assessments for a fluid catalytic c

assessments for a fluid catalytic cracking reactor and a
hydrodealkylization of toluene (HDA) process.62,63 Weitz
and Lewin introduced the disturbance cost (DC) for dynamic
controllability, which was similar in principle to the disturbance
condition number.28 Trierweiler and Engell64 introduced
the robust performance number (RPN) and the robust
performance number of a plant set (RPPN), which allowed a
systematic analysis of the controllability of the system
including many different aspects that must be considered in
control structure design. Zhao and Skogestad applied the
partial disturbance gain (PDG) to assess the controllability of
continuous bioreactors for the control configuration selection.
65 Hernandez and Jimenez analyzed the controllability
properties of thermally coupled distillation sequences.66
Vaca compared two different steady-state designs for a direct
thermally coupled distillation sequence for ternary separations,
using controllability indices, which were provided by
condition number (CN) and SVD.67 All of these indices rely
on a linear model describing the effect of control variable on
the process outputs. Therefore, they are readily integrated
with existing design procedures.
Remarks. Linear analysis is normally performed around a
nominal operating condition that is normally the most common
operating regime in the process but can also be calculated
from a prior static optimization of the process.68–70
There are several limitations of these techniques. First, both
functional controllability and dynamic resilience may be
used to rank different processes with similar economics but
it may be impossible to compare processes with quite different
economics and robustness indices. This is because chemical
process typically exhibit more than one inherent property
that presents limitations on the performance of the control
system, in which case comparisons based on single
controllability indicator become ambiguous. To address this
drawback, Swartz and coworkers proposed a methodology
where they attempted to pose controllability assessment
within an optimization framework.71–73 Second, the relationship
between the indices and the closed-loop performance is
often unclear. Although the use of these indices may be
adequate in some cases, it is quite unpredictable whether the
conclusions drawn are correct or not. Third, these indices are
based on input–output linear static systems, In particular,
when nonlinear characteristics are important, closed-loop
dynamic simulations are usually required. Finally, most of
the indices are based on the frequency domain specification.
Recently, Gabor and Mizsey presented a methodology for
the simple determination of controllability indices in the frequency
domain,74 with this methodology, the process of
making open loop simulations to approximate transfer function
matrices can be avoided. However, most of existing
methods to calculate these indices are complex. In practice,
time domain performances are more favorable. It is worth
highlighting here that limited work has resolved the relationship
between measures and scaling satisfactorily. Therefore,
controllability analysis that is directly applicable to the nonlinear
model of the chemical process would be more useful.