Artificial neural networks, because they are nets of basis functions, can provide good empirical models of complex nonlinear processes that are useful for many purposes including process control. The modelling of a packed distillation column described here provides an interesting example of complex modeling because the column exhibits a change in the sign of the gain under various operating conditions. We show how artificial neural networks can model the column, and demonstrate that the network model is as good or better than a simplified first principles model when used for model predictive control.