In order to investigate the feasibility of constrained multivariable control of a heat-integrated cryogenic distillation process, a rigorous first principles dynamic model was developed and tested against a limited number of experiments. It was found that the process variables showed a large amount of interaction, which is responsible for the difficulties with the presently used, PID-based, control scheme, especially in load-following situations, which are common in air separation plants such as for instance integrated coal gasification combined cycle plants. Contrary to what is suggested in the literature, it was found that vapor hold-up in low-temperature, high-pressure columns does not play a significant role in the process dynamics. Despite large throughput changes and non-linear process behavior, multivariable model predictive control using a linearized model for average operating conditions, could work well provided all process flows have sufficient range. Due to the strong interactive nature of the process variables, process changes have to be made slowly, since otherwise manipulated variables easily saturate and process output targets cannot be maintained.