![](bg7.png)
to ensure possibly highest modeling accuracy of the
process dynamics. For this purpose, a range of data
driven methods for designing the adaptive soft
sensors (Fortuna
et al., 2007; Lin et al., 2007;
Kadlec et. al, 2011) can be considered and combined
with the model (7).
As one of the key aspects of the proposed
method's success is either the availability of the
measurements or their robust estimation procedure
the data driven soft sensors could also be employed
in the case of individual measurements prediction
like in the case of values which are only infrequently
measured (e.g. pressure values
p
1
and p
2
from our
example) or for the smoothing/interpolation
purposes to avoid numerical problems resulting from
the usage of inaccurate hard sensors (e.g. controlled
pressure
p
3
in our example).
There have been great advancements made in the
learning algorithms used for the construction and
adaptation of soft sensors and their multitude of
applications and successful deployments have been
summarized in comprehensive reviews (Lin
et al.,
2007; Kadlec et. al, 2009; Kadlec et. al 2011) and
textbooks, e.g. (Fortuna
et al., 2007). The illustrated
ability to start working with only few historical
samples available (Kadlec and Gabrys, 2010) or to
adapt and provide robust prediction in dynamically
changing environments with noisy measurements
(Kadlec and Gabrys, 2008, 2009, 2011) make the
modern, intelligent soft sensing approaches a very
attractive proposition to combine with model-based
control approaches either as a replacement of the
traditional observers (which require the knowledge
of the plant model) or by providing information
about variables which cannot be measured or can be
measured only infrequently making them of limited
use for control purposes. Such variables can be
modeled and predicted on the basis of other
measurable process variables which soft sensor
techniques successfully exploit. Our future work will
therefore focus on enhancing and robust evaluation
of the proposed nonlinear model-based control
algorithms dedicated for the processes of the higher
relative degree, utilizing a variety of data driven soft
sensing approaches. One possibility is to substitute
the first-principle process model by the data-driven
soft sensor based on the initial off-line learning from
the measurement data and providing the prediction
of the required state and controlled variables. The
other approach could be based on the adaptive data-
driven update of the existing first-principle model to
ensure the on-line compensation for modeling
inaccuracies. In the latter, if the compensation was
accurate, it would be possible to remove the
estimation procedure for the additive parameter
Y
R
ˆ
from the final form of the controller that now
ensures the offset-free control in the presence of the
steady state modeling inaccuracy.
The results presented in this paper show that the
example pneumatic process is of the 3
rd
relative
degree but not very nonlinear. In fact, the simplified
model (7) describes its dynamics with relatively high
accuracy. Apart of what is described above, the
future work will also concentrate on the practical
validation of the suggested control strategy in the
application of the higher order systems with stronger
nonlinearities.
ACKNOWLEDGEMENTS
M. Szymura was supported by the Human Capital
Operational Programme and was co-financed by the
European Union from the financial resources of the
European Social Fund, project no. POKL.04.01.02-
00-209/11. B. Gabrys was supported by funding from
the European Commission within the Marie Curie
Industry and Academia Partnerships and Pathways
(IAPP) programme under grant agreement n. 251617.
The other Authors were supported by the Ministry of
Science and Higher Education under grants:
BKM-UiUA and BK-UiUA.
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