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I have the data of the outside temperatures [8,2,10,13 ..] and I have the thermal inertia (8h) of my building. One of the constraints would be to keep an inside temperature of my building within 20 degrees.

We start at equilibrium and we say that the T_in = 20, T_o = 20 but the T_o in one hour = 18 so the Delta_T_o = 18 and the loss in degrees = 2 / Inertia = 0.22K / h

So we have a T_in = 20-19.78, so the power must react to keep the T_in at 20 by applying the following function: Power = Delta_T (in-out) * U (W / m2.K) * Building area (m2) U being the heat transmission. Suppose that U = 3 and Building Area = 1900 Power = 10146 W.

The purpose of my function would be to minimize the power of my boiler according to the T_o that change and keeping T_in at 20.

See the graph to better visualize the objective.

I thought to use Pyomo or cvxpy but I do not see how to do it to make this MPC (Model Predictive Control)

enter image description here

Georgy
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Dodo3
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1 Answers1

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Logan Beal developed the GEKKO package in Python for MPC (and machine learning, optimization) from an EAGER NSF grant that may be useful for your problem.

pip install gekko

Model Predictive Control

Here is a temperature control lab that teaches how to do modeling, estimation, and control. A first step for your application may be to perform system identification to obtain a time-series model of the dynamic relationship between:

  1. the outside temperature and the inside temperature (disturbance model)
  2. the power input and the inside temperature (control model)

Here is an example Python script with two heaters and two temperatures:

System Identification

from gekko import GEKKO
import pandas as pd
import matplotlib.pyplot as plt

# load data and parse into columns
url = 'http://apmonitor.com/do/uploads/Main/tclab_dyn_data2.txt'
data = pd.read_csv(url)
t = data['Time']
u = data[['H1','H2']]
y = data[['T1','T2']]

# generate time-series model
m = GEKKO(remote=False) # remote=True for MacOS

# system identification
na = 2 # output coefficients
nb = 2 # input coefficients
yp,p,K = m.sysid(t,u,y,na,nb,diaglevel=1)

plt.figure()
plt.subplot(2,1,1)
plt.plot(t,u)
plt.legend([r'$u_0$',r'$u_1$'])
plt.ylabel('MVs')
plt.subplot(2,1,2)
plt.plot(t,y)
plt.plot(t,yp)
plt.legend([r'$y_0$',r'$y_1$',r'$z_0$',r'$z_1$'])
plt.ylabel('CVs')
plt.xlabel('Time')
plt.savefig('sysid.png')
plt.show()

You can replace the input data u and output data y to identify a model for your application.

John Hedengren
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