Nonlinear state estimation for fermentation process using cubature Kalman filter to incorporate delayed measurements

State estimation of biological process variables directly influences the performance of on-line monitoring and optimal control for fermentation process. A novel nonlinear state estimation method for fermentation process is proposed using cubature Kalman filter (CKF) to incorporate delayed measurements. The square-root version of CKF (SCKF) algorithm is given and the system with delayed measurements is described. On this basis, the sample-state augmentation method for the SCKF algorithm is provided and the implementation of the proposed algorithm is constructed. Then a nonlinear state space model for fermentation process is established and the SCKF algorithm incorporating delayed measurements based on fermentation process model is presented to implement the nonlinear state estimation. Finally, the proposed nonlinear state estimation methodology is applied to the state estimation for penicillin and industrial yeast fermentation processes. The simulation results show that the on-line state estimation for fermentation process can be achieved by the proposed method with higher estimation accuracy and better stability.

This figure shows the estimation results of biomass concentration for penicillin fermentation process using the SCKF algorithm to incorporate delayed measurements and the SCKF algorithm with secondary measurements only. The estimates with secondary measurements only cannot track the true state values lacking of sufficient measurement information under incorrect initial conditions, while the SCKF algorithm incorporating delayed measurements converges to the true process state much faster after the first time arrival of the primary measurements. The estimation accuracy of the biomass concentration is improved greatly using the SCKF algorithm with sample-state augmentation, which incorporates delayed measurements efficiently.Figure optionsDownload as PowerPoint slide