Heat integration and dynamic characteristics are critical for the triple-column pressure-swing distillation (TCPSD) processes that are used to separate ternary or multicomponent systems. In this study, rigorous steady-state simulations of heat-integrated TCPSD processes are optimized using Aspen Plus, and dynamic strategies for the different TCPSD processes are explored using Aspen Dynamics. When 20% feed flow rates and composition disturbances are introduced, the composition/temperature cascade control structure (CSB), which uses stage 19 as the temperature-sensitive stage in the second column, exhibits better controllability than the CSA, which uses stage 4 as the temperature-sensitive stage. Three cases of partial heat integration are studied, and the first case, which uses an auxiliary condenser, is the most economic. The dynamic control strategies of the first and second cases handle 10% feed disturbances well; however, the CSE can attain good controllability when 20% feed disturbances are introduced. For the fully heat-integrated TCPSD process, the CSG exhibits good controllability for 20% feed disturbances. The time that the control structures require to reach new steady states varies greatly for different heat integrated processes.