The state estimation and sensor placement for a continuous pulp digester
with delayed measurements are investigated. The underlying model of
interest is heat transfer in a pulp digester modeled by two coupled
hyperbolic partial differential equations and an ordinary differential
equation. Output measurements are considered with delay due to the
possible low sampling rate. The Cayley-Tustin transformation is utilized
to realize model time discretization in a late lumping manner which does
not account for any type of spatial approximation or model reduction.
The discrete Kalman filter is applied to estimate the system states
using the delayed measurements. The selection of sensor location is
addressed along with estimator design accounting for the delayed
measurements and investigated by minimizing the variance of estimation
error. The performance of the state estimator is evaluated, and the
sensor placement is analyzed through simulation studies, which provide
guidance for sensor location selection in industrial applications.