Entrainer-assisted pressure-swing distillation (EA-PSD) is an effective method for separating pressure-insensitive azeotropes, including both minimum-boiling and maximum-boiling azeotropes. The minimum-boiling azeotrope methanol/toluene can be separated by introducing chloroform as a light entrainer (Ind. Eng. Chem. Res. 2017, .56, 4017-4037). However, the methanol product purity of the proposed control strategy shows large negative transient deviations or steady-state deviations under some disturbances. The maximum-boiling azeotrope phenol/cyclohexanone can be separated by introducing acetophenone as a heavy entrainer (Ind. Eng. Chem. Res. 2013, 52, 7836-7853). However, the proposed control strategy involves an online composition controller. In this research, efforts are made to improve the dynamic performance of both EA-PSD processes. New control strategies are classified and established based on the different control modes of the recycling or connecting stream, which is flow controlled at a constant initial value or manipulated to control a certain reflux drum level or base level. Then they are compared with the previous control strategy in which the recycling or connecting stream flow rate is directly proportional to the feed flow rate. The results show that eliminating the ratio of the recycling or connecting stream flow rate to the feed flow rate can lead to better results. In addition, high-selectors can be applied to the deliberately selected feedback control loops of the reflux flow rate or reboiler duty to further improve the dynamic performance. There are a total of 14 control structures for both EA-PSD processes. Overall comparisons and analyses are made for these control structures. The diverse effective control structures are valuable in practice for the control of EA-PSD for separating both minimum-boiling and maximum-boiling azeotropes.