On-line dynamic optimization integrated with generic model control of a batch crystallizer

Batch crystallizers are predominantly used in chemical industries like pharmaceuticals, food industries and specialty chemicals. The nonlinear nature of the batch process leads to difficulties when the objective is to obtain a uniform Crystal Size Distribution (CSD). In this study, a linear PI controller is designed using classical controller tuning methods for controlling the crystallizer outlet temperature by manipulating the inlet jacket temperature; however, the response is not satisfactory. A simple PID controller cannot guarantee a satisfactory response that is why an optimal controller is designed to keep the concentration and temperature in a range that suits our needs. Any typical process operation has constraints on states, inputs and outputs. So, a nonlinear process needs to be operated satisfying the constraints. Hence, a nonlinear controller like Generic Model Controller (GMC) which is similar in structure to the PI controller is implemented. It minimizes the derivative of the squared error, thus improving the output response of the process. Minimization of crystal size variation is considered as an objective function in this study. Model predictive control is also designed that uses advanced optimization algorithm to minimize the error while linearizing the process. Constraints are fed into the MPC toolbox in MATLAB and Prediction, Control horizons and Performance weights are tuned using Sridhar and Cooper Method. Performances of all the three controllers (PID, GMC and MPC) are compared and it is found that MPC is the most superior one in terms of settling time and percentage overshoot.

Crystal size distribution (CSD) is an essential criterion for determining the production of high-quality crystals since it influences the efficiency of the crystallization process. Producing specified CSD in the crystallization process represents a main challenge as it depends on temperature control, which indirectly regulates the solution’s concentration and affects the crystal’s evolution. Different temperature profiles may influence the distribution of crystal products, and a suitable optimization algorithm is required to produce an optimum temperature trajectory that produces the desired CSD. Thus, this study aims to maximize the CSD of the grown seed crystals while minimizing the nucleus-grown crystals by employing the best optimization algorithm for the potash alum crystallization process. The crystallization process was developed and simulated in Matlab software using a potash alum in the water system. Four optimization algorithms were proposed with different objective functions, such as maximizing mean crystal size (I), minimizing coefficient of variation (II), minimizing nucleus-grown crystals (III), and maximizing CSD (IV). Based on the simulation results, optimization IV, which maximizes CSD, performs best with a large mean crystal size of 490 µm. Furthermore, the number of fine crystals was among the lowest at a volume distribution of 0.00071 m3/m compared to the linear profile at 0.00191 m3/m. Optimization IV employs a dissolution strategy, which manipulates two quality specifications in one algorithm (size of crystals and number of fines), which is considered the best optimal cooling profile for seeded batch crystallization by maximizing CSD and minimizing the generation of nucleus-grown crystals.

Kinetic parameter estimation for most batch crystallization processes is necessary because nucleation and crystal growth kinetic parameters are often not available. The existing identification methods are generally based on simplified population balance models such as moment equations, which contain insufficient information on the crystal size distribution (CSD). To deal with these problems, a new optimization‐based identification approach for general batch cooling seeded crystallization is proposed in this study. The final‐time CSD is directly used for identification. A novel effective method for solving the population balance equation is developed and used to identify nucleation and growth kinetic parameters. Cooling crystallization of ammonium sulfate in water was experimentally investigated, where the concentration was measured by an on‐line density meter and the final‐time CSD was analyzed by a Malvern Mastersizer 2000. Kinetics for ammonium sulfate are determined based on cooling crystallization experiments. Applying these kinetics in simulation provides a good prediction of the product CSD. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1786–1794, 2004

Comparative evaluations of bulk seeded protein crystallization in batch versus continuous slug flow crystallizers

On-line optimization and control of fed-batch fermentation is difficult due to its non linearity and dynamic operation points with uncertainty. A novel cascade optimal control algorithm was proposed to treat these difficulties with the operating points, which maximize the objective function, was defined by Necessary Conditions of Optimization (NCO). Consequently, a nonlinear Generic Model Control (GMC) was applied to eliminate effect of uncertainty. Calculations of Hamilton gradient online and repeated optimization were avoided. The simulation on saccharomyces cerevisiae enzyme cultivation process showed the efficiency and advantage of the proposed method.

Battery Management Systems (BMS) are critical to safe and efficient operation of lithium-ion batteries and accurate prediction of the internal states [1]. Smarter BMS that can estimate and implement optimal charging profiles in real-time are important for advancement of the Li-ion battery technology. Estimating optimal profiles using physics-based models is computationally expensive because of the non-linear and stiff nature of the model equations, involving the need for constrained non-linear optimization [2-12]. In this work, we present an alternative approach to control batteries applying the concept of differential geometry. This approach is known as Generic Model Control (GMC), or Reference System Synthesis [13,14]. This work enables robust stabilization and control of battery models to set-point as an alternative approach, eliminating the need to perform optimization of nonlinear models. This work builds on our previous work of implementation of GMC for differential variables occurring in a model consisting of differential algebraic equations (DAEs), and extends it to set point based control for algebraic variables. Conventional GMC is applicable for cases in which the output is typically independent of control [13]. We also extend it for cases for which the measured variable can be an explicit function of the manipulated variable. As compared to the generic model control approaches implemented by previous researchers, we have implemented the same concept using direct DAE numerical solvers [15]. The results are presented for single input single objective, and for constrained problems. The proposed approach is compared with standard control approaches and is found to be equally robust if not better. Acknowledgements The work presented herein was funded in part by the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275 and the Clean Energy Institute at the University of Washington, Seattle.

The current clinical standard of Static Cold Storage (SCS) which involves preservation on ice (about +4°C) in a hypoxic state limits storage to a few hours for metabolically active tissues such as the liver and the heart. This period of hypoxia during can generate superoxide and other free radicals from purine metabolism, a well-established component of ischemia/reperfusion injury (IRI). Machine perfusion is at the cutting edge of organ preservation, which provides a functional, oxygenated preservation modality that can avoid/attenuate IRI. In clinical application, perfusion usually follows a period of SCS. This presentation of oxygen following hypoxia can lead to superoxide and hydrogen peroxide generation, but machine perfusion also allows manipulation of the temperature profiles and supply of antioxidant treatments, which could be used to minimize such issues. However, metabolomic data is difficult to gather, and there are currently no mathematical models present to allow rational design of experiments or guide clinical practice. In this article, the effects of a gradual warming temperature policy and glutathione supplementation to minimize oxidative stress are studied. An optimal gradual warming temperature policy for mid-thermic machine perfusion of a liver metabolic model is determined using a combination of Nash Equilibrium and Monte Carlo optimization. Using this optimal gradual warming temperature policy, minimum GSH requirements to maintain hydrogen peroxide concentrations in the normal region are calculated using a different Monte Carlo optimization methodology. In addition, the dynamic behavior of key metabolites and cofactors are determined. Results show that the minimum GSH requirement increases and that the ratio of GSH/GSSG decreases with increasing hydrogen peroxide concentration. In addition, at high concentrations of hydrogen peroxide it is shown that cytochrome C undergoes dysfunction leading to a decrease in useful oxygen consumption and ATP synthesis from the electron transport chain and an overall reduction in the energy charge for the liver cells.

Experimental implementation of a Quality-by-Control (QbC) framework using a mechanistic PBM-based nonlinear model predictive control involving chord length distribution measurement for the batch cooling crystallization of l-ascorbic acid

Non-linear adaptive control of fermentation processes utilizing a priori modelling knowledge

GMC-fuzzy control of pH during enzymatic hydrolysis of cheese whey proteins

The study of an optimal cooling control strategy for a batch white sugar crystallization process is reported in this paper. Within the proposed control strategy, a dynamic optimization algorithm (DOA) and a generic model control (GMC) algorithm were compared with respect to the final process quality achieved. The linear models required in the controller structures were extracted applying two identification alternatives. The GMC algorithm cases seem to guarantee more satisfactory end point quality of the process. However, only the DOA of the supersaturation manipulating the steam flowrate makes feasible all conflicting control objectives.

Molecular weight is one of the influential attributes in a polymerization process and its control in semi-batch operation poses considerable difficulty due to complexities of the process. The present study focuses on the development of different control strategies for controlling the molecular weight by tracking reactor temperature and composition control using jacket temperature and feed flow rate as manipulated variables. The copolymerization of styrene acrylonitrile with xylene as solvent and AIBN as initiator is considered for the present study. The control strategies evaluated are Multi-loop-proportional integral (PI) control, multivariable-PI control and nonlinear generic model control (GMC). The present study showed that control of temperature and composition has resulted in achieving the desired molecular weight. Nonlinear GMC control is able achieve targeted molecular weight closely even in the presence of unmeasured load disturbances in the monomer feed concentration and initial initiator concentration, whereas multi-loop and multivariable PI controllers resulted in some offset.

Optimal temperature policy in a riser reactor

Continuous processing gains importance in the fine chemical and pharmaceutical industries where crystallization is an important downstream operation. Seeded cooling crystallization of the l-alanine/water system was investigated under similar conditions, i.e., temperature interval, cooling rate, and seed material, both in a stirred batch vessel and in a continuous plug flow crystallizer in the coiled flow inverter (CFI) design with horizontal helical tube coils (ID = 4 mm) and frequent 90° bends of the coils. Short-cut calculations based on characteristic time scales and the Damköhler number allow for comparing the batch and continuous crystallization processes. The experimental results reveal crystal growth and growth rate dispersion to be dominating on the product crystal size distribution (CSD). However, at low flow rates of approximately 31 g min–1, a moving sediment flow of the slurry was present in the CFI crystallizer, resulting in further size dispersion effects. Elevated flow rates of approximately 40 g min–1 resulted in a more homogeneous suspension flow and a product CSD comparable to batch quality. Simulation studies based on a population balance equation model strengthen the hypothesis of the solid phase residence time distribution (RTDS) to be more spread in the moving sediment flow regime, leading to a wider product CSD.

Characterization of the anti-solvent batch, plug flow and MSMPR crystallization of benzoic acid