Mathematical modelling and optimal multivariable control of chemical processes
This work reports the developnent of a mathenatical model
and distributed, multi variable computer-control for a pilot plant
double-effect climbing-film evaporator.
A distributed-parameter model of the plant has been
developed and the time-domain model transformed into the Laplace
domain. The model has been further transformed into an integral
domain confooning to an algebraic ring of polynomials, to eliminate
the transcendental terms which arise in the Laplace domain due to the
distributed nature of the plant model. This has made possible the
application of linear control theories to a set of linear-partial
differential equations •
. The models obtained have well tracked the experimental
results of the plant.
A distributed-computer network has been interfaced with the
plant to implement digital controllers in a hierarchical structure.
. A modern rnultivariable Wiener-Hopf controller has been
applled to the plant model. The application has revealed a limitation
condition that the plant matrix should .be positive-definite along the
infinite frequency axis.
A new multi variable control theory has emerged fram this
study, which avoids the above limitation. The controller has the
structure of the modern Wiener-Hopf controller, but with a unique
feature enabling a designer to specify the closed-loop poles in
advance and to shape the sensitivity matrix as required. In this way,
the method treats directly the interaction problems found in the
chemical processes with good tracking and regulation perfo~noes.
Though the ability of the analytical design methods to determine once
and for all whether a given set of specifications can be met is one of
its chief advantages over the conventional trial-and-error design
procedures. However, one disadvantage that offsets to some degree the
eno~us advantages is the relatively complicated algebra that must be
employed in working out all but the simplest problem •
. Mathematical algorithms and computer software have been
developed to treat some of the mathematical operations defined over
the integral domain, such as matrix fraction description, spectral
factorization, the Bezout identity, and the general manipulation of
polynomial matrices. Hence, the design problems of Wiener-Hopf type
of controllers and other similar algebraic design methods can be