An improved instant wave velocity is first derived for the heat integrated air separation column (HIASC), which is more simplified and accurate than the traditional one. Based on the simplified wave velocity, a nonlinear wave model of the high-purity HIASC is further established. Combined with the proposed wave model, a novel generalized generic model control scheme (SW-GGMC) is carried out, which is compared with the generic model controllers based on the traditional wave model (Wave-GMC) and data-driven model (Data-GMC), respectively. In both servo control and regulatory control, SW-GGMC exhibits the best performances. Detailed research results confirm the efficiency of the simplified wave model and the advantages of the proposed SW-GGMC control scheme. (C) 2016 Elsevier Ltd. All rights reserved.