帶 GEKKO 的 MPC 中的變量邊界

Question

我正在嘗試使用 MPC 和 GEKKO 實現恆溫器控制。

狀態變量（溫度）應該在下面代碼中預先指定的下限和上限溫度值temp_low和temp_upper內。

兩者的界限在一天中都不同：每小時一個值。

目標函數是使用加熱的成本。 價格也隨着一天而變化， TOU如下。 T_external是在T_external的房間外部溫度。

如何實現它以使其優化？

這是我的嘗試：

from gekko import GEKKO
import numpy as np

m = GEKKO(remote=False)
m.time = np.linspace(0,23,24)

#initialize variables
T_external = [50.,50.,50.,50.,45.,45.,45.,60.,60.,63.,64.,45.,45.,50.,52.,53.,53.,54.,54.,53.,52.,51.,50.,45.]
temp_low = [55.,55.,55.,55.,55.,55.,55.,68.,68.,68.,68.,55.,55.,68.,68.,68.,68.,55.,55.,55.,55.,55.,55.,55.]
temp_upper = [75.,75.,75.,75.,75.,75.,75.,70.,70.,70.,70.,75.,75.,70.,70.,70.,70.,75.,75.,75.,75.,75.,75.,75.]
TOU = [0.05,0.05,0.05,0.05,0.05,0.05,0.05,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,0.05,0.05,0.05]

b = m.Param(value=1.)
k = m.Param(value=0.05)
T_e = m.Param(value=T_external)

u = m.MV(value=[0]*24, lb=[0.0]*24, ub=[1.]*24)
u.STATUS = 1  # allow optimizer to change

# Controlled Variable
T = m.SV(value=[60]*24, lb=temp_low, ub=temp_upper)

m.Equation(T.dt() == k*(T_e-T) + b*u)

m.Obj(np.dot(TOU,u))

m.options.IMODE = 6
m.solve(debug=True)

當我運行這個時，我得到：

@error: Model Expression
 *** Error in syntax of function string: Missing operator

Position: 4                   
 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
    ?

Answer 1

Gekko 需要將約束作為不等式表達式，其中將變量T與上TH或下TL值進行比較。 如果你有b=1. ，這導致了一個不可行的解決方案，因為加熱器的功率不足以將溫度保持在上限和下限內。 我將值更改為b=10以獲得可行的解決方案。

from gekko import GEKKO
import numpy as np

m = GEKKO(remote=False)
m.time = np.linspace(0,23,24)

#initialize variables
T_external = [50.,50.,50.,50.,45.,45.,45.,60.,60.,63.,\
              64.,45.,45.,50.,52.,53.,53.,54.,54.,\
              53.,52.,51.,50.,45.]
temp_low = [55.,55.,55.,55.,55.,55.,55.,68.,68.,68.,68.,\
            55.,55.,68.,68.,68.,68.,55.,55.,55.,55.,55.,55.,55.]
temp_upper = [75.,75.,75.,75.,75.,75.,75.,70.,70.,70.,70.,75.,\
              75.,70.,70.,70.,70.,75.,75.,75.,75.,75.,75.,75.]
TOU_v = [0.05,0.05,0.05,0.05,0.05,0.05,0.05,200.,200.,200.,200.,\
         200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,0.05,\
         0.05,0.05]

b = m.Param(value=10.)
k = m.Param(value=0.05)
T_e = m.Param(value=T_external)
TL = m.Param(value=temp_low)
TH = m.Param(value=temp_upper)
TOU = m.Param(value=TOU_v)

u = m.MV(lb=0, ub=1)
u.STATUS = 1  # allow optimizer to change

# Controlled Variable
T = m.SV(value=60)

m.Equations([T>=TL,T<=TH])
m.Equation(T.dt() == k*(T_e-T) + b*u)

m.Minimize(TOU*u)

m.options.IMODE = 6
m.solve(disp=True,debug=True)

一個可能更好的解決方案是通過將限制重新定義為錯誤來設置軟約束。 您可以將誤差降至最低以保持在限制范圍內。 即使不能保持在限制范圍內，優化器也會盡其所能將不可行性降到最低。 這也允許您同時權衡多個目標，例如在舒適度和成本之間。

from gekko import GEKKO
import numpy as np

m = GEKKO(remote=False)
m.time = np.linspace(0,23,24)

#initialize variables
T_external = [50.,50.,50.,50.,45.,45.,45.,60.,60.,63.,\
              64.,45.,45.,50.,52.,53.,53.,54.,54.,\
              53.,52.,51.,50.,45.]
temp_low = [55.,55.,55.,55.,55.,55.,55.,68.,68.,68.,68.,\
            55.,55.,68.,68.,68.,68.,55.,55.,55.,55.,55.,55.,55.]
temp_upper = [75.,75.,75.,75.,75.,75.,75.,70.,70.,70.,70.,75.,\
              75.,70.,70.,70.,70.,75.,75.,75.,75.,75.,75.,75.]
TOU_v = [0.05,0.05,0.05,0.05,0.05,0.05,0.05,200.,200.,200.,200.,\
         200.,200.,200.,200.,200.,200.,200.,200.,200.,200.,0.05,\
         0.05,0.05]

b = m.Param(value=10.)
k = m.Param(value=0.05)
T_e = m.Param(value=T_external)
TL = m.Param(value=temp_low)
TH = m.Param(value=temp_upper)
TOU = m.Param(value=TOU_v)

u = m.MV(lb=0, ub=1)
u.STATUS = 1  # allow optimizer to change

# Controlled Variable
T = m.SV(value=60)

# Soft constraints
eH = m.CV(value=0)
eL = m.CV(value=0)

eH.SPHI=0; eH.WSPHI=100; eH.WSPLO=0  ; eH.STATUS = 1
eL.SPLO=0; eL.WSPHI=0  ; eL.WSPLO=100; eL.STATUS = 1

m.Equations([eH==T-TH,eL==T-TL])

m.Equation(T.dt() == k*(T_e-T) + b*u)

m.Minimize(TOU*u)

m.options.IMODE = 6
m.solve(disp=True,debug=True)

import matplotlib.pyplot as plt
plt.subplot(2,1,1)
plt.plot(m.time,temp_low,'k--')
plt.plot(m.time,temp_upper,'k--')
plt.plot(m.time,T.value,'r-')
plt.ylabel('Temperature')
plt.subplot(2,1,2)
plt.step(m.time,u.value,'b:')
plt.ylabel('Heater')
plt.xlabel('Time (hr)')
plt.show()