Observability analysis and model formulation for nonlinear state estimation

A suitable design of state estimators for advanced control requires a detailed and representative mathematical model for capturing the nonlinear process behavior. The system observability, i.e. when the set of measurements provides enough information to estimate all the system states, is not a premise of the derivation of the Kalman filter. However, this propriety can improve the state estimator performance. On the basis of these design tasks, we outline a state estimation tuning strategy for different model formulations and present an algorithm to select the smallest number of measured variables to guarantee the system observability. The Williams–Otto semi-batch reactor was selected as case study, since its model formulation can be represented by two different set of states: (a) a mass basis states set and (b) a mass fraction basis states set. While the process-noise covariance matrix Q in the state estimator can be a diagonal and constant for the first model formulation, the matrix Q is not diagonal and time-varying for the second one due to their highly correlated states. Our results have shown how to convert the tuning matrices between different state definitions so that similar estimation results can be achieved.