Low order models for nonlinear process control

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 which are mathematically concise and also capture the essential nonlinear behavior of a process. A low order model developed for a high-purity distillation column using the traveling wave phenomenon captures the inherent dynamics of the column. Differential geometry is invoked to achieve input-output linearization of the distillation column based on the nonlinear 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 is presented. The nonlinear controller outperforms the linear controller in tight control of both the overhead and the bottoms composition.; An extension of the traveling wave theory is used to develop a low order model for a batch reactive distillation column. The formation of traveling waves is qualitatively captured by the reduced model. The reduced model is used in nonlinear model predictive control algorithm to produce a specified amount of distillate. The purity of the distillate obtained is controlled via constraints on the tray temperatures in the nonlinear optimization program. The use of reduced model results in significant reduction in the computational requirements.; Since most models do not capture the entire range of behavior exhibited by a chemical process, it is necessary to study the impact of plant-model mismatch. As input-output linearization is used to decouple and control an ill-conditioned process such as the binary distillation column in our work, the impact of uncertainty on the input-output linearization controller performance is studied. It is shown that for an input-output controller the robustness properties depend on the characteristic matrix and not on the nature of the gain matrix as is perceived in the literature.