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Control of Multiproduct Batch Plants

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Abstract

In the chemical industries, discontinuously operated multiproduct plants are widely used for the production of fine, or specialty, chemicals. Control of such plants is a highly nontrivial hybrid control problem. In practice, recipe-based approaches prevail. They provide solutions, which are (i) often even nominally far from optimal and (ii) open-loop and therefore extremely sensitive to unforeseen disturbances. In this project we both attempt to improve standard recipe-based approaches, and we investigate alternative (feedback) strategies that are based on recent results from hierarchical hybrid control theory.


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Description

Multiproduct batch plants possess a high degree of flexibility and are therefore particularly attractive for producing small amounts of several high-value products. From a control engineering point of view, one faces a hybrid control problem, as both continuous input signals and discrete decisions are involved. It is well known that hybrid control problems and, in particular, hybrid optimal control problems are extremely difficult to solve. Indeed, any attempt to solve such problems for plant models of a realistic size without a-priori imposing additional structure seems doomed to fail because of computational complexity. In industrial practice, structure is provided by determining "standard production recipes" and "assembling" the overall production schedule from these recipes. This removes (most) degrees of freedom, hence makes the problem computationally tractable, but provides results that are suboptimal, and very often far from optimal [1].

In B.V. Mishra's Ph.D. thesis [2] this standard recipe based approach is improved by parametrising each task on each unit by two recipes. This increases the available degrees of freedom, and, for a number of examples, has been shown to dramatically improve performance.

We have also investigated an alternative approach, where recent results from our project on hierarchical control theory have been applied to a specific example. The example is idealised to a certain extent but is general enough to capture most of the problems that characterise multiproduct batch plants. The plant is used to produce three kinds of colour pigments, using similar production methods (Fig. 1): from one of the storage tanks B1, B2, or B3, solvent is pumped into either a large reactor R1 or a small reactor R2. Reactant Ai, i=1,2,3, is added to start reaction i delivering the desired product Pi. It is accompanied by a parallel reaction resulting in the waste product Wi. If, at the end of the reaction step, concentration of Wi is above a given threshold Wi,max, product quality is unacceptable and the batch is spoilt. For the duration of the reaction, there are two control inputs: the feed rate of the reactant and the heating/cooling rate for the reactor.

Figure 1: Example plant.

After the reaction is finished, the contents of the reactors is filtered through either F1, F2, or F3, and the solvent is collected in the corresponding tank B1, B2, or B3. The solvent can subsequently be fed back into either of the two reactors. If, in any of the filters, darker colours are filtered before lighter ones (say P3 before P1 or P2, and P2 before P1), an additional cleaning process between the two filtration tasks is needed, taking time tc. The feed rates into the reactors are discrete-valued control inputs as are the decision variables (realised by discrete valve positions) that determine whether a particular reactor is emptied through a particular filter system. Heating/cooling rates for R1 and R2 are continuous-valued control inputs. A typical overall aim is to produce the demanded product volumes with minimal operating costs, while satisfying quality constraints (upper bounds for the concentration of waste products) and safety constraints (upper bounds for reactor temperatures). Details of plant model, specifications, and solution approach are described in [3] and [4].

Publications

  1. Brahmdatt V. Mishra, Eckart Mayer, Jörg Raisch, Achim Kienle. Short-Term Scheduling of Batch Processes. A Comparative Study of Different Approaches. Industrial and Engineering Chemistry Research, 44 (11):4022–4034, 2005.
  2. Brahmdatt V. Mishra. Optimal Operation of Multiproduct Batch Plants. Otto-von-Guericke Universität, Magdeburg, Germany, 2006.
  3. Thomas Moor, Jörg Raisch. Hierarchical Hybrid Control of a Multiproduct Batch Plant. In Proc. 16th IFAC World Congress, Prague, Czech Republic, 2005.
  4. Jörg Raisch, Thomas Moor. Hierarchical Hybrid Control Synthesis and its Application to a Multiproduct Batch Plant, volume 322 of Lecture Notes in Control and Information Sciences, pages 199–216. Springer-Verlag, Berlin, Germany, 2005.

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