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A batch process is characterized by the repetition of time-varying operations of finite duration. Due to this repetition, there are two independent “time” variables, namely, the run time within a batch and the batch index. Accordingly, the optimization objective can be defined for a given batch or over several batches. This chapter formulates the dynamic optimization problem for a given batch and shows that it can be reformulated as a static optimization problem to be solved over several batches. Furthermore, it is shown how optimization can be seen as self-optimizing control that is implemented both within batch and in a batch-to-batch manner. The use of feedback control is of particular interest in the presence of uncertainty. This chapter describes how to set up the various control loops and implement optimizing feedback control. The approach is illustrated via the optimization of a batch distillation column.

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Renewable energies are extensively utilized in smart grids. Due to the widespread use of information and communication technologies in such networks, their security has become a critical issue. This paper aims to enhance the information security of renewable smart grids under cyber-physical attacks. In this regard, it is assumed that the non-legitimate agents manipulate the data of solar and wind sensors to deteriorate the safe operation. Here, a stochastic real-time procedure based on the observation-action method is utilized to simulate the behavior of attackers. Then, to improve the security and mitigate the impact of such a vulnerability, an integrated framework composed of offline and online units is designed. To construct the offline framework, a data mining process including k-nearest neighbour and support vector machine algorithms is implemented based on real historical data. Furthermore, the online framework tracks the real-time data according to a sensor pre-secured by a firewall. The results show that the proposed framework is capable to relieve the influence of cyber-physical attacks where at least 79% of success rate will be achievable under simultaneous false data injection attacks.

A batch process is characterized by the repetition of time-varying operations of finite duration. Due to the repetition, there are two independent "time" variables, namely, the run time during a batch and the batch index. Accordingly, the control and optimization objectives can be defined for a given batch or over several batches. This chapter describes the various control and optimization strategies available for the operation of batch processes. These include online and run-to-run control on the one hand, and repeated numerical optimization and optimizing control on the other. Several case studies are presented to illustrate the various approaches.

This paper presents an overview of the recent developments of modifier-adaptation
schemes for real-time optimization of uncertain processes. These schemes have the ability to
reach plant optimality upon convergence despite the presence of structural plant-model mismatch.
Modifier Adaptation has its origins in the technique of Integrated System Optimization and Parameter
Estimation, but differs in the definition of the modifiers and in the fact that no parameter estimation
is required. This paper reviews the fundamentals of Modifier Adaptation and provides an overview
of several variants and extensions. Furthermore, the paper discusses different methods for estimating
the required gradients (or modifiers) from noisy measurements. We also give an overview of the
application studies available in the literature. Finally, the paper briefly discusses open issues so as to
promote future research in this area.

Measurements can be used in an optimization framework to compensate the effects of uncertainty in the form of model mismatch or process disturbances. Among the various options for input adaption, a promising approach consists of directly enforcing the necessary conditions of optimality (NCO) that include two parts, the active constraints and the sensitivities. In this paper, the variations of the NCO due to parametric uncertainty are studied and used to design appropriate adaptation laws. The inputs are separated into constraint-seeking and sensitivity-seeking directions depending on which part of the NCO they enforce. In addition, the directional influence of uncertainty is used to reduce the number of variables to adapt. The theoretical concepts are illustrated in simulation via the run-to-run optimization of a batch emulsion polymerization reactor.

This paper presents a personal, thus necessarily subjective, view of the operation of batch and semi-batch reactors. The emphasis is on safety, product quality and scale-up. Key characteristics of discontinuous reaction systems are discussed, along with the resulting implications for monitoring, control and optimization. The industrial needs are compared with the research solutions proposed by academia. It is argued that, in industry, measurement and modeling issues are often more important than the algorithmic aspects related to the computation of control and optimization strategies. Major challenges and selected research opportunities are discussed.

Challenges in real-time process optimization mainly arise from the inability to build and adapt accurate models for complex physico-chemical processes. This paper surveys different ways of using measurements to compensate for model uncertainty in the context of process optimization. Three approaches can be distinguished according to the quantities that are adapted: model-parameter adaptation updates the parameters of the process model and repeats the optimization, modifier adaptation modifies the constraints and gradients of the optimization problem and repeats the optimization, while direct input adaptation turns the optimization problem into a feedback control problem and implements optimality via tracking of appropriate controlled variables. This paper argues in favor of modifier adaptation, since it uses a model parameterization and an update criterion that are well tailored to meeting the KKT conditions of optimality. These considerations are illustrated with the real-time optimization of a semi-batch reactor system.

As a real-time optimization technique, modifier adaptation (MA) has gained much significance in recent years. This is mainly due to the fact that MA can deal explicitly with structural plant-model mismatch and unknown disturbances. MA is an iterative technique that is ideally suited to real-life applications. Its two main features are the way measurements are used to correct the model and the role played by the model in actually computing the next inputs. This paper analyzes these two features and shows that, although MA computes the next inputs via numerical optimization, it can be viewed as a feedback control scheme, with optimization implementing feedback to match the plant KKT conditions. As a result, the role of the model is downplayed to the point that model accuracy is not an important issue. The key issues are gradient estimation and model adequacy, the latter requiring that the model possesses the correct curvature of the cost function at the plant optimum. The main role of optimization is to identify the proper set of controlled variables (the active constraints and reduced gradients) as these might change with the operating point and disturbances. Thanks to this reduced requirement on model accuracy, MA is ideally suited to drive real-life processes to optimality. This is illustrated through two experimental systems with very different optimization features, namely, a commercial fuel-cell system and an experimental kite setup for harnessing wind energy.played by the model in actually computing the next inputs. This paper analyzes these two features and shows that, although MA computes the next inputs via numerical optimization, it can be viewed as a feedback control scheme, with optimization implementing feedback to match the plant KKT conditions. As a result, the role of the model is downplayed to the point that model accuracy is not an important issue. The key issues are gradient estimation and model adequacy, the latter requiring that the model possess the correct curvature of the cost function at the plant optimum. The main role of optimization is to identify the proper set of controlled variables (the active constraints and reduced gradients) as these might change with the operating point and due to disturbances. The inputs are computed by enforcing the plant KKT conditions. Thanks to this reduced requirement on model accuracy, MA is ideally suited to drive real-life processes to optimality. This is illustrated through two experimental systems with very different optimization features, namely, a commercial fuel-cell system, the optimality of which is fully determined by active constraints, and an experimental kite setup for harnessing wind energy that has no active constraint.

This paper describes an optimization strategy for operating solid-oxide fuel-cell systems at optimal efficiency. Specifically, we present the experimental validation of a real-time optimization (RTO) strategy applied to a commercial solid-oxide fuel-cell system. The proposed RTO scheme effectively pushes the system to higher levels of efficiency and maintains the system there despite perturbations by tracking active constraints. The optimization approach uses either steady-state measurements, or transient measurements in combination with a dynamic model, and can deal effectively with plant-model mismatch. In the reported experiments, the approach drives the system to the desired power demand at optimal efficiency. The experimental fuel-cell system reached 65% DC electrical efficiency. As such, the proposed RTO scheme is a promising candidate for enforcing optimal micro-CHP operation. In addition, the approach can deal with slow drifts such as degradation without compromising on efficiency. Finally, and important from a practical point of view, we suggest guidelines for safe and optimal operation.

This chapter presents recent developments in the field of process optimization. In the presence of uncertainty in the form of plant-model mismatch and process disturbances, the standard model-based optimization techniques might not achieve optimality for the real process or, worse, they might violate some of the process constraints. To avoid constraints violations, a potentially large amount of conservatism is generally introduced, thus leading to suboptimal performance. Fortunately, process measurements can be used to reduce this suboptimality, while guaranteeing satisfaction of process constraints. Measurement-based optimization schemes can be classified depending on the way measurements are used to compensate the effect of uncertainty. Three classes of measurement-based real-time optimization (RTO) methods are discussed and compared. Finally, four representative application problems are presented and solved using some of the proposed RTO schemes.

Plantwide control is concerned with the structural decisions involved in the control system design of a chemical plant (C.S. Foss, Critique of chemical process control theory, AIChE Journal 19(2), 1973) 209–214; “Which variables should be controlled, which variables should be measured, which inputs should be manipulated, and which links should be made between them?” In particular, the first issue about which variables to control has received little attention. It is argued that the answer is related to finding a simple and robust way of implementing the economically optimal operating policy. The goal is to find a set of controlled variables which, when kept at constant setpoints, indirectly lead to near-optimal operation with acceptable loss. This is denoted “self-optimizing” control. Since the economics are determined by the overall plant behavior, it is necessary to take a plantwide perspective. A systematic procedure for finding suitable controlled variables based on only steady-state information is presented. Important steps are degree of freedom analysis, definition of optimal operation (cost and constraints), and evaluation of the loss when the controlled variables are kept constant rather than optimally adjusted. A case study yields very interesting insights into the control and maximum throughput of distillation columns.

A fast, accurate model for batch distillation simulation will be useful both in batch distillation synthesis and in batch process design. A shortcut model using the Fenske-Underwood-Gilliland (FUG) equations of continuous distillation design was developed. The model consists of stepping forward in time using a first-order explicit integration scheme with a variable time step and solving the FUG equations at each time step. A large number of example problems were used for model testing and validation. Agreement between the shortcut model and rigorous simulation was excellent. The model is a powerful and computationally fast tool that can be used both in batch process design and in synthesis of batch distillation systems.

One of the simplest measures of the success of an optimization system is its ability to correctly identify the optimum process operations policy. In the case of a model-based real-time optimization system, few tools are available to the system designer for investigating the suitability of a candidate process mode for use in such systems. This paper presents point-wise model adequacy checking methods, both analytical and numerical, for determining the ability of the model-based optimization system to have an optimum coincident with that of the true process. The paper concludes with a case study using the reactor for the Williams-Otto plant, where two different approximations to the reaction sequence are tested for point-wise model adequacy.

The issue in this paper is to select controlled variables c as combinations of the measurements y. The objective is to obtain self-optimizing control, which is when we can achieve near-optimal steady-state operation with constant setpoints for the controlled variables, without the need to reoptimize when new disturbances perturb the plant. The null space method yields locally optimal controlled variables c = Hy that are linear combinations of measurements y. The requirement is that we at least have as many measurements as there are unconstrained degrees of freedom, including disturbances, and that the implementation error is neglected. The method is surprisingly simple. From a steady-state model of the plant, the first step is to obtain the optimal sensitivity matrix F, with respect to the disturbances. The optimal matrix H satisfies HF = 0; therefore, the next step is to obtain H in the left null space of F. As an illustration, the method is used to obtain temperature combinations for control of a Petlyuk distillation column.

The use of measurements to compensate for the effect of uncertainty has recently gained attention in the context of real-time optimization of dynamic systems. The commonly used approach consists of updating a process model and performing numerical optimization using the refined model. In contrast, this paper presents a two-level approach that does not require repeating the optimization: At the upper level, the constraints that are active in the optimal solution are identified from optimization of a nominal process model; at the lower level, feedback control is used to enforce the necessary conditions of optimality, i.e., meet the identified active constraints and push selected gradients to zero. A key feature of this self-optimizing control scheme is the use of an input parametrization that is tailored to the identified active constraints. Another feature that is specific to batch processes is the possibility to meet the control objectives either online or on a run-to-run basis. The self-optimizing control approach is illustrated on a semibatch reactor example.

This paper considers the optimization of transient systems consisting of a fixed number of stages,
each of which is described by an index-1 system of differential-algebraic equations (DAE). General initial conditions at the start of the first stage and junction conditions between stages are allowed, as well as point equality and inequality constraints at the end of each stage. A control vector parametrization approach is used to convert the above problem to a finite dimensional nonlinear programming (NLP) problem. The function gradients required for the solution of the NLP are calculated through the solution of a multistage DAE system in the variable sensitivities.

Batch control has traditionally addressed the problems related to the absence of a steady-state and the finite batch duration. Recently, batch control has added the dimension that arises naturally from the possibility of applying run-to-run control, i.e. it exploits the fact that most batch process are repeated over time. Hence, batch control calls for tools that are tailored to these new challenges and specificities of batch operations. These include a mathematical representation that explicitly shows the two independent time variables (the run time t and the run index k), two types of inputs (both constant and time-varying within a run) as well as two types of outputs (the run-time and run-end outputs). This paper introduces a definition of batch-output controllability that considers the two types of inputs and outputs. Also, a quantitative notion of stability that takes into account the finite-time nature of batch processes and typical phenomena such as the batch kick is presented. The tools required for evaluating these properties are readily adapted from the literature. As illustration, a semi-batch reactor example is considered in simulation. Various approaches to batch control are demonstrated and the associated controllability and stability issues discussed.

Real-time steady-state optimization (RTO) has become increasing popular in recent years. But how should this optimal policy be implemented in the control system? It is argued that the goal is to find a set of controlled variables which, when kept at constant setpoints, indirectly lead to near-optimal operation with acceptable loss. This is denoted ‘self-optimizing’ control.

The ability of a model-based real-time optimization scheme to converge to the plant optimum relies on the ability of the underlying process model to predict the plant's necessary conditions of optimality (NCO). These include the values and gradients of the active constraints as well as the gradient of the cost function. Hence, in the presence of plant-model mismatch or unmeasured disturbances, one could measure the plant NCO and use them for tracking the plant optimum. This paper shows how the optimization problem can be modified to incorporate information regarding the plant NCO. The so-called modifiers, which express the difference between the measured or estimated plant NCO and those predicted by the model, are added to the constraint and cost functions in a modified optimization problem and are adapted iteratively. Local convergence and model-adequacy issues are analyzed. The modifier-adaptation scheme is tested experimentally on a three-tank system.

In the framework of real-time optimization, measurement-based schemes have been developed to deal with plant-model mismatch and process variations. These schemes differ in how the feedback information from the plant is used to adapt the inputs. A recent idea therein is to use the feedback information to adapt the constraints of the optimization problem instead of updating the model parameters. These methods are based on the observation that, for many problems, most of the optimization potential arises from activating the correct set of constraints. In this paper, we provide a theoretical justification of these methods based on a variational analysis. Then, various aspects of the constraint-adaptation algorithm are discussed, including the detection of active constraints and convergence issues. Finally, the applicability and suitability of the constraint-adaptation algorithm is demonstrated with the case study of an isothermal stirred-tank reactor.

In industrial polymerization processes, several grades of polymer are frequently produced in the same plant by changing the operating conditions. Transitions between the different grades are rather slow and result in the production of a considerable amount of off-specification polymer. Grade transition improvement is viewed here as a dynamic optimization problem, for which numerous approaches exist. Open-loop implementation of the input profiles obtained from numerical optimization of a nominal process model is often insufficient, due to the presence of uncertainty in the form of model mismatch and process disturbances. A novel measurement-based approach that consists of tracking the necessary conditions of optimality (NCO tracking) using a solution model and measurements is considered. The solution model consists of state-event-triggered controllers sequenced according to the structure of the nominal optimal solution computed offline. The solution model is generated by expressing the input profiles in terms of arcs and switching times, which are then related to the various parts of the NCO, that is, to the active constraints and sensitivities. These arcs and switching times are then adapted online using appropriate measurements. The application of NCO tracking to an industrial polymerization process for implementing optimal grade transitions is investigated in simulation. The grade transition problem. is fairly complex due to a large-scale process model, many degrees of freedom, as well as path and endpoint constraints. A solution model is generated from the nominal optimal solution, and a control superstructure is considered to handle the possible activation of nominally-inactive constraints. Simple PI-type controllers are used to implement the solution model. For different uncertainty scenarios, simulation of the NCO-tracking approach shows that considerable reduction in transition time is possible, while still guaranteeing feasible operation.

This paper presents a new measurement-based optimization framework for batch processes whereby optimal operation can be achieved via the tracking of active constraints. It is shown that, under mild assumptions and to a first-order approximation, tracking the necessary conditions of optimality is equivalent to tracking active constraints (both during the batch and at the end of the batch). Thus the optimal input trajectories can be adjusted using measurements without the use of a model of the process. When only batch-end measurements are available, the proposed method leads itself to an efficient batch-to-batch optimization scheme. The approach is illustrated via the simulation of a semibatch reactor under uncertainty.

Modeling and Real-Time Optimization of Batch Distillation Processes (Master’s thesis)

- G Rizzi