def run_demo(with_plots=True):
"""
Static calibration of the quad tank model.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
jmu_name = compile_jmu("QuadTank_pack.QuadTank_Static", curr_dir + "/files/QuadTank.mop")
# Load static calibration model
qt_static = JMUModel(jmu_name)
# Set control inputs
qt_static.set("u1", 2.5)
qt_static.set("u2", 2.5)
# Save nominal values
a1_nom = qt_static.get("a1")
a2_nom = qt_static.get("a2")
init_res = qt_static.initialize(options={"stat": 1})
print "Optimal parameter values:"
print "a1: %2.2e (nominal: %2.2e)" % (qt_static.get("a1"), a1_nom)
print "a2: %2.2e (nominal: %2.2e)" % (qt_static.get("a2"), a2_nom)
assert N.abs(qt_static.get("a1") - 7.95797110936e-06) < 1e-3
assert N.abs(qt_static.get("a2") - 7.73425542448e-06) < 1e-3
def run_demo(with_plots=True):
"""
Static calibration of the quad tank model.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
jmu_name = compile_jmu("QuadTank_pack.QuadTank_Static",
curr_dir + "/files/QuadTank.mop")
# Load static calibration model
qt_static = JMUModel(jmu_name)
# Set control inputs
qt_static.set("u1", 2.5)
qt_static.set("u2", 2.5)
# Save nominal values
a1_nom = qt_static.get("a1")
a2_nom = qt_static.get("a2")
init_res = qt_static.initialize(options={'stat': 1})
print "Optimal parameter values:"
print "a1: %2.2e (nominal: %2.2e)" % (qt_static.get("a1"), a1_nom)
print "a2: %2.2e (nominal: %2.2e)" % (qt_static.get("a2"), a2_nom)
assert N.abs(qt_static.get("a1") - 7.95797110936e-06) < 1e-3
assert N.abs(qt_static.get("a2") - 7.73425542448e-06) < 1e-3
def run_demo(with_plots=True, with_blocking_factors=False):
"""
Load change of a distillation column. The distillation column model is
documented in the paper:
@Article{hahn+02,
title={An improved method for nonlinear model reduction using balancing of
empirical gramians},
author={Hahn, J. and Edgar, T.F.},
journal={Computers and Chemical Engineering},
volume={26},
number={10},
pages={1379-1397},
year={2002}
}
Note: This example requires Ipopt with MA27.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("DISTLib.Binary_Dist_initial",
curr_dir + "/files/DISTLib.mo")
# Load a model instance into Python
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
rr_0_A = 3.0
init_model.set('rr', rr_0_A)
init_result = init_model.initialize()
# Store stationary point A
y_A = N.zeros(32)
x_A = N.zeros(32)
print(' *** Stationary point A ***')
print '(Tray index, x_i_A, y_i_A)'
for i in range(N.size(y_A)):
y_A[i] = init_model.get('y[' + str(i + 1) + ']')
x_A[i] = init_model.get('x[' + str(i + 1) + ']')
print '(' + str(i + 1) + ', %f, %f)' % (x_A[i], y_A[i])
# Set inputs for stationary point B
rr_0_B = 2.0
init_model.set('rr', rr_0_B)
init_result = init_model.initialize()
# Store stationary point B
y_B = N.zeros(32)
x_B = N.zeros(32)
print(' *** Stationary point B ***')
print '(Tray index, x_i_B, y_i_B)'
for i in range(N.size(y_B)):
y_B[i] = init_model.get('y[' + str(i + 1) + ']')
x_B[i] = init_model.get('x[' + str(i + 1) + ']')
print '(' + str(i + 1) + ', %f, %f)' % (x_B[i], y_B[i])
# Set up and solve an optimal control problem.
# Compile the JMU
jmu_name = compile_jmu(
"DISTLib_Opt.Binary_Dist_Opt1",
(curr_dir + "/files/DISTLib.mo", curr_dir + "/files/DISTLib_Opt.mop"),
compiler_options={'state_start_values_fixed': True})
# Load the dynamic library and XML data
model = JMUModel(jmu_name)
# Initialize the model with parameters
# Initialize the model to stationary point A
for i in range(N.size(x_A)):
model.set('x_0[' + str(i + 1) + ']', x_A[i])
# Set the target values to stationary point B
model.set('rr_ref', rr_0_B)
model.set('y1_ref', y_B[0])
n_e = 100 # Number of elements
hs = N.ones(n_e) * 1. / n_e # Equidistant points
n_cp = 3
# Number of collocation points in each element
# Solve the optimization problem
if with_blocking_factors:
# Blocking factors for control parametrization
blocking_factors = 4 * N.ones(n_e / 4, dtype=N.int)
opt_opts = model.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = n_cp
opt_opts['hs'] = hs
opt_opts['blocking_factors'] = blocking_factors
opt_res = model.optimize(options=opt_opts)
else:
opt_res = model.optimize(options={'n_e': n_e, 'n_cp': n_cp, 'hs': hs})
# Extract variable profiles
u1_res = opt_res['rr']
u1_ref_res = opt_res['rr_ref']
y1_ref_res = opt_res['y1_ref']
time = opt_res['time']
x_res = []
x_ref_res = []
for i in range(N.size(x_B)):
x_res.append(opt_res['x[' + str(i + 1) + ']'])
y_res = []
for i in range(N.size(x_B)):
y_res.append(opt_res['y[' + str(i + 1) + ']'])
if with_blocking_factors:
assert N.abs(opt_res.final('cost') / 1.e1 - 2.8549683) < 1e-3
else:
assert N.abs(opt_res.final('cost') / 1.e1 - 2.8527469) < 1e-3
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.title('Liquid composition')
plt.plot(time, x_res[0])
plt.ylabel('x1')
plt.grid()
plt.subplot(312)
plt.plot(time, x_res[16])
plt.ylabel('x17')
plt.grid()
plt.subplot(313)
plt.plot(time, x_res[31])
plt.ylabel('x32')
plt.grid()
plt.xlabel('t [s]')
plt.show()
# Plot the results
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.title('Vapor composition')
plt.plot(time, y_res[0])
plt.plot(time, y1_ref_res, '--')
plt.ylabel('y1')
plt.grid()
plt.subplot(312)
plt.plot(time, y_res[16])
plt.ylabel('y17')
plt.grid()
plt.subplot(313)
plt.plot(time, y_res[31])
plt.ylabel('y32')
plt.grid()
plt.xlabel('t [s]')
plt.show()
plt.figure(3)
plt.clf()
plt.hold(True)
plt.plot(time, u1_res)
plt.ylabel('u')
plt.plot(time, u1_ref_res, '--')
plt.xlabel('t [s]')
plt.title('Reflux ratio')
plt.grid()
plt.show()
def run_demo(with_plots=True, with_blocking_factors = False):
"""
Load change of a distillation column. The distillation column model is
documented in the paper:
@Article{hahn+02,
title={An improved method for nonlinear model reduction using balancing of
empirical gramians},
author={Hahn, J. and Edgar, T.F.},
journal={Computers and Chemical Engineering},
volume={26},
number={10},
pages={1379-1397},
year={2002}
}
Note: This example requires Ipopt with MA27.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("DISTLib.Binary_Dist_initial",
curr_dir+"/files/DISTLib.mo")
# Load a model instance into Python
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
rr_0_A = 3.0
init_model.set('rr',rr_0_A)
init_result = init_model.initialize()
# Store stationary point A
y_A = N.zeros(32)
x_A = N.zeros(32)
print(' *** Stationary point A ***')
print '(Tray index, x_i_A, y_i_A)'
for i in range(N.size(y_A)):
y_A[i] = init_model.get('y['+ str(i+1) +']')
x_A[i] = init_model.get('x['+ str(i+1) +']')
print '(' + str(i+1) + ', %f, %f)' %(x_A[i], y_A[i])
# Set inputs for stationary point B
rr_0_B = 2.0
init_model.set('rr',rr_0_B)
init_result = init_model.initialize()
# Store stationary point B
y_B = N.zeros(32)
x_B = N.zeros(32)
print(' *** Stationary point B ***')
print '(Tray index, x_i_B, y_i_B)'
for i in range(N.size(y_B)):
y_B[i] = init_model.get('y[' + str(i+1) + ']')
x_B[i] = init_model.get('x[' + str(i+1) + ']')
print '(' + str(i+1) + ', %f, %f)' %(x_B[i], y_B[i])
# Set up and solve an optimal control problem.
# Compile the JMU
jmu_name = compile_jmu("DISTLib_Opt.Binary_Dist_Opt1",
(curr_dir+"/files/DISTLib.mo",curr_dir+"/files/DISTLib_Opt.mop"),
compiler_options={'state_start_values_fixed':True})
# Load the dynamic library and XML data
model = JMUModel(jmu_name)
# Initialize the model with parameters
# Initialize the model to stationary point A
for i in range(N.size(x_A)):
model.set('x_0[' + str(i+1) + ']', x_A[i])
# Set the target values to stationary point B
model.set('rr_ref',rr_0_B)
model.set('y1_ref',y_B[0])
n_e = 100 # Number of elements
hs = N.ones(n_e)*1./n_e # Equidistant points
n_cp = 3; # Number of collocation points in each element
# Solve the optimization problem
if with_blocking_factors:
# Blocking factors for control parametrization
blocking_factors=4*N.ones(n_e/4,dtype=N.int)
opt_opts = model.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['n_cp'] = n_cp
opt_opts['hs'] = hs
opt_opts['blocking_factors'] = blocking_factors
opt_res = model.optimize(options=opt_opts)
else:
opt_res = model.optimize(options={'n_e':n_e, 'n_cp':n_cp, 'hs':hs})
# Extract variable profiles
u1_res = opt_res['rr']
u1_ref_res = opt_res['rr_ref']
y1_ref_res = opt_res['y1_ref']
time = opt_res['time']
x_res = []
x_ref_res = []
for i in range(N.size(x_B)):
x_res.append(opt_res['x[' + str(i+1) + ']'])
y_res = []
for i in range(N.size(x_B)):
y_res.append(opt_res['y[' + str(i+1) + ']'])
if with_blocking_factors:
assert N.abs(opt_res.final('cost')/1.e1 - 2.8549683) < 1e-3
else:
assert N.abs(opt_res.final('cost')/1.e1 - 2.8527469) < 1e-3
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.title('Liquid composition')
plt.plot(time, x_res[0])
plt.ylabel('x1')
plt.grid()
plt.subplot(312)
plt.plot(time, x_res[16])
plt.ylabel('x17')
plt.grid()
plt.subplot(313)
plt.plot(time, x_res[31])
plt.ylabel('x32')
plt.grid()
plt.xlabel('t [s]')
plt.show()
# Plot the results
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.title('Vapor composition')
plt.plot(time, y_res[0])
plt.plot(time, y1_ref_res, '--')
plt.ylabel('y1')
plt.grid()
plt.subplot(312)
plt.plot(time, y_res[16])
plt.ylabel('y17')
plt.grid()
plt.subplot(313)
plt.plot(time, y_res[31])
plt.ylabel('y32')
plt.grid()
plt.xlabel('t [s]')
plt.show()
plt.figure(3)
plt.clf()
plt.hold(True)
plt.plot(time, u1_res)
plt.ylabel('u')
plt.plot(time, u1_ref_res, '--')
plt.xlabel('t [s]')
plt.title('Reflux ratio')
plt.grid()
plt.show()
def run_demo(with_plots=True):
"""
This example is based on a system composed of two Continously Stirred Tank
Reactors (CSTRs) in series. The example demonstrates the following steps:
1. How to solve a DAE initialization problem. The initialization model have
equations specifying that all derivatives should be identically zero,
which implies that a stationary solution is obtained. Two stationary
points, corresponding to different inputs, are computed. We call the
stationary points A and B respectively. For more information about the
DAE initialization algorithm, see http://www.jmodelica.org/page/10.
2. An optimal control problem is solved where the objective is to transfer
the state of the system from stationary point A to point B. Here, it is
also demonstrated how to set parameter values in a model. More
information about the simultaneous optimization algorithm can be found at
http://www.jmodelica.org/page/10.
3. The optimization result is saved to file and then the important variables
are plotted.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
# Compile the stationary initialization model into a DLL
jmu_name = compile_jmu("CSTRLib.Components.Two_CSTRs_stat_init",
os.path.join(curr_dir, "files", "CSTRLib.mo"))
# Load a JMU model instance
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
u1_0_A = 1
u2_0_A = 1
init_model.set('u1',u1_0_A)
init_model.set('u2',u2_0_A)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point A
CA1_0_A = init_model.get('CA1')
CA2_0_A = init_model.get('CA2')
T1_0_A = init_model.get('T1')
T2_0_A = init_model.get('T2')
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('u = [%f,%f]' % (u1_0_A,u2_0_A))
print('CAi = [%f,%f]' % (CA1_0_A,CA2_0_A))
print('Ti = [%f,%f]' % (T1_0_A,T2_0_A))
# Set inputs for stationary point B
u1_0_B = 1.1
u2_0_B = 0.9
init_model.set('u1',u1_0_B)
init_model.set('u2',u2_0_B)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Stationary point B
CA1_0_B = init_model.get('CA1')
CA2_0_B = init_model.get('CA2')
T1_0_B = init_model.get('T1')
T2_0_B = init_model.get('T2')
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('u = [%f,%f]' % (u1_0_B,u2_0_B))
print('CAi = [%f,%f]' % (CA1_0_B,CA2_0_B))
print('Ti = [%f,%f]' % (T1_0_B,T2_0_B))
## Set up and solve an optimal control problem.
# Compile the Model
jmu_name = compile_jmu("CSTR2_Opt",
[os.path.join(curr_dir, "files", "CSTRLib.mo"), os.path.join(curr_dir, "files", "CSTR2_Opt.mop")],
compiler_options={'enable_variable_scaling':True, 'index_reduction':True})
# Load the dynamic library and XML data
model = JMUModel(jmu_name)
# Initialize the model with parameters
# Initialize the model to stationary point A
model.set('cstr.two_CSTRs_Series.CA1_0',CA1_0_A)
model.set('cstr.two_CSTRs_Series.CA2_0',CA2_0_A)
model.set('cstr.two_CSTRs_Series.T1_0',T1_0_A)
model.set('cstr.two_CSTRs_Series.T2_0',T2_0_A)
# Set the target values to stationary point B
model.set('u1_ref',u1_0_B)
model.set('u2_ref',u2_0_B)
model.set('CA1_ref',CA1_0_B)
model.set('CA2_ref',CA2_0_B)
# Initialize the optimization mesh
n_e = 50 # Number of elements
hs = N.ones(n_e)*1./n_e # Equidistant points
n_cp = 3; # Number of collocation points in each element
res = model.optimize(
options={'n_e':n_e, 'hs':hs, 'n_cp':n_cp,
'blocking_factors':2*N.ones(n_e/2,dtype=N.int),
'IPOPT_options':{'tol':1e-4}})
# Extract variable profiles
CA1_res=res['cstr.two_CSTRs_Series.CA1']
CA2_res=res['cstr.two_CSTRs_Series.CA2']
T1_res=res['cstr.two_CSTRs_Series.T1']
T2_res=res['cstr.two_CSTRs_Series.T2']
u1_res=res['cstr.two_CSTRs_Series.u1']
u2_res=res['cstr.two_CSTRs_Series.u2']
der_u2_res=res['der_u2']
CA1_ref_res=res['CA1_ref']
CA2_ref_res=res['CA2_ref']
u1_ref_res=res['u1_ref']
u2_ref_res=res['u2_ref']
cost=res['cost']
time=res['time']
assert N.abs(res.final('cost') - 1.4745648e+01) < 1e-3
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time,CA1_res)
plt.plot([time[0],time[-1]],[CA1_ref_res, CA1_ref_res],'--')
plt.ylabel('Concentration reactor 1 [J/l]')
plt.grid()
plt.subplot(212)
plt.plot(time,CA2_res)
plt.plot([time[0],time[-1]],[CA2_ref_res, CA2_ref_res],'--')
plt.ylabel('Concentration reactor 2 [J/l]')
plt.xlabel('t [s]')
plt.grid()
plt.show()
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time,T1_res)
plt.ylabel('Temperature reactor 1 [K]')
plt.grid()
plt.subplot(212)
plt.plot(time,T2_res)
plt.ylabel('Temperature reactor 2 [K]')
plt.grid()
plt.xlabel('t [s]')
plt.show()
plt.figure(3)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time,u2_res)
plt.ylabel('Input 2')
plt.plot([time[0],time[-1]],[u2_ref_res, u2_ref_res],'--')
plt.grid()
plt.subplot(212)
plt.plot(time,der_u2_res)
plt.ylabel('Derivative of input 2')
plt.xlabel('t [s]')
plt.grid()
plt.show()
def run_demo(with_plots=True):
"""
This example is based on a system composed of two Continously Stirred Tank
Reactors (CSTRs) in series. The example demonstrates the following steps:
1. How to solve a DAE initialization problem. The initialization model have
equations specifying that all derivatives should be identically zero,
which implies that a stationary solution is obtained. Two stationary
points, corresponding to different inputs, are computed. We call the
stationary points A and B respectively. For more information about the
DAE initialization algorithm, see http://www.jmodelica.org/page/10.
2. An optimal control problem is solved where the objective is to transfer
the state of the system from stationary point A to point B. Here, it is
also demonstrated how to set parameter values in a model. More
information about the simultaneous optimization algorithm can be found at
http://www.jmodelica.org/page/10.
3. The optimization result is saved to file and then the important variables
are plotted.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
# Compile the stationary initialization model into a DLL
jmu_name = compile_jmu("CSTRLib.Components.Two_CSTRs_stat_init",
os.path.join(curr_dir, "files", "CSTRLib.mo"))
# Load a JMU model instance
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
u1_0_A = 1
u2_0_A = 1
init_model.set('u1', u1_0_A)
init_model.set('u2', u2_0_A)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point A
CA1_0_A = init_model.get('CA1')
CA2_0_A = init_model.get('CA2')
T1_0_A = init_model.get('T1')
T2_0_A = init_model.get('T2')
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('u = [%f,%f]' % (u1_0_A, u2_0_A))
print('CAi = [%f,%f]' % (CA1_0_A, CA2_0_A))
print('Ti = [%f,%f]' % (T1_0_A, T2_0_A))
# Set inputs for stationary point B
u1_0_B = 1.1
u2_0_B = 0.9
init_model.set('u1', u1_0_B)
init_model.set('u2', u2_0_B)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Stationary point B
CA1_0_B = init_model.get('CA1')
CA2_0_B = init_model.get('CA2')
T1_0_B = init_model.get('T1')
T2_0_B = init_model.get('T2')
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('u = [%f,%f]' % (u1_0_B, u2_0_B))
print('CAi = [%f,%f]' % (CA1_0_B, CA2_0_B))
print('Ti = [%f,%f]' % (T1_0_B, T2_0_B))
## Set up and solve an optimal control problem.
# Compile the Model
jmu_name = compile_jmu("CSTR2_Opt", [
os.path.join(curr_dir, "files", "CSTRLib.mo"),
os.path.join(curr_dir, "files", "CSTR2_Opt.mop")
],
compiler_options={
'enable_variable_scaling': True,
'index_reduction': True
})
# Load the dynamic library and XML data
model = JMUModel(jmu_name)
# Initialize the model with parameters
# Initialize the model to stationary point A
model.set('cstr.two_CSTRs_Series.CA1_0', CA1_0_A)
model.set('cstr.two_CSTRs_Series.CA2_0', CA2_0_A)
model.set('cstr.two_CSTRs_Series.T1_0', T1_0_A)
model.set('cstr.two_CSTRs_Series.T2_0', T2_0_A)
# Set the target values to stationary point B
model.set('u1_ref', u1_0_B)
model.set('u2_ref', u2_0_B)
model.set('CA1_ref', CA1_0_B)
model.set('CA2_ref', CA2_0_B)
# Initialize the optimization mesh
n_e = 50 # Number of elements
hs = N.ones(n_e) * 1. / n_e # Equidistant points
n_cp = 3
# Number of collocation points in each element
res = model.optimize(
options={
'n_e': n_e,
'hs': hs,
'n_cp': n_cp,
'blocking_factors': 2 * N.ones(n_e / 2, dtype=N.int),
'IPOPT_options': {
'tol': 1e-4
}
})
# Extract variable profiles
CA1_res = res['cstr.two_CSTRs_Series.CA1']
CA2_res = res['cstr.two_CSTRs_Series.CA2']
T1_res = res['cstr.two_CSTRs_Series.T1']
T2_res = res['cstr.two_CSTRs_Series.T2']
u1_res = res['cstr.two_CSTRs_Series.u1']
u2_res = res['cstr.two_CSTRs_Series.u2']
der_u2_res = res['der_u2']
CA1_ref_res = res['CA1_ref']
CA2_ref_res = res['CA2_ref']
u1_ref_res = res['u1_ref']
u2_ref_res = res['u2_ref']
cost = res['cost']
time = res['time']
assert N.abs(res.final('cost') - 1.4745648e+01) < 1e-3
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time, CA1_res)
plt.plot([time[0], time[-1]], [CA1_ref_res, CA1_ref_res], '--')
plt.ylabel('Concentration reactor 1 [J/l]')
plt.grid()
plt.subplot(212)
plt.plot(time, CA2_res)
plt.plot([time[0], time[-1]], [CA2_ref_res, CA2_ref_res], '--')
plt.ylabel('Concentration reactor 2 [J/l]')
plt.xlabel('t [s]')
plt.grid()
plt.show()
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time, T1_res)
plt.ylabel('Temperature reactor 1 [K]')
plt.grid()
plt.subplot(212)
plt.plot(time, T2_res)
plt.ylabel('Temperature reactor 2 [K]')
plt.grid()
plt.xlabel('t [s]')
plt.show()
plt.figure(3)
plt.clf()
plt.hold(True)
plt.subplot(211)
plt.plot(time, u2_res)
plt.ylabel('Input 2')
plt.plot([time[0], time[-1]], [u2_ref_res, u2_ref_res], '--')
plt.grid()
plt.subplot(212)
plt.plot(time, der_u2_res)
plt.ylabel('Derivative of input 2')
plt.xlabel('t [s]')
plt.grid()
plt.show()