Batch-to-batch learning for model-based control of process systems with application to cooling crystallization

From an engineering perspective, the term process refers to a conversion of raw materials into intermediate or final products using chemical, physical, or biological operations. Industrial processes can be performed either in continuous or in batch mode. There exist for instance continuous and batch units for reaction, distillation, and crystallization. In batch mode, the raw materials are loaded in the unit only at the beginning of the process. Subsequently, the desired transformation takes place inside the unit, and the products are eventually removed altogether after the processing time. In order to obtain the desired production volume, several batches are repeated. In an industrial process, several variables such as temperatures, pressures, and concentrations have to be regulated in order to ensure safety, maintain the product quality, and optimize economic criteria. In principle, model-based control techniques available in the literature could be systematically utilized in order to achieve these goals. However, a limitation to the applicability of model-based techniques for batch process control is that the available models of batch processes often suffer from severe uncertainties. In this thesis, we have investigated the use of measured data in order to improve the performance of model-based control of batch processes. Our approach consists in using the measured data in order to refine from batch to batch the model that is used to design the controller. By doing so, the performance delivered by the model-based controller is expected to improve. We have developed the parametric model update technique Iterative Identification Control (IIC) and non-parametric model update technique Iterative Learning Control (ILC). While in IIC the measured batch data are used to update from batch to batch parameter estimates for the uncertain physical coefficients, in ILC the data are used to compute a non-parametric, additive correction term for a nominal process model. We have tested the ILC and IIC algorithms for the batch cooling crystallization process both in a simulation environment and on a real pilot-scale crystallization setup. We have shown that the two approaches have complementary advantages. On the one hand, the parametric approach allows for a faster learning since it produces a parsimonious representation of the process. On the other hand, the nonparametric approach can cope effectively with the serious issue of structural mismatches owing to the use of a more flexible representation. Furthermore, we have investigated the use of excitation signals to enhance the performance of parametric model update techniques in an iterative identification/controller design scheme similar to IIC. The excitation signals have a dual effect on the overall control performance. On the one hand, the application of an excitation signal superposed to the normal control input leads after identification to an increased model accuracy, and thus a better control performance. On the other hand, the excitation signal also causes a temporary performance degradation, since it acts as a disturbance while it is applied to control system. For linear dynamical systems, we have shown that the problem of designing the excitation signals aiming to maximize the overall control performance can be approximated as a convex optimization problem. The lack of generally applicable and computationally efficient experiment design tools for nonlinear systems is the main bottleneck for the optimal design of the excitation signals in the case of batch processes. In this thesis, we have developed a novel experiment design method applicable to the class of fading memory nonlinear system. Limiting the excitation signals to a finite number of levels, the information matrix can be expressed as a linear function of the frequency of occurrence of each possible pattern having duration equal to the memory of the system. Exploiting the linear relation between the frequencies and the information matrix, several experiment design problems can be formulated as convex optimization problems.