def __init__(self, body, sc, method, nb_seg, order, solver, ode_class, ode_kwargs, ph_name, snopt_opts=None,
rec_file=None):
NLP.__init__(self, body, sc, method, nb_seg, order, solver, snopt_opts=snopt_opts, rec_file=rec_file)
# Transcription object
if self.method == 'gauss-lobatto':
self.transcription = GaussLobatto(num_segments=self.nb_seg, order=self.order, compressed=True)
elif self.method == 'radau-ps':
self.transcription = Radau(num_segments=self.nb_seg, order=self.order, compressed=True)
elif self.method == 'runge-kutta':
self.transcription = RungeKutta(num_segments=self.nb_seg, order=self.order, compressed=True)
else:
raise ValueError('method must be either gauss-lobatto or radau-ps')
# Phase object
self.phase = self.trajectory.add_phase(ph_name, Phase(ode_class=ode_class, ode_init_kwargs=ode_kwargs,
transcription=self.transcription))
self.phase_name = ''.join(['traj.', ph_name])
# discretization nodes
self.state_nodes = None
self.control_nodes = None
self.t_all = None
self.t_state = None
self.t_control = None
self.idx_state_control = None
# time of flight
self.tof = None
def test_solver_defects_single_phase_reverse_propagation(self):
prob = Problem()
num_seg = 5
seg_ends, _ = lgl(num_seg + 1)
# First phase: normal operation.
transcription = Radau(num_segments=5,
order=5,
segment_ends=seg_ends,
compressed=True)
phase0 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = prob.model.add_subsystem('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.set_state_options('state_of_charge',
fix_initial=True,
fix_final=False,
solve_segments=True)
prob.setup()
prob['phase0.t_initial'] = 0
prob['phase0.t_duration'] = -1.0 * 3600
prob['phase0.states:state_of_charge'][:] = 0.63464982
prob.set_solver_print(level=0)
prob.run_model()
soc0 = prob['phase0.states:state_of_charge']
assert_rel_error(self, soc0[-1], 1.0, 1e-6)
def __init__(self, body, sc, method, nb_seg, order, solver, ode_class, ode_kwargs, ph_name, snopt_opts=None,
rec_file=None):
if isinstance(order, int):
order = tuple(order for _ in range(len(nb_seg)))
if isinstance(method, str):
method = tuple(method for _ in range(len(nb_seg)))
NLP.__init__(self, body, sc, method, nb_seg, order, solver, snopt_opts=snopt_opts, rec_file=rec_file)
# Transcription objects list
self.transcription = []
for i in range(len(self.nb_seg)):
if self.method[i] == 'gauss-lobatto':
t = GaussLobatto(num_segments=self.nb_seg[i], order=self.order[i], compressed=True)
elif self.method[i] == 'radau-ps':
t = Radau(num_segments=self.nb_seg[i], order=self.order[i], compressed=True)
elif self.method[i] == 'runge-kutta':
t = RungeKutta(num_segments=self.nb_seg[i], order=self.order[i], compressed=True)
else:
raise ValueError('method must be either gauss-lobatto, radau-ps or runge-kutta')
self.transcription.append(t)
# Phase objects list
self.phase = []
self.phase_name = []
for i in range(len(self.nb_seg)):
ph = self.trajectory.add_phase(ph_name[i], Phase(ode_class=ode_class[i], ode_init_kwargs=ode_kwargs[i],
transcription=self.transcription[i]))
self.phase.append(ph)
self.phase_name.append(''.join(['traj.', ph_name[i]]))
def test_control_rate2_path_constraint_radau(self):
from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Phase, Radau
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
phase = Phase(ode_class=BrachistochroneODE,
transcription=Radau(num_segments=10, compressed=False))
p.model.add_subsystem('phase0', phase)
phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10))
phase.set_state_options('x', fix_initial=True, fix_final=True)
phase.set_state_options('y', fix_initial=True, fix_final=True)
phase.set_state_options('v', fix_initial=True)
phase.add_control('theta', units='deg', lower=0.01, upper=179.9)
phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', scaler=10)
phase.add_path_constraint('theta_rate2',
lower=-200,
upper=200,
units='rad/s**2')
p.model.linear_solver = DirectSolver()
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,
p.get_val('phase0.timeseries.time')[-1],
1.8016,
tolerance=1.0E-3)
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_solver_defects_reverse_propagation(self):
prob = Problem()
num_seg = 5
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
transcription = Radau(num_segments=5,
order=5,
segment_ends=seg_ends,
compressed=True)
phase0 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = traj.add_phase('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.set_state_options('state_of_charge',
fix_initial=True,
fix_final=False,
solve_segments=True)
# Second phase: normal operation.
phase1 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p1 = traj.add_phase('phase1', phase1)
traj_p1.set_time_options(fix_initial=False, fix_duration=True)
traj_p1.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments=True)
traj_p1.add_objective('time', loc='final')
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'],
connected=True)
prob.setup()
prob['traj.phase0.t_initial'] = 0
prob['traj.phase0.t_duration'] = -1.0 * 3600
prob['traj.phase0.states:state_of_charge'][:] = 0.23794217
prob['traj.phase1.t_initial'] = 0
prob['traj.phase1.t_duration'] = -1.0 * 3600
prob.set_solver_print(level=0)
prob.run_model()
soc1 = prob['traj.phase1.states:state_of_charge']
assert_rel_error(self, soc1[-1], 1.0, 1e-6)
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 test_radau(self):
p = Problem(model=Group())
phase = Phase(ode_class=MyODE,
ode_init_kwargs={'n_traj': n_traj},
transcription=Radau(num_segments=25,
order=3,
compressed=True))
p.model.add_subsystem('phase0', phase)
phase.add_input_parameter('alpha', val=np.ones((n_traj, 2)), units='m')
try:
p.setup()
except Exception as e:
self.fail('Exception encountered in setup:\n' + str(e))
def test_timeseries_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=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.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()
gd = phase.options['transcription'].grid_data
state_input_idxs = gd.subset_node_indices['state_input']
control_input_idxs = gd.subset_node_indices['control_input']
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])
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 test_reentry_radau_dymos(self):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.declare_coloring()
traj = p.model.add_subsystem("traj", Trajectory())
phase0 = traj.add_phase(
"phase0",
Phase(ode_class=ShuttleODE,
transcription=Radau(num_segments=50, order=3)))
phase0.set_time_options(fix_initial=True, units="s", duration_ref=200)
phase0.set_state_options("h",
fix_initial=True,
fix_final=True,
units="ft",
rate_source="hdot",
targets=["h"],
lower=0,
ref0=75000,
ref=300000,
defect_ref=1000)
phase0.set_state_options("gamma",
fix_initial=True,
fix_final=True,
units="rad",
rate_source="gammadot",
targets=["gamma"],
lower=-89. * np.pi / 180,
upper=89. * np.pi / 180)
phase0.set_state_options("phi",
fix_initial=True,
fix_final=False,
units="rad",
rate_source="phidot",
lower=0,
upper=89. * np.pi / 180)
phase0.set_state_options("psi",
fix_initial=True,
fix_final=False,
units="rad",
rate_source="psidot",
targets=["psi"],
lower=0,
upper=90. * np.pi / 180)
phase0.set_state_options("theta",
fix_initial=True,
fix_final=False,
units="rad",
rate_source="thetadot",
targets=["theta"],
lower=-89. * np.pi / 180,
upper=89. * np.pi / 180)
phase0.set_state_options("v",
fix_initial=True,
fix_final=True,
units="ft/s",
rate_source="vdot",
targets=["v"],
lower=0,
ref0=2500,
ref=25000)
phase0.add_control("alpha",
units="rad",
opt=True,
lower=-np.pi / 2,
upper=np.pi / 2,
targets=["alpha"])
phase0.add_control("beta",
units="rad",
opt=True,
lower=-89 * np.pi / 180,
upper=1 * np.pi / 180,
targets=["beta"])
phase0.add_path_constraint("q",
lower=0,
upper=70,
units="Btu/ft**2/s",
ref=70)
phase0.add_objective("theta", loc="final", ref=-0.01)
p.driver.options["optimizer"] = 'SNOPT'
p.driver.opt_settings["iSumm"] = 6
p.setup(check=True)
p.set_val("traj.phase0.states:h",
phase0.interpolate(ys=[260000, 80000], nodes="state_input"),
units="ft")
p.set_val("traj.phase0.states:gamma",
phase0.interpolate(ys=[-1 * np.pi / 180, -5 * np.pi / 180],
nodes="state_input"),
units="rad")
p.set_val("traj.phase0.states:phi",
phase0.interpolate(ys=[0, 75 * np.pi / 180],
nodes="state_input"),
units="rad")
p.set_val("traj.phase0.states:psi",
phase0.interpolate(ys=[90 * np.pi / 180, 10 * np.pi / 180],
nodes="state_input"),
units="rad")
p.set_val("traj.phase0.states:theta",
phase0.interpolate(ys=[0, 25 * np.pi / 180],
nodes="state_input"),
units="rad")
p.set_val("traj.phase0.states:v",
phase0.interpolate(ys=[25600, 2500], nodes="state_input"),
units="ft/s")
p.set_val("traj.phase0.t_initial", 0, units="s")
p.set_val("traj.phase0.t_duration", 2000, units="s")
p.set_val("traj.phase0.controls:alpha",
phase0.interpolate(
ys=[17.4 * np.pi / 180, 17.4 * np.pi / 180],
nodes="control_input"),
units="rad")
p.set_val("traj.phase0.controls:beta",
phase0.interpolate(ys=[-75 * np.pi / 180, 0 * np.pi / 180],
nodes="control_input"),
units="rad")
p.run_driver()
print(p.get_val("traj.phase0.timeseries.time")[-1])
print(p.get_val("traj.phase0.timeseries.states:theta")[-1])
assert_rel_error(self,
p.get_val("traj.phase0.timeseries.time")[-1],
2181.90371131,
tolerance=1e-3)
assert_rel_error(self,
p.get_val("traj.phase0.timeseries.states:theta")[-1],
.53440626,
tolerance=1e-3)
def test_solver_defects(self):
prob = Problem()
num_seg = 5
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
transcription = Radau(num_segments=5,
order=5,
segment_ends=seg_ends,
compressed=True)
phase0 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = traj.add_phase('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.set_state_options('state_of_charge',
fix_initial=True,
fix_final=False,
solve_segments=True)
# Second phase: normal operation.
phase1 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p1 = traj.add_phase('phase1', phase1)
traj_p1.set_time_options(fix_initial=False, fix_duration=True)
traj_p1.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments=True)
traj_p1.add_objective('time', loc='final')
# Second phase, but with battery failure.
phase1_bfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_battery': 2},
transcription=transcription)
traj_p1_bfail = traj.add_phase('phase1_bfail', phase1_bfail)
traj_p1_bfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_bfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments=True)
# Second phase, but with motor failure.
phase1_mfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_motor': 2},
transcription=transcription)
traj_p1_mfail = traj.add_phase('phase1_mfail', phase1_mfail)
traj_p1_mfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_mfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False,
solve_segments=True)
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_bfail'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_mfail'],
vars=['state_of_charge', 'time'],
connected=True)
prob.setup()
prob['traj.phase0.t_initial'] = 0
prob['traj.phase0.t_duration'] = 1.0 * 3600
prob['traj.phase1.t_initial'] = 1.0 * 3600
prob['traj.phase1.t_duration'] = 1.0 * 3600
prob['traj.phase1_bfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_bfail.t_duration'] = 1.0 * 3600
prob['traj.phase1_mfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_mfail.t_duration'] = 1.0 * 3600
prob['traj.phase0.states:state_of_charge'][:] = 1.0
prob.set_solver_print(level=0)
prob.run_model()
soc0 = prob['traj.phase0.states:state_of_charge']
soc1 = prob['traj.phase1.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.states:state_of_charge']
# Final value for State of Charge in each segment should be a good test.
assert_rel_error(self, soc0[-1], 0.63464982, 1e-6)
assert_rel_error(self, soc1[-1], 0.23794217, 1e-6)
assert_rel_error(self, soc1b[-1], 0.0281523, 1e-6)
assert_rel_error(self, soc1m[-1], 0.18625395, 1e-6)
def test_optimizer_segments_direct_connections(self):
prob = Problem()
if optimizer == 'SNOPT':
opt = prob.driver = pyOptSparseDriver()
opt.options['optimizer'] = optimizer
opt.options['dynamic_simul_derivs'] = True
opt.opt_settings['Major iterations limit'] = 1000
opt.opt_settings['Major feasibility tolerance'] = 1.0E-6
opt.opt_settings['Major optimality tolerance'] = 1.0E-6
opt.opt_settings["Linesearch tolerance"] = 0.10
opt.opt_settings['iSumm'] = 6
else:
opt = prob.driver = ScipyOptimizeDriver()
opt.options['dynamic_simul_derivs'] = True
num_seg = 5
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
transcription = Radau(num_segments=5,
order=5,
segment_ends=seg_ends,
compressed=True)
phase0 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = traj.add_phase('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.set_state_options('state_of_charge',
fix_initial=True,
fix_final=False)
# Second phase: normal operation.
phase1 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p1 = traj.add_phase('phase1', phase1)
traj_p1.set_time_options(fix_initial=False, fix_duration=True)
traj_p1.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
traj_p1.add_objective('time', loc='final')
# Second phase, but with battery failure.
phase1_bfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_battery': 2},
transcription=transcription)
traj_p1_bfail = traj.add_phase('phase1_bfail', phase1_bfail)
traj_p1_bfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_bfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
# Second phase, but with motor failure.
phase1_mfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_motor': 2},
transcription=transcription)
traj_p1_mfail = traj.add_phase('phase1_mfail', phase1_mfail)
traj_p1_mfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_mfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_bfail'],
vars=['state_of_charge', 'time'],
connected=True)
traj.link_phases(phases=['phase0', 'phase1_mfail'],
vars=['state_of_charge', 'time'],
connected=True)
prob.model.options['assembled_jac_type'] = 'csc'
prob.model.linear_solver = DirectSolver(assemble_jac=True)
prob.setup()
prob['traj.phase0.t_initial'] = 0
prob['traj.phase0.t_duration'] = 1.0 * 3600
prob['traj.phase1.t_initial'] = 1.0 * 3600
prob['traj.phase1.t_duration'] = 1.0 * 3600
prob['traj.phase1_bfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_bfail.t_duration'] = 1.0 * 3600
prob['traj.phase1_mfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_mfail.t_duration'] = 1.0 * 3600
prob.set_solver_print(level=0)
prob.run_driver()
soc0 = prob['traj.phase0.states:state_of_charge']
soc1 = prob['traj.phase1.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.states:state_of_charge']
# Final value for State of Chrage in each segment should be a good test.
assert_rel_error(self, soc0[-1], 0.63464982, 1e-6)
assert_rel_error(self, soc1[-1], 0.23794217, 1e-6)
assert_rel_error(self, soc1b[-1], 0.0281523, 1e-6)
assert_rel_error(self, soc1m[-1], 0.18625395, 1e-6)
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, ScipyOptimizeDriver, SqliteRecorder, CaseReader, IndepVarComp
from dymos import Trajectory, GaussLobatto, Phase, Radau
from shuttle_ode import ShuttleODE
prob = Problem(model=Group())
traj = prob.model.add_subsystem("traj", Trajectory())
phase0 = Phase(ode_class=ShuttleODE, transcription=Radau(num_segments=20, order=3))
traj.add_phase(name="phase0", phase=phase0)
phase0.set_time_options(fix_initial=True, units="s", duration_ref=200)#, duration_ref=2000, duration_bounds=(50, 3000)
phase0.set_state_options("h", fix_initial=True, fix_final=True, units="ft", rate_source="hdot", targets=["h"], lower=0)#, ref=260000, defect_ref=260000, ref0=80000
phase0.set_state_options("gamma", fix_initial=True, fix_final=True, units="rad", rate_source="gammadot", targets=["gamma"], lower=-89.*np.pi/180, upper=89.*np.pi/180)
phase0.set_state_options("phi", fix_initial=True, fix_final=False, units="rad", rate_source="phidot", lower=0, upper=89.*np.pi/180)
phase0.set_state_options("psi", fix_initial=True, fix_final=False, units="rad", rate_source="psidot", targets=["psi"], lower=0, upper=90.*np.pi/180)
phase0.set_state_options("theta", fix_initial=True, fix_final=False, units="rad", rate_source="thetadot", targets=["theta"], lower=-89.*np.pi/180, upper=89.*np.pi/180)
phase0.set_state_options("v", fix_initial=True, fix_final=True, units="ft/s", rate_source="vdot", targets=["v"], lower=0)#, ref=25600, defect_ref=25600, ref0=2500
phase0.add_control("alpha", units="rad", opt=True, lower=-np.pi/2, upper=np.pi/2, targets=["alpha"])
phase0.add_control("beta", units="rad", opt=True, lower=-89*np.pi/180, upper=1*np.pi/180, targets=["beta"])
phase0.add_path_constraint("q", lower=0, upper=70, units="Btu/ft**2/s", ref=70)#
phase0.add_objective("theta", loc="final", ref=-1)
prob.driver = ScipyOptimizeDriver()
prob.driver.declare_coloring()
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)
def brachistochrone_min_time(transcription='gauss-lobatto',
num_segments=8,
transcription_order=3,
compressed=True,
sim_record='brach_min_time_sim.db',
optimizer='SLSQP',
dynamic_simul_derivs=True,
force_alloc_complex=False,
solve_segments=False,
run_driver=True):
p = Problem(model=Group())
if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
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
else:
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = dynamic_simul_derivs
if transcription == 'runge-kutta':
transcription = RungeKutta(num_segments=num_segments,
compressed=compressed)
elif transcription == 'gauss-lobatto':
transcription = GaussLobatto(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
elif transcription == 'radau-ps':
transcription = Radau(num_segments=num_segments,
order=transcription_order,
compressed=compressed)
phase = Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=transcription)
p.model.add_subsystem('phase0', phase)
phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
fix_final = not solve_segments # can't fix final position if you're solving the segments
phase.set_state_options('pos',
fix_initial=True,
fix_final=fix_final,
solve_segments=solve_segments)
phase.set_state_options('v',
fix_initial=True,
fix_final=False,
solve_segments=solve_segments)
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)
p.model.linear_solver = DirectSolver()
p.setup(check=True, force_alloc_complex=force_alloc_complex)
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_model()
if run_driver:
p.run_driver()
# Plot results
if SHOW_PLOTS:
p.run_driver()
exp_out = phase.simulate(record_file=sim_record)
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')
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_basic(self):
import matplotlib.pyplot as plt
from openmdao.api import Problem, ScipyOptimizeDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from dymos import Trajectory, Phase, Radau
from dymos.examples.battery_multibranch.battery_multibranch_ode import BatteryODE
from dymos.utils.lgl import lgl
prob = Problem()
opt = prob.driver = ScipyOptimizeDriver()
opt.options['dynamic_simul_derivs'] = True
opt.options['optimizer'] = 'SLSQP'
num_seg = 5
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
transcription = Radau(num_segments=num_seg,
order=5,
segment_ends=seg_ends,
compressed=False)
phase0 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p0 = traj.add_phase('phase0', phase0)
traj_p0.set_time_options(fix_initial=True, fix_duration=True)
traj_p0.set_state_options('state_of_charge',
fix_initial=True,
fix_final=False)
# Second phase: normal operation.
phase1 = Phase(ode_class=BatteryODE, transcription=transcription)
traj_p1 = traj.add_phase('phase1', phase1)
traj_p1.set_time_options(fix_initial=False, fix_duration=True)
traj_p1.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
traj_p1.add_objective('time', loc='final')
# Second phase, but with battery failure.
phase1_bfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_battery': 2},
transcription=transcription)
traj_p1_bfail = traj.add_phase('phase1_bfail', phase1_bfail)
traj_p1_bfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_bfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
# Second phase, but with motor failure.
phase1_mfail = Phase(ode_class=BatteryODE,
ode_init_kwargs={'num_motor': 2},
transcription=transcription)
traj_p1_mfail = traj.add_phase('phase1_mfail', phase1_mfail)
traj_p1_mfail.set_time_options(fix_initial=False, fix_duration=True)
traj_p1_mfail.set_state_options('state_of_charge',
fix_initial=False,
fix_final=False)
traj.link_phases(phases=['phase0', 'phase1'],
vars=['state_of_charge', 'time'])
traj.link_phases(phases=['phase0', 'phase1_bfail'],
vars=['state_of_charge', 'time'])
traj.link_phases(phases=['phase0', 'phase1_mfail'],
vars=['state_of_charge', 'time'])
prob.model.options['assembled_jac_type'] = 'csc'
prob.model.linear_solver = DirectSolver(assemble_jac=True)
prob.setup()
prob['traj.phase0.t_initial'] = 0
prob['traj.phase0.t_duration'] = 1.0 * 3600
prob['traj.phase1.t_initial'] = 1.0 * 3600
prob['traj.phase1.t_duration'] = 1.0 * 3600
prob['traj.phase1_bfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_bfail.t_duration'] = 1.0 * 3600
prob['traj.phase1_mfail.t_initial'] = 1.0 * 3600
prob['traj.phase1_mfail.t_duration'] = 1.0 * 3600
prob.set_solver_print(level=0)
prob.run_driver()
soc0 = prob['traj.phase0.states:state_of_charge']
soc1 = prob['traj.phase1.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.states:state_of_charge']
# Final value for State of Chrage in each segment should be a good test.
print('State of Charge after 1 hour')
assert_rel_error(self, soc0[-1], 0.63464982, 1e-6)
print('State of Charge after 2 hours')
assert_rel_error(self, soc1[-1], 0.23794217, 1e-6)
print('State of Charge after 2 hours, battery fails at 1 hour')
assert_rel_error(self, soc1b[-1], 0.0281523, 1e-6)
print('State of Charge after 2 hours, motor fails at 1 hour')
assert_rel_error(self, soc1m[-1], 0.18625395, 1e-6)
# Plot Results
t0 = prob['traj.phases.phase0.time.time'] / 3600
t1 = prob['traj.phases.phase1.time.time'] / 3600
t1b = prob['traj.phases.phase1_bfail.time.time'] / 3600
t1m = prob['traj.phases.phase1_mfail.time.time'] / 3600
plt.subplot(2, 1, 1)
plt.plot(t0, soc0, 'b')
plt.plot(t1, soc1, 'b')
plt.plot(t1b, soc1b, 'r')
plt.plot(t1m, soc1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('State of Charge (percent)')
I_Li0 = prob['traj.phases.phase0.rhs_all.pwr_balance.I_Li']
I_Li1 = prob['traj.phases.phase1.rhs_all.pwr_balance.I_Li']
I_Li1b = prob['traj.phases.phase1_bfail.rhs_all.pwr_balance.I_Li']
I_Li1m = prob['traj.phases.phase1_mfail.rhs_all.pwr_balance.I_Li']
plt.subplot(2, 1, 2)
plt.plot(t0, I_Li0, 'b')
plt.plot(t1, I_Li1, 'b')
plt.plot(t1b, I_Li1b, 'r')
plt.plot(t1m, I_Li1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Line Current (A)')
plt.legend([
'Phase 1', 'Phase 2', 'Phase 2 Battery Fail', 'Phase 2 Motor Fail'
],
loc=2)
plt.show()
def test_dynamic_input_params(self):
prob = Problem(model=Group())
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
# NOTE: using RK4 integration here
P_DEMAND = 2.0
phase0 = Phase(ode_class=BatteryODE, transcription=RungeKutta(num_segments=200))
phase0.set_time_options(fix_initial=True, fix_duration=True)
phase0.set_state_options('state_of_charge', fix_initial=True, fix_final=False)
phase0.add_timeseries_output('battery.V_oc', output_name='V_oc', units='V')
phase0.add_timeseries_output('battery.V_pack', output_name='V_pack', units='V')
phase0.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li', units='A')
phase0.add_input_parameter('P_demand', val=P_DEMAND, units='W')
traj.add_phase('phase0', phase0)
# Second phase: normal operation.
transcription = Radau(num_segments=5, order=5, compressed=True)
phase1 = Phase(ode_class=BatteryODE, transcription=transcription)
phase1.set_time_options(fix_initial=False, fix_duration=True)
phase1.set_state_options('state_of_charge', fix_initial=False, fix_final=False, solve_segments=True)
phase1.add_timeseries_output('battery.V_oc', output_name='V_oc', units='V')
phase1.add_timeseries_output('battery.V_pack', output_name='V_pack', units='V')
phase1.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li', units='A')
phase1.add_input_parameter('P_demand', val=P_DEMAND, units='W')
traj.add_phase('phase1', phase1)
# Second phase, but with battery failure.
phase1_bfail = Phase(ode_class=BatteryODE, ode_init_kwargs={'num_battery': 2},
transcription=transcription)
phase1_bfail.set_time_options(fix_initial=False, fix_duration=True)
phase1_bfail.set_state_options('state_of_charge', fix_initial=False, fix_final=False, solve_segments=True)
phase1_bfail.add_timeseries_output('battery.V_oc', output_name='V_oc', units='V')
phase1_bfail.add_timeseries_output('battery.V_pack', output_name='V_pack', units='V')
phase1_bfail.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li', units='A')
phase1_bfail.add_input_parameter('P_demand', val=P_DEMAND, units='W')
traj.add_phase('phase1_bfail', phase1_bfail)
# Second phase, but with motor failure.
phase1_mfail = Phase(ode_class=BatteryODE, ode_init_kwargs={'num_motor': 2},
transcription=transcription)
phase1_mfail.set_time_options(fix_initial=False, fix_duration=True)
phase1_mfail.set_state_options('state_of_charge', fix_initial=False, fix_final=False, solve_segments=True)
phase1_mfail.add_timeseries_output('battery.V_oc', output_name='V_oc', units='V')
phase1_mfail.add_timeseries_output('battery.V_pack', output_name='V_pack', units='V')
phase1_mfail.add_timeseries_output('pwr_balance.I_Li', output_name='I_Li', units='A')
phase1_mfail.add_input_parameter('P_demand', val=P_DEMAND, units='W')
traj.add_phase('phase1_mfail', phase1_mfail)
traj.link_phases(phases=['phase0', 'phase1'], vars=['state_of_charge', 'time'], connected=True)
traj.link_phases(phases=['phase0', 'phase1_bfail'], vars=['state_of_charge', 'time'], connected=True)
traj.link_phases(phases=['phase0', 'phase1_mfail'], vars=['state_of_charge', 'time'], connected=True)
# prob.model.linear_solver = DirectSolver(assemble_jac=True)
prob.setup()
prob.final_setup()
prob['traj.phases.phase0.time_extents.t_initial'] = 0
prob['traj.phases.phase0.time_extents.t_duration'] = 1.0*3600
# prob['traj.phases.phase1.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1.time_extents.t_duration'] = 1.0*3600
# prob['traj.phases.phase1_bfail.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1_bfail.time_extents.t_duration'] = 1.0*3600
# prob['traj.phases.phase1_mfail.time_extents.t_initial'] = 1.0*3600
prob['traj.phases.phase1_mfail.time_extents.t_duration'] = 1.0*3600
prob.set_solver_print(level=0)
prob.run_model()
plot = True
if plot:
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
t0 = prob['traj.phase0.timeseries.time']
t1 = prob['traj.phase1.timeseries.time']
t1b = prob['traj.phase1_bfail.timeseries.time']
t1m = prob['traj.phase1_mfail.timeseries.time']
soc0 = prob['traj.phase0.timeseries.states:state_of_charge']
soc1 = prob['traj.phase1.timeseries.states:state_of_charge']
soc1b = prob['traj.phase1_bfail.timeseries.states:state_of_charge']
soc1m = prob['traj.phase1_mfail.timeseries.states:state_of_charge']
plt.subplot(2, 2, 1)
plt.plot(t0, soc0, 'b')
plt.plot(t1, soc1, 'b')
plt.plot(t1b, soc1b, 'r')
plt.plot(t1m, soc1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('State of Charge (percent)')
V_oc0 = prob['traj.phase0.timeseries.V_oc']
V_oc1 = prob['traj.phase1.timeseries.V_oc']
V_oc1b = prob['traj.phase1_bfail.timeseries.V_oc']
V_oc1m = prob['traj.phase1_mfail.timeseries.V_oc']
plt.subplot(2, 2, 2)
plt.plot(t0, V_oc0, 'b')
plt.plot(t1, V_oc1, 'b')
plt.plot(t1b, V_oc1b, 'r')
plt.plot(t1m, V_oc1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Open Circuit Voltage (V)')
V_pack0 = prob['traj.phase0.timeseries.V_pack']
V_pack1 = prob['traj.phase1.timeseries.V_pack']
V_pack1b = prob['traj.phase1_bfail.timeseries.V_pack']
V_pack1m = prob['traj.phase1_mfail.timeseries.V_pack']
plt.subplot(2, 2, 3)
plt.plot(t0, V_pack0, 'b')
plt.plot(t1, V_pack1, 'b')
plt.plot(t1b, V_pack1b, 'r')
plt.plot(t1m, V_pack1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Terminal Voltage (V)')
I_Li0 = prob['traj.phase0.timeseries.I_Li']
I_Li1 = prob['traj.phase1.timeseries.I_Li']
I_Li1b = prob['traj.phase1_bfail.timeseries.I_Li']
I_Li1m = prob['traj.phase1_mfail.timeseries.I_Li']
plt.subplot(2, 2, 4)
plt.plot(t0, I_Li0, 'b')
plt.plot(t1, I_Li1, 'b')
plt.plot(t1b, I_Li1b, 'r')
plt.plot(t1m, I_Li1m, 'c')
plt.xlabel('Time (hour)')
plt.ylabel('Line Current (A)')
plt.show()
def test_brachistochrone_undecorated_ode_radau(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, 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),
units='s')
phase.set_state_options('x',
fix_initial=True,
fix_final=True,
rate_source='xdot',
units='m')
phase.set_state_options('y',
fix_initial=True,
fix_final=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'])
# 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)
from __future__ import print_function, division, absolute_import
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group
from dymos import Phase, Radau
from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE
p = Problem(model=Group())
phase = Phase(ode_class=BrachistochroneODE,
transcription=Radau(num_segments=4, order=[3, 5, 3, 5]))
p.model.add_subsystem('phase0', phase)
p.setup()
p['phase0.t_initial'] = 1.0
p['phase0.t_duration'] = 9.0
p.run_model()
grid_data = phase.options['transcription'].grid_data
t_all = p.get_val('phase0.timeseries.time')
t_disc = t_all[grid_data.subset_node_indices['state_disc'], 0]
t_col = t_all[grid_data.subset_node_indices['col'], 0]
def f(x): # pragma: no cover
return np.sin(x) / x + 1
def test_reentry_mixed_controls(self):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring(tol=1.0E-12)
p.driver.options['optimizer'] = 'IPOPT'
p.driver.opt_settings['alpha_for_y'] = 'safer-min-dual-infeas'
p.driver.opt_settings['print_level'] = 5
p.driver.opt_settings['nlp_scaling_method'] = 'gradient-based'
p.driver.opt_settings['mu_strategy'] = 'monotone'
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=ShuttleODE,
transcription=Radau(num_segments=30, order=3)))
phase0.set_time_options(fix_initial=True, units='s', duration_ref=200)
phase0.add_state('h',
fix_initial=True,
fix_final=True,
units='ft',
rate_source='hdot',
targets=['h'],
lower=0,
ref0=75000,
ref=300000,
defect_ref=1000)
phase0.add_state('gamma',
fix_initial=True,
fix_final=True,
units='rad',
rate_source='gammadot',
targets=['gamma'],
lower=-89. * np.pi / 180,
upper=89. * np.pi / 180)
phase0.add_state('phi',
fix_initial=True,
fix_final=False,
units='rad',
rate_source='phidot',
lower=0,
upper=89. * np.pi / 180)
phase0.add_state('psi',
fix_initial=True,
fix_final=False,
units='rad',
rate_source='psidot',
targets=['psi'],
lower=0,
upper=90. * np.pi / 180)
phase0.add_state('theta',
fix_initial=True,
fix_final=False,
units='rad',
rate_source='thetadot',
targets=['theta'],
lower=-89. * np.pi / 180,
upper=89. * np.pi / 180)
phase0.add_state('v',
fix_initial=True,
fix_final=True,
units='ft/s',
rate_source='vdot',
targets=['v'],
lower=500,
ref0=2500,
ref=25000)
phase0.add_control('alpha',
units='rad',
opt=True,
lower=-np.pi / 2,
upper=np.pi / 2)
phase0.add_polynomial_control('beta',
order=9,
units='rad',
opt=True,
lower=-89 * np.pi / 180,
upper=1 * np.pi / 180)
phase0.add_objective('theta', loc='final', ref=-0.01)
phase0.add_path_constraint('q', lower=0, upper=70, ref=70)
p.setup(check=True, force_alloc_complex=True)
p.set_val('traj.phase0.states:h',
phase0.interp('h', [260000, 80000]),
units='ft')
p.set_val('traj.phase0.states:gamma',
phase0.interp('gamma', [-1 * np.pi / 180, -5 * np.pi / 180]),
units='rad')
p.set_val('traj.phase0.states:phi',
phase0.interp('phi', [0, 75 * np.pi / 180]),
units='rad')
p.set_val('traj.phase0.states:psi',
phase0.interp('psi', [90 * np.pi / 180, 10 * np.pi / 180]),
units='rad')
p.set_val('traj.phase0.states:theta',
phase0.interp('theta', [0, 25 * np.pi / 180]),
units='rad')
p.set_val('traj.phase0.states:v',
phase0.interp('v', [25600, 2500]),
units='ft/s')
p.set_val('traj.phase0.t_initial', 0, units='s')
p.set_val('traj.phase0.t_duration', 2000, units='s')
p.set_val('traj.phase0.controls:alpha',
phase0.interp('alpha', [17.4, 17.4]),
units='deg')
p.set_val('traj.phase0.polynomial_controls:beta',
phase0.interp('beta', [-20, 0]),
units='deg')
run_problem(p, simulate=True)
sol = om.CaseReader('dymos_solution.db').get_case('final')
sim = om.CaseReader('dymos_simulation.db').get_case('final')
from scipy.interpolate import interp1d
t_sol = sol.get_val('traj.phase0.timeseries.time')
beta_sol = sol.get_val(
'traj.phase0.timeseries.polynomial_controls:beta', units='deg')
t_sim = sim.get_val('traj.phase0.timeseries.time')
beta_sim = sim.get_val(
'traj.phase0.timeseries.polynomial_controls:beta', units='deg')
sol_interp = interp1d(t_sol.ravel(), beta_sol.ravel())
sim_interp = interp1d(t_sim.ravel(), beta_sim.ravel())
t = np.linspace(0, t_sol.ravel()[-1], 1000)
assert_near_equal(sim_interp(t), sol_interp(t), tolerance=0.01)
assert_near_equal(p.get_val('traj.phase0.timeseries.time')[-1],
expected_results['constrained']['time'],
tolerance=1e-2)
assert_near_equal(p.get_val('traj.phase0.timeseries.states:theta',
units='deg')[-1],
expected_results['constrained']['theta'],
tolerance=1e-2)
def test_brachistochrone_vector_ode_path_constraints_radau_no_indices(
self):
p = Problem(model=Group())
p.driver = ScipyOptimizeDriver()
p.driver.options['dynamic_simul_derivs'] = True
phase = Phase(ode_class=BrachistochroneVectorStatesODE,
transcription=Radau(num_segments=20, order=3))
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=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)
phase.add_path_constraint('pos_dot',
shape=(2, ),
units='m/s',
lower=-4,
upper=12)
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=50)
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 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_battery_power(self):
"""
for battery explicit integration testings
"""
_, local_opt = set_pyoptsparse_opt('SNOPT')
if local_opt != 'SNOPT':
raise unittest.SkipTest("pyoptsparse is not providing SNOPT")
p = om.Problem()
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SNOPT'
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major optimality tolerance'] = 5.0E-3
p.driver.opt_settings['Major feasibility tolerance'] = 1e-6
p.driver.opt_settings['iSumm'] = 6
transcription = Radau(num_segments=15, order=3, compressed=True)
phase0 = Phase(transcription=transcription, ode_class=BatteryGroup)
phase0.set_time_options(fix_initial=True, duration_bounds=(30, 30))
p.model.add_subsystem(name='phase0', subsys=phase0)
phase0.add_state('SOC',
fix_initial=True,
rate_source='dXdt:SOC',
lower=0.0,
upper=1.)
phase0.add_state('U_Th',
units='V',
fix_initial=False,
rate_source='dXdt:V_{thev}',
lower=0.0,
upper=5.0)
# phase0.add_parameter('P_out', units='W', opt=False)
# phase0.add_boundary_constraint('U_pack', units='V', loc='initial', equals=5100)
phase0.add_objective('time', loc='final', ref=1)
p.model.linear_solver = om.DirectSolver(assemble_jac=True)
phase0.add_timeseries_output('Q_{batt}',
output_name='Q_{batt}',
units='W')
# phase0.add_timeseries_output('U_pack', output_name='V', units='V')
p.setup()
# p.check_partials()
T0 = 10 + 273
p['phase0.t_initial'] = 0.0
p['phase0.t_duration'] = 30
p['phase0.states:SOC'] = phase0.interpolate(ys=[1.0, 0.0],
nodes='state_input')
p['phase0.states:U_Th'] = phase0.interpolate(ys=[0.1, 0.1],
nodes='state_input')
# p['phase0.parameters:P_out'][:] = 72000.
p.run_driver()
fig, ax = plt.subplots(3, 1, sharex=True)
fig.suptitle('Temperature Plots')
t_opt = p.get_val('phase0.timeseries.time')
SOC_opt = p.get_val('phase0.timeseries.states:SOC', units=None)
Q_batt_opt = p.get_val('phase0.timeseries.Q_{batt}', units='kW')
ax[1].plot(t_opt, Q_batt_opt * 128 * 40, 'r', label='$Q_{cell}$')
ax[2].plot(t_opt, SOC_opt, 'r', label='$SOC$')
#spot check final values
# assert_rel_error(self, T_batt_opt[-1], 1.25934406, tolerance=1.0E-6)
# ax[3].plot(t_opt, V_opt, 'r', label='$Voltage$')
# axarr = fig.add_subplot(1, 2, 2)
# axarr.plot(sim_out.get_values('time'),sim_out.get_values('electric.battery.I_Li'), 'b')
# # # axarr.plot(p['phase0.state_interp.state_col:r'],
# # # p['phase0.controls:h'], 'bo', ms=4)
# axarr.set_ylabel('I_Li, amps')
# axarr.set_xlabel('time, s')
# axarr.axes.get_xaxis().set_visible(True)
import matplotlib
matplotlib.use(
'agg') # <--- comment out if you want to show this plot.
plt.show()
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()