Abstract 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.