Ниже приведен мой код PYTHON:
У меня есть CSTR, и я пытаюсь контролировать высоту бака и температуру, одновременно управляя входным потоком и температурой охлаждения.Проблема в том, что резюме не отслеживают их соответствующие уставки.Я пытался решить проблему только для 1 CV и 1 MV, это сработало очень хорошо.
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
from gekko import GEKKO
# Steady State Initial Condition
u1_ss = 280.0
u2_ss=100.0
# 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
h_ss=94.77413303
V_ss=8577.41330293
x0 = np.empty(4)
x0[0] = Ca_ss
x0[1] = T_ss
x0[2]= h_ss
x0[3]= V_ss
#%% GEKKO nonlinear MPC
m = GEKKO(remote=False)
m.time = [0,0.02,0.04,0.06,0.08,0.1,0.12,0.15,0.2]
c1=10.0
Ac=100.0
# 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
h0=94.77413303
q0=100.0
V0=8577.41330293
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.h= m.CV(value=h0)
m.rA = m.Var(value=0)
m.Ca = m.CV(value=Ca_ss,lb=0,ub=1)
m.V= m.CV(value=V_ss,lb=0,ub=100000)
m.q=m.MV(value=q0,lb=0,ub=100000)
m.Equation(m.rA == k0*m.exp(-EoverR/m.T)*m.Ca)
m.Equation(m.T.dt() == m.q/m.V*(Tf - m.T) \
+ mdelH/(rho*Cp)*m.rA \
+ UA/m.V/rho/Cp*(m.Tc-m.T))
m.Equation(m.Ca.dt() == m.q/m.V*(Caf - m.Ca) - m.rA)
m.Equation(m.h.dt()==(m.q-c1*m.h**0.5)/Ac)
m.Equation(m.V.dt() == m.q- c1*m.h**0.5)
#MV tuning
m.Tc.STATUS = 1
m.Tc.FSTATUS = 0
m.Tc.DMAX = 100
m.Tc.DMAXHI = 20
m.Tc.DMAXLO = -100
m.q.STATUS = 1
m.q.FSTATUS = 0
m.q.DMAX = 10
#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.h.STATUS = 1
m.h.FSTATUS = 1
m.h.TR_INIT = 1
m.h.TAU = 1.0
m.Ca.STATUS = 1
m.Ca.FSTATUS = 0 # no measurement
m.Ca.TR_INIT = 0
m.V.STATUS = 1
m.V.FSTATUS = 0 # no measurement
m.V.TR_INIT = 0
m.options.CV_TYPE = 1
m.options.IMODE = 6
m.options.SOLVER = 3
#%% define CSTR model
def cstr(x,t,u1,u2,Tf,Caf,Ac):
# Inputs (3):
# Temperature of cooling jacket (K)
Tc = u1
q=u2
# 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]
# the height of the tank (m)
h=x[2]
V=x[3]
# Parameters:
# 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)
# Calculate height derivative
dhdt=(q-c1*h**0.5)/Ac
if x[2]>=300 and dhdt>0:
dhdt = 0
dVdt= q-c1*h**0.5
# Return xdot:
xdot = np.zeros(4)
xdot[0] = dCadt
xdot[1] = dTdt
xdot[2]= dhdt
xdot[3]= dVdt
return xdot
# Time Interval (min)
t = np.linspace(0,8,401)
# Store results for plotting
Ca = np.ones(len(t)) * Ca_ss
V=np.ones(len(t))*V_ss
T = np.ones(len(t)) * T_ss
Tsp = np.ones(len(t)) * T_ss
hsp=np.ones(len(t))*h_ss
h=np.ones(len(t))*h_ss
u1 = np.ones(len(t)) * u1_ss
u2 = np.ones(len(t)) * u2_ss
# Set point steps
Tsp[0:100] = 330.0
Tsp[100:200] = 350.0
Tsp[230:260] = 370.0
Tsp[260:290] = 390.0
hsp[0:100] = 30.0
hsp[100:200] =60.0
hsp[200:250]=90.0
# 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=(u1[i+1],u2[i+1],Tf,Caf,Ac))
# retrieve measurements
Ca[i+1] = y[-1][0]
T[i+1] = y[-1][1]
h[i+1]= y[-1][2]
V[i+1]= y[-1][3]
# insert measurement
m.T.MEAS = T[i+1]
m.h.MEAS=h[i+1]
# solve MPC
m.solve(disp=True)
m.T.SPHI = Tsp[i+1] + DT
m.T.SPLO = Tsp[i+1] - DT
m.h.SPHI = hsp[i+1] + DT
m.h.SPLO = hsp[i+1] - DT
# retrieve new Tc value
u1[i+1] = m.Tc.NEWVAL
u2[i+1] = m.q.NEWVAL
# update initial conditions
x0[0] = Ca[i+1]
x0[1] = T[i+1]
x0[2]= h[i+1]
x0[3]= V[i+1]
#%% Plot the results
plt.clf()
plt.subplot(6,1,1)
plt.plot(t[0:i],u1[0:i],'b--',linewidth=3)
plt.ylabel('Cooling T (K)')
plt.legend(['Jacket Temperature'],loc='best')
plt.subplot(6,1,2)
plt.plot(t[0:i],u2[0:i],'b--',linewidth=3)
plt.ylabel('inlet flow')
plt.subplot(6,1,3)
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(6,1,4)
plt.plot(t[0:i],V[0:i],'g--',linewidth=3)
plt.xlabel('time')
plt.ylabel('Volume of Tank')
plt.subplot(6,1,5)
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')
plt.subplot(6,1,6)
plt.plot(t[0:i],hsp[0:i],'g--',linewidth=3,label=r'$h_{sp}$')
plt.plot(t[0:i],h[0:i],'k.-',linewidth=3,label=r'$h_{meas}$')
plt.xlabel('time')
plt.ylabel('tank level')
plt.legend(loc='best')
plt.draw()
plt.pause(0.01)