The following is related to this question : predictive control model using GEKKO

I am still traying applying MPC to maintain the temperature of a room within a defined range(16,18), as Professor @John explained last time.the gain is normally listed as K=array([[0.93705481,−12.24012156]]). Thus, an increase in β by +1 leads to a decrease in T by -12.24, while an increase in Text by +1 leads to an increase in T by +0.937.

In my case, I tried to implement an external temperature profile for a day (sinusoidal), and I modified the control to vary between 0 and 1, not just 0 or 1, since the equipment can operate within this range. I also adjusted m.bint.MV_STEP_HOR=1 so that the control is updated at each iteration. However, the control still does not react! Even when the external temperature increases or decreases, the control remains unchanged.
I run the corrected code from my previous question:

# Import library
import numpy as np
import pandas as pd
import time
from gekko import GEKKO
from numpy import array

total_minutes_in_day = 24 * 60
interval = 5  # minutes
num_points = total_minutes_in_day // interval

# Générer les points de temps
time_points = np.linspace(0, total_minutes_in_day, num_points)

temperature = 8.5 + 11.5 * np.sin((2 * np.pi / total_minutes_in_day) * time_points - (np.pi / 2))
temperature = np.clip(temperature, -3, 20)


plt.plot(time_points, temperature)
plt.xlabel('Temps (minutes)')
plt.ylabel('Température (°C)')
plt.title('Variation de Tex sur une journée')
plt.savefig('Tex pour une jrn')
plt.grid(True)
plt.show()


K = array([[  0.93705481, -12.24012156]])
p =  {'a': array([[ 1.08945247],
        [-0.00242145],
        [-0.00245978],
        [-0.00272713],
        [-0.00295845],
        [-0.00319119],
        [-0.00343511],
        [-0.00366243],
        [-0.00394247],
        [-0.06665054]]),
 'b': array([[[-0.05160235, -0.01039767],
         [ 0.00173511, -0.01552485],
         [ 0.00174602, -0.01179519],
         [ 0.00180031, -0.01052658],
         [ 0.00186416, -0.00822121],
         [ 0.00193947, -0.00570905],
         [ 0.00202877, -0.00344507],
         [ 0.00211395, -0.00146947],
         [ 0.00223514,  0.00021945],
         [ 0.03800987,  0.04243736]]]),
 'c': array([0.0265903])}

# i have used only 200 mes of T_externel
T_externel = temperature
m = GEKKO(remote=False)
m.y = m.Array(m.CV,1)
m.u = m.Array(m.MV,2)
m.arx(p,m.y,m.u)

# rename CVs
m.T = m.y[0]

# rename MVs
m.beta = m.u[1]
m.free(m.beta)
m.bint = m.MV(0,lb=0,ub=1)
m.Equation(m.beta==m.bint)


# distrubance
m.d = m.u[0]

# distrubance and parametres
m.d = m.Param(T_externel[0])

m.bias = m.Param(0)
m.Tb = m.CV()
m.Equation(m.Tb==m.T+m.bias)

# steady state initialization
m.options.IMODE = 1
m.solve(disp=False)

# set up MPC
m.d.value = T_externel

m.options.IMODE   = 6 # MPC
m.options.CV_TYPE = 1 # the objective is an l1-norm (region)
m.options.NODES   = 2 # Collocation nodes
m.options.SOLVER  = 3 # IPOPT
m.time = np.arange(0,len(T_externel)*300,300) # step time = 300s

# Manipulated variables
m.bint.STATUS = 1  # calculated by the optimizer
m.bint.FSTATUS = 0 # use measured value
m.bint.DCOST = 0.0 # Delta cost penalty for MV movement
m.bint.UPPER = 1.0 # Upper bound
m.bint.LOWER = 0.0 # Lower bound
m.bint.MV_STEP_HOR = 1
m.bint.value = 0

# Controlled variables
m.Tb.STATUS = 1        # drive to set point
m.Tb.FSTATUS = 0       # receive measurement
m.Tb.SPHI = 18         # set point high level
m.Tb.SPLO = 16         # set point low level
m.Tb.WSPHI = 100       # set point high priority
m.Tb.WSPLO = 100       # set point low priority

T_MEAS = 20 # Temperature starts at 17
m.Tb.value = T_MEAS
m.bias.value = T_MEAS - m.T.value[0]

m.options.SOLVER = 1
m.solve(disp=False)

if m.options.APPSTATUS == 1:
   # Retrieve new values
   beta  = m.beta.NEWVAL
else:
   # Solution failed
   beta  = 0.0