A hybrid control scheme consisting of an online concentration estimator and an extended generic model controller (EGMC) is proposed for the high-purity control of the heat integrated distillation column (HIDiC). The estimator is designed based on a principal component analysis (PCA) based method and the nonlinear wave theory of HIDiC. The PCA-based method is introduced to determine the locations of a limited number of measurements, while the nonlinear wave theory is presented to estimate the stage concentration according to the wave profile parameters estimated from the selected measurements. Then the EGMC controller coupling with the online estimation is established. A benzene-toluene system is taken as an illustration, and a comparative simulation study is carried out among the proposed EGMC, a nonlinear-wave-based classical generic model controller (WGMC), proportional-integral-derivative control (PID), and a model predictive control scheme (MPC). Finally, EGMC shows a superior performance over the other control schemes, which confirms the validity of the proposed control scheme.