(468e) Experimental Implementation of a Model-Free Feedback Controller for the Size and Shape of Needle-like Crystals Growing in Suspension

Particle size and shape have a major impact on downstream processes in a crystallization process. The size and shape influences the physical characteristics of the final product obtained at the end of a crystallization step. Feedback control-based approaches have been proposed to control the size and shape of a population of crystals. Application of feedback control in a process can be particularly powerful as they have the ability to guide a population towards a desired target despite the presence of un-modeled phenomena and process disturbances. The prerequisite for the development and implementation of such feedback controllers are the availability of online monitoring and characterization tools for both the solid and liquid phase.

Studies aimed at experimental application of feedback control for size and shape control are scarce in literature [1]. This could be partly attributed to the unavailability of tools that could characterize the size and shape of a population of crystals. Recent advancements in imaging based tools have nevertheless addressed the above-mentioned issue of solid phase characterization [2]. Independent simulation studies performed using model-based and model-free feedback controllers in a growth-dominated seeded batch cooling crystallization process have led us to conclude that a model-free controller can robustly reach final target dimensions with a comparatively low level of complexity. The model-free approach requires only knowledge of the thermodynamics eliminating the need to develop multi-dimensional kinetic models for the system-of-interest [3].

In this work, a feedback controller was implemented in a lab scale batch crystallizer to guide two different seed populations of β L-glutamic acid in water towards desired target dimensions under growth-dominated conditions. The size and shape of the population of crystals was characterized using the online monitoring tool, µ-DISCO [2]. The experimental campaign was a two-step process, involving namely constant supersaturation controller (CSC) and model-free path following controller (PFC) experiments. The CSC experiments were performed at four different constant supersaturation levels to serve two purposes. First, to verify the monotonic behavior of the ratio of the rate of change of the average particle dimensions in the population with temperature, which is essential for the PFC. Second, to estimate an attainable region in the particle size and shape space where the controller could act on the population of crystals.

Upon the completion of the first step, PFC experiments were performed on both population of crystals, to reach two different target dimensions that falls within the attainable region. Repeatability experiments for all the PFC experiments were also performed. The controller was able to successfully reach target dimensions with only the thermodynamic knowledge of the system despite the controller acting on different batches of seed crystals, and operating conditions. The robustness provided by the controller used and experimental verification of the same leads us to conclude that model-free approach towards size and shape control could be a promising alternative to model-based control strategies.

References

[1] Eisenschmidt, H.; Bajcinca, N.; Sundmacher, K. Optimal Control of Crystal Shapes in Batch Crystallization Experiments by Growth-Dissolution Cycles. Cryst. Growth Des. 2016, 16 (6), 3297–3306.

[2] Rajagopalan, A. K.; Schneeberger, J.; Salvatori, F.; Bötschi, S.; Ochsenbein, D. R.; Oswald, M. R.; Pollefeys, M.; Mazzotti, M. A Comprehensive Shape Analysis Pipeline for Stereoscopic Measurements of Particulate Populations in Suspension. Powder Technol. 2017, 321, 479–493.

[3] Ochsenbein, D. R.; Schorsch, S.; Vetter, T.; Mazzotti, M.; Morari, M. Growth Rate Estimation of β L-Glutamic Acid from Online Measurements of Multidimensional Particle Size Distributions and Concentration. Ind. Eng. Chem. Res. 2014, 53 (22), 9136–9148.