Robust Multivariable Control of Ill-Conditioned Plants – A Case Study for High-Purity Distillation

Distillation is one of the most important unit operations in the chemical industry. Among various distillation operations, control of high-purity column poses difficult control due to a number of characteristics of these systems, including strong directionality, ill-conditioning and strongly nonlinear behavior. At the same time, the potential benefits that can be obtained through tight and economic control of the product compositions are very large. This is due to different reasons including the large energy consumption required by the columns and the market requirements which are becoming stricter and stricter. Because of these obvious features of high-purity distillation, this type of column has been studied extensively. Control systems for chemical processes are typically designed using an approximate, linear, time-invariant model of the plant. The actual plant may differ from the nominal model due to many sources of uncertainty, such as nonlinearity, the selection of low-order models to represent a plant with inherently high-order dynamics, inaccurate identification of model parameters due to poor measurements or incomplete knowledge, and uncertainty in the manipulative variables. Considering the differences between the actual plant and nominal model, it is necessary to insure that the control system will be stable and meet some predetermined performance criteria when applied to the actual plant. The identification and control of distillation columns have been subjects of frequent study due to the illconditioned nature of the distillation process. An ill-conditioned plant is very close to singular, and unless care is taken, very small errors can make the model useless. In distillation, this means that a model may have features that are in conflict with physical knowledge (Luyben, 1987; Jacobsen & Skogestad, 1994; Boling & Haggblom, 1996). In addition, ill-conditioned dynamics of high-purity distillation columns leads to high sensitivity to uncertainties in the manipulated variables (Skogestad & Morari, 1988). This effect causes even small errors in the manipulated variables show significant deterioration of the product quality, a fact which explains why open-loop control of high-purity distillation columns is hardly ever satisfactory. The model of a high-purity distillation process has a steady-state gain matrix with a high condition number. The gain matrix is almost singular and its determinant may be affected by quite small model errors, and if

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