Civil Engineering Reference
In-Depth Information
5.5.2.1 Cost Function
In the case study of the CDdI-CIESOL-ARFRISOL building, the cost function
defined by Eq.
5.36
is used. This cost function tries to find the best future change in
the control signals set,
u
, which is able to minimise the tracking error, that can be
defined as the difference between the future predicted outputs (
y
), the PMV index
and the IAQ index, and the reference value for these indices (
w
), that in both cases
is equal to zero. In addition, at the same time, changes in the future control action,
that is, changes in the impulse air temperature,
T
a
imp
, and the aperture of the window,
A
dr
window
, are penalised by means of their associated weighting factors.
ˆ
2
N
2
N
u
2
2
J
=
1
˃
i
[ˆ
y
i
(
k
+
j
|
k
)
−
w
i
(
k
+
j
)
]
+
1
ˉ
c
[
u
c
(
k
+
j
−
1
)
]
(5.36)
i
=
1
j
=
c
=
1
j
=
where, in this case,
y
i
(
ˆ
k
+
j
|
k
)
is the prediction of the PMV and IAQ indices,
y
1
and
ˆ
is the future change in the control signal
c
,in
which
u
1
is the impulse air temperature,
T
a
imp
, and
u
2
is the aperture of the window,
A
dr
wi ndow
.
y
2
respectively, and
ˆ
u
c
(
k
+
t
−
1
)
5.5.2.2 Constraints
Besides, the optimisation problem is subject to several systems constraints given by
Eqs.
5.37
and
5.38
. The first constraint, Eq.
5.37
, limits the maximum and minimum
change in the control signal at each sample time whereas the second constraint,
Eq.
5.38
, makes reference to hard constraints of the fancoil unit and the window, in
other words, it takes into account the minimum and maximum impulse air temper-
ature and window aperture, [
u
c
min
,
u
c
max
], which can be achieved with the current
actuators.
u
1
min
u
1
(
k
+
j
−
1
)
u
1
max
≤
≤
∀
j
=
1
,...,
N
u
(5.37)
u
2
min
u
2
(
k
+
j
−
1
)
u
2
max
u
1
min
u
2
min
u
1
(
u
1
max
u
2
max
k
+
j
−
1
)
≤
≤
∀
j
=
1
,...,
N
u
.
(5.38)
u
2
(
k
+
j
−
1
)
5.5.3 Results
This section displays the real results obtained for the proposed multivariable
nonlinear control approach when it has been tested inside a typical room of the
CDdI-CIESOL-ARFRISOL building during the summer period. This strategy is an
