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Some chemical plants such as distillation column have highly nonlinear behavior. These processes demand a powerful identification method such as linear and nonlinear models. In this paper, a distillation column is simulated in a rather realistic environment by HYSYS and the obtained data is in connection with MATLAB for identification and control purpose. In this case, the identified model is characterized by two structures, Linear model structure based on ARX (Autoregressive with external input) and nonlinear model structure based on neural network. For control goals, two linear and nonlinear model predictive controllers are applied. General predict control (GPC) and nonlinear predict control (NPC) are compared based adaptive identification of model. Since, practical systems change with time and the parameters of system are time varying, using real-time identification based recursive parameter estimation is necessary, although, desired control strategy is reached with a good parameter estimation. The algorithm has been tested on an distillation column. The resulting performances show the successful and promising capabilities of the proposed algorithm.