您引用的示例问题使用默认IPOPT求解器。要获得二进制或整数解决方案，请切换到APOPT求解器。
m.options.SOLVER = 1
您还需要做另一件事，因为您Q1从更改m.MV()为一种m.Intermediate类型。在您访问该Q1值的循环中，进行以下修改：
Q1s[i+1] = Q1.value[1]
Q2s[i+1] = Q2.NEWVAL
Q2仍然是 0 到 100% 之间的连续值，您仍然可以使用该Q2.NEWVAL参数访问移动计划的第一步。对于Q1，您需要使用Q1.value[1]来访问第一步，因为它是一种m.Intermediate()类型并且没有NEWVAL属性。make_mp4=True该脚本会在安装时生成视频动画ffmpeg。动画显示Q1现在是ON/OFF（0 或 1）并且Q2仍然是 0 到 100% 之间的连续值。
具有二元变量的模型预测控制
import numpy as np
import time
import matplotlib.pyplot as plt
import random
import json
# get gekko package with:
# pip install gekko
from gekko import GEKKO
# get tclab package with:
# pip install tclab
from tclab import TCLab
# Connect to Arduino
a = TCLab()
# Make an MP4 animation?
make_mp4 = False
if make_mp4:
import imageio # required to make animation
import os
try:
os.mkdir('./figures')
except:
pass
# Final time
tf = 10 # min
# number of data points (every 3 seconds)
n = tf * 10 + 1
# Percent Heater (0-100%)
Q1s = np.zeros(n)
Q2s = np.zeros(n)
# Temperatures (degC)
T1m = a.T1 * np.ones(n)
T2m = a.T2 * np.ones(n)
# Temperature setpoints
T1sp = T1m[0] * np.ones(n)
T2sp = T2m[0] * np.ones(n)
# Heater set point steps about every 150 sec
T1sp[3:] = 40.0
T2sp[20:] = 30.0
T1sp[40:] = 32.0
T2sp[60:] = 35.0
T1sp[80:] = 45.0
#########################################################
# Initialize Model
#########################################################
# use remote=True for MacOS
m = GEKKO(name='tclab-mpc',remote=False)
# with a local server
#m = GEKKO(name='tclab-mpc',server='http://127.0.0.1',remote=True)
# Control horizon, non-uniform time steps
m.time = [0,6,10,20,30,40,50,60]
# Parameters from Estimation
K1 = m.FV(value=0.607)
K2 = m.FV(value=0.293)
K3 = m.FV(value=0.24)
tau12 = m.FV(value=192)
tau3 = m.FV(value=15)
# don't update parameters with optimizer
K1.STATUS = 0
K2.STATUS = 0
K3.STATUS = 0
tau12.STATUS = 0
tau3.STATUS = 0
# Manipulated variables
Q1b = m.MV(value=0,lb=0,ub=1,name='q1',integer=True)
Q1b.STATUS = 1 # manipulated
Q1b.FSTATUS = 0 # not measured
Q1b.DMAX = 1.0
Q1b.DCOST = 0.1
Q1 = m.Intermediate(Q1b*100)
Q2 = m.MV(value=0,name='q2')
Q2.STATUS = 1 # manipulated
Q2.FSTATUS = 0 # not measured
Q2.DMAX = 30.0
Q2.DCOST = 0.1
Q2.UPPER = 100.0
Q2.LOWER = 0.0
# State variables
TH1 = m.SV(value=T1m[0])
TH2 = m.SV(value=T2m[0])
# Controlled variables
TC1 = m.CV(value=T1m[0],name='tc1')
TC1.STATUS = 1 # drive to set point
TC1.FSTATUS = 1 # receive measurement
TC1.TAU = 40 # response speed (time constant)
TC1.TR_INIT = 1 # reference trajectory
TC1.TR_OPEN = 0
TC2 = m.CV(value=T2m[0],name='tc2')
TC2.STATUS = 1 # drive to set point
TC2.FSTATUS = 1 # receive measurement
TC2.TAU = 0 # response speed (time constant)
TC2.TR_INIT = 0 # dead-band
TC2.TR_OPEN = 1
Ta = m.Param(value=23.0) # degC
# Heat transfer between two heaters
DT = m.Intermediate(TH2-TH1)
# Empirical correlations
m.Equation(tau12 * TH1.dt() + (TH1-Ta) == K1*Q1 + K3*DT)
m.Equation(tau12 * TH2.dt() + (TH2-Ta) == K2*Q2 - K3*DT)
m.Equation(tau3 * TC1.dt() + TC1 == TH1)
m.Equation(tau3 * TC2.dt() + TC2 == TH2)
# Global Options
m.options.IMODE = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES = 3 # Collocation nodes
m.options.SOLVER = 1 # IPOPT
m.options.COLDSTART = 1 # COLDSTART on first cycle
##################################################################
# Create plot
plt.figure(figsize=(10,7))
plt.ion()
plt.show()
# Main Loop
start_time = time.time()
prev_time = start_time
tm = np.zeros(n)
try:
for i in range(1,n-1):
# Sleep time
sleep_max = 6.0
sleep = sleep_max - (time.time() - prev_time)
if sleep>=0.01:
time.sleep(sleep-0.01)
else:
time.sleep(0.01)
# Record time and change in time
t = time.time()
dt = t - prev_time
prev_time = t
tm[i] = t - start_time
# Read temperatures in Celsius
T1m[i] = a.T1
T2m[i] = a.T2
# Insert measurements
TC1.MEAS = T1m[i]
TC2.MEAS = T2m[i]
# Adjust setpoints
db1 = 1.0 # dead-band
TC1.SPHI = T1sp[i] + db1
TC1.SPLO = T1sp[i] - db1
db2 = 0.2
TC2.SPHI = T2sp[i] + db2
TC2.SPLO = T2sp[i] - db2
# Adjust heaters with MPC
m.solve()
if m.options.APPSTATUS == 1:
# Retrieve new values
Q1s[i+1] = Q1.value[1]
Q2s[i+1] = Q2.NEWVAL
# get additional solution information
with open(m.path+'//results.json') as f:
results = json.load(f)
else:
# Solution failed
Q1s[i+1] = 0.0
Q2s[i+1] = 0.0
# Write new heater values (0-100)
a.Q1(Q1s[i])
a.Q2(Q2s[i])
# Plot
plt.clf()
ax=plt.subplot(3,1,1)
ax.grid()
plt.plot(tm[0:i+1],T1sp[0:i+1]+db1,'k-',\
label=r'$T_1$ target',linewidth=3)
plt.plot(tm[0:i+1],T1sp[0:i+1]-db1,'k-',\
label=None,linewidth=3)
plt.plot(tm[0:i+1],T1m[0:i+1],'r.',label=r'$T_1$ measured')
plt.plot(tm[i]+m.time,results['tc1.bcv'],'r-',\
label=r'$T_1$ predicted',linewidth=3)
plt.plot(tm[i]+m.time,results['tc1.tr_hi'],'k--',\
label=r'$T_1$ trajectory')
plt.plot(tm[i]+m.time,results['tc1.tr_lo'],'k--')
plt.ylabel('Temperature (degC)')
plt.legend(loc=2)
ax=plt.subplot(3,1,2)
ax.grid()
plt.plot(tm[0:i+1],T2sp[0:i+1]+db2,'k-',\
label=r'$T_2$ target',linewidth=3)
plt.plot(tm[0:i+1],T2sp[0:i+1]-db2,'k-',\
label=None,linewidth=3)
plt.plot(tm[0:i+1],T2m[0:i+1],'b.',label=r'$T_2$ measured')
plt.plot(tm[i]+m.time,results['tc2.bcv'],'b-',\
label=r'$T_2$ predict',linewidth=3)
plt.plot(tm[i]+m.time,results['tc2.tr_hi'],'k--',\
label=r'$T_2$ range')
plt.plot(tm[i]+m.time,results['tc2.tr_lo'],'k--')
plt.ylabel('Temperature (degC)')
plt.legend(loc=2)
ax=plt.subplot(3,1,3)
ax.grid()
plt.plot([tm[i],tm[i]],[0,100],'k-',\
label='Current Time',linewidth=1)
plt.plot(tm[0:i+1],Q1s[0:i+1],'r.-',\
label=r'$Q_1$ history',linewidth=2)
plt.plot(tm[i]+m.time,Q1.value,'r-',\
label=r'$Q_1$ plan',linewidth=3)
plt.plot(tm[0:i+1],Q2s[0:i+1],'b.-',\
label=r'$Q_2$ history',linewidth=2)
plt.plot(tm[i]+m.time,Q2.value,'b-',
label=r'$Q_2$ plan',linewidth=3)
plt.plot(tm[i]+m.time[1],Q1.value[1],color='red',\
marker='.',markersize=15)
plt.plot(tm[i]+m.time[1],Q2.value[1],color='blue',\
marker='X',markersize=8)
plt.ylabel('Heaters')
plt.xlabel('Time (sec)')
plt.legend(loc=2)
plt.draw()
plt.pause(0.05)
if make_mp4:
filename='./figures/plot_'+str(i+10000)+'.png'
plt.savefig(filename)
# Turn off heaters and close connection
a.Q1(0)
a.Q2(0)
a.close()
# Save figure
plt.savefig('tclab_mpc.png')
# generate mp4 from png figures in batches of 350
if make_mp4:
images = []
iset = 0
for i in range(1,n-1):
filename='./figures/plot_'+str(i+10000)+'.png'
images.append(imageio.imread(filename))
if ((i+1)%350)==0:
imageio.mimsave('results_'+str(iset)+'.mp4', images)
iset += 1
images = []
if images!=[]:
imageio.mimsave('results_'+str(iset)+'.mp4', images)
# Allow user to end loop with Ctrl-C
except KeyboardInterrupt:
# Turn off heaters and close connection
a.Q1(0)
a.Q2(0)
a.close()
print('Shutting down')
plt.savefig('tclab_mpc.png')
# Make sure serial connection still closes when there's an error
except:
# Disconnect from Arduino
a.Q1(0)
a.Q2(0)
a.close()
print('Error: Shutting down')
plt.savefig('tclab_mpc.png')
raise