Main

Nonlinear Model Predictive Control

Main.NonlinearControl History

Hide minor edits - Show changes to output

April 03, 2018, at 01:08 AM by 174.148.130.212 -
Deleted line 172:
#m.server = 'http://127.0.0.1'
Deleted line 343:
m.server='http://127.0.0.1'
March 26, 2018, at 03:59 PM by 10.4.53.207 -
Added lines 314-520:
   plt.draw()
    plt.pause(0.01)
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(:div id=gekko_nmpc:)
(:source lang=python:)
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from gekko import gekko


# Steady State Initial Condition
u_ss = 280.0
# Feed Temperature (K)
Tf = 350
# Feed Concentration (mol/m^3)
Caf = 1

# Steady State Initial Conditions for the States
Ca_ss = 1
T_ss = 304
x0 = np.empty(2)
x0[0] = Ca_ss
x0[1] = T_ss

#%% GEKKO nonlinear MPC
m = gekko()
m.server='http://127.0.0.1'
m.time = [0,0.02,0.04,0.06,0.08,0.1,0.12,0.15,0.2]

# Volumetric Flowrate (m^3/sec)
q = 100
# Volume of CSTR (m^3)
V = 100
# Density of A-B Mixture (kg/m^3)
rho = 1000
# Heat capacity of A-B Mixture (J/kg-K)
Cp = 0.239
# Heat of reaction for A->B (J/mol)
mdelH = 5e4
# E - Activation energy in the Arrhenius Equation (J/mol)
# R - Universal Gas Constant = 8.31451 J/mol-K
EoverR = 8750
# Pre-exponential factor (1/sec)
k0 = 7.2e10
# U - Overall Heat Transfer Coefficient (W/m^2-K)
# A - Area - this value is specific for the U calculation (m^2)
UA = 5e4

# initial conditions
Tc0 = 280
T0 = 304
Ca0 = 1.0

tau = m.Const(value=0.5)
Kp = m.Const(value=1)

m.Tc = m.MV(value=Tc0,lb=250,ub=350)
m.T = m.CV(value=T_ss)
m.rA = m.Var(value=0)
m.Ca = m.CV(value=Ca_ss)

m.Equation(m.rA == k0*m.exp(-EoverR/m.T)*m.Ca)

m.Equation(m.T.dt() == q/V*(Tf - m.T) \
            + mdelH/(rho*Cp)*m.rA \
            + UA/V/rho/Cp*(m.Tc-m.T))

m.Equation(m.Ca.dt() == q/V*(Caf - m.Ca) - m.rA)

#MV tuning
m.Tc.STATUS = 1
m.Tc.FSTATUS = 0
m.Tc.DMAX = 100
m.Tc.DMAXHI = 20  # constrain movement up
m.Tc.DMAXLO = -100 # quick action down

#CV tuning
m.T.STATUS = 1
m.T.FSTATUS = 1
m.T.TR_INIT = 1
m.T.TAU = 1.0
DT = 0.5 # deadband

m.Ca.STATUS = 0
m.Ca.FSTATUS = 0 # no measurement
m.Ca.TR_INIT = 0

m.options.CV_TYPE = 1
m.options.IMODE = 6
m.options.SOLVER = 3

#%% define CSTR model
def cstr(x,t,u,Tf,Caf):
    # Inputs (3):
    # Temperature of cooling jacket (K)
    Tc = u
    # Tf = Feed Temperature (K)
    # Caf = Feed Concentration (mol/m^3)

    # States (2):
    # Concentration of A in CSTR (mol/m^3)
    Ca = x[0]
    # Temperature in CSTR (K)
    T = x[1]

    # Parameters:
    # Volumetric Flowrate (m^3/sec)
    q = 100
    # Volume of CSTR (m^3)
    V = 100
    # Density of A-B Mixture (kg/m^3)
    rho = 1000
    # Heat capacity of A-B Mixture (J/kg-K)
    Cp = 0.239
    # Heat of reaction for A->B (J/mol)
    mdelH = 5e4
    # E - Activation energy in the Arrhenius Equation (J/mol)
    # R - Universal Gas Constant = 8.31451 J/mol-K
    EoverR = 8750
    # Pre-exponential factor (1/sec)
    k0 = 7.2e10
    # U - Overall Heat Transfer Coefficient (W/m^2-K)
    # A - Area - this value is specific for the U calculation (m^2)
    UA = 5e4
    # reaction rate
    rA = k0*np.exp(-EoverR/T)*Ca

    # Calculate concentration derivative
    dCadt = q/V*(Caf - Ca) - rA
    # Calculate temperature derivative
    dTdt = q/V*(Tf - T) \
            + mdelH/(rho*Cp)*rA \
            + UA/V/rho/Cp*(Tc-T)

    # Return xdot:
    xdot = np.zeros(2)
    xdot[0] = dCadt
    xdot[1] = dTdt
    return xdot

# Time Interval (min)
t = np.linspace(0,8,401)

# Store results for plotting
Ca = np.ones(len(t)) * Ca_ss
T = np.ones(len(t)) * T_ss
Tsp = np.ones(len(t)) * T_ss
u = np.ones(len(t)) * u_ss

# Set point steps
Tsp[0:100] = 330.0
Tsp[100:200] = 350.0
Tsp[200:300] = 370.0
Tsp[300:] = 390.0

# Create plot
plt.figure(figsize=(10,7))
plt.ion()
plt.show()

# Simulate CSTR
for i in range(len(t)-1):
    # simulate one time period (0.05 sec each loop)
    ts = [t[i],t[i+1]]
    y = odeint(cstr,x0,ts,args=(u[i],Tf,Caf))
    # retrieve measurements
    Ca[i+1] = y[-1][0]
    T[i+1] = y[-1][1]
    # insert measurement
    m.T.MEAS = T[i+1]
    # solve MPC
    m.solve(disp=True,remote=True) # remote=False for local solve

    m.T.SPHI = Tsp[i+1] + DT
    m.T.SPLO = Tsp[i+1] - DT

    # retrieve new Tc value
    u[i+1] = m.Tc.NEWVAL
    # update initial conditions
    x0[0] = Ca[i+1]
    x0[1] = T[i+1]

    #%% Plot the results
    plt.clf()
    plt.subplot(3,1,1)
    plt.plot(t[0:i],u[0:i],'b--',linewidth=3)
    plt.ylabel('Cooling T (K)')
    plt.legend(['Jacket Temperature'],loc='best')

    plt.subplot(3,1,2)
    plt.plot(t[0:i],Ca[0:i],'b.-',linewidth=3,label=r'$C_A$')
    plt.plot([0,t[i-1]],[0.2,0.2],'r--',linewidth=2,label='limit')
    plt.ylabel(r'$C_A$ (mol/L)')
    plt.legend(loc='best')

    plt.subplot(3,1,3)
    plt.plot(t[0:i],Tsp[0:i],'k-',linewidth=3,label=r'$T_{sp}$')
    plt.plot(t[0:i],T[0:i],'b.-',linewidth=3,label=r'$T_{meas}$')
    plt.plot([0,t[i-1]],[400,400],'r--',linewidth=2,label='limit')
    plt.ylabel('T (K)')
    plt.xlabel('Time (min)')
    plt.legend(loc='best')
March 08, 2018, at 03:48 PM by 45.56.3.173 -
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March 08, 2018, at 03:47 PM by 45.56.3.173 -
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(:toggle hide python button show="Show Python Simulation Code":)
(:div id=python:)
(:source lang=python:)
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from gekko import gekko

# Steady State Initial Condition
u_ss = 280.0
# Feed Temperature (K)
Tf = 350
# Feed Concentration (mol/m^3)
Caf = 1

# Steady State Initial Conditions for the States
Ca_ss = 1
T_ss = 304
x0 = np.empty(2)
x0[0] = Ca_ss
x0[1] = T_ss

#%% GEKKO linear MPC
m = gekko()
#m.server = 'http://127.0.0.1'
m.time = [0,0.02,0.04,0.06,0.08,0.1,0.15,0.2,0.3,0.4,0.5]

# initial conditions
Tc0 = 280
T0 = 304
Ca0 = 1.0

tau = m.Const(value = 0.5)
Kp = m.Const(value = 1)

m.Tc = m.MV(value = Tc0,lb=250,ub=350)
m.T = m.CV(value = T_ss)

m.Equation(tau * m.T.dt() == -(m.T - T0) + Kp * (m.Tc - Tc0))

#MV tuning
m.Tc.STATUS = 1
m.Tc.FSTATUS = 0
m.Tc.DMAX = 100
m.Tc.DMAXHI = 5  # constrain movement up
m.Tc.DMAXLO = -100 # quick action down
#CV tuning
m.T.STATUS = 1
m.T.FSTATUS = 1
m.T.SP = 330
m.T.TR_INIT = 2
m.T.TAU = 1.0
m.options.CV_TYPE = 2
m.options.IMODE = 6
m.options.SOLVER = 3

#%% define CSTR model
def cstr(x,t,u,Tf,Caf):
    # Inputs (3):
    # Temperature of cooling jacket (K)
    Tc = u
    # Tf = Feed Temperature (K)
    # Caf = Feed Concentration (mol/m^3)

    # States (2):
    # Concentration of A in CSTR (mol/m^3)
    Ca = x[0]
    # Temperature in CSTR (K)
    T = x[1]

    # Parameters:
    # Volumetric Flowrate (m^3/sec)
    q = 100
    # Volume of CSTR (m^3)
    V = 100
    # Density of A-B Mixture (kg/m^3)
    rho = 1000
    # Heat capacity of A-B Mixture (J/kg-K)
    Cp = 0.239
    # Heat of reaction for A->B (J/mol)
    mdelH = 5e4
    # E - Activation energy in the Arrhenius Equation (J/mol)
    # R - Universal Gas Constant = 8.31451 J/mol-K
    EoverR = 8750
    # Pre-exponential factor (1/sec)
    k0 = 7.2e10
    # U - Overall Heat Transfer Coefficient (W/m^2-K)
    # A - Area - this value is specific for the U calculation (m^2)
    UA = 5e4
    # reaction rate
    rA = k0*np.exp(-EoverR/T)*Ca

    # Calculate concentration derivative
    dCadt = q/V*(Caf - Ca) - rA
    # Calculate temperature derivative
    dTdt = q/V*(Tf - T) \
            + mdelH/(rho*Cp)*rA \
            + UA/V/rho/Cp*(Tc-T)

    # Return xdot:
    xdot = np.zeros(2)
    xdot[0] = dCadt
    xdot[1] = dTdt
    return xdot

# Time Interval (min)
t = np.linspace(0,10,501)

# Store results for plotting
Ca = np.ones(len(t)) * Ca_ss
T = np.ones(len(t)) * T_ss
Tsp = np.ones(len(t)) * T_ss
u = np.ones(len(t)) * u_ss

# Set point steps
Tsp[0:100] = 330.0
Tsp[100:200] = 350.0
Tsp[200:300] = 370.0
Tsp[300:] = 390.0

# Create plot
plt.figure(figsize=(10,7))
plt.ion()
plt.show()

# Simulate CSTR
for i in range(len(t)-1):
    # simulate one time period (0.05 sec each loop)
    ts = [t[i],t[i+1]]
    y = odeint(cstr,x0,ts,args=(u[i],Tf,Caf))
    # retrieve measurements
    Ca[i+1] = y[-1][0]
    T[i+1] = y[-1][1]
    # insert measurement
    m.T.MEAS = T[i+1]
    # update setpoint
    m.T.SP = Tsp[i+1]
    # solve MPC
    m.solve(disp=True,remote=True) # remote=False for local solve
    # change to a fixed starting point for trajectory
    m.T.TR_INIT = 2
    # retrieve new Tc value
    u[i+1] = m.Tc.NEWVAL
    # update initial conditions
    x0[0] = Ca[i+1]
    x0[1] = T[i+1]

    #%% Plot the results
    plt.clf()
    plt.subplot(3,1,1)
    plt.plot(t[0:i],u[0:i],'b--',linewidth=3)
    plt.ylabel('Cooling T (K)')
    plt.legend(['Jacket Temperature'],loc='best')

    plt.subplot(3,1,2)
    plt.plot(t[0:i],Ca[0:i],'r-',linewidth=3)
    plt.ylabel('Ca (mol/L)')
    plt.legend(['Reactor Concentration'],loc='best')

    plt.subplot(3,1,3)
    plt.plot(t[0:i],Tsp[0:i],'k-',linewidth=3,label=r'$T_{sp}$')
    plt.plot(t[0:i],T[0:i],'b.-',linewidth=3,label=r'$T_{meas}$')
    plt.ylabel('T (K)')
    plt.xlabel('Time (min)')
    plt.legend(['Reactor Temperature'],loc='best')
    plt.draw()
    plt.pause(0.01)
March 08, 2018, at 01:44 PM by 45.56.3.173 -
Changed lines 149-154 from:
Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|ODEINT Python Solution for CSTR Control (PID)]] - [[https://youtu.be/tSOMSxGLzQo|Solution Video]]

Attach:zip.png [[Attach:cstr_mpc2_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]] - [[https://youtu.be/nqv6jFeVUYA|Solution Video]]

Attach:zip.png [[Attach:cstr_nmpc_solution_Python.zip|APM Python Solution for CSTR Control (Nonlinear MPC)]] - [[https://youtu.be/Jxpk4-daDLI|Solution Video]]
to:
Attach:download.png [[Attach:cstr_pid_solution_Python.zip|PID for CSTR Control (Python)]] - [[https://youtu.be/tSOMSxGLzQo|Solution Video]]

Attach:download.png [[Attach:cstr_mpc2_solution_Python.zip|Linear MPC for CSTR Control (APM Python)]] - [[https://youtu.be/nqv6jFeVUYA|Solution Video]]

Attach:download.png [[Attach:cstr_nmpc_solution_Python.zip|Nonlinear MPC for CSTR Control (APM Python)]] - [[https://youtu.be/Jxpk4-daDLI|Solution Video]]
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Attach:download.png [[Attach:cstr_control_solution_PID.zip|Solution 1: PID CSTR Control]] - [[https://youtu.be/sfhHcSF2i90|Solution Video]]

Attach:download.png [[Attach:cstr_control_solution_Linear_MPC.zip|Solution 2: Linear MPC CSTR Control]] - [[https://youtu.be/lBx10LvT8uA|Solution Video]]

Attach:download.png [[Attach:cstr_control_solution_Nonlinear_MPC.zip|Solution 3: Nonlinear MPC CSTR Control]] - [[https://youtu.be/PyrLMlht-PU|Solution Video]]
to:
Attach:download.png [[Attach:cstr_control_solution_PID.zip|PID for CSTR Control (Simulink)]] - [[https://youtu.be/sfhHcSF2i90|Solution Video]]

Attach:download.png [[Attach:cstr_control_solution_Linear_MPC.zip|Linear MPC for CSTR Control (Simulink)]] - [[https://youtu.be/lBx10LvT8uA|Solution Video]]

Attach:download.png [[Attach:cstr_control_solution_Nonlinear_MPC.zip|Nonlinear MPC for CSTR Control (Simulink)]] - [[https://youtu.be/PyrLMlht-PU|Solution Video]]
March 08, 2018, at 01:40 PM by 45.56.3.173 -
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Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|ODEINT Python Solution for CSTR Control (PID)]]

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https://www.youtube.com/embed/tSOMSxGLzQo" frameborder="0" allowfullscreen></iframe>
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Attach:zip
.png [[Attach:cstr_mpc2_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]]

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https://www.youtube.com/embed/nqv6jFeVUYA" frameborder="0" allowfullscreen></iframe>
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Attach:zip
.png [[Attach:cstr_nmpc_solution_Python.zip|APM Python Solution for CSTR Control (Nonlinear MPC)]]

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https://www.youtube.com/embed/Jxpk4-daDLI" frameborder="0" allowfullscreen></iframe>
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to:
Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|ODEINT Python Solution for CSTR Control (PID)]] - [[https://youtu.be/tSOMSxGLzQo|Solution Video]]

Attach:zip.png [[Attach
:cstr_mpc2_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]] - [[https://youtu.be/nqv6jFeVUYA|Solution Video]]

Attach:zip.png [[Attach
:cstr_nmpc_solution_Python.zip|APM Python Solution for CSTR Control (Nonlinear MPC)]] - [[https://youtu.be/Jxpk4-daDLI|Solution Video]]
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Attach:download.png [[Attach:cstr_control_solution_PID.zip|Solution 1: PID CSTR Control]]

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https://www.youtube.com/embed/sfhHcSF2i90" frameborder="0" allowfullscreen></iframe>
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Attach:download.png [[Attach:cstr_control_solution_
Linear_MPC.zip|Solution 2: Linear MPC CSTR Control]]

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<iframe width="560" height="315" src="
https://www.youtube.com/embed/lBx10LvT8uA" frameborder="0" allowfullscreen></iframe>
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Attach:download.png [[Attach:cstr_control_solution_
Nonlinear_MPC.zip|Solution 3: Nonlinear MPC CSTR Control]]

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to:
Attach:download.png [[Attach:cstr_control_solution_PID.zip|Solution 1: PID CSTR Control]] - [[https://youtu.be/sfhHcSF2i90|Solution Video]]

Attach:download.png [[Attach
:cstr_control_solution_Linear_MPC.zip|Solution 2: Linear MPC CSTR Control]] - [[https://youtu.be/lBx10LvT8uA|Solution Video]]

Attach:download.png [[Attach
:cstr_control_solution_Nonlinear_MPC.zip|Solution 3: Nonlinear MPC CSTR Control]] - [[https://youtu.be/PyrLMlht-PU|Solution Video]]
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June 21, 2017, at 09:40 PM by 10.5.113.130 -
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[[Attach:cstr_control.pdf|Problem Information]]

Attach:download.png [[Attach:cstr_control.zip|CSTR Source Files]]
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Attach:download.png [[Attach:cstr_control.zip|CSTR Source Files]] | [[Attach:cstr_control.pdf|Problem Information]]
June 21, 2017, at 09:39 PM by 10.5.113.130 -
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%width=300px%Attach:cstr.png
March 13, 2017, at 10:42 AM by 82.217.12.178 -
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March 11, 2017, at 07:31 AM by 45.56.3.173 -
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March 11, 2017, at 06:33 AM by 45.56.3.173 -
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March 11, 2017, at 06:06 AM by 45.56.3.173 -
Deleted lines 150-151:

Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and MPC compared)]]
March 11, 2017, at 05:09 AM by 45.56.3.173 -
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and MPC - 2nd approach)]]
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and MPC compared)]]
March 11, 2017, at 05:09 AM by 45.56.3.173 -
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and Linear MPC Solution 2)]]
to:
Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and MPC - 2nd approach)]]
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Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]]

Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and Linear MPC)]]
to:
Attach:zip.png [[Attach:cstr_mpc2_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]]

Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and Linear MPC Solution 2)]]
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Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|APM Python Solution for CSTR Control (Linear MPC)]]
March 10, 2017, at 04:13 PM by 10.5.113.121 -
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A step test is required to obtain a process model for the PID controller and the linear model predictive controller. It is a first step in developing a controller. The following code implements a doublet test. A doublet test starts with the system at steady state. Three moves of Manipulated Variable (MV) are made with sufficient time to nearly reach steady state conditions at two other operating points. The steps are above and below the nominal operating conditions. In this case, the cooling jacket temperature is raised, lowered, and brought back to 300 K (nominal operating condition.
March 10, 2017, at 04:09 PM by 10.5.113.121 -
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!!!! Step Test (Doublet)

%width=550px%Attach:cstr_doublet.png

(:source lang=python:)
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# define CSTR model
def cstr(x,t,u,Tf,Caf):
    # Inputs (3):
    # Temperature of cooling jacket (K)
    Tc = u
    # Tf = Feed Temperature (K)
    # Caf = Feed Concentration (mol/m^3)

    # States (2):
    # Concentration of A in CSTR (mol/m^3)
    Ca = x[0]
    # Temperature in CSTR (K)
    T = x[1]

    # Parameters:
    # Volumetric Flowrate (m^3/sec)
    q = 100
    # Volume of CSTR (m^3)
    V = 100
    # Density of A-B Mixture (kg/m^3)
    rho = 1000
    # Heat capacity of A-B Mixture (J/kg-K)
    Cp = 0.239
    # Heat of reaction for A->B (J/mol)
    mdelH = 5e4
    # E - Activation energy in the Arrhenius Equation (J/mol)
    # R - Universal Gas Constant = 8.31451 J/mol-K
    EoverR = 8750
    # Pre-exponential factor (1/sec)
    k0 = 7.2e10
    # U - Overall Heat Transfer Coefficient (W/m^2-K)
    # A - Area - this value is specific for the U calculation (m^2)
    UA = 5e4
    # reaction rate
    rA = k0*np.exp(-EoverR/T)*Ca

    # Calculate concentration derivative
    dCadt = q/V*(Caf - Ca) - rA
    # Calculate temperature derivative
    dTdt = q/V*(Tf - T) \
            + mdelH/(rho*Cp)*rA \
            + UA/V/rho/Cp*(Tc-T)
   
    # Return xdot:
    xdot = np.zeros(2)
    xdot[0] = dCadt
    xdot[1] = dTdt
    return xdot

# Steady State Initial Conditions for the States
Ca_ss = 0.87725294608097
T_ss = 324.475443431599
x0 = np.empty(2)
x0[0] = Ca_ss
x0[1] = T_ss

# Steady State Initial Condition
u_ss = 300.0
# Feed Temperature (K)
Tf = 350
# Feed Concentration (mol/m^3)
Caf = 1

# Time Interval (min)
t = np.linspace(0,25,251)

# Store results for plotting
Ca = np.ones(len(t)) * Ca_ss
T = np.ones(len(t)) * T_ss
u = np.ones(len(t)) * u_ss

# Step cooling temperature to 295
u[10:100] = 303.0
u[100:190] = 297.0
u[190:] = 300.0

# Simulate CSTR
for i in range(len(t)-1):
    ts = [t[i],t[i+1]]
    y = odeint(cstr,x0,ts,args=(u[i+1],Tf,Caf))
    Ca[i+1] = y[-1][0]
    T[i+1] = y[-1][1]
    x0[0] = Ca[i+1]
    x0[1] = T[i+1]

# Construct results and save data file
# Column 1 = time
# Column 2 = cooling temperature
# Column 3 = reactor temperature
data = np.vstack((t,u,T)) # vertical stack
data = data.T            # transpose data
np.savetxt('data_doublet.txt',data,delimiter=',')
   
# Plot the results
plt.figure()
plt.subplot(3,1,1)
plt.plot(t,u,'b--',linewidth=3)
plt.ylabel('Cooling T (K)')
plt.legend(['Jacket Temperature'],loc='best')

plt.subplot(3,1,2)
plt.plot(t,Ca,'r-',linewidth=3)
plt.ylabel('Ca (mol/L)')
plt.legend(['Reactor Concentration'],loc='best')

plt.subplot(3,1,3)
plt.plot(t,T,'k.-',linewidth=3)
plt.ylabel('T (K)')
plt.xlabel('Time (min)')
plt.legend(['Reactor Temperature'],loc='best')

plt.show()
(:sourceend:)
March 10, 2017, at 04:05 PM by 10.5.113.121 -
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(:title Model Predictive Control:)
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(:title Nonlinear Model Predictive Control:)
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(:title Nonlinear Model Predictive Control:)
(:keywords Nonlinear, Model Predictive Control, real-time, tutorial:)
to:
(:title Model Predictive Control:)
(:keywords Nonlinear, PID, Model Predictive Control, real-time, tutorial:)
March 10, 2017, at 04:02 PM by 10.5.113.121 -
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control (PID and Linear MPC)]]

Attach:zip.png [[Attach:cstr_nmpc_solution_Python.zip|Python Solution for CSTR Control (Nonlinear MPC)]]
to:
Attach:zip.png [[Attach:cstr_pid_solution_Python.zip|ODEINT Python Solution for CSTR Control (PID)]]

Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|APM Python Solution for CSTR Control (PID and Linear MPC)]]

Attach:zip.png [[Attach:cstr_nmpc_solution_Python.zip|APM
Python Solution for CSTR Control (Nonlinear MPC)]]
March 09, 2016, at 01:40 AM by 10.5.113.128 -
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control]]
to:
Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control (PID and Linear MPC)]]

Attach:zip.png [[Attach:cstr_nmpc_solution_Python.zip|Python Solution for CSTR Control (Nonlinear MPC)
]]
March 05, 2016, at 05:21 PM by 45.56.3.173 -
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Attach:download.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control]]
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Attach:zip.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control]]
March 04, 2016, at 06:20 PM by 10.4.53.157 -
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!!!! Solution
to:
!!!! Solution in Python

Attach:download.png [[Attach:cstr_mpc_solution_Python.zip|Python Solution for CSTR Control]]

!!!! Solution in Simulink
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<iframe width="560" height="315" src="https://www.youtube.com/embed/qH55ym1g-NM" frameborder="0" allowfullscreen></iframe>
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Attach:download.png [[Attach:cstr_control_solution_PID.zip|Solution 1: PID CSTR Control]]
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Attach:download.png [[Attach:cstr_control_solution_Linear_MPC.zip|Linear MPC CSTR Control]]

Attach:download.png [[Attach:cstr_control_solution_Nonlinear_MPC.zip|Nonlinear MPC CSTR Control]]
to:
Attach:download.png [[Attach:cstr_control_solution_Linear_MPC.zip|Solution 2: Linear MPC CSTR Control]]

Attach:download.png [[Attach:cstr_control_solution_Nonlinear_MPC.zip|Solution 3: Nonlinear MPC CSTR Control]]
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Attach:download.png [[Attach:cstr_control_solution.zip|All CSTR Control Solution Files]]

Attach:download.png [[Attach:cstr_control_solution_PID.zip|PID CSTR Control]]
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See additional information on this application on the [[http://apmonitor.com/che436/index.php/Main/CaseStudyCSTR|Process Control Class Web-page]].
May 23, 2015, at 08:24 PM by 174.148.103.31 -
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Attach:download.png [[Attach:cstr_control_solution_Nonlinear_MPC.zip|Nonlinear MPC CSTR Control]]
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Attach:download.png [[Attach:cstr_control_solution_Linear_MPC.zip|Linear MPC CSTR Control]]
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Attach:download.png [[Attach:cstr_control_solution.zip|CSTR Control Solution Files]]
to:
Attach:download.png [[Attach:cstr_control_solution.zip|All CSTR Control Solution Files]]

Attach:download.png [[Attach:cstr_control_solution_PID.zip|PID CSTR Control]]

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A reactor is used to convert a hazardous chemical '''A''' to an acceptable chemical '''B''' in waste stream before entering a nearby lake. This particular reactor is dynamically modeled as a Continuously Stirred Tank Reactor (CSTR) with a simplified kinetic mechanism that describes the conversion of reactant '''A''' to product '''B''' with an irreversible and exothermic reaction. It is desired to maintain the temperature at a constant setpoint that maximizes the destruction of A (highest possible temperature).
to:
A reactor is used to convert a hazardous chemical '''A''' to an acceptable chemical '''B''' in waste stream before entering a nearby lake. This particular reactor is dynamically modeled as a Continuously Stirred Tank Reactor (CSTR) with a simplified kinetic mechanism that describes the conversion of reactant '''A''' to product '''B''' with an irreversible and exothermic reaction. It is desired to maintain the temperature at a constant setpoint that maximizes the destruction of A (highest possible temperature). Adjust the jacket temperature (''T'_c_''') to maintain a desired  reactor temperature and minimize the concentration of '''A'''. The reactor temperature should never exceed 400 K. The cooling jacket temperature can be adjusted between 250 K and 350 K.
May 22, 2015, at 06:36 PM by 10.5.113.160 -
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Attach:download.png [[Attach:cstr_control_solution.zip|CSTR Control Solution Files]]
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[[Attach:cstr_control.pdf|Problem Statement]]
to:
[[Attach:cstr_control.pdf|Problem Information]]
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'''Objective:''' Design a controller to maintain temperature of a chemical reactor. Develop 3 separate controllers (PID, Linear MPC, Nonlinear MPC) in Python or MATLAB/Simulink. Demonstrate controller performance with steps in the set point and disturbance changes. ''Estimated time: 3 hours.''
to:
'''Objective:''' Design a controller to maintain temperature of a chemical reactor. Develop 3 separate controllers (PID, Linear MPC, Nonlinear MPC) in Python, MATLAB, or Simulink. Demonstrate controller performance with steps in the set point and disturbance changes. ''Estimated time: 3 hours.''
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'''Objective:''' Design a model predictive controller to maintain temperature of a chemical reactor. Develop a linear, first-order model of the reactor and implement the controller in Python or MATLAB/Simulink. Demonstrate controller performance with steps in the set point and disturbance changes. ''Estimated time: 3 hours.''
to:
'''Objective:''' Design a controller to maintain temperature of a chemical reactor. Develop 3 separate controllers (PID, Linear MPC, Nonlinear MPC) in Python or MATLAB/Simulink. Demonstrate controller performance with steps in the set point and disturbance changes. ''Estimated time: 3 hours.''
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!!!! Exercise

'''Objective:''' Design a model predictive controller to maintain temperature of a chemical reactor. Develop a linear, first-order model of the reactor and implement the controller in Python or MATLAB/Simulink. Demonstrate controller performance with steps in the set point and disturbance changes. ''Estimated time: 3 hours.''

[[Attach:cstr_control.pdf|Problem Statement]]

Attach:download.png [[Attach:cstr_control.zip|CSTR Source Files]]

Attach:cstr.png

A reactor is used to convert a hazardous chemical '''A''' to an acceptable chemical '''B''' in waste stream before entering a nearby lake. This particular reactor is dynamically modeled as a Continuously Stirred Tank Reactor (CSTR) with a simplified kinetic mechanism that describes the conversion of reactant '''A''' to product '''B''' with an irreversible and exothermic reaction. It is desired to maintain the temperature at a constant setpoint that maximizes the destruction of A (highest possible temperature).

!!!! Solution

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Dynamic control is also known as Nonlinear Model Predictive Control (NMPC) or simply as Nonlinear Control (NLC). NLC with predictive models is a dynamic optimization approach that seeks to follow a trajectory or drive certain values to maximum or minimum levels.
to:
Dynamic control is also known as Nonlinear Model Predictive Control (NMPC) or simply as Nonlinear Control (NLC). NLC with predictive models is a dynamic optimization approach that seeks to follow a trajectory or drive certain values to maximum or minimum levels.

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(:title Nonlinear Model Predictive Control:)
(:keywords Nonlinear, Model Predictive Control, real-time, tutorial:)
(:description Nonlinear Control (NLC) with predictive models is a dynamic optimization approach that seeks to follow a trajectory or drive certain values to maximum or minimum levels:)

Dynamic control is also known as Nonlinear Model Predictive Control (NMPC) or simply as Nonlinear Control (NLC). NLC with predictive models is a dynamic optimization approach that seeks to follow a trajectory or drive certain values to maximum or minimum levels.