The trade-off between model accuracy and computation tractability for model-based control applications is well known. While nonlinear models are needed to capture the detailed behavior of many chemical processes, the resultant structures may not lead to straightforward control implementation. The current work advocates the use of low-order nonlinear models based on wave propagation that are mathematically concise and capture the essential nonlinear behavior of a process. In this work, differential geometry is invoked to achieve input - output linearization of a high-purity distillation column based on a traveling-wave model. A Kalman filter is used to recursively update the parameter values. Comparison with a linear controller based on a two-time constant model shows that the nonlinear controller outperforms the linear controller in tight control of both the overhead and the bottoms composition.