def test_control_rate_path_constraint_gl(self): from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase, GaussLobatto from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() phase = Phase(ode_class=BrachistochroneODE, transcription=GaussLobatto(num_segments=10)) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='deg', rate_continuity=False, lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) phase.add_path_constraint('theta_rate', lower=0, upper=100, units='deg/s') p.model.linear_solver = DirectSolver() p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, p.get_val('phase0.timeseries.time')[-1], 1.8016, tolerance=1.0E-3)
def test_record_specified_file(self, transcription='gauss-lobatto', top_level_jacobian='csc', optimizer='slsqp'): p = Problem(model=Group()) if optimizer == 'SNOPT': p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = OPTIMIZER p.driver.opt_settings['Major iterations limit'] = 100 p.driver.opt_settings['iSumm'] = 6 p.driver.opt_settings['Verify level'] = 3 else: p.driver = ScipyOptimizeDriver() phase = Phase(transcription, ode_class=BrachistochroneODE, num_segments=8, transcription_order=3) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='deg', rate_continuity=True, lower=0.01, upper=179.9) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.options['assembled_jac_type'] = top_level_jacobian.lower() p.model.linear_solver = DirectSolver(assemble_jac=True) p.setup() p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') p.run_driver() exp_out = phase.simulate(times=np.linspace(p['phase0.t_initial'], p['phase0.t_initial'] + p['phase0.t_duration'], 50), record_file='brachistochrone_sim.db') loaded_exp_out = load_simulation_results('brachistochrone_sim.db') for var in ['time', 'x', 'y', 'v', 'theta']: assert_almost_equal(exp_out.get_values(var).ravel(), loaded_exp_out.get_values(var).ravel())
def test_ex_brachistochrone_vs_rungekutta_compressed(self): from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from dymos import Phase, RungeKutta from dymos.examples.brachistochrone.brachistochrone_vector_states_ode import \ BrachistochroneVectorStatesODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase(ode_class=BrachistochroneVectorStatesODE, transcription=RungeKutta(num_segments=20, compressed=True)) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10)) phase.set_state_options('pos', fix_initial=True, fix_final=False) phase.set_state_options('v', fix_initial=True, fix_final=False) phase.add_control('theta', continuity=True, rate_continuity=True, units='deg', lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) phase.add_boundary_constraint('pos', loc='final', lower=[10, 5]) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver() p.setup(check=True, force_alloc_complex=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 1.80162174 pos0 = [0, 10] posf = [10, 5] p['phase0.states:pos'] = phase.interpolate(ys=[pos0, posf], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[0.46, 100.22900215], nodes='control_input') p['phase0.design_parameters:g'] = 9.80665 p.run_driver() self.assert_results(p) self.tearDown()
def setUpClass(cls): import matplotlib matplotlib.use('Agg') from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from dymos import Phase, load_simulation_results from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() phase = Phase('gauss-lobatto', ode_class=BrachistochroneODE, num_segments=10) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='rad', rate_continuity=False, lower=0.001, upper=3.14) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = 'csc' p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') # Solve for the optimal trajectory p.run_driver() cls.exp_out = phase.simulate( times=100, record_file='phase_simulation_test_sim.db') cls.exp_out_loaded = load_simulation_results( 'phase_simulation_test_sim.db')
def test_unbounded_time(self): p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase('gauss-lobatto', ode_class=BrachistochroneODE, num_segments=8, transcription_order=3) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=False, fix_duration=False) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True, fix_final=False) phase.add_control('theta', continuity=True, rate_continuity=True, units='deg', lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) phase.add_boundary_constraint('time', loc='initial', equals=0) p.model.options['assembled_jac_type'] = 'csc' p.model.linear_solver = DirectSolver(assemble_jac=True) p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100], nodes='control_input') p['phase0.design_parameters:g'] = 9.80665 p.run_driver() self.assertTrue(p.driver.result.success, msg='Brachistochrone with outbounded times has failed')
def test_objective_design_parameter_radau(self): p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase(ode_class=BrachistochroneODE, transcription=Radau(num_segments=20, order=3, compressed=True)) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, duration_bounds=(4, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True, fix_final=False) phase.add_control('theta', continuity=True, rate_continuity=True, units='deg', lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=True, val=9.80665) # Minimize time at the end of the phase phase.add_objective('g') p.model.options['assembled_jac_type'] = 'csc' p.model.linear_solver = DirectSolver() p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100], nodes='control_input') p['phase0.design_parameters:g'] = 9.80665 p.run_driver() assert_rel_error(self, p['phase0.t_duration'], 10, tolerance=1.0E-3)
def double_integrator_direct_collocation(transcription='gauss-lobatto', top_level_jacobian='csc', compressed=True): p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase(transcription, ode_class=DoubleIntegratorODE, num_segments=20, transcription_order=3, compressed=compressed) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, fix_duration=True) phase.set_state_options('x', fix_initial=True) phase.set_state_options('v', fix_initial=True, fix_final=True) phase.add_control('u', units='m/s**2', scaler=0.01, continuity=False, rate_continuity=False, rate2_continuity=False, lower=-1.0, upper=1.0) # Maximize distance travelled in one second. phase.add_objective('x', loc='final', scaler=-1) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = top_level_jacobian.lower() p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 1.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 0.25], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 0], nodes='state_input') p['phase0.controls:u'] = phase.interpolate(ys=[1, -1], nodes='control_input') p.run_driver() return p
def test_brachistochrone_backward_shooting(self): from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase, RungeKutta from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase(ode_class=BrachistochroneODE, transcription=RungeKutta(num_segments=20)) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(-2.0, -0.5)) phase.set_state_options('x', fix_initial=True) phase.set_state_options('y', fix_initial=True) phase.set_state_options('v', fix_initial=False) phase.add_control('theta', units='deg', lower=0.01, upper=179.9, ref0=0, ref=180.0, rate_continuity=True, rate2_continuity=True) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Final state values can't be controlled with simple bounds in ExplicitPhase, # so use nonlinear boundary constraints instead. phase.add_boundary_constraint('x', loc='final', equals=0) phase.add_boundary_constraint('y', loc='final', equals=10) phase.add_boundary_constraint('v', loc='final', equals=0) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=-1) p.model.linear_solver = DirectSolver() p.setup(check=True) p['phase0.t_initial'] = 1.8016 p['phase0.t_duration'] = -1.8016 p['phase0.states:x'] = 10 p['phase0.states:y'] = 5 p['phase0.states:v'] = 10 p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, p['phase0.time'][-1], -1.8016, tolerance=1.0E-3) # Generate the explicitly simulated trajectory exp_out = phase.simulate() assert_rel_error(self, exp_out.get_val('phase0.timeseries.states:x')[-1, 0], 0, tolerance=1.0E-3) assert_rel_error(self, exp_out.get_val('phase0.timeseries.states:y')[-1, 0], 10, tolerance=1.0E-3)
def _make_problem(self, transcription, num_seg, transcription_order=3): p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() # Compute sparsity/coloring when run_driver is called p.driver.options['dynamic_simul_derivs'] = True t = {'gauss-lobatto': GaussLobatto(num_segments=num_seg, order=transcription_order), 'radau-ps': Radau(num_segments=num_seg, order=transcription_order), 'runge-kutta': RungeKutta(num_segments=num_seg)} phase = Phase(ode_class=_BrachistochroneTestODE, transcription=t[transcription]) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(1, 1), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True) phase.set_state_options('y', fix_initial=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='deg', rate_continuity=True, lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) phase.add_boundary_constraint('x', loc='final', equals=10) phase.add_boundary_constraint('y', loc='final', equals=5) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver() p.setup() p['phase0.t_initial'] = 1.0 p['phase0.t_duration'] = 3.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') return p
def test_min_time_climb_for_docs_gauss_lobatto(self): import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase from dymos.examples.min_time_climb.min_time_climb_ode import MinTimeClimbODE p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = 'SLSQP' # Compute sparsity/coloring when run_driver is called p.driver.options['dynamic_simul_derivs'] = True phase = Phase('gauss-lobatto', ode_class=MinTimeClimbODE, num_segments=12, compressed=True, transcription_order=3) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, duration_bounds=(50, 400), duration_ref=100.0) phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E6, ref=1.0E3, defect_ref=1000.0, units='m') phase.set_state_options('h', fix_initial=True, lower=0, upper=20000.0, ref=1.0E2, defect_ref=100.0, units='m') phase.set_state_options('v', fix_initial=True, lower=10.0, ref=1.0E2, defect_ref=0.1, units='m/s') phase.set_state_options('gam', fix_initial=True, lower=-1.5, upper=1.5, ref=1.0, defect_scaler=1.0, units='rad') phase.set_state_options('m', fix_initial=True, lower=10.0, upper=1.0E5, ref=1.0E3, defect_ref=0.1) rate_continuity = True phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0, rate_continuity=rate_continuity, rate_continuity_scaler=100.0, rate2_continuity=False) phase.add_design_parameter('S', val=49.2386, units='m**2', opt=False) phase.add_design_parameter('Isp', val=1600.0, units='s', opt=False) phase.add_design_parameter('throttle', val=1.0, opt=False) phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m') phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None) phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad') phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000) phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8) phase.add_path_constraint(name='alpha', lower=-8, upper=8) # Minimize time at the end of the phase phase.add_objective('time', loc='final') p.driver.options['dynamic_simul_derivs'] = True p.model.options['assembled_jac_type'] = 'csc' p.model.linear_solver = DirectSolver(assemble_jac=True) p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 500 p['phase0.states:r'] = phase.interpolate(ys=[0.0, 50000.0], nodes='state_input') p['phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input') p['phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input') p['phase0.states:m'] = phase.interpolate(ys=[19030.468, 10000.], nodes='state_input') p['phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, p.model.phase0.get_values('time')[-1], 321.0, tolerance=2) exp_out = phase.simulate(times=50) fig, axes = plt.subplots(2, 1, sharex=True) axes[0].plot(phase.get_values('time'), phase.get_values('h'), 'ro') axes[0].plot(exp_out.get_values('time'), exp_out.get_values('h'), 'b-') axes[0].set_xlabel('time (s)') axes[0].set_ylabel('altitude (m)') axes[1].plot(phase.get_values('time'), phase.get_values('alpha', units='deg'), 'ro') axes[1].plot(exp_out.get_values('time'), exp_out.get_values('alpha', units='deg'), 'b-') axes[1].set_xlabel('time (s)') axes[1].set_ylabel('alpha (deg)') plt.show()
def test_brachistochrone_recording(self): import matplotlib matplotlib.use('Agg') from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver, \ SqliteRecorder, CaseReader from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase, GaussLobatto from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() phase = Phase(ode_class=BrachistochroneODE, transcription=GaussLobatto(num_segments=10)) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='deg', rate_continuity=False, lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver() # Recording rec = SqliteRecorder('brachistochrone_solution.db') p.driver.recording_options['record_desvars'] = True p.driver.recording_options['record_responses'] = True p.driver.recording_options['record_objectives'] = True p.driver.recording_options['record_constraints'] = True p.model.recording_options['record_metadata'] = True p.driver.add_recorder(rec) p.model.add_recorder(rec) phase.add_recorder(rec) p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, p.get_val('phase0.timeseries.time')[-1], 1.8016, tolerance=1.0E-3) cr = CaseReader('brachistochrone_solution.db') system_cases = cr.list_cases('root') case = cr.get_case(system_cases[-1]) outputs = dict([ (o[0], o[1]) for o in case.list_outputs(units=True, shape=True, out_stream=None) ]) assert_rel_error( self, p['phase0.controls:theta'], outputs['phase0.control_group.indep_controls.controls:theta'] ['value'])
def ex_aircraft_steady_flight(optimizer='SLSQP', transcription='gauss-lobatto'): p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = optimizer p.driver.options['dynamic_simul_derivs'] = True if optimizer == 'SNOPT': p.driver.opt_settings['Major iterations limit'] = 1000 p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6 p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6 p.driver.opt_settings["Linesearch tolerance"] = 0.10 p.driver.opt_settings['iSumm'] = 6 num_seg = 15 seg_ends, _ = lgl(num_seg + 1) phase = Phase(transcription, ode_class=AircraftODE, num_segments=num_seg, segment_ends=seg_ends, transcription_order=5, compressed=False) # Pass Reference Area from an external source assumptions = p.model.add_subsystem('assumptions', IndepVarComp()) assumptions.add_output('S', val=427.8, units='m**2') assumptions.add_output('mass_empty', val=1.0, units='kg') assumptions.add_output('mass_payload', val=1.0, units='kg') p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(300, 10000), duration_ref=3600) phase.set_state_options('range', units='NM', fix_initial=True, fix_final=False, scaler=0.001, defect_scaler=1.0E-2) phase.set_state_options('mass_fuel', units='lbm', fix_initial=True, fix_final=True, upper=1.5E5, lower=0.0, scaler=1.0E-5, defect_scaler=1.0E-1) phase.add_control('alt', units='kft', opt=True, lower=0.0, upper=50.0, rate_param='climb_rate', rate_continuity=True, rate_continuity_scaler=1.0, rate2_continuity=True, rate2_continuity_scaler=1.0, ref=1.0, fix_initial=True, fix_final=True) phase.add_control('mach', units=None, opt=False) phase.add_input_parameter('S', units='m**2') phase.add_input_parameter('mass_empty', units='kg') phase.add_input_parameter('mass_payload', units='kg') phase.add_path_constraint('propulsion.tau', lower=0.01, upper=1.0) phase.add_path_constraint('alt_rate', units='ft/min', lower=-3000, upper=3000, ref=3000) p.model.connect('assumptions.S', 'phase0.input_parameters:S') p.model.connect('assumptions.mass_empty', 'phase0.input_parameters:mass_empty') p.model.connect('assumptions.mass_payload', 'phase0.input_parameters:mass_payload') phase.add_objective('range', loc='final', ref=-1.0) p.model.linear_solver = DirectSolver(assemble_jac=True) p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 3600.0 p['phase0.states:range'] = phase.interpolate(ys=(0, 1000.0), nodes='state_input') p['phase0.states:mass_fuel'] = phase.interpolate(ys=(30000, 0), nodes='state_input') p['phase0.controls:mach'][:] = 0.8 p['phase0.controls:alt'][:] = 10.0 p['assumptions.S'] = 427.8 p['assumptions.mass_empty'] = 0.15E6 p['assumptions.mass_payload'] = 84.02869 * 400 p.run_driver() exp_out = phase.simulate( times=np.linspace(0, p['phase0.t_duration'], 500), record=True, record_file='test_ex_aircraft_steady_flight_rec.db') plt.plot(phase.get_values('time', nodes='all'), phase.get_values('alt', nodes='all'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('alt'), 'b-') plt.suptitle('altitude vs time') plt.figure() plt.plot(phase.get_values('time', nodes='all'), phase.get_values('alt_rate', nodes='all', units='ft/min'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('alt_rate', units='ft/min'), 'b-') plt.suptitle('altitude rate vs time') plt.figure() plt.plot(phase.get_values('time', nodes='all'), phase.get_values('mass_fuel', nodes='all'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('mass_fuel'), 'b-') plt.suptitle('fuel mass vs time') plt.figure() plt.plot(phase.get_values('time', nodes='all'), phase.get_values('propulsion.dXdt:mass_fuel', nodes='all'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('propulsion.dXdt:mass_fuel'), 'b-') plt.suptitle('fuel mass flow rate vs time') plt.figure() plt.plot(phase.get_values('time', nodes='all'), phase.get_values('mach', nodes='all'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('mach'), 'b-') plt.suptitle('mach vs time') plt.figure() plt.plot(phase.get_values('time', nodes='all'), phase.get_values('mach_rate', nodes='all'), 'ro') plt.plot(exp_out.get_values('time'), exp_out.get_values('mach_rate'), 'b-') plt.suptitle('mach rate vs time') print('time') print(phase.get_values('time', nodes='all').T) print('alt') print(phase.get_values('alt', nodes='all').T) print('alt_rate') print(phase.get_values('alt_rate', nodes='all').T) print('alt_rate2') print(phase.get_values('alt_rate2', nodes='all').T) print('range') print(phase.get_values('range', nodes='all').T) print('flight path angle') print(phase.get_values('gam_comp.gam').T) print('true airspeed') print(phase.get_values('tas_comp.TAS', units='m/s').T) print('coef of lift') print(phase.get_values('aero.CL').T) print('coef of drag') print(phase.get_values('aero.CD').T) print('atmos density') print(phase.get_values('atmos.rho').T) print('alpha') print(phase.get_values('flight_equilibrium.alpha', units='rad').T) print('coef of thrust') print(phase.get_values('flight_equilibrium.CT').T) print('fuel flow rate') print(phase.get_values('propulsion.dXdt:mass_fuel').T) print('max_thrust') print(phase.get_values('propulsion.max_thrust', units='N').T) print('tau') print(phase.get_values('propulsion.tau').T) print('dynamic pressure') print(phase.get_values('q_comp.q', units='Pa').T) print('S') print(phase.get_values('S', units='m**2').T) plt.show() return p
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() prob.driver.options["maxiter"] = 100 prob.setup(check=True) prob.set_val("traj.phase0.states:h", phase0.interpolate(ys=[260000, 80000], nodes="state_input"), units="ft") prob.set_val("traj.phase0.states:gamma", phase0.interpolate(ys=[-1*np.pi/180, -5*np.pi/180], nodes="state_input"), units="rad") prob.set_val("traj.phase0.states:phi", phase0.interpolate(ys=[0, 75*np.pi/180], nodes="state_input"), units="rad") prob.set_val("traj.phase0.states:psi", phase0.interpolate(ys=[90*np.pi/180, 10*np.pi/180], nodes="state_input"), units="rad") prob.set_val("traj.phase0.states:theta", phase0.interpolate(ys=[0, 25*np.pi/180], nodes="state_input"), units="rad") prob.set_val("traj.phase0.states:v", phase0.interpolate(ys=[25600, 2500], nodes="state_input"), units="ft/s") prob.set_val("traj.phase0.t_initial", 0, units="s") prob.set_val("traj.phase0.t_duration", 2000, units="s") prob.set_val("traj.phase0.controls:alpha", phase0.interpolate(ys=[17.4*np.pi/180, 17.4*np.pi/180], nodes="control_input"), units="rad") prob.set_val("traj.phase0.controls:beta", phase0.interpolate(ys=[-75*np.pi/180, 0*np.pi/180], nodes="control_input"), units="rad") recorder = SqliteRecorder("reentry.sql") prob.driver.add_recorder(recorder) prob.run_driver() # prob.run_model()
def test_brachistochrone_for_docs_gauss_lobatto_without_simul_derivs(self): from openmdao.api import Problem, Group, pyOptSparseDriver, DirectSolver from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase from dymos.examples.brachistochrone.brachistochrone_ode import BrachistochroneODE p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = 'SLSQP' phase = Phase('gauss-lobatto', ode_class=BrachistochroneODE, num_segments=100, transcription_order=3, compressed=True) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.add_control('theta', units='deg', rate_continuity=False, lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = 'csc' p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100.5], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, phase.get_values('time')[-1], 1.8016, tolerance=1.0E-3)
def min_time_climb_problem(num_seg=3, transcription_order=5, transcription='gauss-lobatto', top_level_densejacobian=True): p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = 'SNOPT' p.driver.opt_settings['Major iterations limit'] = 500 p.driver.opt_settings['Iterations limit'] = 1000000000 p.driver.opt_settings['iSumm'] = 6 p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-10 p.driver.opt_settings['Major optimality tolerance'] = 1.0E-10 p.driver.opt_settings['Verify level'] = 1 p.driver.opt_settings['Function precision'] = 1.0E-6 p.driver.opt_settings['Linesearch tolerance'] = .1 p.driver.options['dynamic_simul_derivs'] = True phase = Phase(transcription, ode_class=MinTimeClimbODE, num_segments=num_seg, transcription_order=transcription_order) p.model.add_subsystem('phase', phase) phase.set_time_options(opt_initial=False, duration_bounds=(100, 100), duration_ref=100.0) phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E8, scaler=1.0E-4, defect_scaler=1.0E-3, units='m') phase.set_state_options('h', lower=0, upper=20000.0, scaler=1.0E-3, defect_scaler=1.0E-3, units='m') phase.set_state_options('v', lower=10.0, upper=500., scaler=1.0E-2, defect_scaler=1.0E-2, units='m/s') phase.set_state_options('gam', lower=-1.5, upper=1.5, ref=1.0, defect_scaler=1.0, units='rad') phase.set_state_options('m', fix_initial=True, lower=10.0, upper=1.0E5, scaler=1.0E-3, defect_scaler=1.0E-3, units='kg') phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0, rate_continuity=True) phase.add_control('S', val=49.2386, units='m**2', dynamic=False, opt=False) phase.add_control('throttle', val=1.0, opt=True, lower=0., upper=1., rate_continuity=False) phase.add_path_constraint(name='h', lower=1e4, upper=1e4, ref=20000, units='m') phase.add_path_constraint(name='aero.mach', lower=1.2, upper=1.2) phase.add_objective('time', loc='final', ref=-100.0) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = 'csc' p.setup(mode='fwd', check=True) p['phase.t_initial'] = 0.0 p['phase.t_duration'] = 2000. p['phase.states:r'] = phase.interpolate(ys=[0.0, 1e6], nodes='disc') p['phase.states:h'][:] = 1e4 p['phase.states:v'][:] = 250. p['phase.states:gam'][:] = 0. p['phase.states:m'] = phase.interpolate(ys=[50e3, 49e3], nodes='disc') 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 brachistochrone_min_time(transcription='gauss-lobatto', num_segments=8, transcription_order=3, run_driver=True, compressed=True, optimizer='SLSQP'): p = Problem(model=Group()) # if optimizer == 'SNOPT': p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = optimizer p.driver.options['dynamic_simul_derivs'] = True if transcription == 'gauss-lobatto': t = GaussLobatto(num_segments=num_segments, order=transcription_order, compressed=compressed) elif transcription == 'radau-ps': t = Radau(num_segments=num_segments, order=transcription_order, compressed=compressed) elif transcription == 'runge-kutta': t = RungeKutta(num_segments=num_segments, order=transcription_order, compressed=compressed) phase = Phase(ode_class=BrachistochroneODE, transcription=t) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=False, solve_segments=False) phase.set_state_options('y', fix_initial=True, fix_final=False, solve_segments=False) phase.set_state_options('v', fix_initial=True, fix_final=False, solve_segments=False) phase.add_control('theta', continuity=True, rate_continuity=True, units='deg', lower=0.01, upper=179.9) phase.add_input_parameter('g', units='m/s**2', val=9.80665) phase.add_boundary_constraint('x', loc='final', equals=10) phase.add_boundary_constraint('y', loc='final', equals=5) # Minimize time at the end of the phase phase.add_objective('time_phase', loc='final', scaler=10) p.model.linear_solver = DirectSolver() p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100], nodes='control_input') p['phase0.input_parameters:g'] = 9.80665 p.run_model() if run_driver: p.run_driver() # Plot results if SHOW_PLOTS: exp_out = phase.simulate() fig, ax = plt.subplots() fig.suptitle('Brachistochrone Solution') x_imp = p.get_val('phase0.timeseries.states:x') y_imp = p.get_val('phase0.timeseries.states:y') x_exp = exp_out.get_val('phase0.timeseries.states:x') y_exp = exp_out.get_val('phase0.timeseries.states:y') ax.plot(x_imp, y_imp, 'ro', label='implicit') ax.plot(x_exp, y_exp, 'b-', label='explicit') ax.set_xlabel('x (m)') ax.set_ylabel('y (m)') ax.grid(True) ax.legend(loc='upper right') fig, ax = plt.subplots() fig.suptitle('Brachistochrone Solution') x_imp = p.get_val('phase0.timeseries.time_phase') y_imp = p.get_val('phase0.timeseries.controls:theta') x_exp = exp_out.get_val('phase0.timeseries.time_phase') y_exp = exp_out.get_val('phase0.timeseries.controls:theta') ax.plot(x_imp, y_imp, 'ro', label='implicit') ax.plot(x_exp, y_exp, 'b-', label='explicit') ax.set_xlabel('time (s)') ax.set_ylabel('theta (rad)') ax.grid(True) ax.legend(loc='lower right') plt.show() return p
def escort_problem(optimizer='SLSQP', num_seg=3, transcription_order=5, transcription='gauss-lobatto', meeting_altitude=14000., climb_time=350., starting_mass=19030.468): p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = optimizer if optimizer == 'SNOPT': p.driver.opt_settings['Major iterations limit'] = 1000 p.driver.opt_settings['Iterations limit'] = 100000000 p.driver.opt_settings['iSumm'] = 6 p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6 p.driver.opt_settings['Major optimality tolerance'] = 1.0E-5 p.driver.opt_settings['Verify level'] = -1 p.driver.opt_settings['Function precision'] = 1.0E-6 p.driver.opt_settings['Linesearch tolerance'] = 0.10 p.driver.opt_settings['Major step limit'] = 0.5 phase_class = _phase_map[transcription] climb = Phase('gauss-lobatto', ode_class=MinTimeClimbODE, num_segments=num_seg, transcription_order=transcription_order) climb.set_time_options(duration_bounds=(50, climb_time), duration_ref=100.0) climb.set_state_options('r', fix_initial=True, lower=0, upper=1.0E6, scaler=1.0E-3, defect_scaler=1.0E-2, units='m') climb.set_state_options('h', fix_initial=True, lower=0, upper=20000.0, scaler=1.0E-3, defect_scaler=1.0E-3, units='m') climb.set_state_options('v', fix_initial=True, lower=10.0, scaler=1.0E-2, defect_scaler=1.0E-2, units='m/s') climb.set_state_options('gam', fix_initial=True, lower=-1.5, upper=1.5, ref=1.0, defect_scaler=1.0, units='rad') climb.set_state_options('m', fix_initial=True, lower=10.0, upper=1.0E5, scaler=1.0E-3, defect_scaler=1.0E-3) climb.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0, rate_continuity=True) climb.add_control('S', val=49.2386, units='m**2', dynamic=False, opt=False) climb.add_control('Isp', val=5000.0, units='s', dynamic=False, opt=False) climb.add_control('throttle', val=1.0, dynamic=False, opt=False) climb.add_boundary_constraint('h', loc='final', equals=meeting_altitude, scaler=1.0E-3, units='m') climb.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None) climb.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad') # climb.add_boundary_constraint('time', loc='final', upper=climb_time, units='s') climb.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000) climb.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8) # Minimize time at the end of the climb climb.set_objective('time', loc='final', ref=100.0) p.model.add_subsystem('climb', climb) escort = Phase('gauss-lobatto', ode_class=MinTimeClimbODE, num_segments=num_seg * 2, transcription_order=transcription_order) escort.set_time_options(duration_bounds=(50, 10000), opt_initial=True, duration_ref=100.0) escort.set_state_options('r', lower=0, upper=1.0E6, scaler=1.0E-3, defect_scaler=1.0E-2, units='m') escort.set_state_options('h', lower=0, upper=20000.0, scaler=1.0E-3, defect_scaler=1.0E-3, units='m') escort.set_state_options('v', lower=10.0, scaler=1.0E-2, defect_scaler=1.0E-2, units='m/s') escort.set_state_options('gam', lower=-1.5, upper=1.5, ref=1.0, defect_scaler=1.0, units='rad') escort.set_state_options('m', lower=10.0, upper=1.0E5, scaler=1.0E-3, defect_scaler=1.0E-3) escort.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0, rate_continuity=True) escort.add_control('S', val=49.2386, units='m**2', dynamic=False, opt=False) escort.add_control('Isp', val=1600.0, units='s', dynamic=False, opt=False) escort.add_control('throttle', val=1.0, lower=0., upper=1., opt=True) # escort.add_control('throttle', val=1.0, dynamic=False, opt=False) # escort.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3, units='m') # escort.add_boundary_constraint('aero.mach', loc='final', equals=1.0, units=None) # escort.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad') escort.add_boundary_constraint('m', loc='final', equals=15000.0, units='kg') escort.add_path_constraint(name='h', lower=meeting_altitude, upper=meeting_altitude, ref=meeting_altitude) escort.add_path_constraint(name='aero.mach', equals=1.0) # Maximize distance at the end of the escort # escort.set_objective('r', loc='final', ref=-1e5) p.model.add_subsystem('escort', escort) # Connect the phases linkage_comp = PhaseLinkageComp() linkage_comp.add_linkage(name='L01', vars=['t'], units='s', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['r'], units='m', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['h'], units='m', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['v'], units='m/s', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['gam'], units='rad', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['m'], units='kg', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['alpha'], units='rad', equals=0.0, linear=True) linkage_comp.add_linkage(name='L01', vars=['throttle'], equals=0.0, linear=True) p.model.connect('climb.time++', 'linkages.L01_t:lhs') p.model.connect('escort.time--', 'linkages.L01_t:rhs') p.model.connect('climb.states:r++', 'linkages.L01_r:lhs') p.model.connect('escort.states:r--', 'linkages.L01_r:rhs') p.model.connect('climb.states:h++', 'linkages.L01_h:lhs') p.model.connect('escort.states:h--', 'linkages.L01_h:rhs') # p.model.connect('climb.states:v++', 'linkages.L01_v:lhs') p.model.connect('escort.states:v--', 'linkages.L01_v:rhs') # p.model.connect('climb.states:gam++', 'linkages.L01_gam:lhs') p.model.connect('escort.states:gam--', 'linkages.L01_gam:rhs') p.model.connect('climb.states:m++', 'linkages.L01_m:lhs') p.model.connect('escort.states:m--', 'linkages.L01_m:rhs') p.model.connect('climb.controls:alpha++', 'linkages.L01_alpha:lhs') p.model.connect('escort.controls:alpha--', 'linkages.L01_alpha:rhs') p.model.connect('climb.controls:throttle++', 'linkages.L01_throttle:lhs') p.model.connect('escort.controls:throttle--', 'linkages.L01_throttle:rhs') p.model.add_subsystem('linkages', linkage_comp) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = 'csc' # p.driver.add_recorder(SqliteRecorder('escort.db')) p.setup(mode='fwd', check=True) p['climb.t_initial'] = 0.0 p['climb.t_duration'] = 200. p['climb.states:r'] = climb.interpolate(ys=[0.0, 111319.54], nodes='disc') p['climb.states:h'] = climb.interpolate(ys=[100.0, 20000.0], nodes='disc') p['climb.states:v'] = climb.interpolate(ys=[135.964, 283.159], nodes='disc') p['climb.states:gam'] = climb.interpolate(ys=[0.0, 0.0], nodes='disc') p['climb.states:m'] = climb.interpolate(ys=[starting_mass, 16841.431], nodes='disc') p['climb.controls:alpha'] = climb.interpolate(ys=[0.0, 0.0], nodes='all') p['escort.t_initial'] = 200. p['escort.t_duration'] = 1000. p['escort.states:r'] = escort.interpolate(ys=[111319.54, 400000.], nodes='disc') p['escort.states:h'] = escort.interpolate( ys=[meeting_altitude, meeting_altitude], nodes='disc') p['escort.states:v'] = escort.interpolate(ys=[250., 250.], nodes='disc') p['escort.states:gam'] = escort.interpolate(ys=[0.0, 0.0], nodes='disc') p['escort.states:m'] = escort.interpolate(ys=[17000., 15000.], nodes='disc') p['escort.controls:alpha'] = escort.interpolate(ys=[0.0, 0.0], nodes='all') return p
def test_battery_power(self): """ for battery explicit integration testings """ _, local_opt = set_pyoptsparse_opt('SNOPT') if local_opt != 'SNOPT': raise unittest.SkipTest("pyoptsparse is not providing SNOPT") p = om.Problem() p.driver = om.pyOptSparseDriver() p.driver.options['optimizer'] = 'SNOPT' p.driver.opt_settings['Major iterations limit'] = 100 p.driver.opt_settings['Major optimality tolerance'] = 5.0E-3 p.driver.opt_settings['Major feasibility tolerance'] = 1e-6 p.driver.opt_settings['iSumm'] = 6 transcription = Radau(num_segments=15, order=3, compressed=True) phase0 = Phase(transcription=transcription, ode_class=BatteryGroup) phase0.set_time_options(fix_initial=True, duration_bounds=(30, 30)) p.model.add_subsystem(name='phase0', subsys=phase0) phase0.add_state('SOC', fix_initial=True, rate_source='dXdt:SOC', lower=0.0, upper=1.) phase0.add_state('U_Th', units='V', fix_initial=False, rate_source='dXdt:V_{thev}', lower=0.0, upper=5.0) # phase0.add_parameter('P_out', units='W', opt=False) # phase0.add_boundary_constraint('U_pack', units='V', loc='initial', equals=5100) phase0.add_objective('time', loc='final', ref=1) p.model.linear_solver = om.DirectSolver(assemble_jac=True) phase0.add_timeseries_output('Q_{batt}', output_name='Q_{batt}', units='W') # phase0.add_timeseries_output('U_pack', output_name='V', units='V') p.setup() # p.check_partials() T0 = 10 + 273 p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 30 p['phase0.states:SOC'] = phase0.interpolate(ys=[1.0, 0.0], nodes='state_input') p['phase0.states:U_Th'] = phase0.interpolate(ys=[0.1, 0.1], nodes='state_input') # p['phase0.parameters:P_out'][:] = 72000. p.run_driver() fig, ax = plt.subplots(3, 1, sharex=True) fig.suptitle('Temperature Plots') t_opt = p.get_val('phase0.timeseries.time') SOC_opt = p.get_val('phase0.timeseries.states:SOC', units=None) Q_batt_opt = p.get_val('phase0.timeseries.Q_{batt}', units='kW') ax[1].plot(t_opt, Q_batt_opt * 128 * 40, 'r', label='$Q_{cell}$') ax[2].plot(t_opt, SOC_opt, 'r', label='$SOC$') #spot check final values # assert_rel_error(self, T_batt_opt[-1], 1.25934406, tolerance=1.0E-6) # ax[3].plot(t_opt, V_opt, 'r', label='$Voltage$') # axarr = fig.add_subplot(1, 2, 2) # axarr.plot(sim_out.get_values('time'),sim_out.get_values('electric.battery.I_Li'), 'b') # # # axarr.plot(p['phase0.state_interp.state_col:r'], # # # p['phase0.controls:h'], 'bo', ms=4) # axarr.set_ylabel('I_Li, amps') # axarr.set_xlabel('time, s') # axarr.axes.get_xaxis().set_visible(True) import matplotlib matplotlib.use( 'agg') # <--- comment out if you want to show this plot. plt.show()
def thermal_mission_problem(num_seg=5, transcription_order=3, meeting_altitude=20000., Q_env=0., Q_sink=0., Q_out=0., m_recirculated=0., opt_m_recirculated=False, opt_m_burn=False, opt_throttle=True, engine_heat_coeff=0., pump_heat_coeff=0., T=None, T_o=None, opt_m=False, m_initial=20.e3, transcription='gauss-lobatto'): p = Problem(model=Group()) p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = 'SNOPT' p.driver.opt_settings['Major iterations limit'] = 5000 p.driver.opt_settings['Iterations limit'] = 5000000000000000 p.driver.opt_settings['iSumm'] = 6 p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-8 p.driver.opt_settings['Major optimality tolerance'] = 1.0E-8 p.driver.opt_settings['Verify level'] = -1 p.driver.opt_settings['Linesearch tolerance'] = .1 p.driver.opt_settings['Major step limit'] = .1 p.driver.options['dynamic_simul_derivs'] = True phase = Phase(transcription, ode_class=ThermalMissionODE, ode_init_kwargs={'engine_heat_coeff':engine_heat_coeff, 'pump_heat_coeff':pump_heat_coeff}, num_segments=num_seg, transcription_order=transcription_order) p.model.add_subsystem('phase', phase) phase.set_time_options(opt_initial=False, duration_bounds=(50, 400), duration_ref=100.0) phase.set_state_options('r', fix_initial=True, lower=0, upper=1.0E6, scaler=1.0E-3, defect_scaler=1.0E-2, units='m') phase.set_state_options('h', fix_initial=True, lower=0, upper=20000.0, scaler=1.0E-3, defect_scaler=1.0E-3, units='m') phase.set_state_options('v', fix_initial=True, lower=10.0, scaler=1.0E-2, defect_scaler=5.0E-0, units='m/s') phase.set_state_options('gam', fix_initial=True, lower=-1.5, upper=1.5, ref=1.0, defect_scaler=1.0, units='rad') phase.set_state_options('m', fix_initial=not opt_m, lower=15.e3, upper=80e3, scaler=1.0E-3, defect_scaler=1.0E-3, units='kg') phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0, rate_continuity=True) phase.add_design_parameter('S', val=1., units='m**2', opt=False) if opt_throttle: phase.add_control('throttle', val=1.0, lower=0.0, upper=1.0, opt=True, rate_continuity=True) else: phase.add_design_parameter('throttle', val=1.0, opt=False) phase.add_design_parameter('W0', val=10.5e3, opt=False, units='kg') phase.add_boundary_constraint('h', loc='final', equals=meeting_altitude, scaler=1.0E-3, units='m') phase.add_boundary_constraint('aero.mach', loc='final', equals=1., units=None) phase.add_boundary_constraint('gam', loc='final', equals=0.0, units='rad') phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000) phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8) # phase.add_path_constraint(name='time', upper=110.) # Minimize time at the end of the phase phase.add_objective('time', loc='final', ref=100.0) # phase.add_objective('energy', loc='final', ref=100.0) # phase.add_objective('m', loc='final', ref=-10000.0) # Set the state options for mass, temperature, and energy. phase.set_state_options('T', fix_initial=True, ref=300, defect_scaler=1e-2) phase.set_state_options('energy', fix_initial=True, ref=10e3, defect_scaler=1e-4) # Allow the optimizer to vary the fuel flow if opt_m_recirculated: phase.add_control('m_recirculated', val=m_recirculated, lower=0., opt=True, rate_continuity=True, ref=20.) else: phase.add_control('m_recirculated', val=m_recirculated, opt=False) phase.add_design_parameter('Q_env', val=Q_env, opt=False) phase.add_design_parameter('Q_sink', val=Q_sink, opt=False) phase.add_design_parameter('Q_out', val=Q_out, opt=False) # Constrain the temperature, 2nd derivative of fuel mass in the tank, and make # sure that the amount recirculated is at least 0, otherwise we'd burn # more fuel than we pumped. if opt_m_recirculated: phase.add_path_constraint('m_flow', lower=0., upper=50., units='kg/s', ref=10.) if T is not None: phase.add_path_constraint('T', upper=T, units='K') if T_o is not None: phase.add_path_constraint('T_o', upper=T_o, units='K', ref=300.) # phase.add_path_constraint('m_flow', lower=0., upper=20., units='kg/s', ref=10.) p.setup(mode='fwd', check=True) p['phase.t_initial'] = 0.0 p['phase.t_duration'] = 200. p['phase.states:r'] = phase.interpolate(ys=[0.0, 111319.54], nodes='state_input') p['phase.states:h'] = phase.interpolate(ys=[100.0, meeting_altitude], nodes='state_input') # p['phase.states:h'][:] = 10000. p['phase.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input') # p['phase.states:v'][:] = 200. p['phase.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input') p['phase.states:m'] = phase.interpolate(ys=[m_initial, 12.e3], nodes='state_input') p['phase.controls:alpha'] = phase.interpolate(ys=[1., 1.], nodes='control_input') # Give initial values for the phase states, controls, and time p['phase.states:T'] = 310. return p
def test_cruise_results_gl(self): p = Problem(model=Group()) if optimizer == 'SNOPT': p.driver = pyOptSparseDriver() p.driver.options['optimizer'] = optimizer p.driver.options['dynamic_simul_derivs'] = True p.driver.opt_settings['Major iterations limit'] = 100 p.driver.opt_settings['Major step limit'] = 0.05 p.driver.opt_settings['Major feasibility tolerance'] = 1.0E-6 p.driver.opt_settings['Major optimality tolerance'] = 1.0E-6 p.driver.opt_settings["Linesearch tolerance"] = 0.10 p.driver.opt_settings['iSumm'] = 6 p.driver.opt_settings['Verify level'] = 3 else: p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True transcription = GaussLobatto(num_segments=1, order=13, compressed=False) phase = Phase(ode_class=AircraftODE, transcription=transcription) p.model.add_subsystem('phase0', phase) # Pass Reference Area from an external source assumptions = p.model.add_subsystem('assumptions', IndepVarComp()) assumptions.add_output('S', val=427.8, units='m**2') assumptions.add_output('mass_empty', val=1.0, units='kg') assumptions.add_output('mass_payload', val=1.0, units='kg') phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(3600, 3600), duration_ref=3600) phase.set_state_options('range', units='km', fix_initial=True, fix_final=False, scaler=0.01, defect_scaler=0.01) phase.set_state_options('mass_fuel', fix_final=True, upper=20000.0, lower=0.0, scaler=1.0E-4, defect_scaler=1.0E-2) phase.set_state_options('alt', units='km', fix_initial=True) phase.add_control('mach', units=None, opt=False) phase.add_control('climb_rate', units='m/s', opt=False) phase.add_input_parameter('S', units='m**2') phase.add_input_parameter('mass_empty', units='kg') phase.add_input_parameter('mass_payload', units='kg') phase.add_path_constraint('propulsion.tau', lower=0.01, upper=1.0, shape=(1, )) phase.add_timeseries_output('tas_comp.TAS', units='m/s') p.model.connect('assumptions.S', 'phase0.input_parameters:S') p.model.connect('assumptions.mass_empty', 'phase0.input_parameters:mass_empty') p.model.connect('assumptions.mass_payload', 'phase0.input_parameters:mass_payload') phase.add_objective('time', loc='final', ref=3600) p.model.linear_solver = DirectSolver() p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 1.515132 * 3600.0 p['phase0.states:range'] = phase.interpolate(ys=(0, 1296.4), nodes='state_input') p['phase0.states:mass_fuel'] = phase.interpolate(ys=(12236.594555, 0), nodes='state_input') p['phase0.states:alt'] = 5.0 p['phase0.controls:mach'] = 0.8 p['phase0.controls:climb_rate'] = 0.0 p['assumptions.S'] = 427.8 p['assumptions.mass_empty'] = 0.15E6 p['assumptions.mass_payload'] = 84.02869 * 400 p.run_driver() time = p.get_val('phase0.timeseries.time') tas = p.get_val('phase0.timeseries.TAS', units='km/s') range = p.get_val('phase0.timeseries.states:range') assert_rel_error(self, range, tas * time, tolerance=1.0E-4)
def test_double_integrator_for_docs(self): import numpy as np import matplotlib.pyplot as plt from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from dymos import Phase from dymos.examples.double_integrator.double_integrator_ode import DoubleIntegratorODE p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase('gauss-lobatto', ode_class=DoubleIntegratorODE, num_segments=20, transcription_order=3, compressed=True) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(1.0, 1.0)) phase.set_state_options('x', fix_initial=True) phase.set_state_options('v', fix_initial=True, fix_final=True) phase.add_control('u', units='m/s**2', scaler=0.01, continuity=False, rate_continuity=False, rate2_continuity=False, lower=-1.0, upper=1.0) # Maximize distance travelled in one second. phase.add_objective('x', loc='final', scaler=-1) p.model.linear_solver = DirectSolver(assemble_jac=True) p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 1.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 0.25], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 0], nodes='state_input') p['phase0.controls:u'] = phase.interpolate(ys=[1, -1], nodes='control_input') p.run_driver() exp_out = phase.simulate(times=np.linspace(p['phase0.t_initial'], p['phase0.t_duration'], 100), record=False) # Plot results fig, axes = plt.subplots(3, 1) fig.suptitle('Double Integrator Direct Collocation Solution') t_imp = phase.get_values('time', nodes='all') x_imp = phase.get_values('x', nodes='all') v_imp = phase.get_values('v', nodes='all') u_imp = phase.get_values('u', nodes='all') t_exp = exp_out.get_values('time') x_exp = exp_out.get_values('x') v_exp = exp_out.get_values('v') u_exp = exp_out.get_values('u') axes[0].plot(t_imp, x_imp, 'ro', label='implicit') axes[0].plot(t_exp, x_exp, 'b-', label='explicit') axes[0].set_xlabel('time (s)') axes[0].set_ylabel('x (m)') axes[0].grid(True) axes[0].legend(loc='best') axes[1].plot(t_imp, v_imp, 'ro', label='implicit') axes[1].plot(t_exp, v_exp, 'b-', label='explicit') axes[1].set_xlabel('time (s)') axes[1].set_ylabel('v (m/s)') axes[1].grid(True) axes[1].legend(loc='best') axes[2].plot(t_imp, u_imp, 'ro', label='implicit') axes[2].plot(t_exp, u_exp, 'b-', label='explicit') axes[2].set_xlabel('time (s)') axes[2].set_ylabel('u (m/s**2)') axes[2].grid(True) axes[2].legend(loc='best') plt.show()
def 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()
units='rad') phase.add_objective('time', loc='final', scaler=1.0) p.model.add_constraint('phase0.rhs_disc.pairwise.dist', lower=20.0) p.setup() phase = p.model.phase0 p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = max_time / 2.0 for i in range(n_traj): theta, heading, start_x, start_y, end_x, end_y = locs[i] p['phase0.states:p%dx' % i] = phase.interpolate(ys=[start_x, end_x], nodes='state_input') p['phase0.states:p%dy' % i] = phase.interpolate(ys=[start_y, end_y], nodes='state_input') #p['phase0.states:p%dmass' % i] = phase.interpolate(ys=[start_mass, start_mass], nodes='state_input') #p['phase0.states:L%d' % i] = phase.interpolate(ys=[0, 0], nodes='state_input') p.run_driver() exp_out = phase.simulate() import matplotlib.pyplot as plt circle = plt.Circle((0, 0), r_space, fill=False) plt.gca().add_artist(circle) t = exp_out.get_val('phase0.timeseries.time')
def test_timeseries_gl(self): p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() p.driver.options['dynamic_simul_derivs'] = True phase = Phase(ode_class=BrachistochroneODE, transcription=GaussLobatto(num_segments=8, order=3, compressed=True)) p.model.add_subsystem('phase0', phase) phase.set_time_options(fix_initial=True, duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True, fix_final=False) phase.add_control('theta', continuity=True, rate_continuity=True, units='deg', lower=0.01, upper=179.9) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time_phase', loc='final', scaler=10) p.model.linear_solver = DirectSolver() p.setup(check=True) p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.controls:theta'] = phase.interpolate(ys=[5, 100], nodes='control_input') p['phase0.design_parameters:g'] = 9.80665 p.run_driver() gd = phase.options['transcription'].grid_data state_input_idxs = gd.subset_node_indices['state_input'] control_input_idxs = gd.subset_node_indices['control_input'] col_idxs = gd.subset_node_indices['col'] assert_rel_error(self, p.get_val('phase0.time'), p.get_val('phase0.timeseries.time')[:, 0]) assert_rel_error(self, p.get_val('phase0.time_phase'), p.get_val('phase0.timeseries.time_phase')[:, 0]) for state in ('x', 'y', 'v'): assert_rel_error( self, p.get_val('phase0.states:{0}'.format(state)), p.get_val('phase0.timeseries.states:' '{0}'.format(state))[state_input_idxs]) assert_rel_error( self, p.get_val('phase0.state_interp.state_col:{0}'.format(state)), p.get_val('phase0.timeseries.states:' '{0}'.format(state))[col_idxs]) for control in ('theta', ): assert_rel_error( self, p.get_val('phase0.controls:{0}'.format(control)), p.get_val('phase0.timeseries.controls:' '{0}'.format(control))[control_input_idxs]) for dp in ('g', ): for i in range(gd.subset_num_nodes['all']): assert_rel_error( self, p.get_val('phase0.design_parameters:{0}'.format(dp))[0, :], p.get_val('phase0.timeseries.design_parameters:{0}'.format( dp))[i])
def test_brachistochrone_integrated_control_radau_ps(self): import numpy as np from openmdao.api import Problem, Group, ScipyOptimizeDriver, DirectSolver from openmdao.utils.assert_utils import assert_rel_error from dymos import Phase, Radau p = Problem(model=Group()) p.driver = ScipyOptimizeDriver() phase = Phase(ode_class=BrachistochroneODE, transcription=Radau(num_segments=10)) p.model.add_subsystem('phase0', phase) phase.set_time_options(initial_bounds=(0, 0), duration_bounds=(.5, 10)) phase.set_state_options('x', fix_initial=True, fix_final=True) phase.set_state_options('y', fix_initial=True, fix_final=True) phase.set_state_options('v', fix_initial=True) phase.set_state_options('theta', targets='theta', fix_initial=False) phase.add_control('theta_dot', units='deg/s', rate_continuity=True, lower=0, upper=60) phase.add_design_parameter('g', units='m/s**2', opt=False, val=9.80665) # Minimize time at the end of the phase phase.add_objective('time', loc='final', scaler=10) p.model.linear_solver = DirectSolver() p.model.options['assembled_jac_type'] = 'csc' p.setup() p['phase0.t_initial'] = 0.0 p['phase0.t_duration'] = 2.0 p['phase0.states:x'] = phase.interpolate(ys=[0, 10], nodes='state_input') p['phase0.states:y'] = phase.interpolate(ys=[10, 5], nodes='state_input') p['phase0.states:v'] = phase.interpolate(ys=[0, 9.9], nodes='state_input') p['phase0.states:theta'] = np.radians( phase.interpolate(ys=[0.05, 100.0], nodes='state_input')) p['phase0.controls:theta_dot'] = phase.interpolate( ys=[50, 50], nodes='control_input') # Solve for the optimal trajectory p.run_driver() # Test the results assert_rel_error(self, p.get_val('phase0.timeseries.time')[-1], 1.8016, tolerance=1.0E-3) sim_out = phase.simulate(times_per_seg=20) x_sol = p.get_val('phase0.timeseries.states:x') y_sol = p.get_val('phase0.timeseries.states:y') v_sol = p.get_val('phase0.timeseries.states:v') theta_sol = p.get_val('phase0.timeseries.states:theta') theta_dot_sol = p.get_val('phase0.timeseries.controls:theta_dot') time_sol = p.get_val('phase0.timeseries.time') x_sim = sim_out.get_val('phase0.timeseries.states:x') y_sim = sim_out.get_val('phase0.timeseries.states:y') v_sim = sim_out.get_val('phase0.timeseries.states:v') theta_sim = sim_out.get_val('phase0.timeseries.states:theta') theta_dot_sim = sim_out.get_val('phase0.timeseries.controls:theta_dot') time_sim = sim_out.get_val('phase0.timeseries.time') x_interp = interp1d(time_sim[:, 0], x_sim[:, 0]) y_interp = interp1d(time_sim[:, 0], y_sim[:, 0]) v_interp = interp1d(time_sim[:, 0], v_sim[:, 0]) theta_interp = interp1d(time_sim[:, 0], theta_sim[:, 0]) theta_dot_interp = interp1d(time_sim[:, 0], theta_dot_sim[:, 0]) assert_rel_error(self, x_interp(time_sol), x_sol, tolerance=1.0E-5) assert_rel_error(self, y_interp(time_sol), y_sol, tolerance=1.0E-5) assert_rel_error(self, v_interp(time_sol), v_sol, tolerance=1.0E-5) assert_rel_error(self, theta_interp(time_sol), theta_sol, tolerance=1.0E-5) assert_rel_error(self, theta_dot_interp(time_sol), theta_dot_sol, tolerance=1.0E-5)
def 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 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
phase.add_objective('m', loc='final', ref=-10000.0) # phase.set_objective('r', loc='final', ref=-100000.0) p.model.linear_solver = DirectSolver(assemble_jac=True) p.model.options['assembled_jac_type'] = 'csc' # p.driver.add_recorder(SqliteRecorder('out.db')) p.setup(mode='fwd', check=True) # from openmdao.api import view_model # view_model(p) # exit() p['phase.t_initial'] = 0.0 p['phase.t_duration'] = 500. p['phase.states:r'] = phase.interpolate(ys=[0.0, 150.], nodes='disc') p['phase.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='disc') p['phase.states:m'] = phase.interpolate(ys=[5e4, 4.9e4], nodes='disc') p['phase.states:h'][:] = 1e4 p['phase.states:h'][0] = 0 p['phase.states:h'][-1] = 0 p['phase.controls:alpha'] = phase.interpolate(ys=[0.1, 0.1], nodes='all') p['phase.states:v'][:] = 200. # Create CRM geometry for phase_name in ['phase.rhs_disc.aero.OAS_group.', 'phase.rhs_col.aero.OAS_group.']: p[phase_name + 'wing_chord_dv'] = np.array([ 107.4 , 285.8 , 536.2 , 285.8 , 107.4 ]) * 0.0254 p[phase_name + 'wing_twist_dv'] = np.array([ -3.75 , 0.76 , 6.72 , 0.76 , -3.75 ]) * np.pi / 180. p[phase_name + 'wing_displacement_x_dv'] = np.array([ 1780 , 1226 , 904 , 1226 , 1780 ]) * 0.0254 p[phase_name + 'wing_displacement_y_dv'] = np.array([ 263.8 , 181.1 , 174.1 , 181.1 , 263.8 ]) * 0.0254
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()