Civil Engineering Reference
In-Depth Information
Fig. 5.4
Basic MPC structure
•
Estimation of the control actions sequence
. The same model is used to estimate
a sequence of control actions,
u
, which satisfy
some optimisation objectives while they are subjected to certain constraints, just
as the minimisation of the error between the predicted output of the model and the
future references, or the minimisation of the control effort necessary to reach the
established reference or setpoint.
=[
u
(
k
),
u
(
k
+
1
),
u
(
k
+
2
),...
]
•
Update of the prediction of the error
. Because obtaining amodel which precisely
reflects the output of the controlled process is an utopia, it is necessary to estimate
prediction error (defined as the difference between the measured output of the
process and its predicted output to update future predictions.
To sum up, it can be established that MPC strategies, whose basic structure can
be observed in Fig.
5.4
, make use of a model of the process mainly to perform the
following tasks:
•
To obtain the explicit prediction, within a prediction horizon, of the future behav-
iour of the controlled process. These future predictions depend on: past outputs of
the system and past and future control signal values and disturbances.
•
Estimation of the required future control signals, within a control horizon, to lead
the predicted output of the systemas closely as possible to an established reference.
It is necessary to use a cost function that will be evaluated and minimised as well as
the established constraints. Generally, this cost function represents the quadratic
error between the predicted output and the future reference.
•
Once a sequence of future control signals has been estimated, the one associated to
the current sampling time is applied to the process and the other ones are rejected.
The same procedure is again performed at the following sampling time. For this
reason, this strategy is known as receding horizon strategy.
