def run_simulation_with_inputs(time, price, pv, bldg, plot=False):
"""
This function runs a simulation that uses inputs data series
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__))
# compile FMU
path = os.path.join(curr_dir, "..", "Models", "ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.Network', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# create input data series for price and current battery
Npoints = len(time)
# for the simulation no current flow
Ibatt = np.zeros(Npoints)
# Build input trajectory matrix for use in simulation
u = np.transpose(np.vstack((t_data, Ibatt, price, np.squeeze(pv[:,0]), np.squeeze(pv[:,1]), \
np.squeeze(pv[:,2]), np.squeeze(bldg[:,0]), np.squeeze(bldg[:,1]), np.squeeze(bldg[:,2]))))
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(input=([
'Ibatt', 'price', 'pv1', 'pv2', 'pv3', 'bldg1', 'bldg2', 'bldg3'
], u),
start_time=0.,
final_time=24.0 * 3600.0)
# Extract variable profiles
Vs_init_sim = res['Vs']
V1_init_sim = res['V1']
V2_init_sim = res['V2']
V3_init_sim = res['V3']
E_init_sim = res['E']
SOC_init_sim = res['SOC']
Money_init_sim = res['Money']
price_init_sim = res['price']
t_init_sim = res['time']
# plot results
if plot:
plotFunction(t_init_sim, Vs_init_sim, V1_init_sim, V2_init_sim, \
V3_init_sim, E_init_sim, SOC_init_sim, Money_init_sim, price_init_sim)
return res
def run_simulation_with_inputs(time, price, pv, bldg, plot = False):
"""
This function runs a simulation that uses inputs data series
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__));
# compile FMU
path = os.path.join(curr_dir,"..","Models","ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.Network', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# create input data series for price and current battery
Npoints = len(time)
# for the simulation no current flow
Ibatt = np.zeros(Npoints)
# Build input trajectory matrix for use in simulation
u = np.transpose(np.vstack((t_data, Ibatt, price, np.squeeze(pv[:,0]), np.squeeze(pv[:,1]), \
np.squeeze(pv[:,2]), np.squeeze(bldg[:,0]), np.squeeze(bldg[:,1]), np.squeeze(bldg[:,2]))))
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(input=(['Ibatt', 'price', 'pv1', 'pv2', 'pv3', 'bldg1', 'bldg2', 'bldg3'], u), start_time=0., final_time=24.0*3600.0)
# Extract variable profiles
Vs_init_sim = res['Vs']
V1_init_sim = res['V1']
V2_init_sim = res['V2']
V3_init_sim = res['V3']
E_init_sim = res['E']
SOC_init_sim = res['SOC']
Money_init_sim = res['Money']
price_init_sim = res['price']
t_init_sim = res['time']
# plot results
if plot:
plotFunction(t_init_sim, Vs_init_sim, V1_init_sim, V2_init_sim, \
V3_init_sim, E_init_sim, SOC_init_sim, Money_init_sim, price_init_sim)
return res
def run_demo(with_plots=True):
"""
An example on how to simulate a model using the DAE simulator. The result
can be compared with that of sim_rlc.py which has solved the same problem
using dymola. Also writes information to a file.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
model_name = "RLC_Circuit"
mofile = curr_dir + "/files/RLC_Circuit.mo"
jmu_name = compile_jmu(model_name, mofile)
model = JMUModel(jmu_name)
init_res = model.initialize()
(E_dae, A_dae, B_dae, F_dae, g_dae, state_names, input_names, algebraic_names, dx0, x0, u0, w0, t0) = linearize_dae(
init_res.model
)
(A_ode, B_ode, g_ode, H_ode, M_ode, q_ode) = linear_dae_to_ode(E_dae, A_dae, B_dae, F_dae, g_dae)
res1 = model.simulate()
jmu_name = compile_jmu("RLC_Circuit_Linearized", mofile)
lin_model = JMUModel(jmu_name)
res2 = lin_model.simulate()
c_v_1 = res1["capacitor.v"]
i_p_i_1 = res1["inductor.p.i"]
i_p1_i_1 = res1["inductor1.p.i"]
t_1 = res1["time"]
c_v_2 = res2["x[1]"]
i_p_i_2 = res2["x[2]"]
i_p1_i_2 = res2["x[3]"]
t_2 = res2["time"]
assert N.abs(res1.final("capacitor.v") - res2.final("x[1]")) < 1e-3
if with_plots:
p.figure(1)
p.hold(True)
p.subplot(311)
p.plot(t_1, c_v_1)
p.plot(t_2, c_v_2, "g")
p.ylabel("c.v")
p.legend(("original model", "linearized ODE"))
p.grid()
p.subplot(312)
p.plot(t_1, i_p_i_1)
p.plot(t_2, i_p_i_2, "g")
p.ylabel("i.p.i")
p.grid()
p.subplot(313)
p.plot(t_1, i_p1_i_1)
p.plot(t_2, i_p1_i_2, "g")
p.ylabel("i.p1.i")
p.grid()
p.show()
def run_demo(with_plots=True):
"""
An example on how to simulate a model using the DAE simulator. The result
can be compared with that of sim_rlc.py which has solved the same problem
using dymola. Also writes information to a file.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
model_name = 'RLC_Circuit'
mofile = curr_dir+'/files/RLC_Circuit.mo'
jmu_name = compile_jmu(model_name, mofile)
model = JMUModel(jmu_name)
init_res = model.initialize()
(E_dae,A_dae,B_dae,F_dae,g_dae,state_names,input_names,algebraic_names, \
dx0,x0,u0,w0,t0) = linearize_dae(init_res.model)
(A_ode,B_ode,g_ode,H_ode,M_ode,q_ode) = linear_dae_to_ode(
E_dae,A_dae,B_dae,F_dae,g_dae)
res1 = model.simulate()
jmu_name = compile_jmu("RLC_Circuit_Linearized",mofile)
lin_model = JMUModel(jmu_name)
res2 = lin_model.simulate()
c_v_1 = res1['capacitor.v']
i_p_i_1 = res1['inductor.p.i']
i_p1_i_1 = res1['inductor1.p.i']
t_1 = res1['time']
c_v_2 = res2['x[1]']
i_p_i_2 = res2['x[2]']
i_p1_i_2 = res2['x[3]']
t_2 = res2['time']
assert N.abs(res1.final('capacitor.v') - res2.final('x[1]')) < 1e-3
if with_plots:
p.figure(1)
p.hold(True)
p.subplot(311)
p.plot(t_1,c_v_1)
p.plot(t_2,c_v_2,'g')
p.ylabel('c.v')
p.legend(('original model','linearized ODE'))
p.grid()
p.subplot(312)
p.plot(t_1,i_p_i_1)
p.plot(t_2,i_p_i_2,'g')
p.ylabel('i.p.i')
p.grid()
p.subplot(313)
p.plot(t_1,i_p1_i_1)
p.plot(t_2,i_p1_i_2,'g')
p.ylabel('i.p1.i')
p.grid()
p.show()
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_simulation_with_inputs(time, price, pv, bldg, plot=False, usePV=True):
"""
This function runs a simulation that uses inputs data series
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__))
# compile FMU
path = os.path.join(curr_dir, "..", "Models", "ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.ACnetwork', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# create input data series for price and current battery
Npoints = len(time)
# for the simulation no power flow in the battery
P = np.zeros(Npoints)
Q = np.zeros(Npoints)
# if pv panels are not used then remove power
if usePV == False:
pv = np.zeros(np.shape(pv))
# Build input trajectory matrix for use in simulation
u = np.transpose(np.vstack((t_data, P, Q, price, -np.squeeze(bldg[:,0]), -np.squeeze(bldg[:,1]), -np.squeeze(bldg[:,2]), \
np.squeeze(pv[:,0]), np.squeeze(pv[:,1]), np.squeeze(pv[:,2]))))
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(input=([
'P_batt', 'Q_batt', 'price', 'P_bldg1', 'P_bldg2', 'P_bldg3', 'P_pv1',
'P_pv2', 'P_pv3'
], u),
start_time=0.,
final_time=24.0 * 3600.0)
# Extract variable profiles
if plot:
plotFunction(res)
return res
def run_simulation_with_inputs(time, price, pv, bldg, plot = False, usePV = True):
"""
This function runs a simulation that uses inputs data series
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__));
# compile FMU
path = os.path.join(curr_dir,"..","Models","ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.ACnetwork', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# create input data series for price and current battery
Npoints = len(time)
# for the simulation no power flow in the battery
P = np.zeros(Npoints)
Q = np.zeros(Npoints)
# if pv panels are not used then remove power
if usePV == False:
pv = np.zeros(np.shape(pv))
# Build input trajectory matrix for use in simulation
u = np.transpose(np.vstack((t_data, P, Q, price, -np.squeeze(bldg[:,0]), -np.squeeze(bldg[:,1]), -np.squeeze(bldg[:,2]), \
np.squeeze(pv[:,0]), np.squeeze(pv[:,1]), np.squeeze(pv[:,2]))))
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(input=(['P_batt', 'Q_batt', 'price', 'P_bldg1', 'P_bldg2', 'P_bldg3', 'P_pv1', 'P_pv2', 'P_pv3'], u), start_time=0., final_time=24.0*3600.0)
# Extract variable profiles
if plot:
plotFunction(res)
return res
def run_simulation(plot = False):
"""
This function runs a simple simulation without input data
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__));
# compile FMU
path = os.path.join(curr_dir,"..","Models","ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.NetworkSim', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(start_time=0., final_time=24.0*3600.0)
# Extract variable profiles
Vs_init_sim = res['n.Vs']
V1_init_sim = res['n.V1']
V2_init_sim = res['n.V2']
V3_init_sim = res['n.V3']
E_init_sim = res['n.E']
SOC_init_sim = res['n.SOC']
Money_init_sim = res['n.Money']
price_init_sim = res['n.price']
t_init_sim = res['time']
# plot results
if plot:
plotFunction(t_init_sim, Vs_init_sim, V1_init_sim, V2_init_sim, \
V3_init_sim, E_init_sim, SOC_init_sim, Money_init_sim, price_init_sim)
def run_simulation(plot=False):
"""
This function runs a simple simulation without input data
"""
# get current directory
curr_dir = os.path.dirname(os.path.abspath(__file__))
# compile FMU
path = os.path.join(curr_dir, "..", "Models", "ElectricalNetwork.mop")
jmu_model = compile_jmu('ElectricNetwork.NetworkSim', path)
# Load the model instance into Python
model = JMUModel(jmu_model)
# Solve the DAE initialization system
model.initialize()
# Simulate
res = model.simulate(start_time=0., final_time=24.0 * 3600.0)
# Extract variable profiles
Vs_init_sim = res['n.Vs']
V1_init_sim = res['n.V1']
V2_init_sim = res['n.V2']
V3_init_sim = res['n.V3']
E_init_sim = res['n.E']
SOC_init_sim = res['n.SOC']
Money_init_sim = res['n.Money']
price_init_sim = res['n.price']
t_init_sim = res['time']
# plot results
if plot:
plotFunction(t_init_sim, Vs_init_sim, V1_init_sim, V2_init_sim, \
V3_init_sim, E_init_sim, SOC_init_sim, Money_init_sim, price_init_sim)
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):
"""
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("JMExamples.Distillation.Distillation1Input_init",
curr_dir+"/files/JMExamples.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(32):
y_A[i] = init_result['y['+ str(i+1) +']'][0]
x_A[i] = init_result['x['+ str(i+1) +']'][0]
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(32):
y_B[i] = init_result['y[' + str(i+1) + ']'][0]
x_B[i] = init_result['x[' + str(i+1) + ']'][0]
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("JMExamples_opt.Distillation1_opt",
(curr_dir+"/files/JMExamples.mo",curr_dir+"/files/JMExamples_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(32):
model.set('x_init[' + str(i+1) + ']', x_A[i])
# Set the target values to stationary point B
model.set('rr_ref',rr_0_B)
model.set('x1_ref',x_B[0])
# Solve the optimization problem
opts = model.optimize_options()
opts['hs'] = N.ones(100)*1./100 # Equidistant points
opts['n_e'] = 100 # Number of elements
opts['n_cp'] = 3 # Number of collocation points in each element
opt_res = model.optimize()
# Extract variable profiles
x1 = opt_res['x[1]']
x8 = opt_res['x[8]']
x16 = opt_res['x[16]']
x24 = opt_res['x[24]']
x32 = opt_res['x[32]']
y1 = opt_res['y[1]']
y8 = opt_res['y[8]']
y16 = opt_res['y[16]']
y24 = opt_res['y[24]']
y32 = opt_res['y[32]']
t = opt_res['time']
rr = opt_res['rr']
assert N.abs(opt_res.final('rr') - 2.0) < 1e-3
# Plot the results
if with_plots:
plt.figure()
plt.subplot(1,2,1)
plt.plot(t,x16,t,x32,t,x1,t,x8,t,x24)
plt.title('Liquid composition')
plt.grid(True)
plt.ylabel('x')
plt.subplot(1,2,2)
plt.plot(t,y16,t,y32,t,y1,t,y8,t,y24)
plt.title('Vapor composition')
plt.grid(True)
plt.ylabel('y')
plt.xlabel('time')
plt.show()
plt.figure(3)
plt.clf()
plt.hold(True)
plt.plot(t,rr)
plt.ylabel('rr')
plt.xlabel('t [s]')
plt.title('Reflux ratio')
plt.show()
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 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. point A corresponds to operating
conditions where the reactor is cold and the reaction rate is low,
whereas point B corresponds to a higher temperature where the reaction
rate is high.
For more information about the DAE initialization algorithm, see
http://www.jmodelica.org/page/10.
2. How to generate an initial guess for a direct collocation method by means
of simulation. The trajectories resulting from simulation are used to
initialize the variables in the transcribed NLP.
3. An optimal control problem is solved where the objective Is to transfer
the state of the system from stationary point A to point B. The challenge
is to ignite the reactor while avoiding uncontrolled temperature
increase. It is also demonstrated how to set parameter and variable
values in a model.
More information about the simultaneous optimization algorithm can be
found at http://www.jmodelica.org/page/10.
4. The optimization result is saved to file and then the important variables
are plotted.
5. Simulate the system with the optimal control profile. This step is
important in order to verify that the approximation in the transcription
step is valid.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("CSTR.CSTR_Init",
os.path.join(curr_dir, "files", "CSTR.mop"),
compiler_options={"enable_variable_scaling": True})
# load the JMU
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
Tc_0_A = 250
init_model.set('Tc', Tc_0_A)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point A
c_0_A = init_result['c'][0]
T_0_A = init_result['T'][0]
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('Tc = %f' % Tc_0_A)
print('c = %f' % c_0_A)
print('T = %f' % T_0_A)
# Set inputs for Stationary point B
Tc_0_B = 280
init_model.set('Tc', Tc_0_B)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point B
c_0_B = init_result['c'][0]
T_0_B = init_result['T'][0]
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('Tc = %f' % Tc_0_B)
print('c = %f' % c_0_B)
print('T = %f' % T_0_B)
# Compute initial guess trajectories by means of simulation
# Compile the optimization initialization model
jmu_name = compile_jmu("CSTR.CSTR_Init_Optimization",
os.path.join(curr_dir, "files", "CSTR.mop"))
# Load the model
init_sim_model = JMUModel(jmu_name)
# Set model parameters
init_sim_model.set('cstr.c_init', c_0_A)
init_sim_model.set('cstr.T_init', T_0_A)
init_sim_model.set('c_ref', c_0_B)
init_sim_model.set('T_ref', T_0_B)
init_sim_model.set('Tc_ref', Tc_0_B)
res = init_sim_model.simulate(start_time=0., final_time=150.)
# Extract variable profiles
c_init_sim = res['cstr.c']
T_init_sim = res['cstr.T']
Tc_init_sim = res['cstr.Tc']
t_init_sim = res['time']
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(t_init_sim, c_init_sim)
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(t_init_sim, T_init_sim)
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(t_init_sim, Tc_init_sim)
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
# Solve the optimal control problem
# Compile model
jmu_name = compile_jmu("CSTR.CSTR_Opt", curr_dir + "/files/CSTR.mop")
# Load model
cstr = JMUModel(jmu_name)
# Set reference values
cstr.set('Tc_ref', Tc_0_B)
cstr.set('c_ref', c_0_B)
cstr.set('T_ref', T_0_B)
# Set initial values
cstr.set('cstr.c_init', c_0_A)
cstr.set('cstr.T_init', T_0_A)
n_e = 100 # Number of elements
# Set options
opt_opts = cstr.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['init_traj'] = res.result_data
res = cstr.optimize(options=opt_opts)
# Extract variable profiles
c_res = res['cstr.c']
T_res = res['cstr.T']
Tc_res = res['cstr.Tc']
time_res = res['time']
c_ref = res['c_ref']
T_ref = res['T_ref']
Tc_ref = res['Tc_ref']
assert N.abs(res.final('cost') / 1.e7 - 1.8585429) < 1e-3
# Plot the results
if with_plots:
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(time_res, c_res)
plt.plot([time_res[0], time_res[-1]], [c_ref, c_ref], '--')
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(time_res, T_res)
plt.plot([time_res[0], time_res[-1]], [T_ref, T_ref], '--')
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(time_res, Tc_res)
plt.plot([time_res[0], time_res[-1]], [Tc_ref, Tc_ref], '--')
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
# Simulate to verify the optimal solution
# Set up the input trajectory
t = time_res
u = Tc_res
u_traj = N.transpose(N.vstack((t, u)))
# Compile the Modelica model to a JMU
jmu_name = compile_jmu("CSTR.CSTR", curr_dir + "/files/CSTR.mop")
# Load model
sim_model = JMUModel(jmu_name)
sim_model.set('c_init', c_0_A)
sim_model.set('T_init', T_0_A)
sim_model.set('Tc', u[0])
res = sim_model.simulate(start_time=0.,
final_time=150.,
input=('Tc', u_traj))
# Extract variable profiles
c_sim = res['c']
T_sim = res['T']
Tc_sim = res['Tc']
time_sim = res['time']
# Plot the results
if with_plots:
plt.figure(3)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(time_res, c_res, '--')
plt.plot(time_sim, c_sim)
plt.legend(('optimized', 'simulated'))
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(time_res, T_res, '--')
plt.plot(time_sim, T_sim)
plt.legend(('optimized', 'simulated'))
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(time_res, Tc_res, '--')
plt.plot(time_sim, Tc_sim)
plt.legend(('optimized', 'simulated'))
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
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 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. point A corresponds to operating
conditions where the reactor is cold and the reaction rate is low,
whereas point B corresponds to a higher temperature where the reaction
rate is high.
For more information about the DAE initialization algorithm, see
http://www.jmodelica.org/page/10.
2. How to generate an initial guess for a direct collocation method by means
of simulation. The trajectories resulting from simulation are used to
initialize the variables in the transcribed NLP.
3. An optimal control problem is solved where the objective Is to transfer
the state of the system from stationary point A to point B. The challenge
is to ignite the reactor while avoiding uncontrolled temperature
increase. It is also demonstrated how to set parameter and variable
values in a model.
More information about the simultaneous optimization algorithm can be
found at http://www.jmodelica.org/page/10.
4. The optimization result is saved to file and then the important variables
are plotted.
5. Simulate the system with the optimal control profile. This step is
important in order to verify that the approximation in the transcription
step is valid.
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("CSTR.CSTR_Init", os.path.join(curr_dir,"files", "CSTR.mop"),
compiler_options={"enable_variable_scaling":True})
# load the JMU
init_model = JMUModel(jmu_name)
# Set inputs for Stationary point A
Tc_0_A = 250
init_model.set('Tc',Tc_0_A)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point A
c_0_A = init_result['c'][0]
T_0_A = init_result['T'][0]
# Print some data for stationary point A
print(' *** Stationary point A ***')
print('Tc = %f' % Tc_0_A)
print('c = %f' % c_0_A)
print('T = %f' % T_0_A)
# Set inputs for Stationary point B
Tc_0_B = 280
init_model.set('Tc',Tc_0_B)
# Solve the DAE initialization system with Ipopt
init_result = init_model.initialize()
# Store stationary point B
c_0_B = init_result['c'][0]
T_0_B = init_result['T'][0]
# Print some data for stationary point B
print(' *** Stationary point B ***')
print('Tc = %f' % Tc_0_B)
print('c = %f' % c_0_B)
print('T = %f' % T_0_B)
# Compute initial guess trajectories by means of simulation
# Compile the optimization initialization model
jmu_name = compile_jmu("CSTR.CSTR_Init_Optimization",
os.path.join(curr_dir, "files", "CSTR.mop"))
# Load the model
init_sim_model = JMUModel(jmu_name)
# Set model parameters
init_sim_model.set('cstr.c_init',c_0_A)
init_sim_model.set('cstr.T_init',T_0_A)
init_sim_model.set('c_ref',c_0_B)
init_sim_model.set('T_ref',T_0_B)
init_sim_model.set('Tc_ref',Tc_0_B)
res = init_sim_model.simulate(start_time=0.,final_time=150.)
# Extract variable profiles
c_init_sim=res['cstr.c']
T_init_sim=res['cstr.T']
Tc_init_sim=res['cstr.Tc']
t_init_sim = res['time']
# Plot the results
if with_plots:
plt.figure(1)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(t_init_sim,c_init_sim)
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(t_init_sim,T_init_sim)
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(t_init_sim,Tc_init_sim)
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
# Solve the optimal control problem
# Compile model
jmu_name = compile_jmu("CSTR.CSTR_Opt", curr_dir+"/files/CSTR.mop")
# Load model
cstr = JMUModel(jmu_name)
# Set reference values
cstr.set('Tc_ref',Tc_0_B)
cstr.set('c_ref',c_0_B)
cstr.set('T_ref',T_0_B)
# Set initial values
cstr.set('cstr.c_init',c_0_A)
cstr.set('cstr.T_init',T_0_A)
n_e = 100 # Number of elements
# Set options
opt_opts = cstr.optimize_options()
opt_opts['n_e'] = n_e
opt_opts['init_traj'] = res.result_data
res = cstr.optimize(options=opt_opts)
# Extract variable profiles
c_res=res['cstr.c']
T_res=res['cstr.T']
Tc_res=res['cstr.Tc']
time_res = res['time']
c_ref=res['c_ref']
T_ref=res['T_ref']
Tc_ref=res['Tc_ref']
assert N.abs(res.final('cost')/1.e7 - 1.8585429) < 1e-3
# Plot the results
if with_plots:
plt.figure(2)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(time_res,c_res)
plt.plot([time_res[0],time_res[-1]],[c_ref,c_ref],'--')
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(time_res,T_res)
plt.plot([time_res[0],time_res[-1]],[T_ref,T_ref],'--')
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(time_res,Tc_res)
plt.plot([time_res[0],time_res[-1]],[Tc_ref,Tc_ref],'--')
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
# Simulate to verify the optimal solution
# Set up the input trajectory
t = time_res
u = Tc_res
u_traj = N.transpose(N.vstack((t,u)))
# Compile the Modelica model to a JMU
jmu_name = compile_jmu("CSTR.CSTR", curr_dir+"/files/CSTR.mop")
# Load model
sim_model = JMUModel(jmu_name)
sim_model.set('c_init',c_0_A)
sim_model.set('T_init',T_0_A)
sim_model.set('Tc',u[0])
res = sim_model.simulate(start_time=0.,final_time=150.,
input=('Tc',u_traj))
# Extract variable profiles
c_sim=res['c']
T_sim=res['T']
Tc_sim=res['Tc']
time_sim = res['time']
# Plot the results
if with_plots:
plt.figure(3)
plt.clf()
plt.hold(True)
plt.subplot(311)
plt.plot(time_res,c_res,'--')
plt.plot(time_sim,c_sim)
plt.legend(('optimized','simulated'))
plt.grid()
plt.ylabel('Concentration')
plt.subplot(312)
plt.plot(time_res,T_res,'--')
plt.plot(time_sim,T_sim)
plt.legend(('optimized','simulated'))
plt.grid()
plt.ylabel('Temperature')
plt.subplot(313)
plt.plot(time_res,Tc_res,'--')
plt.plot(time_sim,Tc_sim)
plt.legend(('optimized','simulated'))
plt.grid()
plt.ylabel('Cooling temperature')
plt.xlabel('time')
plt.show()
def run_demo(with_plots=True):
"""
Distillation4 optimization model
"""
curr_dir = os.path.dirname(os.path.abspath(__file__));
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("JMExamples.Distillation.Distillation1Input_init",
curr_dir+"/files/JMExamples.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(32):
y_A[i] = init_result['y['+ str(i+1) +']'][0]
x_A[i] = init_result['x['+ str(i+1) +']'][0]
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(32):
y_B[i] = init_result['y[' + str(i+1) + ']'][0]
x_B[i] = init_result['x[' + str(i+1) + ']'][0]
print '(' + str(i+1) + ', %f, %f)' %(x_B[i], y_B[i])
# Set up and solve the simulation problem.
fmu_name1 = compile_fmu("JMExamples.Distillation.Distillation1Inputstep",
curr_dir+"/files/JMExamples.mo")
dist1 = load_fmu(fmu_name1)
# Initialize the model with parameters
# Initialize the model to stationary point A
for i in range(32):
dist1.set('x_init[' + str(i+1) + ']', x_A[i])
res = dist1.simulate(final_time=50)
# Extract variable profiles
x1 = res['x[1]']
x8 = res['x[8]']
x16 = res['x[16]']
x24 = res['x[24]']
x32 = res['x[32]']
y1 = res['y[1]']
y8 = res['y[8]']
y16 = res['y[16]']
y24 = res['y[24]']
y32 = res['y[32]']
t = res['time']
rr = res['rr']
print "t = ", repr(N.array(t))
print "x1 = ", repr(N.array(x1))
print "x8 = ", repr(N.array(x8))
print "x16 = ", repr(N.array(x16))
print "x32 = ", repr(N.array(x32))
if with_plots:
# Plot
plt.figure()
plt.subplot(1,3,1)
plt.plot(t,x16,t,x32,t,x1,t,x8,t,x24)
plt.title('Liquid composition')
plt.grid(True)
plt.ylabel('x')
plt.subplot(1,3,2)
plt.plot(t,y16,t,y32,t,y1,t,y8,t,y24)
plt.title('Vapor composition')
plt.grid(True)
plt.ylabel('y')
plt.subplot(1,3,3)
plt.plot(t,rr)
plt.title('Reflux ratio')
plt.grid(True)
plt.ylabel('rr')
plt.xlabel('time')
plt.show()
def run_demo(with_plots=True):
"""
Distillation4 optimization model
"""
curr_dir = os.path.dirname(os.path.abspath(__file__))
# Compile the stationary initialization model into a JMU
jmu_name = compile_jmu("JMExamples.Distillation.Distillation1Input_init",
curr_dir + "/files/JMExamples.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(32):
y_A[i] = init_result['y[' + str(i + 1) + ']'][0]
x_A[i] = init_result['x[' + str(i + 1) + ']'][0]
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(32):
y_B[i] = init_result['y[' + str(i + 1) + ']'][0]
x_B[i] = init_result['x[' + str(i + 1) + ']'][0]
print '(' + str(i + 1) + ', %f, %f)' % (x_B[i], y_B[i])
# Set up and solve the simulation problem.
fmu_name1 = compile_fmu("JMExamples.Distillation.Distillation1Inputstep",
curr_dir + "/files/JMExamples.mo")
dist1 = load_fmu(fmu_name1)
# Initialize the model with parameters
# Initialize the model to stationary point A
for i in range(32):
dist1.set('x_init[' + str(i + 1) + ']', x_A[i])
res = dist1.simulate(final_time=50)
# Extract variable profiles
x1 = res['x[1]']
x8 = res['x[8]']
x16 = res['x[16]']
x24 = res['x[24]']
x32 = res['x[32]']
y1 = res['y[1]']
y8 = res['y[8]']
y16 = res['y[16]']
y24 = res['y[24]']
y32 = res['y[32]']
t = res['time']
rr = res['rr']
print "t = ", repr(N.array(t))
print "x1 = ", repr(N.array(x1))
print "x8 = ", repr(N.array(x8))
print "x16 = ", repr(N.array(x16))
print "x32 = ", repr(N.array(x32))
if with_plots:
# Plot
plt.figure()
plt.subplot(1, 3, 1)
plt.plot(t, x16, t, x32, t, x1, t, x8, t, x24)
plt.title('Liquid composition')
plt.grid(True)
plt.ylabel('x')
plt.subplot(1, 3, 2)
plt.plot(t, y16, t, y32, t, y1, t, y8, t, y24)
plt.title('Vapor composition')
plt.grid(True)
plt.ylabel('y')
plt.subplot(1, 3, 3)
plt.plot(t, rr)
plt.title('Reflux ratio')
plt.grid(True)
plt.ylabel('rr')
plt.xlabel('time')
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, 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()
