Civil Engineering Reference
In-Depth Information
Fig. 4.4
System with additive disturbance.
Source
: (Ljung
1999
)
Table 4.2
Linear models structures
Used polynomials
Model
B
=
0,
C
=
1,
D
=
1
Auto-Regressive (AR)
B
=
0,
D
=
1
Auto-Regressive Moving Average (ARMA)
C
=
1,
D
=
1,
F
=
1
Auto-Regressive with eXogeneus inputs (ARX)
D
=
1,
F
=
1
Auto-Regressive Moving Average with eXogeneus inputs (ARMAX)
A
=
1,
C
=
1,
D
=
1
Output Error (OE)
A
=
1
Box-Jenkins (BJ)
The linear parametric models most used in the literature have the polynomial gen-
eral structure as shown in Eq.
4.6
, see Fig.
4.4
. Hence, transfer functions associated
with the inputs and disturbances can be expressed according to Eqs.
4.7
and
4.8
,
respectively. Therefore, different model structures can be obtained as a function of
the polynomials which are used, see Table
4.2
.
z
−
1
z
−
1
B
(
)
C
(
)
z
−
1
A
(
)
y
(
k
)
=
u
(
k
)
+
v
(
k
)
(4.6)
F
(
z
−
1
)
D
(
z
−
1
)
z
−
1
B
(
)
z
−
1
G
(
)
=
(4.7)
z
−
1
z
−
1
A
(
)
F
(
)
z
−
1
C
(
)
z
−
1
H
(
)
=
(4.8)
z
−
1
z
−
1
A
(
)
D
(
)
Apart from the fact that the AR and ARMA models do not considered the inputs,
B
0, the main difference among model structures lies in the consideration of
disturbances. AR and ARX structures suppose that disturbances are a white noise,
=
