Real-time feasibility of nonlinear model predictive control for semi-batch reactors subject to uncertainty and disturbances

This paper presents two nonlinear model predictive control based methods for solving closed-loop stochastic dynamic optimisation problems, ensuring both robustness and feasibility with respect to state output constraints. The first one is a new deterministic approach, using the wait-and-see strategy. The key idea is to specifically anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a stochastic approach to solve nonlinear chance-constrained dynamic optimisation problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between uncertain inputs and the constrained state outputs. The performance of the proposed methodologies is assessed via an application to a semi-batch reactor under safety constraints, involving strongly exothermic reactions

Model Reduction in Chemical Engineering: Case studies applied to process analysis, design and operation

During the last decades, models have become widely used for supporting a broad range of chemical engineering activities, such as product and process design and development, process monitoring and control, real time optimization of plant operation or supply chain management. Although tremendous advancements continue to take place in the development of numerical techniques and the acceleration of the computing speed, these advancements have been outpaced by the tendency to make rigorous models of much more complicated and extensive systems. Such rigorous models cannot always be effectively used for design and optimisation. A reduction of the model size and complexity is required to make a model-based solution practical. Many current numerical approaches in systems engineering apply order-reduction to a model in its entirety, without preserving the underlying network structure of the process or its multi-scale decomposition. Retaining these meaningful structural features of a process in a reduced model is a necessity for numerous applications. This is the motivation for the research and the results presented in this thesis. The novelty of this thesis is in systematizing and exploiting the essential structural features of a process in model reduction. The model reduction approach aims first at simplifying the physical and the behavioural structure, as well as the systemic level of the chemical process in the model. Only then additional mathematical and numerical (scheme) reductions are selectively applied to individual compartments or units. In the following step, the reduced models of the individual units are connected at system level and the reduced model of the full process is obtained. In this way, the model reduction procedure is able to preserve the essential structural features of the process. Moreover, the physical meaning of the variables and equations is kept as much as possible. The feasibility and the advantages of the approach are presented for two types of applications: (1) the iso-butane alkylation process, an example of a complex process with relatively simple (one-phase) products; and (2) the freezing step in ice cream manufacture, an example of a single process unit with a complex product. The model reduction procedures works well for the cases considered. The resulting models are solved in acceptable amounts of time. Moreover, they are successfully used for applications such as assessment of the plantwide control structures and the dynamic optimization of the plant operation for the iso-butane alkylation process, and the sensitivity analysis of the model’s parameters in the case of the ice cream freezing process. However, the issue of the optimality with respect to the level of the multi-scale decomposition when developing the reduced model is still open.Chemical EngineeringApplied Science

A first-principles model for the freezing step in ice cream manufacture

This contribution deals with the development of a first-principles model for ice cream formation in the freezing unit to support product design and plant operation. Conservation equations for the mass, energy and momentum, considering axial flow assumptions are taken into account. The distributed features of the ice crystals and air bubbles are considered. Information related to the phase equilibrium conditions, the equations of state and the rate equations are added to the model. Some model reduction is already present, regarding the complex laminar fluid flow. The essential uncertainty of the model is in the simplification of the fluid flow, as well as in the structure and parameters of the rate laws. The structure of the model is presented, as well as preliminary computational results

A reduced model for the freezing step in ice cream manufacture

This contribution deals with the development of a reduced yet complex model, to support process design and operation. The model is computationally effective. The main physical phenomena considered in the model are the axial convective transport of mass, the radial outflow of heat at coolant wall to the refrigerant, the growth of the frozen ice layer, the periodic removal of the ice crystals by scraping and the melting of the ice crystal population in the bulk liquid. Rate equations for the relevant physical phenomena, as well as phase equilibrium conditions and thermodynamic equations of state are also present. The target output variables to meet the product quality specifications are the ice crystals size and the air content. Results of some preliminary steady state simulations are presented

Automated control loop selection via multistage optimal control formulation and nonlinear programming

In this work, a novel approach based on the multistage optimal control formulation of the control loop selection problem is introduced. Currently, state-of-the-art approaches for controller loop design have been focused on data that yield only the pairings between input-output variables, and are not able to incorporate path and end-point constraints. Thus, they only produce the optimal loops for control purposes, without the simultaneous consideration of their optimal tuning. This formulation overcomes these drawbacks by producing an automated integrated solution for the task of control loop design, which also obviates the need for any form of combinatorial optimisastion to be used. To illustrate the procedure, as well as the advantages of the proposed scheme, different practical case studies are discussed and the results compared with those obtained with standard controller loop selection methods and their tuning. The results of the proposed approach show improved performance over previous methodologies found in the literature. Furthermore, the framework is extended to the selection of the control loops that must obey path and end-point constraints imposed by the underlying dynamical process. This task is usually difficult for classical methods, which violate them or exhibit underdamped response in some cases

Maintenance scheduling optimisation of Reverse Osmosis Networks (RONs) via a multistage Optimal Control reformulation

State-of-the-art approaches for membrane cleaning scheduling have focused on the Mixed-Integer Nonlinear Programming (MINLP) formulation so far, a strategy leading to a combinatorial problem that does not capture accurately the dynamic behaviour of the system. In this work, the Reverse Osmosis (RO) cleaning scheduling problem is solved using a novel approach based on the Multistage Integer Nonlinear Optimal Control Problem (MSINOCP) formulation. The approach produces an automated solution for the membrane cleaning scheduling, which also obviates the need for any form of combinatorial optimisation. Two different simulations, for 26 and 52 periods of operation (each period with a duration of one week), are carried out to illustrate the application of the proposed framework and the total cost is 1.17 and 2.48 107 €, respectively. The RO network configuration considers 2 stages, each with 3 individual RO modules. The results show evidently that the new proposed solution framework can solve successfully this type of problems, even for large scale configurations, long time horizons and arbitrary realistic complexity of the underlying dynamic model of the RO process considered

A first-principles model for the freezing step in ice cream manufacture

This contribution deals with the development of a first-principles model for ice cream formation in the freezing unit to support product design and plant operation. Conservation equations for the mass, energy and momentum, considering axial flow assumptions are taken into account. The distributed features of the ice crystals and air bubbles are considered. Information related to the phase equilibrium conditions, the equations of state and the rate equations are added to the model. Some model reduction is already present, regarding the complex laminar fluid flow. The essential uncertainty of the model is in the simplification of the fluid flow, as well as in the structure and parameters of the rate laws. The structure of the model is presented, as well as preliminary computational results

A reduced model for the freezing step in ice cream manufacture

This contribution deals with the development of a reduced yet complex model, to support process design and operation. The model is computationally effective. The main physical phenomena considered in the model are the axial convective transport of mass, the radial outflow of heat at coolant wall to the refrigerant, the growth of the frozen ice layer, the periodic removal of the ice crystals by scraping and the melting of the ice crystal population in the bulk liquid. Rate equations for the relevant physical phenomena, as well as phase equilibrium conditions and thermodynamic equations of state are also present. The target output variables to meet the product quality specifications are the ice crystals size and the air content. Results of some preliminary steady state simulations are presented