The pressure-swing distillation (PSD) processes with varied-diameter columns (VDCs) for separating methanol-chloroform and n-heptane-isobutanol are studied. Furthermore, two heat-integrated PSD processes, partial integration and full heat integration, are discussed with ordinary and VDCs. The results show that whether it is heat integrated or non-heat integrated, the processes using VDC have an advantage in the economy. Based on the minimum total annual cost (TAC), the dynamic controllability without and with full heat integration for an azeotrope system methanol/chloroform is explored. The dynamic controllability without and with partial heat integration for the azeotrope system n-heptane/isobutanol is discussed. The results indicated that compared with the dynamic responses without heat integration process, the heat-integrated PSD with a VDC did not increase the control difficulty while maintaining its economy. More azeotropic systems should be studied to investigate their economics and control effects, which will benefit PSD design and industrial application.