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TCLab B - MIMO Digital Twin

The TCLab is a hands-on application of machine learning and advanced temperature control with two heaters and two temperature sensors. The labs reinforce principles of model development, estimation, and advanced control methods. This is the second exercise to simulate an energy balance and compare the predictions to deep learning with a multi-layered neural network. The additional feature over the first lab is that the model is extended to two heaters and two temperature sensors.

Lab Problem Statement

Data and Solutions

import numpy as np
import pandas as pd
import tclab
import time
import matplotlib.pyplot as plt

# generate step test data on Arduino
filename = 'tclab_dyn_data2.csv'

# heater steps
Q1d = np.zeros(601)
Q1d[10:200] = 80
Q1d[200:280] = 20
Q1d[280:400] = 70
Q1d[400:] = 50

Q2d = np.zeros(601)
Q2d[120:320] = 100
Q2d[320:520] = 10
Q2d[520:] = 80

# Connect to Arduino
a = tclab.TCLab()
fid = open(filename,'w')
fid.write('Time,H1,H2,T1,T2\n')
fid.close()

# run step test (10 min)
for i in range(601):
    # set heater values
    a.Q1(Q1d[i])
    a.Q2(Q2d[i])
    print('Time: ' + str(i) + \
          ' H1: ' + str(Q1d[i]) + \
          ' H2: ' + str(Q2d[i]) + \
          ' T1: ' + str(a.T1)   + \
          ' T2: ' + str(a.T2))
    # wait 1 second
    time.sleep(1)
    fid = open(filename,'a')
    fid.write(str(i)+','+str(Q1d[i])+','+str(Q2d[i])+',' \
              +str(a.T1)+','+str(a.T2)+'\n')
# close connection to Arduino
a.close()

# read data file
data = pd.read_csv(filename)

# plot measurements
plt.figure()
plt.subplot(2,1,1)
plt.plot(data['Time'],data['H1'],'r-',label='Heater 1')
plt.plot(data['Time'],data['H2'],'b--',label='Heater 2')
plt.ylabel('Heater (%)')
plt.legend(loc='best')
plt.subplot(2,1,2)
plt.plot(data['Time'],data['T1'],'r.',label='Temperature 1')
plt.plot(data['Time'],data['T2'],'b.',label='Temperature 2')
plt.ylabel('Temperature (degC)')
plt.legend(loc='best')
plt.xlabel('Time (sec)')
plt.savefig('tclab_dyn_meas2.png')

plt.show()

import numpy as np
import matplotlib.pyplot as plt
from gekko import GEKKO

#initialize GEKKO model
m = GEKKO()

#model discretized time
n = 60*10+1  # Number of second time points (10min)
m.time = np.linspace(0,n-1,n) # Time vector

# Parameters
# Percent Heater (0-100%)
Q1d = np.zeros(n)
Q1d[10:200] = 80
Q1d[200:280] = 20
Q1d[280:400] = 70
Q1d[400:] = 50
Q1 = m.Param()
Q1.value = Q1d

Q2d = np.zeros(n)
Q2d[120:320] = 100
Q2d[320:520] = 10
Q2d[520:] = 80
Q2 = m.Param()
Q2.value = Q2d# Heaters as time-varying inputs
Q1 = m.Param(value=Q1d) # Percent Heater (0-100%)
Q2 = m.Param(value=Q2d) # Percent Heater (0-100%)

T0 = m.Param(value=19.0+273.15)     # Initial temperature
Ta = m.Param(value=19.0+273.15)     # K
U =  m.Param(value=10.0)            # W/m^2-K
mass = m.Param(value=4.0/1000.0)    # kg
Cp = m.Param(value=0.5*1000.0)      # J/kg-K    
A = m.Param(value=10.0/100.0**2)    # Area not between heaters in m^2
As = m.Param(value=2.0/100.0**2)    # Area between heaters in m^2
alpha1 = m.Param(value=0.01)        # W / % heater
alpha2 = m.Param(value=0.005)      # W / % heater
eps = m.Param(value=0.9)            # Emissivity
sigma = m.Const(5.67e-8)            # Stefan-Boltzman

# Temperature states as GEKKO variables
T1 = m.Var(value=T0)
T2 = m.Var(value=T0)        

# Between two heaters
Q_C12 = m.Intermediate(U*As*(T2-T1)) # Convective
Q_R12 = m.Intermediate(eps*sigma*As*(T2**4-T1**4)) # Radiative

m.Equation(T1.dt() == (1.0/(mass*Cp))*(U*A*(Ta-T1) \
                    + eps * sigma * A * (Ta**4 - T1**4) \
                    + Q_C12 + Q_R12 \
                    + alpha1*Q1))

m.Equation(T2.dt() == (1.0/(mass*Cp))*(U*A*(Ta-T2) \
                    + eps * sigma * A * (Ta**4 - T2**4) \
                    - Q_C12 - Q_R12 \
                    + alpha2*Q2))

#simulation mode
m.options.IMODE = 4

#simulation model
m.solve()

#plot results
plt.figure(1)
plt.subplot(2,1,1)
plt.plot(m.time/60.0,np.array(T1.value)-273.15,'b-')
plt.plot(m.time/60.0,np.array(T2.value)-273.15,'r--')
plt.legend([r'$T_1$',r'$T_2$'],loc='best')
plt.ylabel('Temperature (degC)')

plt.subplot(2,1,2)
plt.plot(m.time/60.0,np.array(Q1.value),'b-')
plt.plot(m.time/60.0,np.array(Q2.value),'r--')
plt.legend([r'$Q_1$',r'$Q_2$'],loc='best')
plt.ylabel('Heaters (%)')

plt.xlabel('Time (min)')
plt.show()

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.preprocessing import MinMaxScaler
from gekko import GEKKO

import time

# -------------------------------------
# import or generate data
# -------------------------------------
filename = 'tclab_ss_data2.csv'
try:
    try:
        data = pd.read_csv(filename)
    except:
        url = 'https://apmonitor.com/do/uploads/Main/tclab_ss_data2.txt'
        data = pd.read_csv(url)
except:
    # generate training data if data file not available
    import tclab
    # Connect to Arduino
    a = tclab.TCLab()
    fid = open(filename,'w')
    fid.write('Heater 1,Heater 2,Temperature 1,Temperature 2\n')
    fid.close()
    # data collection takes 6 hours = 120 pts * 3 minutes each
    npts = 120
    for i in range(npts):
        # set random heater values
        Q1 = np.random.rand()*100
        Q2 = np.random.rand()*100
        a.Q1(Q1)
        a.Q2(Q2)
        print('Heater 1: ' + str(Q1) + ' %')
        print('Heater 2: ' + str(Q2) + ' %')
        # wait 3 minutes
        time.sleep(3*60)
        # record temperature and heater value
        print('Temperature 1: ' + str(a.T1) + ' degC')
        print('Temperature 2: ' + str(a.T2) + ' degC')
        fid = open(filename,'a')
        fid.write(str(Q1)+','+str(Q2)+','+str(a.T1)+','+str(a.T2)+'\n')
        fid.close()
    # close connection to Arduino
    a.close()
    # read data file
    data = pd.read_csv(filename)

# -------------------------------------
# scale data
# -------------------------------------
s = MinMaxScaler(feature_range=(0,1))
sc_train = s.fit_transform(data)

# partition into inputs and outputs
xs = sc_train[:,0:2] # 2 heaters
ys = sc_train[:,2:4] # 2 temperatures

# -------------------------------------
# build neural network
# -------------------------------------
nin = 2  # inputs
n1 = 2   # hidden layer 1 (linear)
n2 = 2   # hidden layer 2 (nonlinear)
n3 = 2   # hidden layer 3 (linear)
nout = 2 # outputs

# Initialize gekko models
train = GEKKO()
dyn   = GEKKO()
model = [train,dyn]

for m in model:
    # use APOPT solver
    m.options.SOLVER = 1

    # input(s)
    m.inpt = [m.Param() for i in range(nin)]

    # layer 1 (linear)
    m.w1 = m.Array(m.FV, (nout,nin,n1))
    m.l1 = [[m.Intermediate(sum([m.w1[k,j,i]*m.inpt[j] \
            for j in range(nin)])) for i in range(n1)] \
            for k in range(nout)]

    # layer 2 (tanh)
    m.w2 = m.Array(m.FV, (nout,n1,n2))
    m.l2 = [[m.Intermediate(sum([m.tanh(m.w2[k,j,i]*m.l1[k][j]) \
            for j in range(n1)])) for i in range(n2)] \
            for k in range(nout)]

    # layer 3 (linear)
    m.w3 = m.Array(m.FV, (nout,n2,n3))
    m.l3 = [[m.Intermediate(sum([m.w3[k,j,i]*m.l2[k][j] \
            for j in range(n2)])) for i in range(n3)] \
            for k in range(nout)]

    # outputs
    m.outpt = [m.CV() for i in range(nout)]
    m.Equations([m.outpt[k]==sum([m.l3[k][i] for i in range(n3)]) \
                 for k in range(nout)])

    # flatten matrices
    m.w1 = m.w1.flatten()
    m.w2 = m.w2.flatten()
    m.w3 = m.w3.flatten()

# -------------------------------------
# fit parameter weights
# -------------------------------------
m = train
for i in range(nin):
    m.inpt[i].value=xs[:,i]
for i in range(nout):
    m.outpt[i].value = ys[:,i]
    m.outpt[i].FSTATUS = 1
for i in range(len(m.w1)):
    m.w1[i].FSTATUS=1
    m.w1[i].STATUS=1
    m.w1[i].MEAS=1.0
for i in range(len(m.w2)):
    m.w2[i].STATUS=1
    m.w2[i].FSTATUS=1
    m.w2[i].MEAS=0.5
for i in range(len(m.w3)):
    m.w3[i].FSTATUS=1
    m.w3[i].STATUS=1
    m.w3[i].MEAS=1.0
m.options.IMODE = 2
m.options.EV_TYPE = 2

# solve for weights to minimize loss (objective)
m.solve(disp=True)

# -------------------------------------
# generate dynamic predictions
# -------------------------------------
m = dyn
tf = 600
m.time = np.linspace(0,tf,tf+1)
# load neural network parameters
for i in range(len(m.w1)):
    m.w1[i].MEAS=train.w1[i].NEWVAL
    m.w1[i].FSTATUS = 1
for i in range(len(m.w2)):
    m.w2[i].MEAS=train.w2[i].NEWVAL
    m.w2[i].FSTATUS = 1
for i in range(len(m.w3)):
    m.w3[i].MEAS=train.w3[i].NEWVAL
    m.w3[i].FSTATUS = 1
# step tests
Q1d = np.zeros(tf+1)
Q1d[10:200] = 80
Q1d[200:280] = 20
Q1d[280:400] = 70
Q1d[400:] = 50
Q1 = m.Param()
Q1.value = Q1d

Q2d = np.zeros(tf+1)
Q2d[120:320] = 100
Q2d[320:520] = 10
Q2d[520:] = 80
Q2 = m.Param()
Q2.value = Q2d

# scaled inputs
m.inpt[0].value = Q1d * s.scale_[0] + s.min_[0]
m.inpt[1].value = Q2d * s.scale_[1] + s.min_[1]

# define Temperature output
Q0 = 0   # initial heater
T0 = 19  # ambient temperature
# scaled steady state ouput
T1_ss = m.Var(value=T0)
T2_ss = m.Var(value=T0)
m.Equation(T1_ss == (m.outpt[0]-s.min_[2])/s.scale_[2])
m.Equation(T2_ss == (m.outpt[1]-s.min_[3])/s.scale_[3])
# dynamic prediction
T1 = m.Var(value=T0)
T2 = m.Var(value=T0)
# time constant
tau = m.Param(value=120) # determine in a later exercise
# additional model equation for dynamics
m.Equation(tau*T1.dt()==-(T1-T0)+(T1_ss-T0))
m.Equation(tau*T2.dt()==-(T2-T0)+(T2_ss-T0))

# solve dynamic simulation
m.options.IMODE=4
m.solve()

# generate step test data on Arduino
# -------------------------------------
# import or generate data
# -------------------------------------
filename = 'tclab_dyn_data2.csv'
try:
    try:
        data = pd.read_csv(filename)
    except:
        url = 'https://apmonitor.com/do/uploads/Main/tclab_dyn_data2.txt'
        data = pd.read_csv(url)
except:
    # generate training data if data file not available
    import tclab
    # Connect to Arduino
    a = tclab.TCLab()
    fid = open(filename,'w')
    fid.write('Time,H1,H2,T1,T2\n')
    fid.close()
    # check for cool down
    i = 0
    while i<=10:
        i += 1 # upper limit on wait time
        T1m = a.T1
        T2m = a.T2
        print('T1: ' + str(a.T1) + ' T2: ' + str(a.T2))
        print('Sleep 30 sec')
        time.sleep(30)
        if (a.T1<30 and a.T2<30 and a.T1>=T1m-0.2 and a.T2>=T2m-0.2):
            break  # continue when conditions met
        else:
            print('Not at ambient temperature')
    # run step test (10 min)
    for i in range(tf+1):
        # set heater values
        a.Q1(Q1d[i])
        a.Q2(Q2d[i])
        print('Time: ' + str(i) + \
              ' H1: ' + str(Q1d[i]) + \
              ' H2: ' + str(Q2d[i]) + \
              ' T1: ' + str(a.T1)   + \
              ' T2: ' + str(a.T2))
        # wait 1 second
        time.sleep(1)
        fid = open(filename,'a')
        fid.write(str(i)+','+str(Q1d[i])+','+str(Q2d[i])+',' \
                  +str(a.T1)+','+str(a.T2)+'\n')
        fid.close()
    # close connection to Arduino
    a.close()
    # read data file
    data = pd.read_csv(filename)

# plot prediction and measurement
plt.figure()
plt.subplot(2,1,1)
plt.plot(m.time,Q1.value,'r-',label='Heater 1')
plt.plot(m.time,Q2.value,'b--',label='Heater 2')
plt.ylabel('Heater (%)')
plt.legend(loc='best')
plt.subplot(2,1,2)
plt.plot(data['Time'],data['T1'],'r.',label='T1 Measured')
plt.plot(data['Time'],data['T2'],'b.',label='T2 Measured')
plt.plot(m.time,T1.value,'k-',label='T1 Predicted')
plt.plot(m.time,T2.value,'k--',label='T2 Predicted')
plt.ylabel('Temperature (degC)')
plt.legend(loc='best')
plt.xlabel('Time (sec)')
plt.savefig('tclab_dyn_pred.png')

plt.show()

See also:

Advanced Control Lab Overview

GEKKO Documentation

TCLab Documentation

TCLab Files on GitHub

Basic (PID) Control Lab