python-3.xgekko
Why the delay parameter affects the prediction curve?
I put the result of Gekko's calculation into the queue, after a delay, write the first value of the queue to TCLab Arduino. I use this method to simulate a factory large time delay system, then I optimize Gekko parameters to achieve better control effect. When I add a delay=1 in the model, I got a pretty good prediction curve:
The final control effect is also pretty good:
But when I set delay=80, no other parameters are modified, the prediction curve is not ideal：
The final control effect is also bad:
Why the delay parameter affects the prediction curve? I think the reference trajectory should also shift with time delay. How could I solve this problem?
Here is the code:
import tclab
import numpy as np
import time
import matplotlib.pyplot as plt
from gekko import GEKKO
import _thread
import queue
import threading
import json
# Connect to Arduino
a = tclab.TCLabModel()
R = threading.Lock()
# Turn LED on
print('LED On')
a.LED(100)
# Simulate a time delay
delay = 80
# Run time in minutes
run_time = 60.0
# Number of cycles
loops = int(60.0*run_time)
tm = np.zeros(loops)
# Temperature (K)
T1 = np.ones(loops) * a.T1 # temperature (degC)
Tsp1 = np.ones(loops) * 40.0 # set point (degC)
# heater values
Q1s = np.ones(loops) * 0.0
#########################################################
# Initialize Model
#########################################################
# use remote=True for MacOS
m = GEKKO(name='tclab-mpc',remote=False)
# 240 second time horizon
m.time = np.linspace(0,240,121)
# Parameters
Q1_ss = m.Param(value=0)
TC1_ss = m.Param(value=a.T1)
Kp = m.Param(value=1.0)
tau = m.Param(value=120.0)
# Manipulated variable
Q1 = m.MV(value=Q1_ss.VALUE, name='q1')
Q1.STATUS = 1 # use to control temperature
Q1.FSTATUS = 0 # no feedback measurement
Q1.LOWER = 0.0
Q1.UPPER = 100.0
Q1.DMAX = 50
Q1.DCOST = 2.0
# Controlled variable
TC1 = m.CV(value=TC1_ss.VALUE, name='tc1')
TC1.STATUS = 1 # minimize error with setpoint range
TC1.FSTATUS = 1 # receive measurement
TC1.TR_INIT = 2 # reference trajectory
TC1.TAU = 30 # time constant for response
# 添加延时
Q1d=m.Var()
m.delay(Q1, Q1d, delay)
# Equation
m.Equation(tau * TC1.dt() + (TC1-TC1_ss) == Kp * Q1d)
# Steady-state initialization
m.options.IMODE = 1
m.solve()
# Global Options
m.options.IMODE = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES = 2 # Collocation nodes
m.options.SOLVER = 1 # 1=APOPT, 3=IPOPT
##################################################################
# Create plot
plt.figure()
plt.ion()
plt.show()
filter_tc1 = []
q = queue.Queue()
flag = False
def setQ1():
global flag
global a
last_time = time.time()
while True:
sleep_max = 2.0
sleep = sleep_max - (time.time() - last_time)
print("q.qsize()", q.qsize())
if sleep >= 0.01:
time.sleep(sleep)
else:
time.sleep(0.01)
# Record time and change in time
last_time = time.time()
while q.qsize() >= delay:
q1 = q.get()
print(f'Q1: {q1} ')
try:
R.acquire()
print("write Q1：", a.Q1(float(q1)))
R.release()
except:
print("convertion error!")
_thread.start_new_thread(setQ1, ())
# Rolling average filtering
def movefilter(predata, new, n):
if len(predata) < n:
predata.append(new)
else:
predata.pop(0)
predata.append(new)
return np.average(predata)
# Main Loop
start_time = time.time()
prev_time = start_time
last_Q1 = 0
try:
for i in range(1,loops):
# Sleep time
sleep_max = 2.0
sleep = sleep_max - (time.time() - prev_time)
print(time.time() - prev_time)
if sleep>=0.01:
time.sleep(sleep)
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 Kelvin
R.acquire()
curr_T1 = a.T1
R.release()
last_T1 = curr_T1
avg_T1 = movefilter(filter_tc1, last_T1, 3)
T1[i] = curr_T1
# T1[i] = a.T1
# T2[i] = a.T2
###############################
### MPC CONTROLLER ###
###############################
TC1.MEAS = avg_T1
# input setpoint with deadband +/- DT
DT = 1.0
TC1.SPHI = Tsp1[i] + DT
TC1.SPLO = Tsp1[i] - DT
try:
# solve MPC
m.solve(disp=False)
except:
pass
# test for successful solution
if (m.options.APPSTATUS==1):
# retrieve the first Q value
Q1s[i] = Q1.NEWVAL
with open(m.path+'//results.json') as f:
results = json.load(f)
else:
# not successful, set heater to zero
Q1s[i] = 0
# Write output (0-100)
q.put(Q1s[i])
# Plot
plt.clf()
ax=plt.subplot(2,1,1)
ax.grid()
plt.plot(tm[0:i],T1[0:i],'ro',markersize=3,label=r'$T_1$')
plt.plot(tm[0:i],Tsp1[0:i],'b-',markersize=3,label=r'$T_1 Setpoint$')
plt.plot(tm[i]+m.time,results['tc1.bcv'],'k-.',\
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='best')
ax=plt.subplot(2,1,2)
ax.grid()
plt.plot(tm[0:i],Q1s[0:i],'r-',linewidth=3,label=r'$Q_1$')
plt.plot(tm[i]+m.time,Q1.value,'k-.',\
label=r'$Q_1$ plan',linewidth=3)
# plt.plot(tm[0:i],Q2s[0:i],'b:',LineWidth=3,label=r'$Q_2$')
plt.ylabel('Heaters')
plt.xlabel('Time (sec)')
plt.legend(loc='best')
plt.draw()
plt.pause(0.05)
# Turn off heaters
a.Q1(0)
a.Q2(0)
print('Shutting down')
a.close()
# Allow user to end loop with Ctrl-C
except KeyboardInterrupt:
# Disconnect from Arduino
a.Q1(0)
a.Q2(0)
print('Shutting down')
a.close()
# Make sure serial connection still closes when there's an error
except:
# Disconnect from Arduino
a.Q1(0)
a.Q2(0)
print('Error: Shutting down')
a.close()
raise
Solution
The controller is working as intended. The problem is a well-known issue with model mismatch and delay. Classical control methods are to use a Smith Predictor to compensate for the delay. With MPC, the delay is built into the model, similar to the function of the Smith Predictor. If you change the model to:
Kp = m.Param(value=0.7)
tau = m.Param(value=180.0)
then the performance is improved:
A modification to the reference trajectory also improves performance because the controller is focused on the long-term target versus the near-term error that it can't control.
Method 1 - Open Reference Trajectory at Beginning
TC1.TR_INIT = 2 # reference trajectory
TC1.TR_OPEN = 20 # more focus on final destination
TC1.TAU = 60 # time constant for response
Method 2 - Start Penalizing Later
Use CV_WGT_START to only penalize after a certain amount of time delay.
TC1.TR_INIT = 0 # reference trajectory
m.options.CV_WGT_START = 80
The parameters need one more adjustment to better match the process.
Kp = m.Param(value=0.8)
tau = m.Param(value=160.0)
Method 3: Define Own Reference Trajectory
If you do want a custom reference trajectory then you can define a new variable SP that is delayed as SPd. Define a new CV error that is the difference between TC1 and the delayed reference trajectory.
SP = m.Var()
m.Equation(30 * SP.dt() == -SP + 40)
SPd = m.Var()
m.delay(SP, SPd, delay)
error = m.CV(value=0)
m.Equation(error==SPd - TC1)
error.STATUS = 1 # minimize error with setpoint range
error.FSTATUS = 0 # receive measurement
error.TR_INIT = 0 # reference trajectory
error.SPHI = 0.5 # drive error close to 0
error.SPLO = -0.5 # drive error close to 0
With this approach, you'll need to work out a method to update the error measurement for measurement feedback.
There are also many times that the MPC calculations slightly exceed the cycle time. This is creating a model mismatch that you can help by increasing the MPC cycle time to 3 seconds.
Modified script
import tclab
import numpy as np
import time
import matplotlib.pyplot as plt
from gekko import GEKKO
import _thread
import queue
import threading
import json
# Connect to Arduino
a = tclab.TCLabModel()
R = threading.Lock()
# Turn LED on
print('LED On')
a.LED(100)
# Simulate a time delay
delay = 80
# Run time in minutes
run_time = 60.0
# Number of cycles
loops = int(60.0*run_time)
tm = np.zeros(loops)
# Temperature (K)
T1 = np.ones(loops) * a.T1 # temperature (degC)
Tsp1 = np.ones(loops) * 40.0 # set point (degC)
# heater values
Q1s = np.ones(loops) * 0.0
#########################################################
# Initialize Model
#########################################################
# use remote=True for MacOS
m = GEKKO(name='tclab-mpc',remote=False)
# 240 second time horizon
m.time = np.linspace(0,240,121)
# Parameters
Q1_ss = m.Param(value=0)
TC1_ss = m.Param(value=a.T1)
Kp = m.Param(value=0.7)
tau = m.Param(value=180.0)
# Manipulated variable
Q1 = m.MV(value=Q1_ss.VALUE, name='q1')
Q1.STATUS = 1 # use to control temperature
Q1.FSTATUS = 0 # no feedback measurement
Q1.LOWER = 0.0
Q1.UPPER = 100.0
Q1.DMAX = 50
Q1.DCOST = 2.0
# Controlled variable
TC1 = m.CV(value=TC1_ss.VALUE, name='tc1')
TC1.STATUS = 1 # minimize error with setpoint range
TC1.FSTATUS = 1 # receive measurement
TC1.TR_INIT = 0 # reference trajectory
m.options.CV_WGT_START = 80
# 添加延时
Q1d=m.Var()
m.delay(Q1, Q1d, delay)
# Equation
m.Equation(tau * TC1.dt() + (TC1-TC1_ss) == Kp * Q1d)
# Steady-state initialization
m.options.IMODE = 1
m.solve()
# Global Options
m.options.IMODE = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES = 2 # Collocation nodes
m.options.SOLVER = 1 # 1=APOPT, 3=IPOPT
##################################################################
# Create plot
plt.figure()
plt.ion()
plt.show()
filter_tc1 = []
q = queue.Queue()
flag = False
def setQ1():
global flag
global a
last_time = time.time()
while True:
sleep_max = 2.0
sleep = sleep_max - (time.time() - last_time)
print("q.qsize()", q.qsize())
if sleep >= 0.01:
time.sleep(sleep)
else:
time.sleep(0.01)
# Record time and change in time
last_time = time.time()
while q.qsize() >= delay:
q1 = q.get()
print(f'Q1: {q1} ')
try:
R.acquire()
print("write Q1：", a.Q1(float(q1)))
R.release()
except:
print("convertion error!")
_thread.start_new_thread(setQ1, ())
# Rolling average filtering
def movefilter(predata, new, n):
if len(predata) < n:
predata.append(new)
else:
predata.pop(0)
predata.append(new)
return np.average(predata)
# Main Loop
start_time = time.time()
prev_time = start_time
last_Q1 = 0
try:
for i in range(1,loops):
# Sleep time
sleep_max = 2.0
sleep = sleep_max - (time.time() - prev_time)
print(time.time() - prev_time)
if sleep>=0.01:
time.sleep(sleep)
else:
print('Warning: Dynamic mismatch from excess MPC time')
print(' Consider increasing the cycle time to 3+ sec')
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 Kelvin
R.acquire()
curr_T1 = a.T1
R.release()
last_T1 = curr_T1
avg_T1 = movefilter(filter_tc1, last_T1, 3)
T1[i] = curr_T1
# T1[i] = a.T1
# T2[i] = a.T2
###############################
### MPC CONTROLLER ###
###############################
TC1.MEAS = avg_T1
# input setpoint with deadband +/- DT
DT = 1.0
TC1.SPHI = Tsp1[i] + DT
TC1.SPLO = Tsp1[i] - DT
try:
# solve MPC
m.solve(disp=False)
except:
pass
# test for successful solution
if (m.options.APPSTATUS==1):
# retrieve the first Q value
Q1s[i] = Q1.NEWVAL
with open(m.path+'//results.json') as f:
results = json.load(f)
else:
# not successful, set heater to zero
Q1s[i] = 0
# Write output (0-100)
q.put(Q1s[i])
# Plot
plt.clf()
ax=plt.subplot(2,1,1)
ax.grid()
plt.plot(tm[0:i],T1[0:i],'ro',markersize=3,label=r'$T_1$')
plt.plot(tm[0:i],Tsp1[0:i],'b-',markersize=3,label=r'$T_1 Setpoint$')
plt.plot(tm[i]+m.time,results['tc1.bcv'],'k-.',\
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='best')
ax=plt.subplot(2,1,2)
ax.grid()
plt.plot(tm[0:i],Q1s[0:i],'r-',linewidth=3,label=r'$Q_1$')
plt.plot(tm[i]+m.time,Q1.value,'k-.',\
label=r'$Q_1$ plan',linewidth=3)
# plt.plot(tm[0:i],Q2s[0:i],'b:',LineWidth=3,label=r'$Q_2$')
plt.ylabel('Heaters')
plt.xlabel('Time (sec)')
plt.legend(loc='best')
plt.draw()
plt.pause(0.05)
# Turn off heaters
a.Q1(0)
a.Q2(0)
print('Shutting down')
a.close()
# Allow user to end loop with Ctrl-C
except KeyboardInterrupt:
# Disconnect from Arduino
a.Q1(0)
a.Q2(0)
print('Shutting down')
a.close()
# Make sure serial connection still closes when there's an error
except:
# Disconnect from Arduino
a.Q1(0)
a.Q2(0)
print('Error: Shutting down')
a.close()
raise
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