def make_problem(self,
transcription=GaussLobatto,
optimizer='SLSQP',
numseg=30):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.declare_coloring()
p.driver.options['optimizer'] = optimizer
if optimizer == 'SNOPT':
p.driver.declare_coloring()
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
elif optimizer == 'IPOPT':
p.driver.opt_settings['hessian_approximation'] = 'limited-memory'
# p.driver.opt_settings['nlp_scaling_method'] = 'user-scaling'
p.driver.opt_settings['print_level'] = 5
p.driver.opt_settings['linear_solver'] = 'mumps'
p.driver.declare_coloring()
else:
p.driver.declare_coloring()
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=HyperSensitiveODE,
transcription=transcription(num_segments=numseg, order=3)))
phase0.set_time_options(fix_initial=True, fix_duration=True)
phase0.add_state('x',
fix_initial=True,
fix_final=False,
rate_source='x_dot',
targets=['x'])
phase0.add_state('xL',
fix_initial=True,
fix_final=False,
rate_source='L',
targets=['xL'])
phase0.add_control('u', opt=True, targets=['u'])
phase0.add_boundary_constraint('x', loc='final', equals=1)
phase0.add_objective('xL', loc='final')
phase0.set_refine_options(refine=True, tol=1e-6, max_order=14)
p.setup(check=True)
p.set_val('traj.phase0.states:x',
phase0.interpolate(ys=[1.5, 1], nodes='state_input'))
p.set_val('traj.phase0.states:xL',
phase0.interpolate(ys=[0, 1], nodes='state_input'))
p.set_val('traj.phase0.t_initial', 0)
p.set_val('traj.phase0.t_duration', tf)
p.set_val('traj.phase0.controls:u',
phase0.interpolate(ys=[-0.6, 2.4], nodes='control_input'))
return p
def make_problem(self, transcription=Radau, optimizer='SLSQP', numseg=30):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.declare_coloring(tol=1.0E-12)
OPT, OPTIMIZER = set_pyoptsparse_opt(optimizer, fallback=False)
p.driver.options['optimizer'] = OPTIMIZER
if OPTIMIZER == 'SNOPT':
p.driver.opt_settings['iSumm'] = 6
p.driver.opt_settings['Verify level'] = 3
elif OPTIMIZER == 'IPOPT':
p.driver.opt_settings['max_iter'] = 500
p.driver.opt_settings['print_level'] = 4
p.driver.opt_settings['tol'] = 1.0E-6
p.driver.opt_settings['acceptable_tol'] = 1.0E-5
traj = p.model.add_subsystem('traj', Trajectory())
phase = traj.add_phase('phase', Phase(ode_class=RobotArmODE,
transcription=transcription(num_segments=numseg, order=3)))
phase.set_time_options(fix_initial=True, fix_duration=False)
phase.add_state('x0', fix_initial=True, fix_final=True, rate_source='x0_dot', units='m')
phase.add_state('x1', fix_initial=True, fix_final=True, rate_source='x1_dot', units='rad')
phase.add_state('x2', fix_initial=True, fix_final=True, rate_source='x2_dot', units='rad')
phase.add_state('x3', fix_initial=True, fix_final=True, rate_source='x3_dot', units='m/s')
phase.add_state('x4', fix_initial=True, fix_final=True, rate_source='x4_dot', units='rad/s')
phase.add_state('x5', fix_initial=True, fix_final=True, rate_source='x5_dot', units='rad/s')
phase.add_control('u0', opt=True, lower=-1, upper=1, scaler=0.1, units='m**2/s**2',
continuity=False, rate_continuity=False)
phase.add_control('u1', opt=True, lower=-1, upper=1, scaler=0.1, units='m**3*rad/s**2',
continuity=False, rate_continuity=False)
phase.add_control('u2', opt=True, lower=-1, upper=1, scaler=0.1, units='m**3*rad/s**2',
continuity=False, rate_continuity=False)
phase.add_path_constraint('u0', lower=-1, upper=1, scaler=0.1)
phase.add_path_constraint('u1', lower=-1, upper=1, scaler=0.1)
phase.add_path_constraint('u2', lower=-1, upper=1, scaler=0.1)
phase.add_objective('time', ref=0.1)
phase.set_refine_options(refine=True, tol=1e-5, smoothness_factor=1.2)
p.setup(check=True, force_alloc_complex=False, mode='auto')
p.set_val('traj.phase.t_initial', 0)
p.set_val('traj.phase.t_duration', 10)
p.set_val('traj.phase.states:x0', phase.interpolate(ys=[4.5, 4.5], nodes='state_input'))
p.set_val('traj.phase.states:x1', phase.interpolate(ys=[0.0, 2 * np.pi / 3], nodes='state_input'))
p.set_val('traj.phase.states:x2', phase.interpolate(ys=[np.pi / 4, np.pi / 4], nodes='state_input'))
p.set_val('traj.phase.states:x3', phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
p.set_val('traj.phase.states:x4', phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
p.set_val('traj.phase.states:x5', phase.interpolate(ys=[0.0, 0.0], nodes='state_input'))
return p
def __init__(self, body, sc, method, nb_seg, order, solver, snopt_opts=None, rec_file=None):
"""Initializes NLP class. """
# input parameters
self.body = body
self.sc = sc
self.method = method
self.nb_seg = nb_seg
self.order = order
self.solver = solver
if self.solver == 'SNOPT':
self.snopt_opts = snopt_opts
else:
self.snopt_opts = None
self.rec_file = rec_file
# Problem object
self.p = Problem(model=Group())
# Problem Driver
self.p.driver = pyOptSparseDriver()
self.p.driver.options['optimizer'] = self.solver
self.p.driver.options['print_results'] = False
self.p.driver.options['dynamic_derivs_sparsity'] = True
if self.snopt_opts is not None:
for k in self.snopt_opts.keys():
self.p.driver.opt_settings[k] = self.snopt_opts[k]
self.p.driver.declare_coloring(show_summary=True, show_sparsity=False)
# Problem Recorder
if rec_file is not None:
recorder = SqliteRecorder(rec_file)
opts = ['record_objectives', 'record_constraints', 'record_desvars']
self.p.add_recorder(recorder)
for opt in opts:
self.p.recording_options[opt] = False
self.p.recording_options['excludes'] = rec_excludes
self.rec_file = rec_file
# Trajectory object
self.trajectory = self.p.model.add_subsystem('traj', Trajectory())
# Problem object for explicit simulation
self.p_exp = None
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=GaussLobatto,
optimizer='SLSQP',
numseg=30):
p = Problem(model=Group())
p.driver = pyOptSparseDriver()
p.driver.declare_coloring()
OPT, OPTIMIZER = set_pyoptsparse_opt(optimizer, fallback=False)
p.driver.options['optimizer'] = OPTIMIZER
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=HyperSensitiveODE,
transcription=transcription(num_segments=numseg, order=3)))
phase0.set_time_options(fix_initial=True, fix_duration=True)
phase0.add_state('x',
fix_initial=True,
fix_final=False,
rate_source='x_dot',
targets=['x'])
phase0.add_state('xL',
fix_initial=True,
fix_final=False,
rate_source='L',
targets=['xL'])
phase0.add_control('u', opt=True, targets=['u'])
phase0.add_boundary_constraint('x', loc='final', equals=1)
phase0.add_objective('xL', loc='final')
p.setup(check=True)
p.set_val('traj.phase0.states:x',
phase0.interpolate(ys=[1.5, 1], nodes='state_input'))
p.set_val('traj.phase0.states:xL',
phase0.interpolate(ys=[0, 1], nodes='state_input'))
p.set_val('traj.phase0.t_initial', 0)
p.set_val('traj.phase0.t_duration', tf)
p.set_val('traj.phase0.controls:u',
phase0.interpolate(ys=[-0.6, 2.4], nodes='control_input'))
return p
def make_problem(transcription=GaussLobatto, num_segments=10, order=3, compressed=True):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
traj = p.model.add_subsystem('traj', Trajectory())
phase = traj.add_phase('phase', Phase(ode_class=crtbp_ode, transcription=transcription(num_segments=num_segments,
order=order,
compressed=compressed)))
phase.set_time_options(fix_initial=True, fix_duration=True)
phase.add_state('x', rate_source='vx', )
phase.add_state('y', rate_source='vz', fix_initial=True)
phase.add_state('z', rate_source='vz')
phase.add_state('x_dot', rate_source='vx_dot', fix_initial=True, units=None)
phase.add_state('y_dot', rate_source='vy_dot', units=None)
phase.add_state('z_dot', rate_source='vz_dot', fix_initial=True, units=None)
p.model.add_subsystem('x_periodic_bc', om.ExecComp('bc_defect=final-initial'))
p.model.connect('traj.phase.timeseries.states:x', 'x_periodic_bc.initial', src_indices=0)
p.model.connect('traj.phase.timeseries.states:x', 'x_periodic_bc.final', src_indices=-1)
p.model.add_constraint('x_periodic_bc.bc_defect', equals=0)
p.model.add_subsystem('z_periodic_bc', om.ExecComp('bc_defect=final-initial'))
p.model.connect('traj.phase.timeseries.states:z', 'z_periodic_bc.initial', src_indices=0)
p.model.connect('traj.phase.timeseries.states:z', 'z_periodic_bc.final', src_indices=-1)
p.model.add_constraint('z_periodic_bc.bc_defect', equals=0)
p.model.add_subsystem('vy_periodic_bc', om.ExecComp('bc_defect=final-initial'))
p.model.connect('traj.phase.timeseries.states:y_dot', 'vy_periodic_bc.initial', src_indices=0)
p.model.connect('traj.phase.timeseries.states:y_dot', 'vy_periodic_bc.final', src_indices=-1)
p.model.add_constraint('vy_periodic_bc.bc_defect', equals=0)
phase.add_objective('time', loc='final')
p.setup(check=True)
return p
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)
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 two_burn_orbit_raise_problem(transcription='gauss-lobatto',
optimizer='SNOPT',
transcription_order=3,
compressed=True,
show_plots=False):
traj = Trajectory()
p = Problem(model=traj)
if optimizer == 'SNOPT':
p.driver = pyOptSparseDriver()
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
p.driver.opt_settings['Major iterations limit'] = 100
p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6
p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6
p.driver.opt_settings['iSumm'] = 6
else:
p.driver = pyOptSparseDriver()
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5, units='DU/TU')
# First Phase (burn)
burn1 = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
# Second Phase (Coast)
coast = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10)
coast.set_state_options('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
# Third Phase (burn)
burn2 = Phase(transcription,
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=transcription_order,
compressed=compressed)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
initial_ref=10)
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-10,
upper=10)
burn2.add_objective('deltav', loc='final', scaler=100.0)
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(SqliteRecorder('two_burn_orbit_raise_example.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('design_parameters:c', value=1.5)
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val(
'burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'),
)
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
# Plot results
exp_out = traj.simulate(times=50, num_procs=3)
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = traj.get_values('time', flat=True)
x_sol = traj.get_values('pos_x', flat=True)
y_sol = traj.get_values('pos_y', flat=True)
dv_sol = traj.get_values('deltav', flat=True)
u1_sol = traj.get_values('u1', units='deg', flat=True)
t_exp = exp_out.get_values('time', flat=True)
x_exp = exp_out.get_values('pos_x', flat=True)
y_exp = exp_out.get_values('pos_y', flat=True)
dv_exp = exp_out.get_values('deltav', flat=True)
u1_exp = exp_out.get_values('u1', units='deg', flat=True)
ax_u1.plot(t_sol, u1_sol, 'ro', ms=3)
ax_u1.plot(t_exp, u1_exp, 'b-')
ax_deltav.plot(t_sol, dv_sol, 'ro', ms=3)
ax_deltav.plot(t_exp, dv_exp, 'b-')
ax_xy.plot(x_sol, y_sol, 'ro', ms=3, label='implicit')
ax_xy.plot(x_exp, y_exp, 'b-', label='explicit')
if show_plots:
plt.show()
return p
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()
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 instantiate_problem(self, idx):
traj = Trajectory()
p = Problem(model=traj)
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=4,
transcription_order=3,
compressed=True)
traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg')
burn1.add_design_parameter('c', opt=False, val=1.5)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
coast.add_design_parameter('c', opt=False, val=1.5)
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=3,
transcription_order=3,
compressed=True)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=1.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
ref0=0,
ref=10)
burn2.add_design_parameter('c', opt=False, val=1.5)
burn2.add_objective('deltav', loc='final')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
rec_file = 'two_burn_orbit_raise_example_{0}.db'.format(idx)
p.driver.add_recorder(SqliteRecorder(rec_file))
p.setup(check=True)
# Set Initial Guesses
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'))
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('burn1.design_parameters:c', value=1.5)
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('coast.design_parameters:c', value=1.5)
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.set_val('burn2.design_parameters:c', value=1.5)
p.run_model()
# Plot results
sim_rec_file = 'traj_sim_{0}.db'.format(idx)
exp_out = traj.simulate(times=50, record_file=sim_rec_file)
loaded_exp_out = load_simulation_results(sim_rec_file)
return exp_out, loaded_exp_out, rec_file, sim_rec_file
def test_reentry_mixed_controls(self):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
OPT, OPTIMIZER = set_pyoptsparse_opt('IPOPT', fallback=False)
p.driver.options['optimizer'] = OPTIMIZER
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=ShuttleODE,
transcription=GaussLobatto(num_segments=20, 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=5,
units='rad',
opt=True,
lower=-89 * np.pi / 180,
upper=1 * np.pi / 180)
phase0.add_objective('theta', loc='final', ref=-0.01)
p.setup(check=True, force_alloc_complex=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.polynomial_controls:beta', np.radians(-75))
p.run_driver()
exp_out = traj.simulate()
from scipy.interpolate import interp1d
t_sol = p.get_val('traj.phase0.timeseries.time')
beta_sol = p.get_val('traj.phase0.timeseries.polynomial_controls:beta')
t_sim = exp_out.get_val('traj.phase0.timeseries.time')
beta_sim = exp_out.get_val(
'traj.phase0.timeseries.polynomial_controls:beta')
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], 100)
assert_near_equal(sim_interp(t), sol_interp(t), tolerance=1.0E-3)
def test_reentry_gauss_lobatto_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=GaussLobatto(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],
2181.88191719,
tolerance=1e-3)
assert_rel_error(self,
p.get_val("traj.phase0.timeseries.states:theta")[-1],
.53440955,
tolerance=1e-3)
def setUpClass(cls):
cls.traj = Trajectory()
p = Problem(model=cls.traj)
# Since we're only testing features like get_values that don't rely on a converged
# solution, no driver is attached. We'll just invoke run_model.
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=4,
transcription_order=3,
compressed=True)
cls.traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=0.1)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg')
burn1.add_design_parameter('c', opt=False, val=1.5)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
cls.traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
coast.add_design_parameter('c', opt=False, val=1.5)
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=3,
transcription_order=3,
compressed=True)
cls.traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10))
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=1.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=0.1)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
ref0=0,
ref=10)
burn2.add_design_parameter('c', opt=False, val=1.5)
burn2.add_objective('deltav', loc='final')
# Link Phases
cls.traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
cls.traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.model.add_recorder(SqliteRecorder('test_trajectory_rec.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'))
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('burn1.design_parameters:c', value=1.5)
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('coast.design_parameters:c', value=1.5)
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.set_val('burn2.design_parameters:c', value=1.5)
p.run_model()
def test_two_burn_orbit_raise_for_docs(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, pyOptSparseDriver, DirectSolver, SqliteRecorder
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=False)
p.driver.options['optimizer'] = 'SNOPT'
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5)
# First Phase (burn)
burn1 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('theta',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vr',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('vt',
fix_initial=True,
fix_final=False,
defect_scaler=100.0)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
# Second Phase (Coast)
coast = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
duration_ref=10)
coast.set_state_options('r',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vr',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('vt',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
# Third Phase (burn)
burn2 = Phase('gauss-lobatto',
ode_class=FiniteBurnODE,
num_segments=10,
transcription_order=3,
compressed=True)
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20),
duration_bounds=(.5, 10),
initial_ref=10)
burn2.set_state_options('r',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('theta',
fix_initial=False,
fix_final=False,
defect_scaler=100.0)
burn2.set_state_options('vr',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('vt',
fix_initial=False,
fix_final=True,
defect_scaler=100.0)
burn2.set_state_options('accel',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.set_state_options('deltav',
fix_initial=False,
fix_final=False,
defect_scaler=1.0)
burn2.add_control('u1',
rate_continuity=True,
rate2_continuity=True,
units='deg',
scaler=0.01,
rate_continuity_scaler=0.001,
rate2_continuity_scaler=0.001,
lower=-30,
upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.options['assembled_jac_type'] = 'csc'
p.model.linear_solver = DirectSolver(assemble_jac=True)
p.driver.add_recorder(
SqliteRecorder('two_burn_orbit_raise_example_for_docs.db'))
p.setup(check=True)
# Set Initial Guesses
p.set_val('design_parameters:c', value=1.5)
p.set_val('burn1.t_initial', value=0.0)
p.set_val('burn1.t_duration', value=2.25)
p.set_val('burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val(
'burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'),
)
p.set_val('burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0],
nodes='control_input'))
p.set_val('coast.t_initial', value=2.25)
p.set_val('coast.t_duration', value=3.0)
p.set_val('coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7],
nodes='state_input'))
p.set_val('coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('coast.controls:u1',
value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('burn2.t_initial', value=5.25)
p.set_val('burn2.t_duration', value=1.75)
p.set_val('burn2.states:r',
value=burn2.interpolate(ys=[1, 3], nodes='state_input'))
p.set_val('burn2.states:theta',
value=burn2.interpolate(ys=[0, 4.0], nodes='state_input'))
p.set_val('burn2.states:vr',
value=burn2.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)],
nodes='state_input'))
p.set_val('burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
traj.get_values('deltav', flat=True)[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate(times=50, num_procs=3)
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = traj.get_values('time')
x_sol = traj.get_values('pos_x')
y_sol = traj.get_values('pos_y')
dv_sol = traj.get_values('deltav')
u1_sol = traj.get_values('u1', units='deg')
t_exp = exp_out.get_values('time')
x_exp = exp_out.get_values('pos_x')
y_exp = exp_out.get_values('pos_y')
dv_exp = exp_out.get_values('deltav')
u1_exp = exp_out.get_values('u1', units='deg')
for phase_name in ['burn1', 'coast', 'burn2']:
ax_u1.plot(t_sol[phase_name], u1_sol[phase_name], 'ro', ms=3)
ax_u1.plot(t_exp[phase_name], u1_exp[phase_name], 'b-')
ax_deltav.plot(t_sol[phase_name], dv_sol[phase_name], 'ro', ms=3)
ax_deltav.plot(t_exp[phase_name], dv_exp[phase_name], 'b-')
ax_xy.plot(x_sol[phase_name],
y_sol[phase_name],
'ro',
ms=3,
label='implicit' if phase_name == 'burn1' else None)
ax_xy.plot(x_exp[phase_name],
y_exp[phase_name],
'b-',
label='explicit' if phase_name == 'burn1' else None)
plt.show()
def test_invalid_linkage_phase(self):
p = Problem(model=Group())
traj = Trajectory()
p.model.add_subsystem('traj', subsys=traj)
# Since we're only testing features like get_values that don't rely on a converged
# solution, no driver is attached. We'll just invoke run_model.
# First Phase (burn)
burn1 = Phase(ode_class=FiniteBurnODE, transcription=GaussLobatto(num_segments=4, order=3))
traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr', fix_initial=True, fix_final=False, defect_scaler=0.1)
burn1.set_state_options('vt', fix_initial=True, fix_final=False, defect_scaler=0.1)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg')
burn1.add_design_parameter('c', opt=False, val=1.5)
# Second Phase (Coast)
coast = Phase(ode_class=FiniteBurnODE, transcription=GaussLobatto(num_segments=10, order=3))
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10))
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=True)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_control('u1', opt=False, val=0.0, units='deg')
coast.add_design_parameter('c', opt=False, val=1.5)
# Third Phase (burn)
burn2 = Phase(ode_class=FiniteBurnODE, transcription=GaussLobatto(num_segments=3, order=3))
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10))
burn2.set_state_options('r', fix_initial=False, fix_final=True, defect_scaler=1.0)
burn2.set_state_options('theta', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.set_state_options('vr', fix_initial=False, fix_final=True, defect_scaler=0.1)
burn2.set_state_options('vt', fix_initial=False, fix_final=True, defect_scaler=0.1)
burn2.set_state_options('accel', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.set_state_options('deltav', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
ref0=0, ref=10)
burn2.add_design_parameter('c', opt=False, val=1.5)
burn2.add_objective('deltav', loc='final')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'foo'], vars=['u1', 'u1'])
# Finish Problem Setup
p.model.linear_solver = DirectSolver()
p.model.add_recorder(SqliteRecorder('test_trajectory_rec.db'))
with self.assertRaises(ValueError) as e:
p.setup(check=True)
self.assertEqual(str(e.exception), 'Invalid linkage. Phase \'foo\' does not exist in '
'trajectory \'traj\'.')
def test_connected_linkages_rk(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 = 20
seg_ends, _ = lgl(num_seg + 1)
traj = prob.model.add_subsystem('traj', Trajectory())
# First phase: normal operation.
transcription = RungeKutta(num_segments=num_seg)
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, 5e-5)
assert_rel_error(self, soc1[-1], 0.23794217, 5e-5)
assert_rel_error(self, soc1b[-1], 0.0281523, 5e-5)
assert_rel_error(self, soc1m[-1], 0.18625395, 5e-5)
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 make_problem(self,
constrained=True,
transcription=GaussLobatto,
optimizer='SLSQP',
numseg=50):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver(optimizer=optimizer)
p.driver.declare_coloring()
if optimizer == 'IPOPT':
p.driver.opt_settings['max_iter'] = 500
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['tol'] = 1.0E-7
p.driver.opt_settings['mu_strategy'] = 'monotone'
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=ShuttleODE,
transcription=transcription(num_segments=numseg, 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,
targets=['alpha'])
phase0.add_control('beta',
units='rad',
opt=True,
lower=-89 * np.pi / 180,
upper=1 * np.pi / 180,
targets=['beta'])
if constrained:
phase0.add_path_constraint('q', lower=0, upper=70, ref=70)
phase0.add_objective('theta', loc='final', ref=-0.01)
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 * np.pi / 180, 17.4 * np.pi / 180]),
units='rad')
p.set_val('traj.phase0.controls:beta',
phase0.interp('beta', [-75 * np.pi / 180, 0 * np.pi / 180]),
units='rad')
return p
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_two_burn_orbit_raise_gl_rk_gl_constrained(self):
import numpy as np
import matplotlib.pyplot as plt
from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver
from openmdao.utils.assert_utils import assert_rel_error
from openmdao.utils.general_utils import set_pyoptsparse_opt
from dymos import Phase, GaussLobatto, RungeKutta, Trajectory
from dymos.examples.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE
traj = Trajectory()
p = Problem(model=Group())
p.model.add_subsystem('traj', traj)
p.driver = pyOptSparseDriver()
_, optimizer = set_pyoptsparse_opt('SNOPT', fallback=True)
p.driver.options['optimizer'] = optimizer
p.driver.options['dynamic_simul_derivs'] = True
traj.add_design_parameter('c', opt=False, val=1.5, units='DU/TU')
# First Phase (burn)
burn1 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
burn1 = traj.add_phase('burn1', burn1)
burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10))
burn1.set_state_options('r', fix_initial=True, fix_final=False)
burn1.set_state_options('theta', fix_initial=True, fix_final=False)
burn1.set_state_options('vr', fix_initial=True, fix_final=False)
burn1.set_state_options('vt', fix_initial=True, fix_final=False)
burn1.set_state_options('accel', fix_initial=True, fix_final=False)
burn1.set_state_options('deltav', fix_initial=True, fix_final=False)
burn1.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
# Second Phase (Coast)
coast = Phase(ode_class=FiniteBurnODE,
transcription=RungeKutta(num_segments=20, compressed=True))
traj.add_phase('coast', coast)
coast.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), duration_ref=10)
coast.set_state_options('r', fix_initial=False, fix_final=False)
coast.set_state_options('theta', fix_initial=False, fix_final=False)
coast.set_state_options('vr', fix_initial=False, fix_final=False)
coast.set_state_options('vt', fix_initial=False, fix_final=False)
coast.set_state_options('accel', fix_initial=True, fix_final=False)
coast.set_state_options('deltav', fix_initial=False, fix_final=False)
coast.add_design_parameter('u1', opt=False, val=0.0)
# Third Phase (burn)
burn2 = Phase(ode_class=FiniteBurnODE,
transcription=GaussLobatto(num_segments=10, order=3, compressed=True))
traj.add_phase('burn2', burn2)
burn2.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 10), initial_ref=10)
burn2.set_state_options('r', fix_initial=False, fix_final=True)
burn2.set_state_options('theta', fix_initial=False, fix_final=False)
burn2.set_state_options('vr', fix_initial=False, fix_final=True)
burn2.set_state_options('vt', fix_initial=False, fix_final=True)
burn2.set_state_options('accel', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.set_state_options('deltav', fix_initial=False, fix_final=False, defect_scaler=1.0)
burn2.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
scaler=0.01, lower=-30, upper=30)
burn2.add_objective('deltav', loc='final', scaler=1.0)
burn1.add_timeseries_output('pos_x', units='DU')
coast.add_timeseries_output('pos_x', units='DU')
burn2.add_timeseries_output('pos_x', units='DU')
burn1.add_timeseries_output('pos_y', units='DU')
coast.add_timeseries_output('pos_y', units='DU')
burn2.add_timeseries_output('pos_y', units='DU')
# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])
traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])
# Finish Problem Setup
p.model.linear_solver = DirectSolver()
p.setup(check=True, force_alloc_complex=True)
# Set Initial Guesses
p.set_val('traj.design_parameters:c', value=1.5)
p.set_val('traj.burn1.t_initial', value=0.0)
p.set_val('traj.burn1.t_duration', value=2.25)
p.set_val('traj.burn1.states:r',
value=burn1.interpolate(ys=[1, 1.5], nodes='state_input'))
p.set_val('traj.burn1.states:theta',
value=burn1.interpolate(ys=[0, 1.7], nodes='state_input'))
p.set_val('traj.burn1.states:vr',
value=burn1.interpolate(ys=[0, 0], nodes='state_input'))
p.set_val('traj.burn1.states:vt',
value=burn1.interpolate(ys=[1, 1], nodes='state_input'))
p.set_val('traj.burn1.states:accel',
value=burn1.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn1.states:deltav',
value=burn1.interpolate(ys=[0, 0.1], nodes='state_input'), )
p.set_val('traj.burn1.controls:u1',
value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))
p.set_val('traj.coast.t_initial', value=2.25)
p.set_val('traj.coast.t_duration', value=3.0)
p.set_val('traj.coast.states:r',
value=coast.interpolate(ys=[1.3, 1.5], nodes='state_input'))
p.set_val('traj.coast.states:theta',
value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))
p.set_val('traj.coast.states:vr',
value=coast.interpolate(ys=[0.3285, 0], nodes='state_input'))
p.set_val('traj.coast.states:vt',
value=coast.interpolate(ys=[0.97, 1], nodes='state_input'))
p.set_val('traj.coast.states:accel',
value=coast.interpolate(ys=[0, 0], nodes='state_input'))
# p.set_val('traj.coast.controls:u1',
# value=coast.interpolate(ys=[0, 0], nodes='control_input'))
p.set_val('traj.burn2.t_initial', value=5.25)
p.set_val('traj.burn2.t_duration', value=1.75)
p.set_val('traj.burn2.states:r',
value=burn2.interpolate(ys=[1.8, 3], nodes='state_input'))
p.set_val('traj.burn2.states:theta',
value=burn2.interpolate(ys=[3.2, 4.0], nodes='state_input'))
p.set_val('traj.burn2.states:vr',
value=burn2.interpolate(ys=[.5, 0], nodes='state_input'))
p.set_val('traj.burn2.states:vt',
value=burn2.interpolate(ys=[1, np.sqrt(1 / 3)], nodes='state_input'))
p.set_val('traj.burn2.states:accel',
value=burn2.interpolate(ys=[0.1, 0], nodes='state_input'))
p.set_val('traj.burn2.states:deltav',
value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('traj.burn2.controls:u1',
value=burn2.interpolate(ys=[1, 1], nodes='control_input'))
p.run_driver()
assert_rel_error(self,
p.get_val('traj.burn2.timeseries.states:deltav')[-1],
0.3995,
tolerance=2.0E-3)
# Plot results
exp_out = traj.simulate()
fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)
span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)
ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')
ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)
ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)
t_sol = dict((phs, p.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_sol = dict((phs, p.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_sol = dict((phs, p.get_val('traj.{0}.timeseries.controls:u1'.format(phs), units='deg'))
for phs in ['burn1', 'burn2'])
t_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.time'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
x_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
y_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
dv_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
for phs in ['burn1', 'coast', 'burn2'])
u1_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.controls:u1'.format(phs),
units='deg'))
for phs in ['burn1', 'burn2'])
for phs in ['burn1', 'coast', 'burn2']:
try:
ax_u1.plot(t_sol[phs], u1_sol[phs], 'ro', ms=3)
ax_u1.plot(t_exp[phs], u1_exp[phs], 'b-')
except KeyError:
pass
ax_deltav.plot(t_sol[phs], dv_sol[phs], 'ro', ms=3)
ax_deltav.plot(t_exp[phs], dv_exp[phs], 'b-')
ax_xy.plot(x_sol[phs], y_sol[phs], 'ro', ms=3, label='implicit')
ax_xy.plot(x_exp[phs], y_exp[phs], 'b-', label='explicit')
plt.show()
def test_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 make_problem(self,
constrained=True,
transcription=GaussLobatto,
optimizer='SLSQP',
numseg=30):
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
OPT, OPTIMIZER = set_pyoptsparse_opt(optimizer, fallback=False)
p.driver.options['optimizer'] = OPTIMIZER
traj = p.model.add_subsystem('traj', Trajectory())
phase0 = traj.add_phase(
'phase0',
Phase(ode_class=ShuttleODE,
transcription=transcription(num_segments=numseg, 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,
targets=['alpha'])
phase0.add_control('beta',
units='rad',
opt=True,
lower=-89 * np.pi / 180,
upper=1 * np.pi / 180,
targets=['beta'])
if constrained:
phase0.add_path_constraint('q', lower=0, upper=70, ref=70)
phase0.add_objective('theta', loc='final', ref=-0.01)
p.setup(check=True, force_alloc_complex=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')
return p
def thermal_mission_trajectory(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'] = 50 #00
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'] = .05
p.driver.options['dynamic_simul_derivs'] = True
traj = p.model.add_subsystem('traj', Trajectory())
ascent = 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)
ascent = traj.add_phase('ascent', ascent)
ascent.set_time_options(opt_initial=False,
duration_bounds=(50, 400),
duration_ref=100.0)
ascent.set_state_options('r',
fix_initial=True,
lower=0,
upper=1.0E6,
scaler=1.0E-3,
defect_scaler=1.0E-2,
units='m')
ascent.set_state_options('h',
fix_initial=True,
lower=0,
upper=20000.0,
scaler=1.0E-3,
defect_scaler=1.0E-3,
units='m')
ascent.set_state_options('v',
fix_initial=True,
lower=10.0,
scaler=1.0E-2,
defect_scaler=5.0E-0,
units='m/s')
ascent.set_state_options('gam',
fix_initial=True,
lower=-1.5,
upper=1.5,
ref=1.0,
defect_scaler=1.0,
units='rad')
ascent.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')
ascent.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True)
ascent.add_design_parameter('S', val=1., units='m**2', opt=False)
if opt_throttle:
ascent.add_control('throttle',
val=1.0,
lower=0.0,
upper=1.0,
opt=True,
rate_continuity=True)
else:
ascent.add_design_parameter('throttle', val=1.0, opt=False)
ascent.add_design_parameter('W0', val=10.5e3, opt=False, units='kg')
ascent.add_boundary_constraint('h',
loc='final',
equals=meeting_altitude,
scaler=1.0E-3,
units='m')
ascent.add_boundary_constraint('aero.mach',
loc='final',
equals=1.,
units=None)
ascent.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad')
ascent.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
ascent.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# ascent.add_path_constraint(name='time', upper=110.)
# Minimize time at the end of the ascent
ascent.add_objective('time', loc='final', ref=100.0)
# ascent.add_objective('energy', loc='final', ref=100.0)
# ascent.add_objective('m', loc='final', ref=-10000.0)
# Set the state options for mass, temperature, and energy.
ascent.set_state_options('T',
fix_initial=True,
ref=300,
defect_scaler=1e-2)
ascent.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:
ascent.add_control('m_recirculated',
val=m_recirculated,
lower=0.,
opt=True,
rate_continuity=True,
ref=20.)
else:
ascent.add_control('m_recirculated', val=m_recirculated, opt=False)
ascent.add_design_parameter('Q_env', val=Q_env, opt=False)
ascent.add_design_parameter('Q_sink', val=Q_sink, opt=False)
ascent.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:
ascent.add_path_constraint('m_flow',
lower=0.,
upper=50.,
units='kg/s',
ref=10.)
if T is not None:
ascent.add_path_constraint('T', upper=T, units='K')
if T_o is not None:
ascent.add_path_constraint('T_o', upper=T_o, units='K', ref=300.)
cruise = 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)
cruise = traj.add_phase('cruise', cruise)
cruise.set_time_options(opt_initial=False,
duration_bounds=(50, 1e4),
duration_ref=100.0)
cruise.set_state_options('r',
lower=0,
upper=1.0E6,
scaler=1.0E-3,
defect_scaler=1.0E-2,
units='m')
cruise.set_state_options('h',
lower=0,
upper=20000.0,
scaler=1.0E-3,
defect_scaler=1.0E-3,
units='m')
cruise.set_state_options('v',
lower=10.0,
scaler=1.0E-2,
defect_scaler=5.0E-0,
units='m/s')
cruise.set_state_options('gam',
lower=-1.5,
upper=1.5,
ref=1.0,
defect_scaler=1.0,
units='rad')
cruise.set_state_options('m',
lower=15.e3,
upper=80e3,
scaler=1.0E-3,
defect_scaler=1.0E-3,
units='kg')
cruise.add_control('alpha',
units='deg',
lower=-8.0,
upper=8.0,
scaler=1.0,
rate_continuity=True)
cruise.add_design_parameter('S', val=1., units='m**2', opt=False)
if opt_throttle:
cruise.add_control('throttle',
val=1.0,
lower=0.0,
upper=1.0,
opt=True,
rate_continuity=True)
else:
cruise.add_design_parameter('throttle', val=1.0, opt=False)
cruise.add_design_parameter('W0', val=10.5e3, opt=False, units='kg')
# Set the state options for mass, temperature, and energy.
cruise.set_state_options('T',
fix_initial=True,
ref=300,
defect_scaler=1e-2)
cruise.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:
cruise.add_control('m_recirculated',
val=m_recirculated,
lower=0.,
opt=True,
rate_continuity=True,
ref=20.)
else:
cruise.add_control('m_recirculated', val=m_recirculated, opt=False)
cruise.add_design_parameter('Q_env', val=Q_env, opt=False)
cruise.add_design_parameter('Q_sink', val=Q_sink, opt=False)
cruise.add_design_parameter('Q_out', val=Q_out, opt=False)
cruise.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
cruise.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Link Phases (link time and all state variables)
traj.link_phases(phases=['ascent', 'cruise'], vars=['*'])
p.setup(mode='fwd', check=True)
p['traj.ascent.t_initial'] = 0.0
p['traj.ascent.t_duration'] = 200.
p['traj.ascent.states:r'] = ascent.interpolate(ys=[0.0, 111319.54],
nodes='state_input')
p['traj.ascent.states:h'] = ascent.interpolate(
ys=[100.0, meeting_altitude], nodes='state_input')
# p['traj.ascent.states:h'][:] = 10000.
p['traj.ascent.states:v'] = ascent.interpolate(ys=[135.964, 283.159],
nodes='state_input')
# p['traj.ascent.states:v'][:] = 200.
p['traj.ascent.states:gam'] = ascent.interpolate(ys=[0.0, 0.0],
nodes='state_input')
p['traj.ascent.states:m'] = ascent.interpolate(ys=[m_initial, 20.e3],
nodes='state_input')
p['traj.ascent.controls:alpha'] = ascent.interpolate(ys=[1., 1.],
nodes='control_input')
# Give initial values for the ascent states, controls, and time
p['traj.ascent.states:T'] = 310.
p['traj.cruise.t_initial'] = 200
p['traj.cruise.t_duration'] = 1000.
p['traj.cruise.states:r'] = cruise.interpolate(ys=[111319.54, 2e6],
nodes='state_input')
p['traj.cruise.states:h'] = cruise.interpolate(
ys=[meeting_altitude, meeting_altitude], nodes='state_input')
# p['traj.cruise.states:h'][:] = 10000.
p['traj.cruise.states:v'] = cruise.interpolate(ys=[283.159, 283.159],
nodes='state_input')
# p['traj.cruise.states:v'][:] = 200.
p['traj.cruise.states:gam'] = cruise.interpolate(ys=[0.0, 0.0],
nodes='state_input')
p['traj.cruise.states:m'] = cruise.interpolate(ys=[14e3, 12.e3],
nodes='state_input')
p['traj.cruise.controls:alpha'] = cruise.interpolate(ys=[1., 1.],
nodes='control_input')
# Give initial values for the cruise states, controls, and time
p['traj.cruise.states:T'] = 310.
return p