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In this paper, we investigate the limits of performance of a binary distillation column regulated by LTI controllers. The disturbance of distillation process is characterized as the input with bounded magnitudes and bounded rates of change. The performance indices of the top and bottom control loops are defined as the maximum magnitudes of top and bottom compositions, respectively. The convex optimization is 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 the limits of performance between the top and bottom compositions. The trade-off curve provides a practical insight of the LTI controllers applied to the distillation column.