Elaboraciones gastronómicas usando flores de Allium

Particulate processes are widely used and applied in industry for the manufacturing of a large variety of products, such as in the crystallisation of proteins (Wiencek, 2002), production of latexes by emulsion polymerisation (Immanuel and Doyle, 2002) and aerosol synthesis of titania powders (Kalani and Christofides, 2000). The PSD of the particulate (dispersed) phase strongly influences both the mechanical and physicochemical properties of the product materials. This has motivated a growing attention on the control of particulate processes and has often resulted in model-based control approaches due to the underlying complexities of the phenomena involved (Braatz, 2002; Christofides et al., 2008; Nagy, 2009).

Model-based control strategies have been widely used for various particulate processes including emulsion polymerisation (Doyle et al., 2002; Immanuel and Doyle, 2003), granulation (Wang et al., 2006), fermentation (Henson et al., 2002; Zhu et al., 2000), cellular biological systems (Stelling et al., 2004), aerosol (Kalani and Christofides, 2002) and thermal spray coating processes (Li et al., 2004). In the last decade much effort has been devoted to the development of model-based control strategies of the CSD for crystallisation processes (Aamir et al., 2010; Aamir et al., 2009b; Braatz and Hasebe, 2002; Ma et al., 2002a; Nagy and Braatz, 2003a; Shi et al., 2006; Shi et al., 2005). Most of the strategies used for control and optimisation rely on lumped parameter system, assuming homogeneous systems. The discrepancies with the experimental data are usually reduced through the adjustment of only few sensitive parameters, generally related to the kinetics of the crystallisation. This makes the updated model/parameters valid only in the vicinity of the

current operating conditions. In light of this, a knowledge-based approach to the problem, based on the actual understanding of the process, the implementation of a detailed mechanistic model and a robust run-to-run or within run adaptive model update are crucial aids to the parameter identification. In recent years, the availability of more accurate mathematical models, solution techniques for complex mathematical systems, advances in on-line measurements and control theory created the ground for advancements in the field of nonlinear optimisation and control of the CSD in crystallisation processes (Braatz, 2002;

Larsen et al., 2006; Yu et al., 2007). Different strategies have been proposed to control the crystal size distribution. They include feed forward (open-loop) control, batch-to-batch strategies and on-line model-based control.

The model-based control approaches for crystallisation processes can be divided in two main categories: (i) open-loop (feed-forward) control and (ii) on-line model-based feedback control approaches. Open-loop (or feed-forward) control approaches are techniques for which the process outputs have no effect on the inputs, whereas feed-back control systems are implemented in a closed-loop setting with the outputs that affect the inputs in such a way to keep the outputs at the desired value (Braatz, 2002; Chew et al., 2007; Immanuel and Doyle, 2002; Nagy and Braatz, 2004). Note that open-loop or closed-loop control approaches are defined with respect to some final product property at the end of the batch. In the case of open-loop control approaches the operating conditions are optimised off-line based on model predictions to achieve a desired product property at the end of the batch (e.g.

maximize mean size). The resulting optimal operating policies (e.g. temperature versus time or anti-solvent addition rate versus time profiles) then are implemented using simple feedback tracking control systems.

The operation of crystallisation processes using programmed temperature profiles, derived based on the assumption of constant supersaturation, was introduced in the 1970s (Jones and Mullin, 1974; Mullin and Nyvlt, 1971). The application of programmed temperature profiles yields better CSD properties compared to the natural or linear cooling, traditionally used for crystallisation operation. Performing the open-loop optimisation off-line with nominal values of the model parameters and then implementing the optimal trajectory is the most frequently used model-based control approach. One of the first applications of optimal control theory to crystallisation processes was reported by Jones and Mullin in (1974). The author computed optimal cooling trajectories that maximized the final size of the seed crystals for a batch crystallisation process. In the past few decades optimal control has been widely recommended to improve batch crystallisation operations (Rawlings et al., 1993).

The final CSD is dependent on the supersaturation profile created over the batch time, hence the supersaturation profile (generated e.g. by cooling, anti-solvent addition or evaporation) is the most important decision variable in the optimisations. Various objective functions have been used in the optimisations. A detailed review of the optimisation approaches for the properties of the CSD expressed by its moments were given by (Ward et al., 2006) and are summarised in the Chapter 3. The optimal operating profile is strongly influenced by the objective optimised. For example the solution of the optimal control problems with the aim to maximize the weight-average mean crystal size generally leads to convex cooling profiles, whereas the minimization of the coefficient of variation of the CSD in un-seeded crystallisation processes results in fast cooling during the initial part of the operation to generate nuclei in short time period (Nagy and Braatz, 2003b). Detailed overviews of model development and advances in crystallisation control approaches are given in several comprehensive review articles (Braatz, 2002; Braatz et al., 2002; Larsen et al., 2006;

Rawlings et al., 1993; Yu et al., 2007). Using optimal temperature trajectories the improvement in the mean crystal size of a potassium nitrate system was reported (Miller and Rawlings, 1994). The mean crystal size and crystal quality of adipic acid was improved using optimal temperature trajectories (Costa et al., 2005).

Anti-solvent addition profile was optimised to improve the product CSD by (Nowee et al., 2008a). More recently model-based optimisation was applied to the combined cooling and anti-solvent crystallisation of lovastatin (Nagy et al., 2008b). The authors showed that the optimal operating trajectories and whether the crystallisation process is controlled by cooling, anti-solvent addition or a combination of the two approaches strongly depend on the objective function used in the optimisation. Hence the model-based optimisation approach in this case has become not only a methodology to determine the best operating curve but also a process design tool, capable of automatically selecting the best supersaturation generation methodology for the process (cooling or anti-solvent addition).

The significant improvement in the computational performance allowed the solution of more complex optimal control problems or the use of more comprehensive models in the optimisation. For example (Ma et al., 2002b) considered two-dimensional growth, solving a corresponding two-dimensional PBE for temperature optimisation in the cooling crystallisation of potassium dihydrogen phosphate (KDP) in water. Costa et al. (2005) incorporated aggregation and (Hu et al., 2005) considered growth rate dispersion in their model-based optimisation studies. The paper by (Woo et al., 2006) provides and exemplary case study of using combined computational fluid dynamics (CFD) and PBM for model-based optimisation. The authors used an efficient high resolution finite volume scheme to

solve the coupled PBM-CFD model, which also incorporated the effect of micromixing, for an anti-solvent crystallisation system. The complex model was used for open-loop optimisation however the approach is computationally too expensive for real-time model predictive control.

Parameter uncertainties can also be considered during the optimisation to achieve robust open-loop optimal operating trajectories (Nagy and Braatz, 2004), which minimizes the variability in the product property due to errors in the model. Open-loop optimisation of the temperature trajectories for polymorphic crystallisation was illustrated by (Hermanto et al., 2007).

In addition to the supersaturation profile the seed mass and seed distribution can also be optimised to achieve a desired product property (Bohlin and Rasmuson, 1996; Chung et al., 1999; Kalbasenka et al., 2007). A more detailed overview of these approaches, as well as a novel methodology that simultaneously designs supersaturation profile and seed recipe, or applies dynamic seeding, for the control of the shape of the CSD are provided in Chapters 7 and 9.

A product engineering approach has been proposed by several authors who considered the integrated design of crystallisation and downstream process units to achieve desired performance of the integrated process chain or to produce target end-product quality (Hounslow and Reynolds, 2006; Wibowo et al., 2001).

In addition to the overview of the open-loop model-based control approaches provided in this section there is a vast literature related to the model-free control (direct design) approaches for crystallisation processes, which are based on the application of supersaturation control approaches to control the crystallisation process in the phase diagram. This literature is briefly reviewed in Chapter 7, for more details see e.g. the review papers by Fujiwara et al. (2005) and Nagy et al., (2008a, b). These approaches provide fast, robust and reliable control, of crystallisation processes, which can be supported in an industrial environment; however they are designed based on heuristics and trial-and-error experimentations. Hence, the application of these approaches to the control of crystallisation systems is not directly within the scope of the thesis; however a novel methodology to analyse and provide a systematic framework for direct design (based on a simplified model-based optimisation approach) is presented in Chapters 7 and 8.

In addition to the open-loop model-based control approaches significant effort has been devoted to the development and implementation of closed-loop model based control approaches (Larsen et al., 2006; Nagy and Braatz, 2003a; Rawlings et al., 1993;

Sheikhzadeh et al., 2008b). Although these control approaches in principle solve similar dynamic optimisation problems as the open-loop model-based control techniques their implementation complexity is significantly larger than in the latter case. The main difficulties arise from the requirement of on-line state and parameter estimation approaches as well as due to the necessity of computing the solution of the optimisation problem within the sampling period in the process (real-time implementation). These approaches provide the benefits of inherent robustness due to their closed-loop architecture and the ability to adapt the operating conditions to unforeseen disturbances. Nevertheless, the practical application of these approaches is still very scarce both in laboratory as well as industrial environments, due the increased complexity of the control algorithm but also because of regulatory constraints related to the changing/adaptation of operating conditions. Due to their currently very limited applicability these approaches are not considered in this thesis and the focus of the research is directed towards the development and evaluation of efficient open-loop model-based optimal control approaches for CSD control in crystallisation processes.