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# Online predictive control of the run-end outputs z in a batch process. The model in the " Model Predictive Controller " block is used to compute z pred (t) fromˆxfromˆ fromˆx(t).

Source publication

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 desc...

## Contexts in source publication

**Context 1**

... P is the predictive control law for run-end outputs and z pred (t) is the prediction of z available at time t as illustrated in Figure 4. ...

**Context 2**

... with forgetting factor converges after 30 runs, while the schemes with time shift of the trajec- tories converge after 25 runs as illustrated in Figure 13. The final tracking error is slightly smaller with the latter methods, especially when the time shift of the feedforward trajectory is reduced to δ u = 0.25 h as shown in Table 3. Figure 14 shows the tracking performance of ILC with input shift after 20 runs. Note that, since it is necessary to have distillate in the product tank to be able to take measurements, tracking starts one sampling time after the start of Phase 2, that is, at at t s + h. ...

## Citations

... 87,88 The inference of these batch properties can be used to inform process operation as well as optimization and control. 89 3.3.3 Uncertainty. ...

In the literature, machine learning (ML) and artificial intelligence (AI) applications tend to start with examples that are irrelevant to process engineers (e.g. classification of images between cats and dogs, house pricing, types of flowers, etc.). However, process engineering principles are also based on pseudo-empirical correlations and heuristics, which are a form of ML. In this work, industrial data science fundamentals will be explained and linked with commonly-known examples in process engineering, followed by a review of industrial applications using state-of-art ML techniques.

... and active biological agents are produced in such systems [5,6], while they are operated under extreme working standards to comply with stringent production regulations and a competitive global market. ...

... Control of chemical and biochemical processes is a challenging task due to nonlinearities associated with their internal states, manipulated variables, and also disturbances [26] as well as their time variability [6], which is inherent to many chemical and biochemical systems [3,27]. ...

Chemical and biochemical processes generally suffer from extreme nonlinearities with respect to internal states, manipulated variables, and also disturbances. These processes have always received special technical and scientific attention due to their importance as the means of large-scale production of chemicals, pharmaceuticals, and biologically active agents. In this work, a general-purpose genetic algorithm (GA)-optimized neural network (NNARX) controller is introduced, which offers a very simple but efficient design. First, the proof of the controller stability is presented, which indicates that the controller is bounded-input bounded-output (BIBO) stable under simple conditions. Then the controller was tested for setpoint tracking, handling modeling error, and disturbance rejection on two nonlinear processes that is, a continuous fermentation and a continuous pH neutralization process. Compared to a conventional proportional-integral (PI) controller, the results indicated better performance of the controller for setpoint tracking and acceptable action for disturbance rejection. Hence, the GA-optimized NNARX controller can be implemented for a variety of nonlinear multi-input multi-output (MIMO) systems with minimal a-priori information of the process and the controller structure.

... While modern batch production is in many cases highly automated and numerous approaches for batch plant control and optimization have been developed, see e.g. [2], many tasks that arise in batch production require manual actions and interventions, including manual steps in single production operations, e.g. harvesting a filter press, and medium-and long-term production decisions by plant management. ...

The complexity of modern industrial batch plants makes it nearly impossible for plant personnel and production managers to predict their future behavior accurately over longer periods of time. This contribution presents the INOSIM Foresight system for predictive decision support that employs highly accurate dynamic material flow simulation to create a transparency and situational awareness that allows the plant operators and management to operate and plan more efficiently, productively, and safely, which can lead to savings in the millions. Intuitive predictive graphical dashboards support plant personnel in a variety of ways. For example, they provide concise guidance to improve production (e.g. by counteracting negative events before they occur and by predicting key KPIs days or even weeks ahead), and they enable the staff to create production, personnel, and in-process maintenance plans that are efficient and non-conservative. The system is currently being deployed at a new, innovative pharma batch plant of CSL Behring GmbH in Marburg, Germany.

... Batch processing offers greater flexibility in the production of speciality and pharmaceutical chemicals. Thus, the trend in the chemical industry towards high added value products has increased interest in the optimal model-based control of batch processes ( Bonvin and François, 2017 ). Due to its ability to include directly constraints in the computation of the control moves, NMPC presents major advantages for the optimal operation of transient chemical plants. ...

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.

... The absence of an operating point means that separation into static and dynamic objectives is not possible. According to [5], there are in practice four approaches to the control of discontinuous processes based on the control objectives and the methods of reaching these objectives. ...

This paper presents a thorough review of control technologies that have been applied to wastewater treatment processes in the environmental engineering regime in the past four decades. It aims to provide a comprehensive technological review for both water engineering professionals and control specialists, giving rise to a suite of up-to-date pathways to impact this field in light of the classified technology hubs. The assessment was conducted with respect to linear control, linearizing control, nonlinear control, and artificial intelligence-based control. The application domain of each technology hub was summarized into a set of comparative tables for a holistic assessment. Challenges and perspectives were offered to these field engineers to help orient their future endeavor.

... Consequently, the application of online, measurement-based, optimizing feedback schemes is of great importance for the optimal operation of batch and semi-batch processes (Eaton and Rawlings, 1990;Ruppen et al., 1995;Ruppen et al., 1998;Bonvin et al., 2001;Bonvin, 2006;Kadam et al., 2007;Welz et al., 2008;Mesbah et al., 2011;Bonvin and François, 2017). ...

... On the other hand, the gas-liquid mass-transfer coefficients (˜K/) are assumed to vary within a batch. The uncertainty ranges for the parameters are given in Table 5 Remark 5.4 The back-off values can also be updated on a batch-to-batch manner so as to increase the performance of future batches (Bonvin and François, 2017). ...

The trend towards high-quality, low-volume and high-added value production has put more emphasis on semi-batch processing due to its increased flexibility of operations. Dynamic optimization plays an important role toward improving the operation of batch and semi-batch. In addition, nonlinear model predictive control (NMPC) is also an important tool for the real-time optimization of batch and semi-batch processes under uncertainty. However, the transient behaviour as well as the flexibility decrease with respect to time make the optimization of such processes very challenging.
The preferred strategy to solve constrained nonlinear dynamic optimization problems is usually to use a so-called direct method. Nevertheless, based on the problem type at hand and the solution algorithm used, direct methods may lead to computational complexity. In particular, the large prediction horizons required in shrinking-horizon NMPC increase the real-time computational effort because of expensive matrix factorizations in the solution steps, especially at the beginning of the batch. The computational delay associated with advanced control methods is usually underestimated in theoretical studies. However, this delay may contribute to suboptimal or, worse, infeasible operation in real-life applications.
Alternatively, indirect methods based on Pontryagin’s Minimum Principle (PMP) could efficiently deal with the optimization of batch and semi-batch processes. In fact, the interplay between states and co-states in the context of PMP might turn out to be computationally quite efficient. The main indirect solution technique is the shooting method, which however often leads to convergence problems and instabilities caused by the integration of the co-state equations forward in time. Generally, it has been extensively argued that indirect methods are non-convergent and inefficient for constrained problems. However, this study proposes an alternative, convergent and effective indirect solution technique. Instead of integrating the states and co-states simultaneously forward in time, the proposed algorithm parameterizes the inputs, and integrates the state equations forward in time and the co-state equations backward in time, thereby leading to a gradient-based optimization approach. Constraints are handled by indirect adjoining to the Hamiltonian function, which allows meeting the active constraints explicitly at every iteration step. The performance of the solution strategy is compared to direct methods through three different case studies. The results show that the proposed PMP-based quasi-Newton strategy is effective in dealing with complicated constraints and is quite competitive computationally.
In addition, this work suggests using the proposed indirect solution technique in the context of shrinking-horizon NMPC under uncertainty. Uncertainties can be handled by the introduction of time-varying backoff terms for the path constraints. The resulting NMPC algorithm is applied to a two-phase semi-batch reactor for the hydroformylation of 1-dodecene in the presence of uncertainty, and its performance is compared to that of NMPC that uses a direct simultaneous optimization method. The results show that the proposed algorithm (i) can enforce feasible operation for different uncertainty realizations both within batch or from batch to batch, and (ii) is significantly faster than direct simultaneous NMPC, especially at the beginning of the batch. In addition, a modification of the PMP-based NMPC scheme is proposed to enforce active constraints via tracking and reduce the real-time computational load further.
This thesis also details the combination of an indirect solution scheme together with a parsimonious input parameterization. The idea is to parameterize the sensitivity-seeking inputs in a parsimonious way so as to decrease the computational load of constrained nonlinear dynamic optimization problems. The proposed method is tested on the simulated examples of a batch binary distillation column with terminal purity constraints and a two-phase semi-batch hydroformylation reactor with a complex path constraint. The performance of the proposed indirect parsimonious solution scheme is compared with those of a fully parameterized PMP-based and a direct simultaneous solution approaches. It is observed that the combination of the indirect approach with parsimonious input parameterization can result in significant reduction in computational time.
Finally, in this work, the combination of simple solution models with parsimonious input parameterization in the context of shrinking-horizon NMPC is suggested in order to minimize the computational delay in feedback. Solution models exploit the nominal optimal solution to suggest parsimonious parameterizations (especially for sensitivity-seeking arcs) that lead to fast optimization. The proposed approach is illustrated in simulation on two case studies in the presence of uncertainty, namely a binary batch distillation column and a semi-batch reactor. The results show that the suggested parsimonious shrinking-horizon NMPC (i) performs very similarly to the standard (fully parameterized) shrinking-horizon NMPC in terms of cost, (ii) is computationally much faster than the standard shrinking-horizon NMPC especially at the beginning of the batch, (iii) is robust to plant-model mismatch

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.

In this chapter, chemical industrial processes are considered, and Linear Algebra-Based Control Design (LAB CD) is the approach used to design the controller. First, the case of dealing with a nonlinear first principles–based model of the process is considered. Then, an experimental linearized model around an operating point is considered, and, again, the LAB CD methodology is applied to design the control. The simple model based on a first-order plus time delay (FOPTD) transfer function is used, and the controlled plant behavior is shown to be appropriate for small changes in the reference. A gain-scheduling adaptation scheme is suggested for larger reference changes. Thence, a design applicable to a large variety of processes is obtained. In order to better illustrate the procedure, the control design for a typical continuous stirred tank reactor (CSTR) is developed.

A new design method of two-dimensional (2D) controller for multi-phase batch processes with time delay and disturbances is proposed to ensure the stability of the control system and realize efficient production in industry. The batch process is first converted to an equivalent but different dimensional 2D-FM switched system. Based on the 2D system framework, then sufficient conditions of a controller existence expressed by linear matrix inequalities (LMIs) that stabilizing system is given by means of the average dwell time method. Meanwhile, robust hybrid 2D controller design containing extended information is proposed and the minimum runtime lower bound of each sub-system is accurately calculated. The design advantages of the controller depend on the size of the time delay so it has a certain degree of robustness. At the same time, considering the exponential stability, the system can have a faster rate of convergence. In addition, the introduction of extended information has improved the control performance of the system to some extent. The acquisition of minimum time at different phases will promote certain production efficiency and thus reduce energy consumption. Finally, an injection process in industrial production process has been taken as an example to verify effectiveness of the proposed method.