Heat integrated distillation columns (HIDiCs) may have multiple steady-states, which may cause abrupt changes in process states. The present work presents two possible approaches to avoiding such multiplicity. The first approach is related to compressor operation strategies in the LV control structure; the strategy of constant compressor rotation speed can realize stable operation without multiple steady-states. The second approach is to adopt the DV or LB control structure. By employing one of these two structures, no multiplicity appears and stable operation of HIDiC can be realized. Herein, the usefulness of the proposed approaches is demonstrated though rigorous dynamic simulations.