Product quality control in reduced dimensional spaces

Effective control of quality variables in high-dimensional processes is considered. Because of the high dimension of the output space, control of a subset of the quality variables is often practiced, to indirectly control the entire quality space. An example of this type of situation is the control of the full molecular weight distribution (MWD). Often, indirect control of the MWD, for example, by controlling an average of the distribution, is practiced instead. It is shown in this paper that, as a controller eliminates a disturbance in the controlled variables (for example, the weight-average chain length), it transfers and can possibly inflate the disturbance in the remaining quality variables (the full MWD). Therefore, while it may appear that good control is being achieved (the average is at its target), the polymer quality has, in fact, degraded. A simple analysis tool, called the disturbance inflation factor (DIF), is introduced to predict this effect. The DIF is used to predict which manipulated variable results in the best control of the full MWD while acting only on a single measured variable such as the weight-average chain length. It is further applied to evaluate if control of the full distribution may be improved by considering other controlled variables, such as the number-average chain length, or other manipulated variables, such as combinations of the existing manipulated variables. The ideas are illustrated on a simulated polystyrene reactor.