python-3.x - 如何在状态空间模型中添加时间延迟

Question

我最近尝试通过状态空间模型控制我的 TCLab Arduino。我参考了State Space Models，将一个一阶线性系统（无时延）转化为状态空间形式，控制效果还不错。现在想用一阶加死时间模型来控制实验室，但不知道如何将FOPDT模型转化为状态空间形式。如何在状态空间模型中添加时间延迟？

这是代码：

import tclab
import numpy as np
import time
import matplotlib.pyplot as plt
from gekko import GEKKO
import json

# Connect to Arduino
# a = tclab.TCLab()
a = tclab.TCLabModel()

# 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

Q1_ss = 0
#########################################################
# Initialize Model
#########################################################
tau = 160.0
kp = 0.6
Am = np.zeros((1,1))
Bm = np.zeros((1,1))
Cm = np.zeros((1,1))

Am[0, 0] = - 1/tau
Bm[0, 0] = kp/tau
Cm[0, 0] = 1

# state space simulation
m = GEKKO(remote=False)
x,y,u = m.state_space(Am,Bm,Cm,D=None)

mv = u[0]
cv = y[0]

mv.VALUE = Q1_ss
mv.STATUS = 1  # use to control temperature
mv.FSTATUS = 0 # no feedback measurement
mv.LOWER = 0.0
mv.UPPER = 100.0
mv.DMAX = 10.0
mv.COST = 0.0
mv.DCOST = 0.1

cv.VALUE = a.T1
cv.STATUS = 1     # minimize error with setpoint range
cv.FSTATUS = 1    # receive measurement
cv.TR_INIT = 2    # reference trajectory
cv.TAU = 60       # time constant for response

m.time = np.linspace(0, 160, 81)
m.options.IMODE   = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES   = 2 # Collocation nodes
m.options.MAX_TIME = 10
##################################################################

# Create plot
plt.figure()
plt.ion()
plt.show()

filter_tc1 = []

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 = Q1_ss
try:
    for i in range(1,loops):
        # Sleep time
        sleep_max = 2.0
        print(time.time() - prev_time)
        sleep = sleep_max - (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
        curr_T1 = a.T1
        last_T1 = curr_T1
        avg_T1 = movefilter(filter_tc1, last_T1, 3)
        T1[i] = curr_T1

        ###############################
        ### MPC CONTROLLER          ###
        ###############################
        cv.MEAS = avg_T1
        # input setpoint with deadband +/- DT
        DT = 0.5
        cv.SPHI = Tsp1[i] + DT
        cv.SPLO = Tsp1[i] - DT
        # solve MPC
        m.solve(disp=False)
        # test for successful solution
        if (m.options.APPSTATUS==1):
            # retrieve the first Q value
            Q1s[i] = mv.NEWVAL
            print('Q1.NEWVAL', mv.NEWVAL)
            with open(m.path+'//results.json') as f:
                results = json.load(f)
        else:
            # not successful, set heater to zero
            Q1s[i] = last_Q1
            print('last_Q1', mv.NEWVAL)
        print(m.path)
        # Write output (0-100)
        a.Q1(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'$T_1 Setpoint$')
        cv_name = cv.NAME + '.bcv'
        print(cv_name)
        plt.plot(tm[i]+m.time,results[cv_name],'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,mv.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()

标签： python-3.xgekko

Answer 1

使用delayGekko 中的功能添加时间延迟。这是一个例子。要将其添加到状态空间模型中，您可以延迟输入mv或输出cv。这是输出延迟的状态空间模型。

# state space simulation
m = GEKKO(remote=False)
x,y,u = m.state_space(Am,Bm,Cm,D=None)
mv = u[0]
cv_in = y[0]

cv = m.CV()
m.delay(cv_in,cv,4) # delay of 4 steps (8 sec)

import tclab
import numpy as np
import time
import matplotlib.pyplot as plt
from gekko import GEKKO
import json

# Connect to Arduino
# a = tclab.TCLab()
a = tclab.TCLabModel()

# 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

Q1_ss = 0
#########################################################
# Initialize Model
#########################################################
tau = 160.0
kp = 0.6
Am = np.zeros((1,1))
Bm = np.zeros((1,1))
Cm = np.zeros((1,1))

Am[0, 0] = - 1/tau
Bm[0, 0] = kp/tau
Cm[0, 0] = 1

# state space simulation
m = GEKKO(remote=False)
x,y,u = m.state_space(Am,Bm,Cm,D=None)
mv = u[0]
cv_in = y[0]

cv = m.CV()
m.delay(cv_in,cv,4) # delay of 4 steps (8 sec)

mv.VALUE = Q1_ss
mv.STATUS = 1  # use to control temperature
mv.FSTATUS = 0 # no feedback measurement
mv.LOWER = 0.0
mv.UPPER = 100.0
mv.DMAX = 10.0
mv.COST = 0.0
mv.DCOST = 0.1

cv.VALUE = a.T1
cv.STATUS = 1     # minimize error with setpoint range
cv.FSTATUS = 1    # receive measurement
cv.TR_INIT = 2    # reference trajectory
cv.TAU = 60       # time constant for response

m.time = np.linspace(0, 160, 81)
m.options.IMODE   = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES   = 2 # Collocation nodes
m.options.MAX_TIME = 10
##################################################################

# Create plot
plt.figure()
plt.ion()
plt.show()

filter_tc1 = []

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 = Q1_ss
try:
    for i in range(1,loops):
        # Sleep time
        sleep_max = 2.0
        print(time.time() - prev_time)
        sleep = sleep_max - (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
        curr_T1 = a.T1
        last_T1 = curr_T1
        avg_T1 = movefilter(filter_tc1, last_T1, 3)
        T1[i] = curr_T1

        ###############################
        ### MPC CONTROLLER          ###
        ###############################
        cv.MEAS = avg_T1
        # input setpoint with deadband +/- DT
        DT = 0.5
        cv.SPHI = Tsp1[i] + DT
        cv.SPLO = Tsp1[i] - DT
        # solve MPC
        m.solve(disp=False)
        # test for successful solution
        if (m.options.APPSTATUS==1):
            # retrieve the first Q value
            Q1s[i] = mv.NEWVAL
            print('Q1.NEWVAL', mv.NEWVAL)
            with open(m.path+'//results.json') as f:
                results = json.load(f)
        else:
            # not successful, set heater to zero
            Q1s[i] = last_Q1
            print('last_Q1', mv.NEWVAL)
        print(m.path)
        # Write output (0-100)
        a.Q1(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'$T_1 Setpoint$')
        cv_name = cv.NAME + '.bcv'
        print(cv_name)
        plt.plot(tm[i]+m.time,results[cv_name],'k-.',\
                 label=r'$T_1$ predicted',lw=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-',lw=3,label=r'$Q_1$')
        plt.plot(tm[i]+m.time,mv.value,'k-.',\
                 label=r'$Q_1$ plan',lw=3)
        # plt.plot(tm[0:i],Q2s[0:i],'b:',lw=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()