State estimation using a multi-rate particle filter for a reactive distillation column described by a DAE model

State estimation for systems that exhibit nonlinear dynamics is a challenging task. Various estimation techniques have been proposed and the applicability of the available techniques has been demonstrated for more or less complex cases. Applications to really large process models are still rare. In this paper, we investigate a reactive distillation (RD) process that is modeled by a high-dimensional nonlinear system that is described by differential and algebraic equations (DAE) with more than one hundred states. The process exhibits highly nonlinear dynamics and only a few states are measured. The measurements include both differential and algebraic states and are available at different frequencies. We present a formulation of the multi-rate particle filtering (PF) state estimation method which is specifically designed to handle models that are described by DAE. Compared to existing publications on multirate particle filtering modifications of the algorithm are required for nonlinear DAE models where algebraic state variables are measured. We demonstrate the computational feasibility of the methods for the high order RD process model and compare the performance of the proposed estimator for the single-rate case where all measurements are available at every sampling instance and for the multi-rate case where the outputs are available at different sampling rates. We also investigate the effect of the number of particles on the mean squared estimation error for the single-rate and for the multi-rate sampling case and show that the proposed particle filtering technique can be applied to this complex system with a reasonable number of particles.