(233q) Application of Model-Predictive Control to a Feeding Blending Unit

Continuous pharmaceutical manufacturing is
pursued by the FDA [1][2]. By continuously monitoring the process and by
actively taking actions in case of deviating process parameters, the product
quality will be improved while the production costs decrease. The proper
operation of the continuous production line requires the development and
implementation of sophisticated control strategies. On the one hand, the control
strategy has to ensure that intermediates of bad quality are discharged. On the
other hand, this missing material has to be compensated by means of adjusting
the production speed of the upstream and/or downstream unit operation. This
operation mode poses the requirement of adjusting the production speed of
individual unit operations.

The paper at hand focuses on the design of
a model predictive control (MPC) strategy [3][4] for a feeding blending unit
(FBU), see Figure 1. The considered setup utilizes two feeders and a blender in
order to create a blend of a given composition. The controller aims at tracking
a prescribed blender outlet mass flow. Simultaneously, the mass hold-up in the
blender, as well as the blender speed should remain within given bounds. A
mathematical model of the plant, which is based on physical relations, is
given. Model parameters have to be identified from measurement data. Based on
the presented plant model, a model predictive control strategy is designed.

Figure 1: Considered setup

The presented plant model is based upon the
idea of dividing the blender into several compartments. For each compartment,
the mass balance equation is solved. The inlet mass flow of the compartments is
known: for the first compartment, it is equal to the sum of the feeder mass
flows, and for the following compartments, the inlet mass flow is equal to the
outlet mass flow of the preceding one. The outlet mass flow of one compartment is
computed from the hold-up in the compartment and the mean residence time of the
material in this compartment. The mean residence time depends on the hold-up
and on the blender speed. A simple relation, which relates the mean residence
time to the blender speed is fitted from measured data. By considering the mass
hold-ups of the individual compartments as state variables, a state space realization
[5] of the plant is derived. The number of state variables equals the number of
compartments.

Furthermore, the input/output behavior of
the blender regarding concentration is modeled by means of a third order low
pass filter with additional dead-time. The time constants and the dead time
have to be identified from measurements.

A model predictive control strategy, which
is based on the presented plant model, is proposed. The formulation of the
objective function is discussed. Constraints on the state and the actuating
signal are taken into account by the suggested control strategy. Several test
scenarios, which investigate the fluctuations of feeder mass flows on the
outlet of the blender are set up.

Simulation studies demonstrate the advantages
of the proposed concept. The tuning of the controller is very intuitive,
multi-input multi-output systems with constraints can be handled naturally.

[1] U.S.
Department of Health and Human Services, “Guidance for Industry - PAT - A Framework
for Innovative Pharmaceutical Development, Manufacturing, and Quality
Assurance,” 2004.

[2] S. Chatterjee,
“FDA Perspective on Continuous Manufacturing,” IFPAC Annual Meeting,
2012. [Online]. Available: http://www.fda.gov/downloads/AboutFDA/CentersOffices/OfficeofMedicalProd....
[Accessed: 21-Mar-2016].

[3] J. B. Rawlings
and D. Q. Mayne, Model Predictive Control: Theory and Design. Nob Hill
Publishing, 2015.

[4] J.
Maciejowski, Predictive Control with Constraints. Prentice Hall, 2001.

[5] B. Friedland, Control
System Design: An Introduction to State-Space Methods. New York:
McGraw-Hill, 1986.