Model-based quality monitoring of batch and semi-batch processes

In this paper, a model-based inferential quality monitoring approach for a class of batch systems is investigated. Given the appropriate model form, the batch quality monitoring problem can be reduced to the problem of state estimation for batch and semi-batch processes. Because feed upsets are often a major source of disturbance in this type of system, it is shown that estimating the initial conditions can lead to improved state estimates throughout the batch as well as improved monitoring and control of end- use quality in many cases. The approach taken in this paper is to reduce the e€ects of the initial uncertainty resulting from feed disturbances by using algorithms designed to perform on-line smoothing of the initial conditions. First, an Extended Kalman Filter- based ®xed-point smoothing algorithm is presented and compared to a popular approach to estimating the initial conditions. Subsequently, a nonlinear optimization-based approach is introduced and analyzed. A sub-optimal on-line approximation to the optimization problem is developed and shown to be directly related to the Extended Kalman Filter-based results. Finally, some practical implementation aspects are discussed, along with simulation results from an industrially relevant example application.