In Australia and around the world, fedbatch crystallization is a key unit operation in the manufacture of raw sugar. In Australia strict quality standards on export raw sugar, coupled with a limited window of opportunity for harvesting the sugar cane, engendered the search for optimal operating policies of the fedbatch sugar crystallizers, commonly referred to as vacuum pans. Previous optimal control studies cast the vacuum pan control problem in terms of two key process variables - the sucrose oversaturation in the mother liquor and the mass fraction of crystal suspended in the mother liquor, commonly known as the crystal content.
The sucrose oversaturation in the mother liquor must be kept high, thus motivating seed crystal growth, but not so high as to exceed the point of crystal nucleation. If this upper limit on oversaturation is exceeded, an avalanche of small, unwanted crystals nucleate from solution, polluting the seed crystal population. Avoiding non-compliance penalties and minimizing downstream processing difficulties demand that these nuclei be removed. Operationally this is achieved by dissolving them back into solution - a procedure leading to batch time inefficiencies, batch scheduling conflicts and the ill-use of steam resources.
The suspension crystal content also needs to be kept high, ensuring adequate surface area for sugar deposition from the mother molasses. However, as the crystal content increases, natural circulation in the vacuum pan stalls, resulting in spatial variations in the molasses/crystal slurry properties. This spatial variation leads to crystal growth rate variations, which combine to broaden the product crystal size distribution. In the worst case pockets of critically oversaturated molasses form, producing the unwanted nuclei previously mentioned.
The vacuum pan control problem therefore is essentially a measurement problem, since no sensors exists which can accurately divine the sucrose oversaturation or the crystal content. While traditional means of control have relied on skilled operators to assess the process condition, present automatic control practice within Australia favours the use of simple output based sensors to assess the process condition. At best, this offers an indirect means of controlling the oversaturation and crystal content.
Thus, the present work addresses the measurement problem via the application of state estimation theory. The ultimate goal of the work was to rigorously determine the oversaturation and crystal content in the vacuum pan throughout the batch time.
While a nonlinear model for the fedbatch vacuum pan had been previously developed, it was not in a form amenable to state estimation theory. To this end the model order was reduced by careful analysis of the mass balance sensitivity to the ancillary model components.
The model state space was then transformed to another basis, a step which was prompted by the observability properties of the reduced order model. This has resulted in a novel model formulation that is more amenable to practical state estimation and describes the system in terms of variables more relevant to operators, sugar technologists and theoreticians.
A series of simulations is carried out, indicating the most promising candidate from the pool of newly derived models. The state estimator employed is developed on a more rigorous basis than is usually the case, since it accommodates model parameter uncertainties by using the model's structure.
After off-line analyses of plant data, the state estimator is deployed in real time. The estimator was employed first in an advisory capacity, enabling operators to assess the now-available oversaturation and crystal content. Ultimately, these state estimates were incorporated into feedback control loops, enabling simultaneous control of the oversaturation and crystal content in the pan.