(344d) Robust State Estimation of Feeder and Blender Systems in Continuous Pharmaceutical Manufacturing Systems

The development and application of advanced monitoring, operational- and design-making strategies for continuous pharmaceutical manufacturing require good understanding of the current state of the system. Moving horizon estimation (MHE) can estimate the current system state by solving a well-defined optimization problem where process complexities are explicitly taken into consideration as constraints. Traditional MHE techniques assume random measurement noise governed by some normal distributions. However, this assumption is not always valid since the actual distributions are often unknown or exhibiting departures from normal form. In addition, conventional state estimators fail to consider gross or systematic errors, such as bias, outliers, and drifts. The presence of gross errors can contaminate the state estimates and the reconciled measurements, causing undesirable “smearing” effects [1]. As a result, research on state estimation is closely related to topics of data reconciliation (DR) and gross error detection (GED).

Robust estimators, also known as the maximum likelihood estimators or M-estimators, are commonly used in reconciling measurements contaminated with gross errors. Robust estimators have been implemented in many research areas, including state estimation, data reconciliation, and parameter estimation [2, 3, 4]. Systematical comparisons between various robust estimators can be found in literature [1, 5]. To improve the accuracy and robustness of state estimation, we incorporate robust estimators within the standard MHE skeleton, leading to an extended MHE for dynamic state estimation with gross errors.

In continuous tablet or capsule production lines, the optimal operation of the feeder-blender system (FBS) is crucial in order to meet the critical quality attributes of the final product. Advanced monitoring and control strategies of FBS require fast and accurate estimates of the current process state. In this work, the proposed MHE framework is implemented on a simple FBS configuration which includes two loss-in-weight (LIW) feeders and one continuous blender. Based on our experiment results, we propose a first-principle dynamic model for screw feeders and a reduced-order, compartment-based model for continuous blenders. Both dynamic models are used in our MHE framework, to result in a dynamic optimization (DO) problem constrained by differential algebraic equations (DAEs).

The proposed MHE strategy is first tested on simulation runs of the FBS where measurements are contaminated with gross errors such as outliers and drifts. Numerical results show significant benefits in applying the extended MHE technique with robust estimators. In addition, we implement our MHE framework in a pilot plant FBS, which is part of a continuous dry granulation line, and demonstrate on-line dynamic state estimation and data reconciliation. Experimental results confirm that the proposed MHE framework is robust to gross errors and can provide accuracy state estimates. Moreover, the efficient solution of the MHE realized in this work, suggests feasible application of on-line state estimation on more complex continuous pharmaceutical processes.

Bibliography

[1] Özyurt, Derya B., and Ralph W. Pike. "Theory and practice of simultaneous data reconciliation and gross error detection for chemical processes." Computers & chemical engineering 28.3 (2004): 381-402.

[2] Tjoa, I. B., and L. T. Biegler. "Simultaneous strategies for data reconciliation and gross error detection of nonlinear systems." Computers & chemical engineering 15.10 (1991): 679-690.

[3] Arora, Nikhil, and Lorenz T. Biegler. "Redescending estimators for data reconciliation and parameter estimation." Computers & Chemical Engineering 25.11 (2001): 1585-1599.

[4] Nicholson, Bethany, Rodrigo López-Negrete, and Lorenz T. Biegler. "On-line state estimation of nonlinear dynamic systems with gross errors." Computers & Chemical Engineering 70 (2014): 149-159.

[5] Prata, Diego Martinez, José Carlos Pinto, and Enrique Luis Lima. "Comparative analysis of robust estimators on nonlinear dynamic data reconciliation." Computer Aided Chemical Engineering 25 (2008): 501-506.