An internal model control scheme based on a second-order internal model (SI-IMC) is proposed for the heat-integrated air separation column (HIASC). An adaptive internal model control (ASI-IMC) scheme is further presented to make the model more accurate. The IMC scheme based on the first-order model (F-IMC) and the multi-loop PID (M-PID) scheme are also explored as the comparison basis of ASI-IMC and SI-IMC schemes. Comparative researches among these four control schemes are carried out in detail. The results indicate that ASI-IMC presents the best performances among the four control schemes in both servo control and regulatory control, which proves the improvement of ASI-IMC over the SI-IMC and the superiority of ASI-IMC for the high-purity HIASC.