An appropriate structure for a reduced-order model of transfer function type is first proposed for an ideal heat integrated distillation column (HIDiC) based on the process dynamics. The reduced-order model could well represent the process not only in steady state but dynamic state as well, A multivariable internal model control (IMC) system is designed and applied to the ideal HIDiC. The simulation results demonstrate that the IMC controller can deal with the interactive nature of the ideal HIDiC more effectively than PI controllers, indicating the IMC controller could be a better means for operation of the ideal HIDiC in the case where high system performance is required, However, the ideal HIDiC is extremely sensitive to changes in operating conditions and this makes it necessary to adopt an on-line model adaptation mechanism to facilitate the performance of the IMC controller.