A Kaibel distillation column separates a feed into four products with significant lower energy consumption than a conventional sequence of binary columns. Optimal operation and control of such systems is an important task in order to obtain the potential energy savings.A laboratory column has been built at NTNU, Department of Chemical Engineering. At the time of the diploma work the laboratory column has unfortunately not been available for MPC experiments.In practical operation a control structure based on temperature measurements is chosen for the given case. This structure gives a four-by-four multivariable system. The candidate shall base his work on a model developed by Jens Strandberg. The motivation of using a Kaibel distillation column is primarily its energy saving potential. There is no reason for using such an energy saving column if the product purities are below some acceptable values. These purities can be kept above these acceptable values by sufficient control of the column.The simulation model of the Kaibel column was extended to include an efficiency parameter which describes an insufficient vapor mixing effect that occurs in distillation columns. This insufficient mixing leads to increased impurity flows in open-loop, but this is counteracted by increased reflux flow in closed-loop. The column can obtain sufficient purities for increasing insufficient mixing until the reflux flow reaches its maximum value.A single layer MPC and a supervisory MPC approach have been described, implemented and tested on the simulation model of the column. These MPCs show improved dynamic responses compared to the existing decentralized control approach. These MPCs have also been compared in a sensitivity analysis part. The sensitivity analysis shows a clear improvement in the robustness properties for a supervisory MPC compared to decentralized control in terms of input uncertainty. The supervisory MPC has also shown to be more robust than the single layer MPC.A brief qualitative discussion regarding alternative MPC approaches has been done, where inferential control is suggested as an alternative MPC approach for the Kaibel column.An MPC implementation has been done for use at the existing laboratory column at Department of Chemical Engineering. Also here, based on implementation issues, the supervisory MPC is preferable compared to a single layer MPC. A parameter adjusted version of the developed simulation model is recommended as the MPC's internal prediction model.