A new model‐based control strategy for the internal thermally coupled distillation column (ITCDIC) is presented. Based on the nonlinear wave theory that describes the nonlinear dynamics in the separation processes, a simplified nonlinear wave model is established that concerns both the wave propagation and the profile shape. An advanced controller (WGGMC) is formulated by combining the nonlinear wave model with a generalized generic model control (GGMC). Compared with a conventional generic model controller based on a data‐driven model (TGMC), and another wave‐model based generic model controller (WGMC) developed in our previous work, WGGMC exhibits the best performances in both servo control and regulatory control. Furthermore, WGGMC can handle a very‐high‐purity system of ITCDIC with top product composition of 0.99999, while the other two controllers fail to work. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4133–4141, 2013