使用GEKKO的MPC中的可变范围 [英] Variable bounds in MPC with GEKKO

问题描述

我正在尝试使用MPC和GEKKO实现恒温器控制.

I'm trying to implement a thermostat control using MPC and GEKKO.

状态变量(温度)应在下面的代码的上限和下限预定温度值temp_low和temp_upper之内.

The state variable (temperature) should be within a lower and upper pre-specified temp values , temp_low and temp_upper in the code below.

两者的界限每天都会变化:每小时一个值.

Both bound vary along the day: one value per hour.

目标函数是使用加热的成本.价格也随一天(TOU)的变化而变化. T_external是房间的外部温度，在微分方程中起作用.

The objective function is the cost-to-go of using the heating. The price also changes along the day, TOU below. T_external is the room's exterior temperature that plays a role in the differential equation.

如何实现此目标以使其优化?

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)

当我运行它时，我得到:

When I run this I get:

@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
    ?

推荐答案

Gekko需要使用约束作为不等式表达式，其中将变量T与较高的TH或较低的TL值进行比较.如果您使用b=1.，则将导致不可行的解决方案，因为加热器的功率不足以将温度保持在上限和下限之内.我将值更改为b=10以获得可行的解决方案.

Gekko needs the constaints as inequality expressions where the variable T is compared to the upper TH or lower TL values. If you have b=1., it leads to an infeasible solution because the heater isn't powerful enough to maintain the temperature within the upper and lower limits. I changed the value to b=10 to get a feasible solution.

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)

一种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.您可以将错误最小化以保持在限制范围内.即使无法保持在限制范围内，优化器也会尽力而为，以最大程度地减少不可行性.这也使您可以同时权衡多个目标，例如在舒适度和舒适度之间进行权衡.费用.

A potentially better solution is to set up soft constraints by redefining the limits as an error. You can 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 simultaneously such as between comfort and cost.

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()

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