The internal thermally coupled distillation column (ITCDIC) is a frontier in energy-saving distillation research. The process inside a high-purity ITCDIC is of great nonlinear dynamics, which trouble the conventional control schemes. A multivariable adaptive robust generic model control (ARGMC) is presented to solve the difficulties, where an ARX model is derived and a recursive least squares estimation (RLSE) method is introduced. The benzene/toluene system is studied as an illustrative example. The results of ARGMC are compared with the robust generic model control (RGMC) and traditional PID control in detail. The performances in both servo control and regulatory control confirm the accuracy and validity of ARGMC for the high-purity ITCDIC process.