The separation of ternary nonideal systems with multi‐azeotrope is very important because they are often found in the waste of chemical and pharmaceutical industries, which is much more difficult due to the formation of multi‐azeotrope and distillation boundary. We propose a systematic procedure for design and control of a triple‐column pressure‐swing distillation for separating ternary systems with three binary minimum azeotropes. This procedure involves thermodynamic insights, a two‐step optimization method, and effective control strategy. The separation of tetrahydrofuran (THF)/ethanol/water is used to illustrate the capability of the proposed procedure. It is found that the pressure limits in columns can be determined through the analysis of residue curve maps, distillation boundary, and isovolatility curves. The optimal triple‐column pressure‐swing distillation is generated with the minimum total annual cost (TAC) of $2.181 × 106 in sequence A. The operating conditions are well controlled approaching their desired specifications in an acceptable time when disturbances occur. © 2019 American Institute of Chemical Engineers AIChE J, 65: 1281–1293, 2019