(494d) A New Methodology for Plant-Wide Control Design for Large Scale Processes

In this work an approach for addressing the problem of design a
plant-wide control structure in a systematical way is presented. The
methodology given here is applied to the Tennessee Eastman challenger
process proposed by Downs
and Vogel, [1992], which is very useful for obtaining
final conclusions and comparing with other results reported
previously. The goals of this work are: operate the process at the
optimum economic operation and reject the disturbances. In order to
do this, a steady-state optimization is done for driving the plant to
that specific working point. Based on the ideas of self-optimizing
control Skogestad,
[2000] and using the optimization results (previous
step), some other controlled variables (CVs) such as levels without
steady-state effect and constrained variables are chosen. The rest of
degrees of freedom can be chosen to be controlled in order to achieve
a better plant controllability.

The main novelties of this methodology consist on proposing an
adequate metric, which is assumed as the objective function very
helpful for searching the rest of CVs supported by genetic algorithm
(GA). It allows to achieve the optimum set that minimize this new
metric without accounting any heuristic concept. The proposed metric
is the sum of square errors (SSE) at steady state of the
non-controlled variables when disturbances and setpoints changes are
present. It can be proofed that the expression of this SSE is

SSE= ns å s=1 ||rows(Ssp)||22+ nd å t=1 ||rowt(Sd)||22,

(1)

where row_s(S_sp)
indicates the row s of S_sp and row_t(S_d)
the row t of S_d, being S_d=[D_r-D_sG_rG_s^-1]
and S_sp=[-G_rG_s^-1],
n_sp and n_d are the number of setpoints and
disturbances that are spected to be changed respectively. G_s
and G_r are the matrix gain of the controlled variables and
remaining variables with respect to the available manipulated
variables respectively. Similarly, D_s and D_r
are the matrix gain of the controlled variables and remaining
variables with respect to the disturbances considered respectively.
In this expression is assumed that the CVs are perfectly controlled.

The main
contribution given here is done in the calculation of the SSE which
previously considered only setpoint changes in specific variables
(first term of the SSE expression ). The second term of this
expression is introduced here for considering the steady-state
disturbance effects. Therefore regulator and servo problems are
accounted.

The GA seems to be a good option for deciding among a great amount of
possible combinations of CV's present in large scale chemical plants.
The set of the founded CVs are paired with the available manipulated
variables (MVs) using relative gain array (RGA) of Bristol,
[1966]. A good RGA is assured due to the used metric for
selecting the set of CV's. By means of this procedure was found the
control structure for the entire plant. The main advantages of this
procedure is that during its steps was not used any heuristic rule or
experience knowledge. In addition, it is only necessary a linear
steady-state model of the process. The developed approach gives an
acceptable control structure in a simpler way, systematic which
provides fewer control loops comparing with other controller
structures proposed by previous works [McAvoy
and YE, 1994,Ricker,
1996,Benjaree
and Arkun, 1995]. As a direct consequence, fewer sensors
and analyzers are necessary for achieve the control objectives. The
tuning of the PI controllers is synthesized with the Internal Model
Control (IMC) rules Rivera
et al., [1986], supported by dynamic models for each
pair MV-CV. The dynamic simulations are done according to some of the
challengers proposed by Downs
and Vogel, [1992]. They show the good behavior of the
controlled process. Finally, the operation cost of the plant is kept
at low magnitude even though different critical conditions are
present. In this way, a good full decentralized control structure was
found ensuring good self-optimizing properties.

References

[Benjaree and Arkun
1995]

A. Benjaree and Y. Arkun. Control configuration design
applied to the tennessee eastman plant-wide control problem.
Computers Chemical Engineering, 19 (4): 453-480, 1995.

[Bristol 1966]

E. H. Bristol. On a measure of interaction for multivaraible
process control. IEEE Trans. Autom. Control, 11: 133-134,
1966.

[Downs and Vogel 1992]

J.J. Downs and E.F. Vogel. A plant-wide industrial process control
problem. Computers and Chemical Engineering, 17 (3):
245-255, 1992.

[McAvoy and YE 1994]

T. McAvoy and N. YE. Base control for the tennessee eastman
challenge process. Computers Chemical Engineering, 18 (5):
383-413, 1994.

[Ricker 1996]

N.L. Ricker. Decentralized control of the tennessee eastman challenge
process. Journal of Process Control, 6 (4): 205-221, 1996.

[Rivera et al.
1986]

D. E. Rivera, M. Morari, and S. Skogestad. Internal
model control. 4. pid controller design. Industrial Engeenering
Chemical Research, 25: 252-265, 1986.

[Skogestad 2000]

S. Skogestad. Plantwide control: the search for self-optimizing
control structure. Journal of Process Control, 10: 487-503,
2000.