Abstract:
The aim of this study was to test the applicability and utility of linear multivariable robust analysis
techniques to a typical chemical process control problem. The fundamental issue in feedback control
is robustness in the face of uncertainty. The integrated nature of the process studied leads to
interaction between process variables, necessitating a multivariable approach.
It was found that robust analysis techniques provide a useful source of information: the traditional
use of safety margins to ensure robustness based on rules of thumb can be replaced by precisely
calculated margins. Robustness of a feedback loop with regard to stability and performance is
evaluated by considering an upper bound on a scalar-valued function of frequency, namely the
structured singular value.
An obvious requirement for the testing of robustness is a description bounding the expected
uncertainty. A description encompassing the entire range of possible plant operating conditions
using a linear nominal plant model with associated bounded perturbation for the system under study,
was derived. The uncertainty description used, independent norm-bounded additive uncertainty in
the transfer function matrix elements, reduces this multivariable description to a number of single
input single output process identification problems. A novel algorithm was used to calculate the
least conservative nominal plant model with norm-bounded uncertainty description.
The calculation algorithm employed for robust analysis requires that the problem statement be given
a specific structure, the so called ~-structure. It was found that it is possible to transform the
evaluation of robust stability and robust performance to this structure.
The major weakness of robust analysis techniques are strong dependence on the validity and
tightness of the uncertainty description. Techniques exist which allow a tighter linear description of
plant uncertainty than the technique used in this study. It is however so that a significant portion of
the uncertainty stems from the fact that a linear model is used to describe an inherently (known) nonlinear plant. It is believed that linear robust analysis techniques provide a significant aid to the
