(669f) Loss Method: A Static Estimator Applied for Product Composition Estimation From Distillation Column Temperature Profile

Loss method: A static
estimator applied for product composition estimation from distillation column
temperature profile

Maryam Ghadrdan¹, Chriss Grimholt¹ ,
Sigurd Skogestad¹, Ivar J. Halvorsen²

¹ Department of
Chemical Engineering, Norwegian
University of
Science and
Technology, N-7491 Trondheim, Norway, Email: ghadrdan@nt.ntnu.no, grimholt@stud.ntnu.no,
skoge@nt.ntnu.no

² SINTEF ICT, Applied Cybernetics, N-7465 Trondheim, Norway, Email: ivar.j.halvorsen@sintef.no

Assuring
the quality of products is a necessity for many processes in order to optimize plant economy and
reduce unwanted emissions. Unfortunately, because of delay in composition
analysers or their offline operations, the product qualities cannot be
monitored in
real time. To overcome the lack of instrumentation for direct measurement of
such parameters,
techniques capable of estimating them based on the information from other
measurable variables are developed and are commonly referred as soft sensor
among other
nomenclatures.

In this
work, we have a presented a static estimator to estimate such immeasurable
parameters from other measurements in the plant. Our estimation method (we call
it Loss method) is a reformulation of the well-developed Self-optimizing method
proposed by Skogestad (2000) to make it adequate for the
purpose of estimation. The idea behind self-optimising control is
to find a variable which characterise operation at the optimum, and the value
of this variable at the optimum should be less sensitive to variations in
disturbances than the optimal value of the remaining degrees of freedom. Thus
if we close a feedback loop with this candidate variable controlled to a
setpoint, we should expect that the operation will be kept closer to optimum
when a disturbance occur, and minimising control loss will be equivalent to
minimising estimation error.

Figure 1 shows the block-diagram of the Loss
method. The objective is to find the optimal H matrix which minimizes the
prediction error which is defined as the difference between the estimated and
real values of the primary variables.

We have
formulated the Loss method for open-loop and closed-loop estimator. With the term ?open-loop? estimator, it is
implied that the predicted variables are not used for control purposes. It
should be noted that this is not the same as implying that variables in a given
system are uncontrolled. We could use an ?open-loop? estimator to predict a
primary variable that are in fact controlled by some other means than the
prediction.

From this, we can think of three main types of
?open-loop? estimators

1. Predicting primary
variables from a open-loop system (no control of
variables).

2. Predicting primary
variables from a closed-loop system where the primary variables are controlled by
manipulating suitable input variables.

3. Predicting primary
variables from a closed-loop system where the secondary variables are
controlled (not by the predicted variable).

Figure 1.
Block diagram for the Loss Method.

The Loss Method is also compared to Partial
Least Squares or Projection to Latent Structures (PLS) which is a family of
multivariate analysis techniques used to extract useful information from
correlated data. This method is used to compress the predictor data into a set of latent variable. There are several
different algorithms generating bases but which all give the same predictor. We
have chosen the interpretation of Di Ruscio (2000) as the PLS solution we
compared with our method, because their interpretation of the method is the
closest and most comparable to our method. Instead of introducing scores and
loadings, they present a non-iterative solution based on some weights which are
the only degrees of freedom in their method. We have applied this method and
compared it with partial least square on a distillation column case. In this
case, the predictors are the temperatures sensed by thermocouples and the
output variables are the composition of the products. Despite the fact that
these two methods are developed in two different contexts, it was interesting
to find out that the results from both are very similar.

References

Di Ruscio, D. (2000). ?A
weighted view on the partial least-squares algorithm.? Automatica 36: 831-850

Skogestad, S. (2000). ?Plantwide
control: the search for the selfoptimizing control
structure.? J. Proc. Control 10: 487-507