• Batch distillation
• batch to batch controller
• Constraint-seeking
• Implicit scheme of optimization
• input parameterization
• modeling
• NCO tracking
• Necessay condition of optimality
• Real-Time optimization
• Sensitivity-seeking

Batch distillation is a chemical process used to separate the different components of a mixture. Even if it is not as used as the continuous operation the batch process still plays an important role in the chemical process industries mostly where the materials to be separated are produced in small quantities or where the main product contains only small amount of impurities. As this operative way of the distillation process is increasing, it is also increasing the research of optimizing the process since it represents the natural choice of reducing production costs and maximize the product yield.
The purpose of this thesis is to analyze the potential of optimizing the process via an implicit scheme of optimization, so called NCO-tracking strategy. Since the batch nature of the process, repeatibility is assumed, thus the process will be optimized over few batches related to the same process specifics (charge and composition).
The different schemes of Real-Time Optimization can be divided into explicit schemes and implicit schemes. While the explicit scheme uses a model-based optimization to update the input parameters related to the process, the implicit scheme computes the update values of the input parameters directly on the bases of measurements, with the use of a high-level controller. The advantages of using an implicit scheme for optimization are related to the possible presence of uncertainties (model mismatches and process disturbances). NCO-tracking compensates the effect of uncertainties through direct input update via the action of a measurement-based controller; while input update, performed via model-based re-optimization (explicit scheme), could be affect by recursive errors and it does not guarantee that active constraints of the real process will be reached.
In order to define the features of NCO-tracking strategy several steps need to be analyzed. These steps are evaluated offline (before running the process) via simulating the process with the use of a reliable model. The first step of the thesis concerns the implementation of a batch distillation model. The short-cut model realized is based on simplified material balances and FUG equations, a set of experimental equations proposed by Fenske-Underwood-Gilliland already tested and proved to be functional for the purpose of modeling distillation processes. The model built for both Matlab and Simulink codes was tested in several simulations, obtaining satisfying results that proved the reliability of the model and its functionality for its role in NCO-tracking definition.
The main principle of NCO tracking is to turn an optimization problem into a control problem and its greatest feature is the definition of the necessary conditions of optimality (NCO). NCO are quantities related to the process that need to be met to allow the process reaching its optimality. Along with the definition of the NCO, this optimization strategy is also characterized by the evaluation of the optimal input profiles and detection of its appropriate parameterization. The optimal input parameterization must be imposed as set-point in order to move the process towards its optimal direction and help meeting the NCO. The control problem is then defined: tracking the NCO by adjusting the parameters that compose the optimal parameterization, via measurement-based controller (Implicit scheme).
Numerical optimization is performed to understand the optimal behavior of the process and detect the NCO and the appropriate parameterization of the key variables for the batch distillation process. This way, the model and numerical optimization are used only offline, before starting the process, to understand and characterize the optimal solution; while, the online operation will track the NCO by adjusting the parameters, leading the process to its optimality.
The thesis focuses on the application of the NCO-tracking strategy to a specific batch distillation process. The objective of the process is to recover a certain desired amount of high purity main product and the optimization concern the minimization of the final batch time.
Performing the numerical optimization via simulation of the process model, it was possible to define the NCO and the input parameterization. The NCO detected was: two terminal constraint-seeking NCO, linked to the recovery of light key and main components and two terminal sensitivity-seeking NCO, linked to the gradient of the cost function (final time). The key variable chosen as key variable was the distillate temperature, which parameterization was detected as a combination of two arcs: (i) constant at the beginning of the process, (ii) linearly increasing for the rest of the process. This optimal trajectory is imposed as set-point and controller by adjusting the internal reflux ratio. Each arc is characterized by two parameters, this way the NCO strategy is defined by:
four NCO and four input parameters.
Once that NCO and the input parameterization was defined, it is possible to transform the optimization problem into a control problem by implementing a high-level control responsible of tracking the NCO by adjusting the input parameters. The application of the NCO-tracking strategy, as a control problem, is determined by a square control configuration for a MIMO system (4_4). In order to built a good controller for this system, a decoupling effect is needed; this problem is solved by performing a SVD decomposition, capable of computing the independent input direction of the process. The controller will track the NCO (CV) by adjusting the input directions (MV) and modifying this way the input parameters, since they can be computed as a linear combination of the input directions.
The NCO detected from numerical optimization are related to terminal conditions and for this reason, the controller will act as a batch-to-batch controller: each batch will be repeated with a new set-point profile for the distillate temperature, determined by the control action on the four parameters.
The batch-to-batch controller will track the necessary conditions of optimality to their set-point values. Sensitivity-seeking NCO will be pushed to 0, thus, the gradient of the final time will be reduced to 0 and the process will reach its optimality. For this reason the batch-to-batch controller can be defined as a Self-Optimizing controller.
The simulation results proposed in this thesis show the potential of NCO-tracking strategy and the possibility of optimizing a repeatable process by meeting the necessary conditions of optimality, reducing the final batch time over consecutive batches.