(509d) Nonlinear Steady-State Data Reconciliation for a Continuous Tableting Line

The robust operation of a continuous process requires a sufficient level and quality of online process measurements and an appropriate level of process control. As the pharmaceutical industry transitions from batch to continuous operation the questions of how many measurement points and what quality of online measurements are necessary or sufficient and the level of sophistication of the process control systems required are very much under discussion. Under the aegis of the NSF ERC on Structured Organic Particulate Systems, we have been investigating these questions in the context of continuous production of tablets. Tablets are the most common dosage form and thus the conversion from batch to continuous production of this drug product form has thus received quite a bit of attention [1].

In this paper we specifically focus on answering questions concerning the selection of and impact of online measurements. To address these questions, we first develop a nonlinear steady state data reconciliation model for a continuous dry granulation line. The data reconciliation model of such a process network consists of the relationship between all of the measured and relevant unmeasured variables of the process together with a description of the error distributions of these measurements [2, 3]. It is assumed that the number of measurements is larger than the degree of freedom of the network model, hence that there is redundancy. Given a set of measurements, an optimization problem is posed which has as its objective function a likelihood type function. This function is the minimization of the difference between the measured values and their best estimates, weighted by the standard deviation of the measurement error of the associated sensor model, with the above mentioned reconciliation model forming the constraint set [3, 4].  

The solution of the maximum likelihood problem constitutes the best real time estimate of the state of a processing system taking into account all of the measurements and their error characteristics. Such an estimate can serve as basis for checking whether all process variables are within acceptable bounds, for identify gross measurement errors, for control action or for process optimization steps. Additionally the reconciliation formulation provides a framework for investigating the impact of adding or eliminating measurements, of replacing instruments with given error characteristics with those with tighter variances or of introducing measurement redundancy [5].

While the data reconciliation problem has received much attention in the process systems engineering literature, most of the attention has been directed at linear models, which consist of the component mass balances of the process [3]. Nonlinearities have principally been introduced through the addition of energy balances, which in their most common form involve equations that are bilinear in flow and composition or flow and temperature [3]. Additionally, it is generally assumed that measurement errors are normally distributed. In this paper we consider nonlinearities which arise because of the inclusion of online measurements of properties such as density and variables such as screw speed, roll speed, etc.  The model nonlinearities have implications on computation performance, which is important for real time application. Finally, given the nature of some of the spectroscopic measurements used in the tableting application [6, 7], the assumption of normality of the measurement error comes into question [5]. We illustrate the approach using case studies carried out on a continuous tableting line.  

References

 [1] Reklaitis G. The Pharmaceutical Manufacturing Institute. 2013, (White Paper) Purdue University, West Lafayette, IN.

 [2] F. Carl Knopf. Modeling, Analysis and Optimization of Process and Energy Systems. First Edition. John Wiley & Sons, Inc. 2002.

[3] Narasimhan S.  & Jordache C. Data reconciliation & Gross Error detection. Houston Texas. Gulf Publishing Company. 2000.

[4] Narasimhan S., Bhatt N. Deconstructing principal component analysis using a data reconciliation perspective. Computers and Chemical Engineering. 2015, 77, 74–84

[5] Cencica O. and Frühwirth R.  A general framework for data reconciliation. Part I: Linear constraints. Computers and Chemical Engineering. 2015, 75, 196–208

[6] Austin, J.; Gupta, A.; McDonnell, R.; Reklaitis, G.V.; Harris, M.T. The use of Near-Infrared and Microwave Resonance Sensing to Monitor a Continuous Roller Compaction Process. Wiley Online Library. 2013.

[7] Austin, J.; Gupta, A.; McDonnell, R.; Reklaitis, G.V.; Harris, M.T. A novel microwave sensor to determine particulate blend composition on-line. Analytica Chimica Acta. 2014, 819, 82-93.