Civil Engineering Reference
In-Depth Information
Algorithm 2
Procedure to estimate
f
and
G
PNMPC
1: To obtain the
y
0
vector with a length
N
,where
N
is the prediction horizon: it is necessary
to execute the model using past inputs, outputs and measurable disturbances, and with
ˆ
u
=
T
. Such that
y
0
f
.
2: To estimate the first column of the
G
PNMPC
matrix. Obtain the
[
00
...
0
]
ˆ
=
y
1
vector, as in the previous step,
the model has to be executed using past inputs, outputs and measurable disturbances, and, in
this case, with
ˆ
u
(
)
1000
.
k
−
1
T
where
ʲ
∗
is a very small value, such as,
u
=[
ʲ
0
...
0
]
−
y
0
ʲ
3: To estimate the second column of the
G
PNMPC
matrix. Obtain the
y
1
G
PNMPC
(
:
,
1
)
=
y
2
vector, the model is executed
ˆ
T
.
using past inputs and outputs, and, with
u
=[
0
ʲ
0
...
0
]
y
2
y
0
ˆ
− ˆ
G
PNMPC
(
:
,
2
)
=
ʲ
4: Continue with the remaining columns of
G
PNMPC
matrix until the last column where the
y
N
u
T
,
vector is obtained executing the model with past inputs and outputs, and with
u
=[
00
... ʲ
]
where
N
u
is the control horizon.
y
N
u
−
y
0
ʲ
G
PNMPC
(
:
,
N
u
)
=
∗
ʲ
is estimated in each case to obtain a good numerical approximation of the derivative of
y
ˆ
•
Multilayer control
. Control of a sub-system is divided into algorithms or layers,
which act at different time intervals. Within its typical structure, see Fig.
5.5
,the
following layers are considered:
-
Regulatory (Follow-up) control
. It is responsible for the estimation of the control
actions,
u
, which are required to obtain a value of the controlled variables,
y
,
equal to the established references,
w
.
-
Optimisation
. It is an algorithm able to determine the optimal values of the
references,
w
, assuming constant values for the characteristic parameters of the
used model.
-
Adaptation
. This layer estimates the best values for each one of the characteristic
parameters of the used model,
ʽ
, to achieve a behaviour as close as possible to
the real plant.
The principal feature of this structure is the interaction which takes place among
all the layers at different instants. Moreover, these instants will be smaller as a
function of the proximity of their associated layer to controlled system.
•
Multilevel control
. In this kind of control strategy, each one of the elements to
control has specific objectives, and thus, it is necessary to use local controllers
which are coordinated by means of a supervisor, see Fig.
5.6
.
Moreover, it is based on decomposition and coordination methods developed in
mathematical programming. This control structure can be used in both open and
