Model-Predictive Design, Control, and Optimization

Currently, there is a high level of interest in the pharmaceutical industry in continuous-manufacturing strategies, integrated with online-monitoring tools, that are designed, optimized, and controlled using advanced, model-predictive systems. These strategies can accelerate the full implementation of the quality-by-design (QbD) paradigm for the next generation of pharmaceutical products. In addition to its flexibility and time- and cost-saving features, continuous manufacturing is intrinsically steady and therefore easily amenable to model predictive design, optimization, and control methods. These methods have proven to be effective approaches to improve operational efficiency and have been widely used in various process industries. Excitingly, in the pharmaceutical industry, the application of the model-predictive design, optimization, and control is virgin territory, wide open to researchers and technology providers.

Using modeling methods

Recently, the pharmaceutical industry as well as FDA have recognized the need for modernizing pharmaceutical manufacturing and have launched an initiative for enhancing process understanding through QbD and process analytical technology (PAT) tools (1-4). Major goals of these efforts include development of the scientific mechanistic understanding of a wide range of processes; harmonization of processes and equipment; development of technologies to perform online measurements of critical material properties during processing; performance of real-time control and optimization; minimization of the need for empirical experimentation and, finally, exploration of process flexibility or design space (5). In many cases, these goals can be achieved effectively and efficiently by the joint application of designed experiments and modeling tools such as discrete element modeling (DEM), computational fluid dynamics (CFD), statistical models, and population balance models (PBM). DEM and CFD are mechanistic in nature and can effectively capture the motion of particles within equipment or their interaction with a stream of fluid. The DEM approach has been implemented in various pharmaceutically relevant unit operations, such as blending, granulation, and coating (6). The application of CFD has been observed in unit operations, such as mixing, granulation, and crystallization (7). Statistical models, such as response-surface methodologies, have been largely used to determine design space and to a lesser extent for optimization (8). PBMs (hyperbolic partial differential equations representing mesoscopic framework) have also been widely implemented on particle-based unit operations, such as granulation, crystallization, and mixing (9).

While application of model-predictive design in pharmaceutical applications is only in its infancy, several successes can be reported. Examples of applications at Rutgers University include stirred tank agitators used as bioreactors (10), roller bottle reactors used for mammalian cell culture of viruses (11), and understanding wall losses in the Anderson Cascade Impactor (12). Many other groups have since used CFD tools for many design applications, including chemical reactors of many different scales, crystallizers, liquid-liquid and liquid-gas reactors, and cleanroom design.

Similarly, use of DEM applications go back well over a decade. Some of the earliest examples of the use of DEM for design purposes in pharmaceutical applications focused on the design of powder blenders, including the V-blender, the double cone, and the bin blender. Since then, many other examples have followed, focusing on hoppers, tablet coating, and tableting, for example.

An additional modeling tool is the use of response-surface models, which are typically developed using data from designed experiments and subsequently used to select process optima and to design control algorithms. While the data-driven models used in this application are largely empirical and do not require a mechanistic understanding of the processes to which they are applied, they are invaluable as tools to aid understanding of the relative importance of process and formulation variables and thus help narrow down the scope of work required to advance process understanding.

These tools are increasingly becoming common components of the pharmaceutical process-design toolbox. They have spread from academia to the largest pharmaceutical companies, many of which have formed process-modeling groups in which researchers are using these tools to design and optimize processes in silico prior to expensive equipment acquisition or to reduce the complexity of designed experiments.

To date, efforts have been piecemeal and typically have focused on individual process components. The emergence of continuous manufacturing as a central focus of attention, however, is now motivating the need to develop modeling frameworks capable of simulating all process components simultaneously, using a variety of tools suited for each specific process. The flowsheet framework meets this need.

Flowsheet modeling

The continuous manufacturing of drugs can be achieved using various routes: direct compaction (DC), roller compaction (dry granulation or DG), or wet granulation (WG), depending on the starting and desired end properties of the formulation. DC is the simplest of the processes mentioned above while DG and WG improve flowability characteristics to prevent ingredient segregation and to increase density. DC (14), DG (15), and WG (16) routes have been explored using model-predictive flowsheet methodologies. Application of advanced modeling techniques for optimization and control (17, 18) on the overall flowsheet instead of the individual unit operations would enable efficient operation of the continuous process.

The challenges associated with developing robust and reliable flowsheet models for solids' processes include:

• Characterization of all unit operations

• Development of models that describe their constituent mechanisms

• Performance of experimental studies for the data acquisition of multi-dimensional key particle properties

• Identification of all the possible manipulated and controlled variables and their interactions (17, 18)

• Integration of process design and control to identify globally valid operating conditions.

Extensive research is ongoing to identify and develop predictive models for all the unit operations involved in the continuous tablet-manufacturing process. For integrating the various unit operations into a flowsheet, it is crucial to correctly identify the critical connecting properties that communicate across units (17). Simulating the overall flowsheet, the variations in the key properties can also be tracked during the transient states involving process start-up, perturbation propagation, dynamic response to change in settings due to control actions, and process shutdown. Furthermore, through the implementation of various operating scenarios, the flowsheet model can be used for the assessment of different process alternatives (so far achieved by expensive laboratory tests), which are then scaled up to the desired plant size. The developed and validated flowsheet-simulation system can also be used for operator training, since any sequences in operating schedules can be performed virtually and analyzed through a computer screen. Using information obtained from the flowsheet models for plant implementation is the next challenge. Incorporating control systems in the actual plant is a crucial task needed for efficient operation and minimal variation from the setpoint values.

Of particular interest from a regulatory perspective is the use of integrated flowsheet models to enable identification of the propagation of noise or upsets in a particular unit operation through the entire continuous line (16, 18). This issue is directly relevant to the assessment of robustness and reliability of the continuous manufacturing system. Process optimization can be achieved by implementing optimization algorithms on the overall integrated model. Figure 1 shows a flowsheet model (simulated in gPROMS, Process Systems Enterprise) of a flexible, continuous, tablet-manufacturing process together with the implemented control system.

Figure 1: Flexible continuous tablet manufacturing process with (1) direct compaction, (2) roller compaction, and (3) wet granulation. (ALL FIGURES COURTESY OF AUTHORS)

Model-predictive control

Various control systems can be implemented on the flowsheet model in the form of simple PID loops (15) or with advanced model-predictive control (MPC) (17). Control loops can be implemented by identifying the control-loop pairings and assessing the need for MPC in each control loop (as opposed to using just PID loops). With this information, the PID controllers are designed and implemented to obtain a predictive model of the plant, thereby suggesting the design of the MPC controller. The designed MPC is then incorporated into a general model for model-based performance evaluation.

As an example, consider integration of control hardware and software in the continuous feeder and blender system, as shown in Figure 2. A PAT system is used to read the near infrared (NIR) spectral data at the blender outlet and communicate it to the multivariable analysis (MVA) model performing principle-component analysis and partial least-squares (PCA/PLS) to provide the API concentration and relative standard deviation (RSD) value. These critical quality attributes (CQAs) are used as inputs to the MPC in the process-control system. The MPC uses the two CQA inputs to drive the feed ratio and the blender speed. The MPC output (feed ratio) gives the feeders' flowrate setpoints, which are then tracked by slave PID controllers. The implemented control scheme utilises a PAT data-management system (synTQ, Optimal) to integrate a digital automation system (DeltaV, Emerson Process Management) with an NIR analyser and MVA model.

Figure 2: Implementation of a model-predictive controller via a process analytical technology (PAT) datamanagement system (1. SynTQ, Optimal), (2. MATLAB OPC, MathWorks), or (3. SiPAT, PCS7, Siemens).

Integrating multiple system parts presented several challenges. A framework, however, is now in place that allows implementation of control architectures for a wide variety of continuous powder processes.

Acknowledgements

This work is supported by the National Science Foundation Engineering Research Center on Structured Organic Particulate Systems, through Grant NSF-ECC 0540855.

The authors are from the Engineering Research Center for Structured Organic Particulate Systems (ERC-SOPS), Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854, USA.

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