Civil Engineering Reference
In-Depth Information
Fig. 4.5
Periodogram power spectral density estimate and evolution in the time domain of the
winter PRBS signal used for the identification procedure
low frequencies and it does not cover the whole frequency range of interest for this
system.
Figure
4.5
shows the periodogram power spectral density estimate and the evolu-
tion in the time domain associated with the PRBS signal for the winter. As the fancoil
unit is an on/off actuator (with only two states), the designed PRBS signal covers all
the operation range of the actuator which is not desirable from a linear control point
of view since linear models are only acceptable for a specific operation point and
its closest surrounding. This issue can be taken into account by designing the PRBS
signal so that the range of the indoor air temperature, see Fig.
4.6
, is tight, 5
◦
C. Thus,
inside this range the nonlinearity of the system is smooth. Moreover, the PRBS has
been designed to obtain an indoor air temperature range which is the typical one to
acquire an optimal thermal comfort, i.e. PMV
0.
Once adequate signals have been calculated to estimate a linear model, the iden-
tification process can start. To do this, the
System Identification Toolbox
of Matlab
is used (Ljung
1999
,
2007
) since it allows to estimate a linear model as a function of
established premises and a desired model structure. As pointed out previously, in this
case an ARX model, whose polynomial general structure is shown in Eq.
4.9
,was
used. In addition, the model structure can also be given by a simple linear difference
equation, see Eq.
4.10
, which relates the current output of the system
y
=
(
k
)
to a finite
number of past outputs and inputs and a white noise,
y
(
k
−
j
)
,
u
(
k
−
j
)
and
v
(
k
)
respectively.
z
−
1
z
−
1
A
(
)
y
(
k
)
=
B
(
)
u
(
k
)
+
v
(
k
)
(4.9)
