Mathematical modelling and optimal multivariable control of chemical processes
Doctoral thesis
English
OPEN
Nawari, Mustafa O.
This work reports the developnent of a mathenatical model and distributed, multi variable computercontrol for a pilot plant doubleeffect climbingfilm evaporator. A distributedparameter model of the plant has been developed and the timedomain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming 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 linearpartial differential equations. The models obtained have well tracked the experimental results of the plant. A distributedcomputer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable WienerHopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positivedefinite 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 WienerHopf controller, but with a unique feature enabling a designer to specify the closedloop 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 performances. 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 trialanderror design procedures. However, one disadvantage that offsets to some degree the enormous 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 WienerHopf type of controllers and other similar algebraic design methods can be easily solved.

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