(62e) Model Predictive Control of Wet Granulation Using an Experimentally Validated Population Balance Model

Granulation is a complex process in which many input variables influence many product properties. As Iveson et al. describe in a review paper (2001), the understanding of the fundamental processes that control granulation behavior and product properties have increased in recent years. This knowledge can be used during process design, in choosing the right formulation and operating conditions, and it can also be used to improve process control.

Although many variables are set constant during process design, variations during production in input variables occur due to the variable nature of the powder feed. Even if all granule properties but size are ignored for process control, a one phase granule size distributions still needs to be represented by multiple output variables, in order to represent the shape of the distribution. (these can be mean sizes (with coefficients of variation), percentile sizes, moments or size bins).

Model Predictive Control (MPC) is an effective method to control multiple input, multiple output processes (García et al. 1989). To be able to control multiple outputs by changing multiple inputs, the controller uses a process model to calculate the influence of input variables on future states of the process. The complex nature of granulation makes MPC an obvious choice as has been suggested by Wang and Cameron (2002) in their review of modeling and control of continuous drum granulation. However there are only few examples of MPC applied on granulation mentioned in literature. Pottmann et al. (2000) fitted a black box, linear discrete-time model to process data. They tested plant-model mismatch by perturbing individual step response gains and time constants and introducing Gaussian measurement noise to the outputs. They conclude: ?Its performance indicates how the unique control objectives of granulation processes can be met effectively by using this approach.? Gatzke and Doyle (2001) introduced soft output constraints and prioritized control objectives to the same MPC setup.

In our current work we introduce a more detailed plant model, and use experimentally validated rate laws in the controller. The plant model is based on work presented by Sanders et al. (2005), granulation kinetics were measured in a 10 liter batch granulator with an experimental design that included four process variables (impeller speed, binder content, binder viscosity and starch/lactose ratio). The aggregation rates were extracted with a Discretized Population Balance model (DPB) (Biggs et al. 2003). Knowledge of the kinetics was used to model a continuous (well mixed) granulator.

The controller model is a linearized state space model, derived from the nonlinear DPB model. It has the four process variables from the experimental design and a feed ratio as input variables. Since the DPB model describes the whole size distribution (GSD), different sets of output variables were chosen and compared.

Preliminary results show successful implementation of Model Predictive Control on a continuous granulator. Further research is needed to test the linear model on an actual pilot plant.

References:

C.A. Biggs, C. Sanders, A.C. Scott, A.W. Willemse, A.C. Hoffman, T. Instone, A.D. Salman and M.J. Hounslow, Coupling granule properties and granulation rates in high-shear granulation, Powder Technology, Volume 130, Issues 1-3, 19 February 2003, Pages 162-168.

E.P. Gatzke and F.J. Doyle, III, Model predictive control of a granulation system using soft output constraints and prioritized control objectives, Powder Technology, Volume 121, Issues 2-3, 26 November 2001, Pages 149-158.

S.M. Iveson, J.D. Litster, K. Hapgood and B.J. Ennis, Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review, Powder Technology, Volume 117, Issues 1-2, 4 June 2001, Pages 3-39.

C.E. García, D.M. Prett and M. Morari, Model predictive control: theory and practice?a survey, Automatica 25 3 (1989), pp. 335?348.

M. Pottmann, B.A. Ogunnaike, A.A. Adetayo and B.J. Ennis, Model-based control of a granulation system, Powder Technology, Volume 108, Issues 2-3, 20 March 2000, Pages 192-201.

C.F.W. Sanders, W. Oostra, A.D. Salman and M.J. Hounslow, Development of a predictive high-shear granulation model; Experimental and modelling results, 7th World Congress of Chemical Engineering , Glasgow 2005

F.Y. Wang and I.T. Cameron, Review and future directions in the modelling and control of continuous drum granulation, Powder Technology, Volume 124, Issue 3, 29 April 2002, Pages 238-253.