| An algorithm is presented which solves the extended Kalman filter equations for a continuous dynamic system that is discretely measured which is the usual structure for model predictive control. For large systems, computational decoupling of the state estimates and covariances in the EKF equations allows a sequential strategy in the solution of these differential equations. The computational algorithm also exploits the symmetric nature of the covariance matrix. The algorithm utilizes implicit simultaneous methods, which are powerful in terms of accuracy and efficiency, for numerical integration and includes an error control strategy that takes into account the behavior of both the state estimates and covariances. The algorithm was validated by successful solution of known test problems. This algorithm can be used for on-line filtering and state estimation, model predictive control and parameter estimation.This algorithm was used to implement an estimation and control of a fed-batch E. Coli fermentor. Large delay times and intermittent measurement of crucial state variables make this reactor system a formidable challenge for on-line optimization and control. Near optimal control of this reactor is achieved using a dual filter strategy i.e., two filters each operating sequentially on different sampling and measurement frequencies. The high frequency filter provides a priori estimates and covariances to the low frequency filter while the low frequency filter provides initial conditions for the high frequency filter. |
