Application of Kalman filters to the regulation of dead time processes

A single-input single-output control algorithm for a process with dead time and dead time uncertainty is described. The process dynamics consist of first-order mixing and pure delay with the pure delay being dominant. The process is disturbed at the upstream end by a disturbance sequence consisting of white noise passed through a first-order shaping filter. The process output is subject to white measurement noise. A discrete Kalman filter is used to produce state estimates for the disturbance mixing and dead time states which are updated from the process output residual error. In order to handle dead time uncertainty of up to a priori established limits, the residual error is passed through a dynamic dead band whose magnitude is a function of the dead time states of a separate process dynamic model driven by the process input. The dead band eliminates dead time error components from the residual. Control is achieved by state feedback from the upstream Kalman filter state estimate. The algorithm is in use on paper machine and bleach plant control applications and gives near minimum variance performance when properly tuned.