Linear controller design and performance limits of binary distillation column subject to disturbances with bounds on magnitudes and rates of change

In this paper, we present an application of linear controller design via convex optimization to a binary distillation column and determine its limits of performance. Disturbances of distillation process are characterized as input signals with bounded magnitudes and rates of change. Performance measures of top and bottom control loops are defined as the maximum deviation magnitudes of top and bottom compositions, respectively. This performance is often referred to as the worst-case norm of convolution systems under such disturbances. The convex optimization and the ellipsoid algorithm are applied to design linear controllers and, at the same time, determine the best achievable performance of the closed-loop system. Then, a series of convex optimization problems are efficiently solved to give a trade-off curve representing limits of performance between the top and bottom compositions. The trade-off curve provides a practical insight into the design specification that cannot be achieved for the distillation column control with dynamic controller configuration. To confirm the results, we undertake computer simulation using nonlinear dynamical model of the distillation column. Closed-loop responses of the chosen optimal linear controller are consistent with the trade-off curve and yields superior performance than that of a conventional decentralized PI controller.