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.

This work explores the model predictive controller design of the continuous pulp digester process consisting of the co-current zone and counter-current zone modelled by a set of nonlinear coupled hyperbolic partial differential equations (PDE). The distributed parameter system of interest is not spectral and slow-fast dynamic separation does not hold. To address this challenge, the nonlinear continuous-time model is linearized and discretized in time utilizing the Cayley-Tustin discretization framework, which ensures system theoretic properties and structure preservation without spatial discretization or model reduction. The discrete model is used in the full state model predictive controller design, which is augmented by the Luenberger observer design to achieve the output constrained regulation. Finally, a numerical example is provided to demonstrate the feasibility and applicability of the proposed controller designs.