python - 如何将 FOPDT 模型的死区时间应用于 MPC gekko 中的操纵变量

Question

我正在尝试使用 FOPDT 方程中先前估计的 k、tau 和 theta 值构建 MPC 模型。我实现了这个建议以使用 cspline 估计死区时间:How to estimate theta value in FOPDT equation using gekko? .

但是，我不能对 MPC 做同样的事情，因为我不能使用 MV 作为 cspline 的第二个参数来应用死区时间。如果我为第二个参数使用 gekko 变量，则 MV 不会改变，因为它们不存在于等式中。我有两个 MV，一个 CV 和两个干扰变量。在这种情况下如何应用死区时间？谢谢

import numpy as np
import time
import plotly.express as px 
from gekko import GEKKO
import json
from datetime import datetime

start_time_count = datetime.now().strftime('%Y-%m-%d %H:%M:%S')
print("start_time: ", start_time_count)

dist1 = d19jcSliceMPC['Cond_PID_SP'].values
mv1 = d19jcSliceMPC['Front_PID_PV'].values
mv2 = d19jcSliceMPC['Rear_PID_PV'].values
dist2 = d19jcSliceMPC['Pull_rolling'].values
cv1 = d19jcSliceMPC['Cond_Center_Btm_TC'].values

run_time = 3.0 * 60.0 
n = int(0.2*run_time)

Tsp1 = 1163.0 #setpoint

m = GEKKO(name='MPCbtmTC',remote=False)
m.time = np.linspace(0,n-1,n)
time_uc = m.Param(m.time)

# MV
Front = m.MV(value=mv1)
Front_ss = m.Param(value=mv1[0])
KpFront = m.Param(value=1.685312)
tauFront = m.Param(value=5.770839)
thetaFront = m.Param(value=0.114705)
t1 = np.linspace(-1,n-1,n)
ucFront = m.Var(); tm1 = m.Var(); m.Equation(tm1==time_uc-thetaFront)
m.cspline(tm1,ucFront,t1,np.array(Front),bound_x=False)

Rear = m.MV(value=mv2)
Rear_ss = m.Param(value=mv2[0])
KpRear = m.Param(value=0.1)
tauRear = m.Param(value=36.0)
thetaRear = m.Param(value=3.779397)
t2 = np.linspace(-4,n-1,n)
ucRear = m.Var(); tm2 = m.Var(); m.Equation(tm2==time_uc-thetaRear)
m.cspline(tm2,ucRear,t2,np.array(Rear),bound_x=False)

Front.STATUS = 1  # use to control temperature
Front.FSTATUS = 0 # no feedback measurement
Front.LOWER = 1160.0
Front.UPPER = 1200.0
Front.DMAX = 2.0
Front.COST = 0.0
Front.DCOST = 1.0e-4

Rear.STATUS = 1  # use to control temperature
Rear.FSTATUS = 0 # no feedback measurement
Rear.LOWER = 1180.0
Rear.UPPER = 1220.0
Rear.DMAX = 2.0
Rear.COST = 0.0
Rear.DCOST = 1.0e-4

# Parameters (disturbance)
CondSP = m.Param(value=dist1)
CondSP_ss = m.Param(value=dist1[0])
KpCondSP = m.Param(value=4.990293)
tauCondSP = m.Param(value=29.272660)
thetaCondSP = m.Param(value=2.554230)
t3 = np.linspace(-3,n-1,n)
ucCondSP = m.Var(); tm3 = m.Var(); m.Equation(tm3==time_uc-thetaCondSP)
m.cspline(tm3,ucCondSP,t3,dist1,bound_x=False)

Pull = m.Param(value=dist2)
Pull_ss = m.Param(value=dist2[0])
KpPull = m.Param(value=0.151304)
tauPull = m.Param(value=4.128567)
thetaPull = m.Param(value=0.0)
t4 = np.linspace(-0,n-1,n)
ucPull = m.Var(); tm4 = m.Var(); m.Equation(tm4==time_uc-thetaPull)
m.cspline(tm4,ucPull,t4,dist2,bound_x=False)

# Controlled variable
TC1_ss = m.Param(value=cv1[0])
TC1 = m.CV(value=TC1_ss.value)
TC1.STATUS = 1     # minimize error with setpoint range
TC1.FSTATUS = 1    # receive measurement
TC1.TR_INIT = 2    # reference trajectory
TC1.TAU = 2       # time constant for response

# Equation
m.Equation(TC1.dt()==(KpFront*(ucFront-Front_ss)-(TC1-TC1_ss))/tauFront + (KpRear*(ucRear-Rear_ss)-(TC1-TC1_ss))/tauRear+ 
                     (KpCondSP*(ucCondSP-CondSP_ss)-(TC1-TC1_ss))/tauCondSP + (KpPull*(ucPull-Pull_ss)-(TC1-TC1_ss))/tauPull)

# Global Options
m.options.IMODE   = 6 # MPC
m.options.CV_TYPE = 1 # Objective type
m.options.NODES   = 3 # Collocation nodes
m.options.SOLVER  = 1 # 1=APOPT, 3=IPOPT

TC1.MEAS = cv1[0]
# input setpoint with deadband +/- DT
DT = 0.1
TC1.SPHI = Tsp1 + DT
TC1.SPLO = Tsp1 - DT
# solve MPC
m.solve(disp=False)    
# get additional solution information
with open(m.path+'//results.json') as f:
    results = json.load(f)

finish_time_count = datetime.now().strftime('%Y-%m-%d %H:%M:%S')
print("end_time: ", finish_time_count)

df_plot = pd.DataFrame({'DateTime' : d19jcSliceMPC.time,
                        'CV (TC1)' : results['v9.bcv'],
                        'SPHI' : results['v9.sp_hi'],
                        'SPLO' : results['v9.sp_lo'],
                        'Front' : Front,
                        'Rear' : Rear})
figGekko = px.line(df_plot, 
                   x='DateTime',
                   y=['CV (TC1)','SPHI','SPLO','Front','Rear'],
                   labels={"value": "Degrees Celsius"},
                   title = "MPC")
figGekko.update_layout(legend_title_text='')
figGekko.show()

编辑:

按照提示，我改成了

ucFront = m.Var(); m.Equation(ucFront==Front) 
tm1 = m.Var(); m.Equation(tm1==time_uc-thetaFront)
m.cspline(tm1,ucFront,t1,np.array(Front),bound_x=False)

但是我得到这个错误:

Error: Exception: Access Violation
At line 359 of file ./f90/cqp.f90
Traceback: not available, compile with -ftrace=frame or -ftrace=full

Error: 'results.json' not found. Check above for additional error details

如果我只保留 MV 作为未移位的输入，我会得到与之前相同的错误

TypeError: y_data must be a python list or numpy array

Answer 1

正如 Junho Park 正确观察到的那样，您可以创建另一个变量 x，例如:

MV = m.MV()  # use MV in MPC application

x  = m.Var() # use x with cspline function
m.Equation(x==MV) # connect x and MV

cspline 对象提示 MV，因为它想要一个计算变量，而不是默认情况下固定且消耗一定自由度的类型。