Page 354 - Design of Simple and Robust Process Plants

340 Chapter 8 Instrumentation, Automation of Operation and Control
The validation of reaction and separations for static models have been addressed
primarily by process designers. Dynamic models require a realistic representation of
the dynamics for the control designer. Key factors for evaluation are the response
time, dead times, and related time constants next to concurrency on process condi-
tions However be aware that any large response time of measurements is included
in the simulation. Measurements on similar equipment can provide a good indica-
tion of these time parameters. Although an error of 15% on response times still
forms a relatively good basis for control design, controllers can still be adjusted with-
in the process.
There are several different types of dynamic interaction analysis, and these are
outlined only briefly at this point (Skogestad, and Postlethwaite 1996).
. The RGA can be expressed as the sum norm (sum of the absolute values of
all elements) of the RGA matrix minus the identity matrix:
k RGA Ik sum
The identity matrix is the ideal RGA matrix if the inputs and outputs are arranged
in such a way that the preferred pairings are at the diagonal. The RGA number
therefore gives a quantitative measure of the non-ideality of the RGA matrix, and
can be used to check whether the steady-state pairing holds over the frequency
range where control is needed.
. Dynamic RGA, (McAvoy, 1983).
. Singular value decomposition.
. Condition number ± this is the ratio between the gains in the strong and
weak directions
.
CN =
A system is said to be ªwell-conditionedº if all output directions can be realized with
roughly the same effort as for the inputs. A high condition number indicates that
the system is ill-conditioned. Some combinations of the input have a strong effect
on the outputs, while other combinations have a weak effect. A condition number of
1 is the preferred situation.

. Morari resilience index. The minimum singular value of the plant is a useful
measure for evaluation the feasibility for achieving acceptable control, (Mor-
ari and Zafiriou, 1989)
. Performance relative gain array, PRGA.
. Static disturbance gain matrix. The static disturbance gain matrix G d is
defined as a linear model that connects the disturbances to the outputs.
When G d is factorized into its singular values, a measure is obtained of the
effect of the disturbances on the outputs.
. Closed loop disturbance gain, CLDG.
. Relative disturbance gain.
For more detailed information on interaction parameters, see Skogestad and Post-
lethwaite (1996).