def _setup_MPC_solver(self,
file_path,
opt_name,
dt,
horizon,
n_e,
par_values,
constr_viol_costs={},
mpc_options={}):
op = transfer_optimization_problem(
opt_name,
file_path,
compiler_options={'state_initial_equations': True})
op.set(par_values.keys(), par_values.values())
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = 2
opt_opts['IPOPT_options']['tol'] = 1e-10
opt_opts['IPOPT_options']['print_time'] = False
if 'IPOPT_options' in mpc_options:
opt_opts['IPOPT_options'].update(mpc_options['IPOPT_options'])
for key in mpc_options:
if key != 'IPOPT_options':
opt_opts[key] = mpc_options[key]
self.solver = MPC(op,
opt_opts,
dt,
horizon,
constr_viol_costs=constr_viol_costs)
def test_get_results_this_sample(self):
"""
Test that get_results_this_sample returns the optimization result for
this optimization.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
op.set('_start_c', float(self.c_0_A))
op.set('_start_T', float(self.T_0_A))
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
seed = 7
cvc = {'T': 1e6}
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
bf = BlockingFactors(factors=factors)
opt_opts['blocking_factors'] = bf
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
constr_viol_costs=cvc,
noise_seed=seed)
MPC_object.update_state()
u_k1 = MPC_object.sample()
result1 = MPC_object.get_results_this_sample()
N.testing.assert_equal(0, result1['time'][0])
N.testing.assert_equal(sample_period * horizon, result1['time'][-1])
MPC_object.update_state()
u_k2 = MPC_object.sample()
result2 = MPC_object.get_results_this_sample()
N.testing.assert_equal(sample_period, result2['time'][0])
N.testing.assert_equal(sample_period * (horizon + 1),
result2['time'][-1])
def test_infeasible_start(self):
"""
Test that the MPC class throws an exception if the first optimization
is unsuccessful.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
cvc = {'T': 1e6}
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
bf = BlockingFactors(factors=factors)
opt_opts['blocking_factors'] = bf
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
constr_viol_costs=cvc)
# Test with infeasible problem
MPC_object.update_state({'_start_c': 900, '_start_T': 700})
N.testing.assert_raises(Exception, MPC_object.sample)
def test_warm_start_options(self):
"""
Test that the warm start options are activated.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
op.set('_start_c', float(self.c_0_A))
op.set('_start_T', float(self.T_0_A))
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
cvc = {'T': 1e6}
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
initial_guess='trajectory',
constr_viol_costs=cvc)
MPC_object.update_state({
'_start_c': 587.47543496,
'_start_T': 345.64619542
})
u_k1 = MPC_object.sample()
MPC_object.update_state()
u_k2 = MPC_object.sample()
N.testing.assert_(MPC_object.collocator.warm_start)
wsip =\
MPC_object.collocator.solver_object.getOption('warm_start_init_point')
mu_init = MPC_object.collocator.solver_object.getOption('mu_init')
prl = MPC_object.collocator.solver_object.getOption('print_level')
N.testing.assert_(wsip == 'yes')
N.testing.assert_equal(mu_init, 1e-3)
N.testing.assert_equal(prl, 0)
def test_du_bounds(self):
"""
Test with blocking_factor du_bounds.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
op.set('_start_c', float(self.c_0_A))
op.set('_start_T', float(self.T_0_A))
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
seed = 7
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
du_bounds = {'Tc': 5}
bf = BlockingFactors(factors=factors, du_bounds=du_bounds)
opt_opts['blocking_factors'] = bf
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
noise_seed=seed,
initial_guess='trajectory')
MPC_object.update_state()
u_k1 = MPC_object.sample()
res = MPC_object.get_results_this_sample()
Tc = res['Tc']
prev_value = Tc[0]
largest_delta = 0
for value in Tc:
delta = value - prev_value
if delta > largest_delta:
largest_delta = delta
prev_value = value
assert largest_delta < 5, "Value {} is not less than {}".format(
largest_delta, 5)
def test_softening_bounds(self):
"""
Test the automatic softening of hard variable bounds.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
# Define some MPC-options
sample_period = 3
horizon = 50
seed = 7
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
bf = BlockingFactors(factors=factors)
opt_opts['blocking_factors'] = bf
opt_opts['IPOPT_options']['print_level'] = 0
cvc = {'T': 1e6}
originalPathConstraints = op.getPathConstraints()
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
constr_viol_costs=cvc,
noise_seed=seed)
# Assert that an optimization with an initial value outside of bounds
# succeeds
MPC_object.update_state({'_start_c': self.c_0_A, '_start_T': 355})
MPC_object.sample()
N.testing.assert_(
'Solve_Succeeded',
MPC_object.collocator.solver_object.getStat('return_status'))
def run_demo(with_plots=True):
"""
This example is based on the Hicks-Ray Continuously Stirred Tank Reactors
(CSTR) system. The system has two states, the concentration and the
temperature. The control input to the system is the temperature of the
cooling flow in the reactor jacket. The chemical reaction in the reactor is
exothermic, and also temperature dependent; high temperature results in
high reaction rate.
The problem is solved using the CasADi-based collocation algorithm through
the MPC-class. FMI is used for initialization and simulation purposes.
The following steps are demonstrated in this example:
1. How to generate an initial guess for a direct collocation method by
means of simulation with a constant input. The trajectories resulting
from the simulation are used to initialize the variables in the
transcribed NLP, in the first sample(optimization).
2. An optimal control problem is defined where the objective is to
transfer the state of the system from stationary point A to point B.
An MPC object for the optimization problem is created. After each
sample the NLP is updated with an estimate of the states in the next
sample. The estimate is done by simulating the model for one sample
period with the optimal input calculated in the optimization as input.
To each estimate a normally distributed noise, with the mean 0
and standard deviation 0.5% of the nominal value of each state, is
added. The MPC object uses the result from the previous optimization as
initial guess for the next optimization (for all but the first
optimization, where the simulation result from #1 is used instead).
(3.) If with_plots is True we compile the same optimization problem again
and define the options so that the op has the same options and
resolution as the op we solved through the MPC-class. By same
resolution we mean that both op should have the same mesh and blocking
factors. This allows us to compare the MPC-results to an open loop
optimization. Note that the MPC-results contains noise while the open
loop optimization does not.
"""
### 1. Compute initial guess trajectories by means of simulation
# Locate the Modelica and Optimica code
file_path = os.path.join(get_files_path(), "CSTR.mop")
# Compile and load the model used for simulation
sim_fmu = compile_fmu("CSTR.CSTR_MPC_Model", file_path,
compiler_options={"state_initial_equations":True})
sim_model = load_fmu(sim_fmu)
# Define stationary point A and set initial values and inputs
c_0_A = 956.271352
T_0_A = 250.051971
sim_model.set('_start_c', c_0_A)
sim_model.set('_start_T', T_0_A)
sim_model.set('Tc', 280)
opts = sim_model.simulate_options()
opts["CVode_options"]["maxh"] = 0.0
opts["ncp"] = 0
init_res = sim_model.simulate(start_time=0., final_time=150, options=opts)
### 2. Define the optimal control problem and solve it using the MPC class
# Compile and load optimization problem
op = transfer_optimization_problem("CSTR.CSTR_MPC", file_path,
compiler_options={"state_initial_equations":True})
# Define MPC options
sample_period = 3 # s
horizon = 33 # Samples on the horizon
n_e_per_sample = 1 # Collocation elements / sample
n_e = n_e_per_sample*horizon # Total collocation elements
finalTime = 150 # s
number_samp_tot = int(finalTime/sample_period) # Total number of samples to do
# Create blocking factors with quadratic penalty and bound on 'Tc'
bf_list = [n_e_per_sample]*(horizon/n_e_per_sample)
factors = {'Tc': bf_list}
du_quad_pen = {'Tc': 500}
du_bounds = {'Tc': 30}
bf = BlockingFactors(factors, du_bounds, du_quad_pen)
# Set collocation options
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = 2
opt_opts['init_traj'] = init_res
opt_opts['blocking_factors'] = bf
if with_plots:
# Compile and load a new instance of the op to compare the MPC results
# with an open loop optimization
op_open_loop = transfer_optimization_problem(
"CSTR.CSTR_MPC", file_path,
compiler_options={"state_initial_equations":True})
op_open_loop.set('_start_c', float(c_0_A))
op_open_loop.set('_start_T', float(T_0_A))
# Copy options from MPC optimization
open_loop_opts = copy.deepcopy(opt_opts)
# Change n_e and blocking_factors so op_open_loop gets the same
# resolution as op
open_loop_opts['n_e'] = number_samp_tot
bf_list_ol = [n_e_per_sample]*(number_samp_tot/n_e_per_sample)
factors_ol = {'Tc': bf_list_ol}
bf_ol = BlockingFactors(factors_ol, du_bounds, du_quad_pen)
open_loop_opts['blocking_factors'] = bf_ol
open_loop_opts['IPOPT_options']['print_level'] = 0
constr_viol_costs = {'T': 1e6}
# Create the MPC object
MPC_object = MPC(op, opt_opts, sample_period, horizon,
constr_viol_costs=constr_viol_costs, noise_seed=1)
# Set initial state
x_k = {'_start_c': c_0_A, '_start_T': T_0_A }
# Update the state and optimize number_samp_tot times
for k in range(number_samp_tot):
# Update the state and compute the optimal input for next sample period
MPC_object.update_state(x_k)
u_k = MPC_object.sample()
# Reset the model and set the new initial states before simulating
# the next sample period with the optimal input u_k
sim_model.reset()
sim_model.set(list(x_k.keys()), list(x_k.values()))
sim_res = sim_model.simulate(start_time=k*sample_period,
final_time=(k+1)*sample_period,
input=u_k, options=opts)
# Extract state at end of sample_period from sim_res and add Gaussian
# noise with mean 0 and standard deviation 0.005*(state_current_value)
x_k = MPC_object.extract_states(sim_res, mean=0, st_dev=0.005)
# Extract variable profiles
MPC_object.print_solver_stats()
complete_result = MPC_object.get_complete_results()
c_res_comp = complete_result['c']
T_res_comp = complete_result['T']
Tc_res_comp = complete_result['Tc']
time_res_comp = complete_result['time']
# Verify solution for testing purposes
try:
import casadi
except:
pass
else:
Tc_norm = N.linalg.norm(Tc_res_comp) / N.sqrt(len(Tc_res_comp))
assert(N.abs(Tc_norm - 311.7362) < 1e-3)
c_norm = N.linalg.norm(c_res_comp) / N.sqrt(len(c_res_comp))
assert(N.abs(c_norm - 653.5369) < 1e-3)
T_norm = N.linalg.norm(T_res_comp) / N.sqrt(len(T_res_comp))
assert(N.abs(T_norm - 328.0852) < 1e-3)
# Plot the results
if with_plots:
### 3. Solve the original optimal control problem without MPC
res = op_open_loop.optimize(options=open_loop_opts)
c_res = res['c']
T_res = res['T']
Tc_res = res['Tc']
time_res = res['time']
# Get reference values
Tc_ref = op.get('Tc_ref')
T_ref = op.get('T_ref')
c_ref = op.get('c_ref')
# Plot
plt.close('MPC')
plt.figure('MPC')
plt.subplot(3, 1, 1)
plt.plot(time_res_comp, c_res_comp)
plt.plot(time_res, c_res )
plt.plot([time_res[0],time_res[-1]],[c_ref,c_ref],'--')
plt.legend(('MPC with noise', 'Open-loop without noise', 'Reference value'))
plt.grid()
plt.ylabel('Concentration')
plt.title('Simulated trajectories')
plt.subplot(3, 1, 2)
plt.plot(time_res_comp, T_res_comp)
plt.plot(time_res, T_res)
plt.plot([time_res[0],time_res[-1]],[T_ref,T_ref], '--')
plt.grid()
plt.ylabel('Temperature [C]')
plt.subplot(3, 1, 3)
plt.step(time_res_comp, Tc_res_comp)
plt.step(time_res, Tc_res)
plt.plot([time_res[0],time_res[-1]],[Tc_ref,Tc_ref], '--')
plt.grid()
plt.ylabel('Cooling temperature [C]')
plt.xlabel('time')
plt.show()
def test_eliminated_variables(self):
"""
Test that the results when using eliminated variables are the same as when not using them.
"""
# Compile and load the model used for simulation
sim_fmu = compile_fmu(
"CSTR.CSTR_MPC_Model",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
sim_model = load_fmu(sim_fmu)
# Compile and load the model with eliminated variables used for simulation
sim_fmu_elim = compile_fmu("CSTR.CSTR_elim_vars_MPC_Model",
self.cstr_file_path,
compiler_options={
"state_initial_equations": True,
'equation_sorting': True,
'automatic_tearing': False
})
sim_model_elim = load_fmu(sim_fmu_elim)
# Define stationary point A and set initial values and inputs
c_0_A = 956.271352
T_0_A = 250.051971
sim_model.set('_start_c', c_0_A)
sim_model.set('_start_T', T_0_A)
sim_model.set('Tc', 280)
init_res = sim_model.simulate(start_time=0., final_time=150)
# Compile and load optimization problems
op = transfer_to_casadi_interface("CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={
"state_initial_equations": True,
"common_subexp_elim": False
})
op_elim = transfer_to_casadi_interface("CSTR.CSTR_elim_vars_MPC",
self.cstr_file_path,
compiler_options={
"state_initial_equations":
True,
'equation_sorting': True,
'automatic_tearing': False,
"common_subexp_elim": False
})
# Define MPC options
sample_period = 5 # s
horizon = 10 # Samples on the horizon
n_e_per_sample = 1 # Collocation elements / sample
n_e = n_e_per_sample * horizon # Total collocation elements
finalTime = 50 # s
number_samp_tot = 5 # Total number of samples to do
# Create blocking factors with quadratic penalty and bound on 'Tc'
bf_list = [n_e_per_sample] * (horizon / n_e_per_sample)
factors = {'Tc': bf_list}
du_quad_pen = {'Tc': 50}
du_bounds = {'Tc': 30}
bf = BlockingFactors(factors, du_bounds, du_quad_pen)
# Set collocation options
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = 2
opt_opts['init_traj'] = init_res
constr_viol_costs = {'T': 1e6}
# Create the MPC object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
constr_viol_costs=constr_viol_costs,
noise_seed=1)
# Set initial state
x_k = {'_start_c': c_0_A, '_start_T': T_0_A}
# Update the state and optimize number_samp_tot times
for k in range(number_samp_tot):
# Update the state and compute the optimal input for next sample period
MPC_object.update_state(x_k)
u_k = MPC_object.sample()
# Reset the model and set the new initial states before simulating
# the next sample period with the optimal input u_k
sim_model.reset()
sim_model.set(list(x_k.keys()), list(x_k.values()))
sim_res = sim_model.simulate(start_time=k * sample_period,
final_time=(k + 1) * sample_period,
input=u_k)
# Extract state at end of sample_period from sim_res and add Gaussian
# noise with mean 0 and standard deviation 0.005*(state_current_value)
x_k = MPC_object.extract_states(sim_res, mean=0, st_dev=0.005)
# Extract variable profiles
complete_result = MPC_object.get_complete_results()
op_elim.eliminateAlgebraics()
assert (len(op_elim.getEliminatedVariables()) == 2)
opt_opts_elim = op_elim.optimize_options()
opt_opts_elim['n_e'] = n_e
opt_opts_elim['n_cp'] = 2
opt_opts_elim['init_traj'] = init_res
# Create the MPC object with eliminated variables
MPC_object_elim = MPC(op_elim,
opt_opts_elim,
sample_period,
horizon,
constr_viol_costs=constr_viol_costs,
noise_seed=1)
# Set initial state
x_k = {'_start_c': c_0_A, '_start_T': T_0_A}
# Update the state and optimize number_samp_tot times
for k in range(number_samp_tot):
# Update the state and compute the optimal input for next sample period
MPC_object_elim.update_state(x_k)
u_k = MPC_object_elim.sample()
# Reset the model and set the new initial states before simulating
# the next sample period with the optimal input u_k
sim_model_elim.reset()
sim_model_elim.set(list(x_k.keys()), list(x_k.values()))
sim_res = sim_model_elim.simulate(start_time=k * sample_period,
final_time=(k + 1) *
sample_period,
input=u_k)
# Extract state at end of sample_period from sim_res and add Gaussian
# noise with mean 0 and standard deviation 0.005*(state_current_value)
x_k = MPC_object_elim.extract_states(sim_res, mean=0, st_dev=0.005)
# Extract variable profiles
complete_result_elim = MPC_object_elim.get_complete_results()
N.testing.assert_array_almost_equal(complete_result['c'],
complete_result_elim['c'])
N.testing.assert_array_almost_equal(complete_result['T'],
complete_result_elim['T'])
N.testing.assert_array_almost_equal(complete_result['Tc'],
complete_result_elim['Tc'])
def test_auto_bl_factors(self):
"""
Test blocking factors generated in the mpc-class.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
# Create MPC-object
MPC_object_auto = MPC(op, opt_opts, sample_period, horizon)
MPC_object_auto.update_state()
MPC_object_auto.sample()
res_auto = MPC_object_auto.get_results_this_sample()
opt_opts_auto = op.optimize_options()
opt_opts_auto['n_e'] = n_e
opt_opts_auto['IPOPT_options']['print_level'] = 0
bf_list = [1] * horizon
factors = {'Tc': bf_list}
bf = BlockingFactors(factors)
opt_opts_auto['blocking_factors'] = bf
MPC_object = MPC(op, opt_opts_auto, sample_period, horizon)
MPC_object.update_state()
MPC_object.sample()
res = MPC_object.get_results_this_sample()
# Assert that res_auto['Tc'] and res['Tc'] are equal
N.testing.assert_array_equal(res_auto['Tc'], res['Tc'])
def test_infeasible_return_input(self):
"""
Test that the input returned from an unsuccessful optimization is the
next input in the last successful optimization.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
seed = 7
cvc = {'T': 1e6}
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
bf = BlockingFactors(factors=factors)
opt_opts['blocking_factors'] = bf
# Create MPC-object
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
constr_viol_costs=cvc,
noise_seed=seed,
create_comp_result=False,
initial_guess='trajectory')
# NOTE: THIS NOT WORKING WITH initial_guess='shift'!!
MPC_object.update_state({
'_start_c': 587.47543496,
'_start_T': 345.64619542
})
u_k1 = MPC_object.sample()
result1 = MPC_object.get_results_this_sample()
# Optimize with infeasible problem
MPC_object.update_state({'_start_c': 900, '_start_T': 400})
u_k2 = MPC_object.sample()
# Assert that problem was infeasible and that the returned input is
# the next input from the last succesful optimization
N.testing.assert_(
'Infeasible_Problem_Detected',
MPC_object.collocator.solver_object.getStat('return_status'))
N.testing.assert_almost_equal(u_k2[1](0)[0],
result1['Tc'][4],
decimal=10)
# Assert that the returned resultfile is that of the last succesful
# optimization
result2 = MPC_object.get_results_this_sample()
assert result1 == result2, "UNEQUAL VALUES. result1={}\nresult2={}".format(
result1, result2)
# Assert that problem was infeasible yet again and that the returned
# input is the next (third) input from the last succesful optimization
MPC_object.update_state({'_start_c': 900, '_start_T': 400})
u_k3 = MPC_object.sample()
N.testing.assert_(
'Infeasible_Problem_Detected',
MPC_object.collocator.solver_object.getStat('return_status'))
N.testing.assert_almost_equal(u_k3[1](0)[0],
result1['Tc'][7],
decimal=10)
class RealTimeMPCBase(RealTimeBase):
"""
A base class for performing real time MPC on a process. Note that
this is an abstract class; to use it, you need to extend it with
the functions send_control_signal and get_values.
"""
def __init__(self,
file_path,
opt_name,
dt,
t_hor,
t_final,
start_values,
par_values,
output_names,
input_names,
par_changes=ParameterChanges(),
mpc_options={},
constr_viol_costs={},
noise=0):
"""
Create a real time MPC object.
Parameters::
file_path --
The path of the .mop file containing the model to be used for
the MPC solver.
opt_name --
The name of the optimization in the file specified by file_path
to be used by the MPC solver.
dt --
The time to wait in between each sample.
t_hor --
The horizon time for the MPC solver. Must be an even multiple
of dt.
t_final --
The total time to run the real time MPC.
start_values --
A dictionary containing the initial state values for the process.
par_values --
A dictionary containing parameter values to be set in the model.
output_names --
A list of the names of all of the output variables used in the
model.
input_names --
A list of the names of all of the input variables used in the
model.
par_changes --
A ParameterChanges object containing parameter changes and the
times they should be applied.
Default: An empty ParameterChanges object
mpc_options --
A dictionary of options to be used for the MPC solver.
constr_viol_costs --
Constraint violation costs used by the MPC solver. See the
documentation of the MPC class for more information.
noise --
Standard deviation of the noise to add to the input signals.
Default: 0
"""
super(RealTimeMPCBase,
self).__init__(dt, t_final, start_values, output_names,
input_names, par_changes, noise)
horizon = int(t_hor / dt)
n_e = horizon
self._setup_MPC_solver(file_path, opt_name, dt, horizon, n_e,
par_values, constr_viol_costs, mpc_options)
self.range_ = []
for i, name in enumerate(self.inputs):
var = self.solver.op.getVariable(name)
self.range_.append(
(var.getMin().getValue(), var.getMax().getValue()))
def _setup_MPC_solver(self,
file_path,
opt_name,
dt,
horizon,
n_e,
par_values,
constr_viol_costs={},
mpc_options={}):
op = transfer_optimization_problem(
opt_name,
file_path,
compiler_options={'state_initial_equations': True})
op.set(par_values.keys(), par_values.values())
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = 2
opt_opts['IPOPT_options']['tol'] = 1e-10
opt_opts['IPOPT_options']['print_time'] = False
if 'IPOPT_options' in mpc_options:
opt_opts['IPOPT_options'].update(mpc_options['IPOPT_options'])
for key in mpc_options:
if key != 'IPOPT_options':
opt_opts[key] = mpc_options[key]
self.solver = MPC(op,
opt_opts,
dt,
horizon,
constr_viol_costs=constr_viol_costs)
def enable_codegen(self, name=None):
"""
Enables use of generated C code for the MPC solver.
Generates and compiles code for the NLP, gradient of f, Jacobian of g,
and Hessian of the Lagrangian of g Function objects, and then replaces
the solver object in the solver's collocator with a new one that makes
use of the compiled functions as ExternalFunction objects.
Parameters::
name --
A string that if it is not None, loads existing files
nlp_[name].so, grad_f_[name].so, jac_g_[name].so and
hess_lag_[name].so as ExternalFunction objects to be used
by the solver rather than generating new code.
Default: None
"""
self.solver.collocator.enable_codegen(name)
def enable_integral_action(self, mu, M, error_names=None, u_e=None):
"""
Enables integral action for the inputs.
If integral action is enabled, in each step the input error is
calculated and used to update the estimation of the error. By
default, the input error is calculated as the matrix M times the
difference between the current state vector as predicted by the
solver in the last time step and as measured from the process
in the current time step; however, this can be changed by
overriding the estimate_input_error method.
The low-pass filter used to update the estimate is
[new estimate] = mu*[old estimate] + (1-mu)*[current estimate]
Parameters::
mu --
Controls the convergence rate of the error estimate.
See above.
M --
A matrix used for calculating the input error from the state
error. See above.
error_names --
A list containing the names of the model variables for
the input errors. If set to None, it is assumed be the
same as the list of input variables with the prefix '_e'
appended to each one.
Default: None
u_e --
A list containing a set of values to be applied as
stationary errors to the input signals. Used for
simulating a stationary error where there otherwise wouldn't
be one. If set to None, no stationary error is applied.
Default: None.
"""
self._ia = True
self.mu = mu
self.M = M
if error_names == None:
self.errors = [name + '_e' for name in self.inputs]
else:
self.errors = error_names
if u_e == None:
self.u_e = N.zeros(len(self.inputs))
else:
self.u_e = N.array(u_e)
self.u_e_e = N.zeros(len(self.inputs))
def run(self, save=False):
"""
Run the real time MPC controller defined by the object.
Parameters::
save --
Determines whether or not to save data after running. If set
to False, the same data can still be saved manually by using
the save_results function.
Default: False
Returns::
The results and statistics from the run.
"""
if self._already_run:
raise RuntimeError('run can only be called once')
self.e_e = []
n_outputs = len(self.outputs)
n_inputs = len(self.inputs)
x_k = self.start_values.copy()
x_k_last = x_k.copy()
time1 = time.clock()
time2 = time.time()
time3 = 0
for k in range(self.n_steps):
new_pars = self.par_changes.get_new_pars(k * self.dt)
if new_pars != None:
self.solver.op.set(new_pars.keys(), new_pars.values())
self.solver.update_state(x_k)
u_k = self.solver.sample()
u_k = self._apply_noise(u_k, std_dev=self.noise)
if self._ia:
u_k_e = self._apply_error(u_k)
if time3 != 0:
solve_time = time.time() - time3
self.solve_times.append(solve_time)
if solve_time > self.dt * 0.2:
print 'WARNING: Control signal late by', solve_time, 's'
if self._ia:
self.send_control_signal(u_k_e)
else:
self.send_control_signal(u_k)
if k == 0:
next_time = time.time() + self.dt
m_k = self.wait_and_get_measurements(next_time)
next_time = time.time() + self.dt
time3 = time.time()
x_k = self.estimate_states(m_k, x_k_last)
x_k_last = x_k.copy()
if self._ia:
self._update_error_estimate(x_k)
for i in range(n_outputs):
self.results[self.outputs[i]].append(x_k['_start_' +
self.outputs[i]])
for i in range(n_inputs):
self.results[self.inputs[i]].append(u_k[1](0)[i])
self.stats.append(self.solver.collocator.solver_object.getStats())
self.ptime = time.clock() - time1
self.rtime = time.time() - time2
print 'Processor time:', self.ptime, 's'
print 'Real time:', self.rtime, 's'
if save:
self.save_results()
self._already_run = True
return self.results, self.stats
def _apply_noise(self, u_k, std_dev=0.0):
if std_dev == 0:
return u_k
inputs = u_k[1](0)
for n in range(len(inputs)):
noise = N.random.normal(0.0, std_dev)
inputs[n] += noise
inputs[n] = max(self.range_[n][0], min(self.range_[n][1],
inputs[n]))
return (u_k[0], lambda t: inputs)
def _apply_error(self, u_k):
u_k_e = []
for i in range(len(self.errors)):
u_k_e.append(
max(self.range_[i][0],
min(self.range_[i][1], u_k[1](0)[i] + self.u_e[i])))
return (u_k[0], lambda t: N.array(u_k_e))
def _update_error_estimate(self, x_k):
e_k = self._calculate_error(x_k)
u_e_e_next = self.estimate_input_error(e_k)
self.u_e_e = (1 - self.mu) * self.u_e_e + self.mu * (u_e_e_next +
self.u_e_e)
for i in range(len(self.errors)):
self.solver.set(self.errors[i], self.u_e_e[i])
self.e_e.append(self.u_e_e)
def estimate_input_error(self, e_k):
"""
Estimates the input error given the state error.
Parameters::
e_k --
The state error vector.
Returns::
The input error vector.
"""
return self.M.dot(e_k)
def _calculate_error(self, x_k):
x_k_a = N.array([x_k['_start_' + name] for name in self.outputs])
res = self.solver.get_results_this_sample()
x_k_e = N.array(
[res[name][self.solver.options['n_cp']] for name in self.outputs])
return x_k_a - x_k_e
def print_stats(self):
"""
Print statistics from the run.
The times printed are the sums of the corresponding
statistics from the NLP solver over all time steps.
"""
if not self._already_run:
raise RuntimeError(
'Stats can only be printed after run() has been called')
stat_names = [
't_callback_fun', 't_callback_prepare', 't_eval_f', 't_eval_g',
't_eval_grad_f', 't_eval_h', 't_eval_jac_g', 't_mainloop'
]
total_times = {}
for name in stat_names:
total_times[name] = 0.
for stat in self.stats:
for name in stat_names:
total_times[name] += stat[name]
t_total = total_times['t_mainloop']
print 'Total times:'
for name in stat_names:
print("%19s: %6.4f s (%7.3f%%)" %
(name, total_times[name], total_times[name] / t_total * 100))
def save_results(self, filename=None):
"""
Pickle and save data from the run to a file name either passed
as an argument or entered by the user. If an empty string is
entered as the file name, no data is saved.
Parameters::
filename --
The file name to save as. If it is not provided, the
user will be prompted to input it.
Default: None
"""
if not self._already_run:
raise RuntimeError(
'Results can only be saved after run() has been called')
result_dict = {}
result_dict['results'] = self.results
result_dict['stats'] = self.stats
result_dict['ptime'] = self.ptime
result_dict['rtime'] = self.rtime
result_dict['noise'] = self.noise
result_dict['late_times'] = self.late_times
result_dict['wait_times'] = self.wait_times
result_dict['solve_times'] = self.solve_times
save_to_file(result_dict, filename)
def test_du_quad_pen(self):
"""
Test with blocking_factor du_quad_pen.
"""
op = transfer_to_casadi_interface(
"CSTR.CSTR_MPC",
self.cstr_file_path,
compiler_options={"state_initial_equations": True})
op.set('_start_c', float(self.c_0_A))
op.set('_start_T', float(self.T_0_A))
# Set options collocation
n_e = 50
opt_opts = op.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['IPOPT_options']['print_level'] = 0
# Define some MPC-options
sample_period = 3
horizon = 50
seed = 7
# Define blocking factors
bl_list = [1] * horizon
factors = {'Tc': bl_list}
bf = BlockingFactors(factors=factors)
opt_opts['blocking_factors'] = bf
# Create MPC-object without du_quad_pen
MPC_object = MPC(op,
opt_opts,
sample_period,
horizon,
noise_seed=seed,
initial_guess='trajectory')
MPC_object.update_state()
MPC_object.sample()
res = MPC_object.get_results_this_sample()
# Create MPC-object with du_quad_pen
opt_opts_quad = op.optimize_options()
opt_opts_quad['n_e'] = n_e
opt_opts_quad['IPOPT_options']['print_level'] = 0
bf_list = [1] * horizon
factors = {'Tc': bf_list}
du_quad_pen = {'Tc': 100}
bf = BlockingFactors(factors, du_quad_pen=du_quad_pen)
opt_opts_quad['blocking_factors'] = bf
MPC_object_quad = MPC(op,
opt_opts_quad,
sample_period,
horizon,
noise_seed=seed,
initial_guess='trajectory')
MPC_object_quad.update_state()
MPC_object_quad.sample()
res_quad = MPC_object_quad.get_results_this_sample()
Tc = res['Tc']
prev_value = Tc[0]
largest_delta = 0
for value in Tc:
delta = value - prev_value
if delta > largest_delta:
largest_delta = delta
prev_value = value
Tc = res_quad['Tc']
prev_value = Tc[0]
largest_delta_quad = 0
for value in Tc:
delta = value - prev_value
if delta > largest_delta_quad:
largest_delta_quad = delta
prev_value = value
N.testing.assert_(largest_delta_quad < largest_delta)