Integrated batch‐to‐batch and nonlinear model predictive control for polymorphic transformation in pharmaceutical crystallization

Abstract

Polymorphism, a phenomenon in which a substance can have more than one crystal form, is a frequently encountered phenomenon in pharmaceutical compounds. Different polymorphs can have very different physical properties such as crystal shape, solubility, hardness, color, melting point, and chemical reactivity, so that it is important to ensure consistent production of the desired polymorph. In this study, an integrated batch-tobatch and nonlinear model predictive control (B2B-NMPC) strategy based on a hybrid model is developed for the polymorphic transformation of L-glutamic acid from the metastable a-form to the stable b-form crystals. The hybrid model comprising of a nominal first-principles model and a correction factor based on an updated PLS model is used to predict the process variables and final product quality. At each sampling instance during a batch, extended predictive self-adaptive control (EPSAC) is employed as a NMPC technique to calculate the control action by using the current hybrid model as a predictor. At the end of the batch, the PLS model is updated by utilizing the measurements from the batch and the above procedure is repeated to obtain new control actions for the next batch. In a simulation study using a previously reported model for a polymorphic crystallization with experimentally determined parameters, the proposed B2B-NMPC control strategy produces better performance, where it satisfies all the state constraints and produces faster and smoother convergence, than the standard batch-to-batch strategy.

Hybrid semi-parametric modeling in process systems engineering: Past, present and future

“…in order to enhance the prediction quality, can also be beneficial in this context. While a parallel set-up (Doyle et al, 2003;Hermanto et al, 2011;Zhang et al, 2012) is relatively easy to apply and might be sufficient in many cases, a serial approach can help to under-stand the complex interactions. For example, Georgieva et al (2003) model the most uncertain parts in a set of material, energy and population balances, namely the agglomeration kernel, the nucleation and growth rate, through nonparametric techniques.…”

“…However, given that the model estimates can be compared to measurements at-time, the model parameters, i.e. mainly the network weights, might be adapted, thus reducing or eliminating the model-plant mismatch (Costa et al, 1998Cubillos & Acuna, 2007;Cubillos & Lima, 1997Hermanto et al, 2011). In such a case, it might be argued that hybrid semi-parametric models bear no advantage over non-parametric models, since those can be adapted in the same way, but (i) the hybrid semi-parametric model is easier to interpret, wherefore the control action can be scrutinized and (ii) the hybrid semi-parametric model might be easier to adapt, e.g.…”

“…Particle size distribution, which is of major interest in many processes, can be modeled with population balances, as for instance in crystallization (Georgieva et al, 2003;Hermanto, Braatz, & Chiu, 2011;Lauret et al, 2000;Zhang, Wang, He, & Jia, 2012), milling (Kumar Akkisetty et al, 2010) or polymerization (Doyle et al, 2003). The application of a complementary nonparametric model, e.g.…”

“…These methods can account for nonlinearities and are relatively computationally inexpensive. In case that the process model equations are not invertible, FLC (Bazaei & Majd, 2003;Hussain, Ho, & Allwright, 2001;Madar, Abonyi, & Szeifert, 2005), sliding mode control (Hussain & Ho, 2004), Model Predictive Con-trol (MPC) (Abonyi et al, 1999;Cubillos, Callejas, Lima, & Vega, 2001;Hermanto et al, 2011;Ibrehem, Hussain, & Ghasem, 2011;Klimasauskas, 1998;Tsen et al, 1996;van Can et al, 1996;Vega et al, 2000;Vega, Lima, & Pinto, 1997), predictive or optimal control (Anderson et al, 2000;Costa et al, 1998;Costa, Henriques, Alves, Maciel Filho, & Lima, 1999;Cubillos & Lima, 1997Schenker & Agarwal, 2000;Vieira et al, 2005) schema can be employed, where FLC and sliding mode control are computational less expensive while MPC or optimal control may provide better performance. When comparing the performances of control schema that utilize hybrid semiparametric models to those using either traditional control methods (such as a self-tuning PID (Xiong & Jutan, 2002), a generalized minimum variance controller (Xiong & Jutan, 2002), a FLC based on a linear model (Hussain et al, 2001) or a MPC based on a linearized model (Anderson et al, 2000)) or to non-parametric model based controllers (Cubillos et al, 2001;Hussain et al, 2001;Ibrehem et al, 2011;Schenker & Agarwal, 2000), it was mostly observed that the hybrid semiparametric model based control schema performed significantly better.…”

Robust PID based indirect-type iterative learning control for batch processes with time-varying uncertainties

“…Combining with the feedback control design, a two-step ILC design [29] was proposed to adjust the process input for improving the output tracking performance against load disturbance and process uncertainties. For highly nonlinear processes such as crystallization processes, hierarchical ILC and nonlinear MPC based ILC methods [30,31] were proposed to track the desired setpoint profile against batch-to-batch uncertainties.…”