Distillation columns have proved to be the most reliable separation method for separating chemical mixtures to their pure components. As the number of components to be separated increases, the number of columns and the energy required to run these columns also increase. This results in huge capital costs that are unaffordable due to limited energy resources. A most "compact" column called the divided wall column appeared to solve this difficulty. This column is capable of separating mixtures of three or more components to high purity products with energy less than that of the conventional multicolumn process. However, the control of these columns is more complicated due to the coupling effect and increased number of variables in these columns. Our focus in this paper is limited to the divided wall columns separating ternary mixtures only. There are three main objectives of this paper. First, the paper presents a survey study about the different control aspects of the divided wall columns, based on the type of control used: composition control, temperature control, or cascaded composition-temperature control. An up-to-date overview of most of the current literature is presented. Second, conventional and adaptive proportional-integral-derivative (PID) controllers are proposed to control a divided wall distillation column separating a ternary mixture of ethanol, propanol, and n-butanol. Fuzzy logic control, neural network control, and adaptive neuro-fuzzy inference systems are suggested for the tuning of the PID controllers. Particle swarm optimization technique is also applied to improve the results obtained by the adaptive PID controllers. Finally, a multi-input-multi-output neural network model reference adaptive controller based on adaptive PID controller tuned by adaptive neuro-fuzzy inference systems based particle swarm optimization is suggested. The results indicate the superiority of the adaptive PID controllers over conventional PID controllers, especially in the case of disturbances.