The heat integrated air separation column (HIASC) is a frontier in the energy-saving distillation research. The dynamic model of HIASC is first proposed. The dynamic behaviours such as strong asymmetric nonlinearity and distinct inverse responses are first investigated based on the simulation results of the dynamic model to give some insight into the dynamic difficulties associated with the control of a high purity HIASC. The multi-loop PID (M-PID) and the autoregressive exogenous (ARX) model based generic model control (GMC) scheme are then explored. Furthermore, a multivariable decoupling ARX model is proposed in order to eliminate the interaction between the two single control loops. At last, an adaptive generic model control (ADGMC) scheme for HIASC is presented. The detailed comparative research works are carried out, and the results show that the ADGMC overcomes the interaction of the control loops and the model mismatch of GMC, and hence improves the control performances.