带有 GEKKO 的 MPC 中的变量边界
Variable bounds in MPC with GEKKO
我正在尝试使用 MPC 和 GEKKO 实现恒温器控制。
状态变量（温度）应在预先指定的下限和上限温度范围内，下面代码中的 temp_low 和 temp_upper。
这两个界限每天都在变化：每小时一个值。
objective函数是使用暖气的成本到去。价格也随着一天的变化而变化，TOU 以下。 T_external 是在微分方程中起作用的房间外部温度。
如何实现才能优化？
这是我的尝试：
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)
当我 运行 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
?
Gekko 需要将约束作为不等式表达式，其中变量 T 与上限 TH 或下限 TL 值进行比较。如果你有 b=1.，它会导致一个不可行的解决方案，因为加热器的功率不足以将温度维持在上限和下限内。我把值改成了b=10来得到一个可行的方案。
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)
一个可能更好的解决方案是通过将限制重新定义为错误来设置软约束。您可以 minimize the error to stay within the limits. Even if it can't stay within the limits, the optimizer will do the best it can to minimize the infeasibility. This also allows you to trade-off multiple objectives 同时兼顾舒适性和成本。
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()
我正在尝试使用 MPC 和 GEKKO 实现恒温器控制。
状态变量（温度）应在预先指定的下限和上限温度范围内，下面代码中的 temp_low 和 temp_upper。
这两个界限每天都在变化：每小时一个值。
objective函数是使用暖气的成本到去。价格也随着一天的变化而变化，TOU 以下。 T_external 是在微分方程中起作用的房间外部温度。
如何实现才能优化？
这是我的尝试：
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)
当我 运行 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
?
Gekko 需要将约束作为不等式表达式，其中变量 T 与上限 TH 或下限 TL 值进行比较。如果你有 b=1.，它会导致一个不可行的解决方案，因为加热器的功率不足以将温度维持在上限和下限内。我把值改成了b=10来得到一个可行的方案。
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)
一个可能更好的解决方案是通过将限制重新定义为错误来设置软约束。您可以 minimize the error to stay within the limits. Even if it can't stay within the limits, the optimizer will do the best it can to minimize the infeasibility. This also allows you to trade-off multiple objectives 同时兼顾舒适性和成本。
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()