A multi-form modelling approach to the dynamics and control of drum granulation processes

Abstract

Drum granulation processes are represented by a set of mass transfer, solid transport, as well as population balance equations. The population balance is mathematically described by partial differential–integral equations. The overall granulation model is highly non-linear, large-scale with multiple coordinates and uncertain parameters, leading to tremendous difficulties for optimisation and control. In our previous work, a two-level control strategy is proposed, which consists of an upper level optimal control for the determination of optimal set-points, and a lower level non-linear model predictive control (NMPC) for the simultaneous computations of uncertain parameters and control variables. However, long computing times and insufficient measurement data prevent industrial applications. In this paper, strategies are developed to improve the applicability of the multi-level, model predictive control scheme (ML-MPC) using the multi-form modelling approach. In the multi-form modelling approach, the granulation plants are represented by a variety of model forms for different end-uses. These include: (1) the distributed parameter population balance model (DP-PBM), (2) the lumped parameter population balance model (LP-PBM), (3) matrix representation with off-line computed matrix elements, (4) local linear models, (5) reduced order models using balanced truncating and methods of moment. It can be shown through dynamic simulations that significant computing time reductions can be achieved with properly selected model forms. Since both open-loop optimal control and closed loop MPC rely on iterative dynamic optimisation, overall computing time reduction makes on-line applications possible. Furthermore, the development of local linear models allows the applications of well-established linear system theory and techniques to process control, parameter identification and model order reduction. The demonstrated advantages of the proposed multi-form modelling approach imply a big step forward towards the industrial applications of model-based control for granulation processes.