Comfort Control Techniques for the Users of a Room - Comfort Control in Buildings - page 199

G 1 , 1 G 1 , 2
G 2 , 1 G 2 , 2

G = (5.31)

u 1

u = (5.32)

u 2

where both the free response, f i , and the forced response, G i , j , matrices are estimated
through the selected algorithm. As mentioned before, such strategy is different from
traditional nonlinear predictive control techniques since it uses linearised models at
each sample time, which are independent of the system operating points, to estimate
each matrix G i , j , whereas, a nonlinear model for f i is calculated doing the con-
trol actions equal to zero and assuming no changes in the disturbances through the
prediction horizon. Therefore, in this strategy the predicted output data vector, y is ˆ

estimated as shown in Eqs. 5.33 - 5.35 :

ˆ f 1

f 2

G PNMPC

y 1
ˆ

u 1

= + (5.33)

y 2 u 2

f i = f ( y i p , u j p , v p ) (5.34)

⊡
⊣

⊤
⊦

y 1
ʨ

ʨ ˆ y 1

ʨ

ʨ ˆ

u 1 u 2

G PNMPC = (5.35)

y 2
ʨ

ʨ ˆ y 2

ʨ

ʨ ˆ

u 1 u 2

v p
are the past increments in the measurable disturbances, y i p are the past and present
values of the system output i , and G PNMPC matrix is the Jacobian of

In previous equations, u j p are the past increments in the control action j ,

y . To estimate f i
and G i , j for each output-manipulated variable set at each sample time, it is necessary
to use Algorithm 2. Finally, the control law is obtained using techniques similar to
the ones used in classical MPC algorithms.
In addition, the existing error between output provided by real measurements
inside the room at the current time instant, and the output of the room model (a sim-
plified version of the first principles model presented in Sect. 4.2.2 of Chap. 4 ) is
filtered by means of a low-pass filter, integrated and added to the predicted output
obtained from the model in the next sampling time. Besides, this technique supposes
that the integral of the filtered error is constant along all the predictions calculated
at instant k .

ˆ