From process knowledge to the design of practical multivariable controllers

The objective of this thesis is to investigate a framework for designing linear or nonlinear multivariable controllers which uses process knowledge instead of a complete dynamic model. The structure of these controllers centers around the extensive variables of the process (e.g. total mass content of a system, reaction rate, etc.) instead of the intensive variables that are usually measured. This technique has been developed for both open-loop unstable and open-loop stable multivariable processes.; In Part I, a multivariable controller (hereafter, MEV) based on the principles of Extensive Variable Control Structures has been developed for distillation columns. The comparison of the performance of MEV with conventional control structures and Dynamic Matrix Control (DMC) for different distillation columns with purity specifications ranging from 10000 ppm to 10 ppm shows that the MEV has superior regulatory performance, particularly in high purity columns where neither classical nor modern approaches are effective. The inability of model-based DMC to handle strong nonlinearities is also addressed. Particularly, we show that for moderate-purity columns (around 10000 ppm of impurity) the performance of DMC is better than that of the conventional structure and comparable to that of MEV. As we move from moderate-purity columns to high-purity columns (1000 ppm) the performance of DMC becomes worse than that of the conventional structure or the MEV structure. This implies that DMC is more sensitive than the PI type structures to process nonlinearities. Based on our process understanding we suggest simple nonlinear output transformations which result in a nonlinear DMC with much better performance than that of standard DMC.; In Part II, a simple and innovative procedure for designing control structures for open-loop unstable multivariable systems is given. We treat the control system as an interacting multi-input multi-output system, rather than in terms of isolated single loops in which each controller responds to charges in a single measurement. At the same time, we retain the attractive multiple single-input single-output control structure. The closed-loop stability, dynamic performance, and robustness of a controller are established by an effective damping coefficient and its corresponding effective closed-loop time constant. These concepts and a multivariable root locus provide a suitable framework for the design of multi-loop single-input single-output controllers. The controller tuning is reduced to an optimization problem. The procedure is illustrated on a complex system of two reactors in series, with a separator and recycle, where exothermic second-order reactions occur. The system is highly nonlinear and has three open-loop poles in the right half of the s-plane. Performance is evaluated by simulation of the nonlinear mathematical model. Finally, the extensive variable control structure introduced in Part I is presented for the above system. The resulting controller is nonlinear since it incorporates the reaction rate explicitly.