100),
duration_ref=100, units='s')
ascent.set_state_options('r', fix_initial=True, fix_final=False)
ascent.set_state_options('h', fix_initial=True, fix_final=False)
ascent.set_state_options('gam', fix_initial=False, fix_final=True)
ascent.set_state_options('v', fix_initial=False, fix_final=False)
# Limit the muzzle energy
ascent.add_boundary_constraint('kinetic_energy.ke', loc='initial', units='J',
upper=400000, lower=0, ref=100000, shape=(1,))
# Second Phase (descent)
transcription = GaussLobatto(num_segments=5, order=3, compressed=True)
descent = Phase(ode_class=CannonballODE, transcription=transcription)
traj.add_phase('descent', descent)
# All initial states and time are free (they will be linked to the final states of ascent.
# Final altitude is fixed (we will set it to zero so that the phase ends at ground impact)
descent.set_time_options(initial_bounds=(.5, 100), duration_bounds=(.5, 100),
duration_ref=100)
descent.set_state_options('r', fix_initial=False, fix_final=False)
descent.set_state_options('h', fix_initial=False, fix_final=True)
descent.set_state_options('gam', fix_initial=False, fix_final=False)
descent.set_state_options('v', fix_initial=False, fix_final=False)
descent.add_objective('r', loc='final', scaler=-1.0)
# Add internally-managed design parameters to the trajectory.
traj.add_design_parameter('CD', val=0.5, units=None, opt=False)
traj.add_design_parameter('CL', val=0.0, units=None, opt=False)
traj.add_design_parameter('T', val=0.0, units='N', opt=False)
traj.add_design_parameter('alpha', val=0.0, units='deg', opt=False)
# Add externally-provided design parameters to the trajectory.
traj.add_input_parameter('mass',
target_params={'ascent': 'm', 'descent': 'm'},
val=1.0)
traj.add_input_parameter('S', val=0.005)
# Link Phases (link time and all state variables)
traj.link_phases(phases=['ascent', 'descent'], vars=['*'])
# Issue Connections
p.model.connect('external_params.radius', 'size_comp.radius')
p.model.connect('external_params.dens', 'size_comp.dens')
p.model.connect('size_comp.mass', 'traj.input_parameters:mass')
p.model.connect('size_comp.S', 'traj.input_parameters:S')
# Finish Problem Setup
p.model.linear_solver = DirectSolver()
p.driver.add_recorder(SqliteRecorder('ex_two_phase_cannonball.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('external_params.radius', 0.05, units='m')
p.set_val('external_params.dens', 7.87, units='g/cm**3')
p.set_val('traj.design_parameters:CD', 0.5)
p.set_val('traj.design_parameters:CL', 0.0)
p.set_val('traj.design_parameters:T', 0.0)
p.set_val('traj.ascent.t_initial', 0.0)
p.set_val('traj.ascent.t_duration', 10.0)
p.set_val('traj.ascent.states:r', ascent.interpolate(ys=[0, 100], nodes='state_input'))
p.set_val('traj.ascent.states:h', ascent.interpolate(ys=[0, 100], nodes='state_input'))
p.set_val('traj.ascent.states:v', ascent.interpolate(ys=[200, 150], nodes='state_input'))
p.set_val('traj.ascent.states:gam', ascent.interpolate(ys=[25, 0], nodes='state_input'),
units='deg')
p.set_val('traj.descent.t_initial', 10.0)
p.set_val('traj.descent.t_duration', 10.0)
p.set_val('traj.descent.states:r', descent.interpolate(ys=[100, 200], nodes='state_input'))
p.set_val('traj.descent.states:h', descent.interpolate(ys=[100, 0], nodes='state_input'))
p.set_val('traj.descent.states:v', descent.interpolate(ys=[150, 200], nodes='state_input'))
p.set_val('traj.descent.states:gam', descent.interpolate(ys=[0, -45], nodes='state_input'),
units='deg')
p.run_driver()
assert_rel_error(self, p.get_val('traj.descent.states:r')[-1],
3183.25, tolerance=1.0E-2)
exp_out = traj.simulate()
print('optimal radius: {0:6.4f} m '.format(p.get_val('external_params.radius',
units='m')[0]))
print('cannonball mass: {0:6.4f} kg '.format(p.get_val('size_comp.mass',
units='kg')[0]))
print('launch angle: {0:6.4f} '
'deg '.format(p.get_val('traj.ascent.timeseries.states:gam', units='deg')[0, 0]))
print('maximum range: {0:6.4f} '
'm '.format(p.get_val('traj.descent.timeseries.states:r')[-1, 0]))
fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(10, 6))
time_imp = {'ascent': p.get_val('traj.ascent.timeseries.time'),
'descent': p.get_val('traj.descent.timeseries.time')}
time_exp = {'ascent': exp_out.get_val('traj.ascent.timeseries.time'),
'descent': exp_out.get_val('traj.descent.timeseries.time')}
r_imp = {'ascent': p.get_val('traj.ascent.timeseries.states:r'),
'descent': p.get_val('traj.descent.timeseries.states:r')}
r_exp = {'ascent': exp_out.get_val('traj.ascent.timeseries.states:r'),
'descent': exp_out.get_val('traj.descent.timeseries.states:r')}
h_imp = {'ascent': p.get_val('traj.ascent.timeseries.states:h'),
'descent': p.get_val('traj.descent.timeseries.states:h')}
h_exp = {'ascent': exp_out.get_val('traj.ascent.timeseries.states:h'),
'descent': exp_out.get_val('traj.descent.timeseries.states:h')}
axes.plot(r_imp['ascent'], h_imp['ascent'], 'bo')
axes.plot(r_imp['descent'], h_imp['descent'], 'ro')
axes.plot(r_exp['ascent'], h_exp['ascent'], 'b--')
axes.plot(r_exp['descent'], h_exp['descent'], 'r--')
axes.set_xlabel('range (m)')
axes.set_ylabel('altitude (m)')
fig, axes = plt.subplots(nrows=4, ncols=1, figsize=(10, 6))
states = ['r', 'h', 'v', 'gam']
for i, state in enumerate(states):
x_imp = {'ascent': p.get_val('traj.ascent.timeseries.states:{0}'.format(state)),
'descent': p.get_val('traj.descent.timeseries.states:{0}'.format(state))}
x_exp = {'ascent': exp_out.get_val('traj.ascent.timeseries.states:{0}'.format(state)),
'descent': exp_out.get_val('traj.descent.timeseries.states:{0}'.format(state))}
axes[i].set_ylabel(state)
axes[i].plot(time_imp['ascent'], x_imp['ascent'], 'bo')
axes[i].plot(time_imp['descent'], x_imp['descent'], 'ro')
axes[i].plot(time_exp['ascent'], x_exp['ascent'], 'b--')
axes[i].plot(time_exp['descent'], x_exp['descent'], 'r--')
params = ['CL', 'CD', 'T', 'alpha', 'm', 'S']
fig, axes = plt.subplots(nrows=6, ncols=1, figsize=(12, 6))
for i, param in enumerate(params):
p_imp = {
'ascent': p.get_val('traj.ascent.timeseries.traj_parameters:{0}'.format(param)),
'descent': p.get_val('traj.descent.timeseries.traj_parameters:{0}'.format(param))}
p_exp = {'ascent': exp_out.get_val('traj.ascent.timeseries.'
'traj_parameters:{0}'.format(param)),
'descent': exp_out.get_val('traj.descent.timeseries.'
'traj_parameters:{0}'.format(param))}
axes[i].set_ylabel(param)
axes[i].plot(time_imp['ascent'], p_imp['ascent'], 'bo')
axes[i].plot(time_imp['descent'], p_imp['descent'], 'ro')
axes[i].plot(time_exp['ascent'], p_exp['ascent'], 'b--')
axes[i].plot(time_exp['descent'], p_exp['descent'], 'r--')
plt.show()
scaler=1.0E-3, defect_scaler=1.0E-3, units='m')
phase.set_state_options('v', fix_initial=True, lower=0.01,
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=1e3, upper=1.0E6,
scaler=1.0E-3, defect_scaler=1.0E-3)
phase.add_control('alpha', units='rad', lower=-8. * np.pi/180., upper=8. * np.pi/180., scaler=1, rate_continuity=True)
phase.add_control('throttle', val=1.0, lower=0., upper=1., opt=True, rate_continuity=True)
phase.add_boundary_constraint('h', loc='final', equals=100., scaler=1.0E-3, units='m')
phase.add_boundary_constraint('r', loc='final', equals=1500., units='km')
# phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
phase.add_path_constraint(name='aero.mach', lower=0.01, upper=.9)
# phase.add_path_constraint(name='prop.m_dot', upper=0.)
# phase.add_path_constraint(name='flight_dynamics.r_dot', lower=0.)
# phase.add_path_constraint(name='m', lower=1e4)
phase.add_path_constraint(name='h', lower=0.)
# phase.set_objective('time', loc='final', ref=10.0)
phase.add_objective('m', loc='final', ref=-10000.0)
# phase.set_objective('r', loc='final', ref=-100000.0)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
def escort_problem(optimizer='SLSQP',
num_seg=3,
transcription_order=5,
transcription='gauss-lobatto',
meeting_altitude=14000.,
climb_time=350.,
starting_mass=19030.468):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
if optimizer == 'SNOPT':
p.driver.opt_settings['Major iterations limit'] = 1000
p.driver.opt_settings['Iterations limit'] = 100000000
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-5
p.driver.opt_settings['Verify level'] = -1
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
phase_class = _phase_map[transcription]
climb = Phase('gauss-lobatto',
ode_class=MinTimeClimbODE,
num_segments=num_seg,
transcription_order=transcription_order)
climb.set_time_options(duration_bounds=(50, climb_time),
duration_ref=100.0)
climb.set_state_options('r',
fix_initial=True,
lower=0,
upper=1.0E6,
scaler=1.0E-3,
defect_scaler=1.0E-2,
units='m')
climb.set_state_options('h',
fix_initial=True,
lower=0,
upper=20000.0,
scaler=1.0E-3,
defect_scaler=1.0E-3,
units='m')
climb.set_state_options('v',
fix_initial=True,
lower=10.0,
scaler=1.0E-2,
defect_scaler=1.0E-2,
units='m/s')
climb.set_state_options('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
ref=1.0,
defect_scaler=1.0,
units='rad')
climb.set_state_options('m',
fix_initial=True,
lower=10.0,
upper=1.0E5,
scaler=1.0E-3,
defect_scaler=1.0E-3)
climb.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True)
climb.add_control('S', val=49.2386, units='m**2', dynamic=False, opt=False)
climb.add_control('Isp', val=5000.0, units='s', dynamic=False, opt=False)
climb.add_control('throttle', val=1.0, dynamic=False, opt=False)
climb.add_boundary_constraint('h',
loc='final',
equals=meeting_altitude,
scaler=1.0E-3,
units='m')
climb.add_boundary_constraint('aero.mach',
loc='final',
equals=1.0,
units=None)
climb.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
# climb.add_boundary_constraint('time', loc='final', upper=climb_time, units='s')
climb.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
climb.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Minimize time at the end of the climb
climb.set_objective('time', loc='final', ref=100.0)
p.model.add_subsystem('climb', climb)
escort = Phase('gauss-lobatto',
ode_class=MinTimeClimbODE,
num_segments=num_seg * 2,
transcription_order=transcription_order)
escort.set_time_options(duration_bounds=(50, 10000),
opt_initial=True,
duration_ref=100.0)
escort.set_state_options('r',
lower=0,
upper=1.0E6,
scaler=1.0E-3,
defect_scaler=1.0E-2,
units='m')
escort.set_state_options('h',
lower=0,
upper=20000.0,
scaler=1.0E-3,
defect_scaler=1.0E-3,
units='m')
escort.set_state_options('v',
lower=10.0,
scaler=1.0E-2,
defect_scaler=1.0E-2,
units='m/s')
escort.set_state_options('gam',
lower=-1.5,
upper=1.5,
ref=1.0,
defect_scaler=1.0,
units='rad')
escort.set_state_options('m',
lower=10.0,
upper=1.0E5,
scaler=1.0E-3,
defect_scaler=1.0E-3)
escort.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True)
escort.add_control('S',
val=49.2386,
units='m**2',
dynamic=False,
opt=False)
escort.add_control('Isp', val=1600.0, units='s', dynamic=False, opt=False)
escort.add_control('throttle', val=1.0, lower=0., upper=1., opt=True)
# escort.add_control('throttle', val=1.0, dynamic=False, opt=False)
# escort.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m')
# escort.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None)
# escort.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
escort.add_boundary_constraint('m',
loc='final',
equals=15000.0,
units='kg')
escort.add_path_constraint(name='h',
lower=meeting_altitude,
upper=meeting_altitude,
ref=meeting_altitude)
escort.add_path_constraint(name='aero.mach', equals=1.0)
# Maximize distance at the end of the escort
# escort.set_objective('r', loc='final', ref=-1e5)
p.model.add_subsystem('escort', escort)
# Connect the phases
linkage_comp = PhaseLinkageComp()
linkage_comp.add_linkage(name='L01',
vars=['t'],
units='s',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['r'],
units='m',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['h'],
units='m',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['v'],
units='m/s',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['gam'],
units='rad',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['m'],
units='kg',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['alpha'],
units='rad',
equals=0.0,
linear=True)
linkage_comp.add_linkage(name='L01',
vars=['throttle'],
equals=0.0,
linear=True)
p.model.connect('climb.time++', 'linkages.L01_t:lhs')
p.model.connect('escort.time--', 'linkages.L01_t:rhs')
p.model.connect('climb.states:r++', 'linkages.L01_r:lhs')
p.model.connect('escort.states:r--', 'linkages.L01_r:rhs')
p.model.connect('climb.states:h++', 'linkages.L01_h:lhs')
p.model.connect('escort.states:h--', 'linkages.L01_h:rhs')
#
p.model.connect('climb.states:v++', 'linkages.L01_v:lhs')
p.model.connect('escort.states:v--', 'linkages.L01_v:rhs')
#
p.model.connect('climb.states:gam++', 'linkages.L01_gam:lhs')
p.model.connect('escort.states:gam--', 'linkages.L01_gam:rhs')
p.model.connect('climb.states:m++', 'linkages.L01_m:lhs')
p.model.connect('escort.states:m--', 'linkages.L01_m:rhs')
p.model.connect('climb.controls:alpha++', 'linkages.L01_alpha:lhs')
p.model.connect('escort.controls:alpha--', 'linkages.L01_alpha:rhs')
p.model.connect('climb.controls:throttle++', 'linkages.L01_throttle:lhs')
p.model.connect('escort.controls:throttle--', 'linkages.L01_throttle:rhs')
p.model.add_subsystem('linkages', linkage_comp)
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.options['assembled_jac_type'] = 'csc'
# p.driver.add_recorder(SqliteRecorder('escort.db'))
p.setup(mode='fwd', check=True)
p['climb.t_initial'] = 0.0
p['climb.t_duration'] = 200.
p['climb.states:r'] = climb.interpolate(ys=[0.0, 111319.54], nodes='disc')
p['climb.states:h'] = climb.interpolate(ys=[100.0, 20000.0], nodes='disc')
p['climb.states:v'] = climb.interpolate(ys=[135.964, 283.159],
nodes='disc')
p['climb.states:gam'] = climb.interpolate(ys=[0.0, 0.0], nodes='disc')
p['climb.states:m'] = climb.interpolate(ys=[starting_mass, 16841.431],
nodes='disc')
p['climb.controls:alpha'] = climb.interpolate(ys=[0.0, 0.0], nodes='all')
p['escort.t_initial'] = 200.
p['escort.t_duration'] = 1000.
p['escort.states:r'] = escort.interpolate(ys=[111319.54, 400000.],
nodes='disc')
p['escort.states:h'] = escort.interpolate(
ys=[meeting_altitude, meeting_altitude], nodes='disc')
p['escort.states:v'] = escort.interpolate(ys=[250., 250.], nodes='disc')
p['escort.states:gam'] = escort.interpolate(ys=[0.0, 0.0], nodes='disc')
p['escort.states:m'] = escort.interpolate(ys=[17000., 15000.],
nodes='disc')
p['escort.controls:alpha'] = escort.interpolate(ys=[0.0, 0.0], nodes='all')
return p
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
def test_control_rate2_boundary_constraint_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=20,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(0.1, 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,
rate2_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('theta_rate2',
loc='final',
equals=0.0,
units='deg/s**2')
# Minimize time at the end of the phase
phase.add_objective('time')
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'] = 8
p.run_driver()
plt.plot(p.get_val('phase0.timeseries.states:x'),
p.get_val('phase0.timeseries.states:y'), 'ko')
plt.figure()
plt.plot(p.get_val('phase0.timeseries.time'),
p.get_val('phase0.timeseries.controls:theta'), 'ro')
plt.plot(p.get_val('phase0.timeseries.time'),
p.get_val('phase0.timeseries.control_rates:theta_rate'), 'bo')
plt.plot(p.get_val('phase0.timeseries.time'),
p.get_val('phase0.timeseries.control_rates:theta_rate2'),
'go')
plt.show()
assert_rel_error(
self,
p.get_val('phase0.timeseries.control_rates:theta_rate2')[-1],
0,
tolerance=1.0E-6)
def test_two_phase_cannonball_for_docs(self):
from openmdao.api import Problem, Group, IndepVarComp, DirectSolver, SqliteRecorder, \
pyOptSparseDriver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, Trajectory, load_simulation_results
from dymos.examples.cannonball.cannonball_ode import CannonballODE
from dymos.examples.cannonball.size_comp import CannonballSizeComp
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.options['dynamic_simul_derivs'] = True
external_params = p.model.add_subsystem('external_params',
IndepVarComp())
external_params.add_output('radius', val=0.10, units='m')
external_params.add_output('dens', val=7.87, units='g/cm**3')
external_params.add_design_var('radius',
lower=0.01,
upper=0.10,
ref0=0.01,
ref=0.10)
p.model.add_subsystem('size_comp', CannonballSizeComp())
traj = p.model.add_subsystem('traj', Trajectory())
# First Phase (ascent)
ascent = Phase('radau-ps',
ode_class=CannonballODE,
num_segments=5,
transcription_order=3,
compressed=True)
ascent = traj.add_phase('ascent', ascent)
# All initial states except flight path angle are fixed
# Final flight path angle is fixed (we will set it to zero so that the phase ends at apogee)
ascent.set_time_options(fix_initial=True,
duration_bounds=(1, 100),
duration_ref=100)
ascent.set_state_options('r', fix_initial=True, fix_final=False)
ascent.set_state_options('h', fix_initial=True, fix_final=False)
ascent.set_state_options('gam', fix_initial=False, fix_final=True)
ascent.set_state_options('v', fix_initial=False, fix_final=False)
# Limit the muzzle energy
ascent.add_boundary_constraint('kinetic_energy.ke',
loc='initial',
units='J',
upper=400000,
lower=0,
ref=100000)
# Second Phase (descent)
descent = Phase('gauss-lobatto',
ode_class=CannonballODE,
num_segments=5,
transcription_order=3,
compressed=True)
traj.add_phase('descent', descent)
# All initial states and time are free (they will be linked to the final states of ascent.
# Final altitude is fixed (we will set it to zero so that the phase ends at ground impact)
descent.set_time_options(initial_bounds=(.5, 100),
duration_bounds=(.5, 100),
duration_ref=100)
descent.set_state_options('r', fix_initial=False, fix_final=False)
descent.set_state_options('h', fix_initial=False, fix_final=True)
descent.set_state_options('gam', fix_initial=False, fix_final=False)
descent.set_state_options('v', fix_initial=False, fix_final=False)
descent.add_objective('r', loc='final', scaler=-1.0)
# Add internally-managed design parameters to the trajectory.
traj.add_design_parameter('CD', val=0.5, units=None, opt=False)
traj.add_design_parameter('CL', val=0.0, units=None, opt=False)
traj.add_design_parameter('T', val=0.0, units='N', opt=False)
traj.add_design_parameter('alpha', val=0.0, units='deg', opt=False)
# Add externally-provided design parameters to the trajectory.
traj.add_input_parameter('mass',
targets={
'ascent': 'm',
'descent': 'm'
},
val=1.0,
units='kg')
traj.add_input_parameter('S', val=0.005, units='m**2')
# Link Phases (link time and all state variables)
traj.link_phases(phases=['ascent', 'descent'], vars=['*'])
# Issue Connections
p.model.connect('external_params.radius', 'size_comp.radius')
p.model.connect('external_params.dens', 'size_comp.dens')
p.model.connect('size_comp.mass', 'traj.input_parameters:mass')
p.model.connect('size_comp.S', 'traj.input_parameters:S')
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(SqliteRecorder('ex_two_phase_cannonball.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('external_params.radius', 0.05, units='m')
p.set_val('external_params.dens', 7.87, units='g/cm**3')
p.set_val('traj.design_parameters:CD', 0.5)
p.set_val('traj.design_parameters:CL', 0.0)
p.set_val('traj.design_parameters:T', 0.0)
p.set_val('traj.ascent.t_initial', 0.0)
p.set_val('traj.ascent.t_duration', 10.0)
p.set_val('traj.ascent.states:r',
ascent.interpolate(ys=[0, 100], nodes='state_input'))
p.set_val('traj.ascent.states:h',
ascent.interpolate(ys=[0, 100], nodes='state_input'))
p.set_val('traj.ascent.states:v',
ascent.interpolate(ys=[200, 150], nodes='state_input'))
p.set_val('traj.ascent.states:gam',
ascent.interpolate(ys=[25, 0], nodes='state_input'),
units='deg')
p.set_val('traj.descent.t_initial', 10.0)
p.set_val('traj.descent.t_duration', 10.0)
p.set_val('traj.descent.states:r',
descent.interpolate(ys=[100, 200], nodes='state_input'))
p.set_val('traj.descent.states:h',
descent.interpolate(ys=[100, 0], nodes='state_input'))
p.set_val('traj.descent.states:v',
descent.interpolate(ys=[150, 200], nodes='state_input'))
p.set_val('traj.descent.states:gam',
descent.interpolate(ys=[0, -45], nodes='state_input'),
units='deg')
p.run_driver()
assert_rel_error(self,
traj.get_values('r')['descent'][-1],
3191.83945861,
tolerance=1.0E-2)
exp_out = traj.simulate(times=100,
record_file='ex_two_phase_cannonball_sim.db')
# exp_out_loaded = load_simulation_results('ex_two_phase_cannonball_sim.db')
print('optimal radius: {0:6.4f} m '.format(
p.get_val('external_params.radius', units='m')[0]))
print('cannonball mass: {0:6.4f} kg '.format(
p.get_val('size_comp.mass', units='kg')[0]))
fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(8, 6))
axes[0].plot(
traj.get_values('r')['ascent'],
traj.get_values('h')['ascent'], 'bo')
axes[0].plot(
traj.get_values('r')['descent'],
traj.get_values('h')['descent'], 'ro')
axes[0].plot(
exp_out.get_values('r')['ascent'],
exp_out.get_values('h')['ascent'], 'b--')
axes[0].plot(
exp_out.get_values('r')['descent'],
exp_out.get_values('h')['descent'], 'r--')
axes[0].set_xlabel('range (m)')
axes[0].set_ylabel('altitude (m)')
# plt.suptitle('Kinetic Energy vs Time')
axes[1].plot(
traj.get_values('time')['ascent'],
traj.get_values('kinetic_energy.ke')['ascent'], 'bo')
axes[1].plot(
traj.get_values('time')['descent'],
traj.get_values('kinetic_energy.ke')['descent'], 'ro')
axes[1].plot(
exp_out.get_values('time')['ascent'],
exp_out.get_values('kinetic_energy.ke')['ascent'], 'b--')
axes[1].plot(
exp_out.get_values('time')['descent'],
exp_out.get_values('kinetic_energy.ke')['descent'], 'r--')
# axes[1].plot(exp_out_loaded.get_values('time')['ascent'],
# exp_out_loaded.get_values('kinetic_energy.ke')['ascent'],
# 'b--')
#
# axes[1].plot(exp_out_loaded.get_values('time')['descent'],
# exp_out_loaded.get_values('kinetic_energy.ke')['descent'],
# 'r--')
axes[1].set_xlabel('time (s)')
axes[1].set_ylabel(r'kinetic energy (J)')
# plt.figure()
axes[2].plot(
traj.get_values('time')['ascent'],
traj.get_values('gam', units='deg')['ascent'], 'bo')
axes[2].plot(
traj.get_values('time')['descent'],
traj.get_values('gam', units='deg')['descent'], 'ro')
axes[2].plot(
exp_out.get_values('time')['ascent'],
exp_out.get_values('gam', units='deg')['ascent'], 'b--')
axes[2].plot(
exp_out.get_values('time')['descent'],
exp_out.get_values('gam', units='deg')['descent'], 'r--')
axes[2].set_xlabel('time (s)')
axes[2].set_ylabel(r'flight path angle (deg)')
plt.show()
def test_brachistochrone_vector_ode_path_constraints_rk_partial_indices(
self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=RungeKutta(num_segments=20))
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', equals=[10, 5])
phase.add_path_constraint('pos_dot',
shape=(2, ),
units='m/s',
indices=[1],
lower=-4,
upper=4)
phase.add_timeseries_output('pos_dot', shape=(2, ), units='m/s')
# 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'] = 2.0
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=[5, 100],
nodes='control_input')
p['phase0.design_parameters:g'] = 9.80665
p.run_driver()
assert_rel_error(self,
np.min(p.get_val('phase0.timeseries.pos_dot')[:, -1]),
-4,
tolerance=1.0E-2)
# Plot results
if SHOW_PLOTS:
exp_out = phase.simulate(times_per_seg=20)
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.states:pos')[:, 0]
y_imp = p.get_val('phase0.timeseries.states:pos')[:, 1]
x_exp = exp_out.get_val('phase0.timeseries.states:pos')[:, 0]
y_exp = exp_out.get_val('phase0.timeseries.states:pos')[:, 1]
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('x (m)')
ax.set_ylabel('y (m)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution\nVelocity')
t_imp = p.get_val('phase0.timeseries.time')
t_exp = exp_out.get_val('phase0.timeseries.time')
xdot_imp = p.get_val('phase0.timeseries.pos_dot')[:, 0]
ydot_imp = p.get_val('phase0.timeseries.pos_dot')[:, 1]
xdot_exp = exp_out.get_val('phase0.timeseries.pos_dot')[:, 0]
ydot_exp = exp_out.get_val('phase0.timeseries.pos_dot')[:, 1]
ax.plot(t_imp, xdot_imp, 'bo', label='implicit')
ax.plot(t_exp, xdot_exp, 'b-', label='explicit')
ax.plot(t_imp, ydot_imp, 'ro', label='implicit')
ax.plot(t_exp, ydot_exp, 'r-', label='explicit')
ax.set_xlabel('t (s)')
ax.set_ylabel('v (m/s)')
ax.grid(True)
ax.legend(loc='upper right')
fig, ax = plt.subplots()
fig.suptitle('Brachistochrone Solution')
x_imp = p.get_val('phase0.timeseries.time')
y_imp = p.get_val('phase0.timeseries.control_rates:theta_rate2')
x_exp = exp_out.get_val('phase0.timeseries.time')
y_exp = exp_out.get_val(
'phase0.timeseries.control_rates:theta_rate2')
ax.plot(x_imp, y_imp, 'ro', label='implicit')
ax.plot(x_exp, y_exp, 'b-', label='explicit')
ax.set_xlabel('time (s)')
ax.set_ylabel('theta rate2 (rad/s**2)')
ax.grid(True)
ax.legend(loc='lower right')
plt.show()
return p
def test_design_parameter_boundary_constraint(self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneODE,
transcription=GaussLobatto(num_segments=20,
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=True, val=9.80665)
# We'll let g vary, but make sure it hits the desired value.
# It's a static design parameter, so it shouldn't matter whether we enforce it
# at the start or the end of the phase, so here we'll do both.
# Note if we make these equality constraints, some optimizers (SLSQP) will
# see the problem as infeasible.
phase.add_boundary_constraint('g',
loc='initial',
units='m/s**2',
upper=9.80665)
phase.add_boundary_constraint('g',
loc='final',
units='m/s**2',
upper=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'] = 5
p.run_driver()
assert_rel_error(self,
p.get_val('phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-4)
assert_rel_error(self,
p.get_val('phase0.timeseries.design_parameters:g')[0],
9.80665,
tolerance=1.0E-6)
assert_rel_error(
self,
p.get_val('phase0.timeseries.design_parameters:g')[-1],
9.80665,
tolerance=1.0E-6)
end_y = center_y + r * np.sin(theta + theta2)
locations.append([start_x, end_x, start_y, end_y])
#print("location", i, locations[-1])
phase.add_input_parameter('sx%d' % i, val=start_x, units='m')
phase.add_input_parameter('sy%d' % i, val=start_y, units='m')
phase.add_input_parameter('ex%d' % i, val=end_x, units='m')
phase.add_input_parameter('ey%d' % i, val=end_y, units='m')
phase.add_input_parameter('ts%d' % i, val=t_start, units='s')
phase.add_input_parameter('te%d' % i, val=t_end, units='s')
phase.set_state_options('x%d' % i, scaler=0.01, defect_scaler=0.1)
phase.set_state_options('y%d' % i, scaler=0.01, defect_scaler=0.1)
phase.add_boundary_constraint('x%d' % i, loc='initial', equals=start_x)
phase.add_boundary_constraint('y%d' % i, loc='initial', equals=start_y)
phase.add_boundary_constraint('x%d' % i, loc='final', equals=end_x)
phase.add_boundary_constraint('y%d' % i, loc='final', equals=end_y)
# phase.set_state_options('v%d' % i, fix_initial=False, fix_final=False,
# scaler=0.01, defect_scaler=0.01, lower=0.0)
phase.add_control('vx%d' % i,
rate_continuity=False,
units='m/s',
opt=True,
upper=10,
lower=-10.0,
scaler=200.0,
adder=-10)
phase.add_control('vy%d' % i,
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
