Distributed economic model predictive control for operational safety of nonlinear processes

Achieving operational safety of chemical processes while operating them in an economically‐optimal manner is a matter of great importance. Our recent work integrated process safety with process control by incorporating safety‐based constraints within model predictive control (MPC) design; however, the safety‐based MPC was developed with a centralized architecture, with the result that computation time limitations within a sampling period may reduce the effectiveness of such a controller design for promoting process safety. To address this potential practical limitation of the safety‐based control design, in this work, we propose the integration of a distributed model predictive control architecture with Lyapunov‐based economic model predictive control (LEMPC) formulated with safety‐based constraints. We consider both iterative and sequential distributed control architectures, and the partitioning of inputs between the various optimization problems in the distributed structure based on their impact on process operational safety. Moreover, sufficient conditions that ensure feasibility and closed‐loop stability of the iterative and sequential safety distributed LEMPC designs are given. A comparison between the proposed safety distributed EMPC controllers and the safety centralized EMPC is demonstrated via a chemical process example. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3404–3418, 2017     

Inferential Control of Reactive Destillation Columns – An Algorithmic Approach

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed‐integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed‐integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.     

Integrated design and control of semicontinuous distillation systems utilizing mixed integer dynamic optimization

Semicontinuous distillation systems are notoriously difficult to design and optimize because the structural parameters, operational parameters, and control system must all be determined simultaneously. In the past 15 years of research into semicontinuous systems, studies of the optimal design of these systems have all been limited in scope to small subsets of the parameters, which yields suboptimal and often unsatisfactory results. In this work, for the first time, the problem of integrated design and control of semicontinuous distillation processes is studied by using a mixed integer dynamic optimization (MIDO) problem formulation to optimize both the structural and control tuning parameters of the system. The public model library (PML) of gPROMS is used to simulate the process and the built-in optimization package of gPROMS is used to solve the MIDO via the deterministic outer approximation method. The optimization results are then compared to the heuristic particle swarm optimization (PSO) method.     

Decentralized Control System Design under Uncertainty Using Mixed‐Integer Optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In this contribution, the optimal control structure and the optimal controller parameters are determined simultaneously using mixed‐integer dynamic optimization (MIDO) under uncertainty, to account for nonlinear process dynamics and various disturbance scenarios. Application of the sigma point method is proposed in order to approximate the expectation and the variance of a chosen performance index with a minimum number of points to solve the MIDO problem under uncertainty. The proposed methodology is demonstrated with a benchmark problem of an inferential control for a reactive distillation column. The results are compared with established heuristic design methods and with previous deterministic approaches.     

A new superstructure optimization paradigm for process synthesis with product distribution optimization: Application to an integrated shale gas processing and chemical manufacturing process

We propose a novel process synthesis framework that combines product distribution optimization of chemical reactions and superstructure optimization of the process flowsheet. A superstructure with a set of technology/process alternatives is first developed. Next, the product distributions of the involved chemical reactions are optimized to maximize the profits of the effluent products. Extensive process simulations are then performed to collect high‐fidelity process data tailored to the optimal product distributions. Based on the simulation results, a superstructure optimization model is formulated as a mixed‐integer nonlinear program (MINLP) to determine the optimal process design. A tailored global optimization algorithm is used to efficiently solve the large‐scale nonconvex MINLP problem. The resulting optimal process design is further validated by a whole‐process simulation. The proposed framework is applied to a comprehensive superstructure of an integrated shale gas processing and chemical manufacturing process, which involves steam cracking of ethane, propane, n‐butane, and i‐butane. © 2017 American Institute of Chemical Engineers AIChE J, 63: 123–143, 2018     

Equation‐oriented simulation and optimization of process flowsheets incorporating detailed spiral‐wound multistream heat exchanger models

Multiple chemical processes rely on multistream heat exchangers (MHEXs) for heat integration, particularly at cryogenic temperatures. Owing to their geometric complexity, the detailed design of MHEXs is typically iterative: the exchanger geometric parameters are selected to match process specifications resulting from a flowsheet optimization step; then, the flowsheet is reoptimized with the predictions of the MHEX model, and these steps are repeated until a convergence criterion is met. This paper presents a novel framework that allows—for the first time, to our knowledge—for the simultaneous optimization of the process flowsheet and the detailed MHEX design. Focusing on spiral‐wound MHEXs, we develop an equation‐oriented exchanger model using industry‐accepted heat transfer and pressure drop correlations for single‐phase and multiphase streams. We embed this model in our previously developed pseudo‐transient equation‐oriented process simulation and optimization framework. We demonstrate our approach on an industrial case study, the PRICO^® natural gas liquefaction process. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3778–3789, 2017     

Simultaneous mixed-integer dynamic optimization for integrated design and control

We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way.     

Optimal PID controller tuning using stochastic programming techniques

We argue that stochastic programming provides a powerful framework to tune and analyze the performance limits of controllers. In particular, stochastic programming formulations can be used to identify controller settings that remain robust across diverse scenarios (disturbances, set‐points, and modeling errors) observed in real‐time operations. We also discuss how to use historical data and sampling techniques to construct operational scenarios and inference analysis techniques to provide statistical guarantees on limiting controller performance. Under the proposed framework, it is also possible to use risk metrics to handle extreme (rare) events and stochastic dominance concepts to conduct systematic benchmarking studies. We provide numerical studies to illustrate the concepts and to demonstrate that modern modeling and local/global optimization tools can tackle large‐scale applications. The proposed work also opens the door to data‐based controller tuning strategies that can be implemented in real‐time operations. © 2017 American Institute of Chemical Engineers AIChE J, 64: 2997–3010, 2018     

A pseudo‐transient optimization framework for periodic processes: Pressure swing adsorption and simulated moving bed chromatography

Periodic systems are widely used in separation processes and in reaction engineering. They are designed for and operated at a cyclic steady state (CSS). Identifying and optimizing the CSS has proven to be computationally challenging. A novel framework for equation‐oriented simulation and optimization of cyclic processes is introduced. A two‐step reformulation of the process model is proposed, comprising, (1) a full discretization of the time and spatial domains and (2) recasting the discretized model as a differential‐algebraic equation system, for which theoretical stability guarantees are provided. Additionally, a mathematical, structural connection between the CSS constraints and material recycling is established, which allows us to deal with these conditions via a “tearing” procedure. These developments are integrated in a pseudo‐transient design optimization framework and two extensive case studies are presented: a simulated moving bed chromatography system and a pressure swing adsorption process. © 2017 American Institute of Chemical Engineers AIChE J, 64: 2982–2996, 2018     

Optimal supply chain design and operations under multi‐scale uncertainties: Nested stochastic robust optimization modeling framework and solution algorithm

Although strategic and operational uncertainties differ in their significance of impact, a “one‐size‐fits‐all” approach has been typically used to tackle all types of uncertainty in the optimal design and operations of supply chains. In this work, we propose a stochastic robust optimization model that handles multi‐scale uncertainties in a holistic framework, aiming to optimize the expected economic performance while ensuring the robustness of operations. Stochastic programming and robust optimization approaches are integrated in a nested manner to reflect the decision maker's different levels of conservativeness toward strategic and operational uncertainties. The resulting multi‐level mixed‐integer linear programming model is solved by a decomposition‐based column‐and‐constraint generation algorithm. To illustrate the application, a county‐level case study on optimal design and operations of a spatially‐explicit biofuel supply chain in Illinois is presented, which demonstrates the advantages and flexibility of the proposed modeling framework and efficiency of the solution algorithm. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3041–3055, 2016     

Multi‐rate observer design for process monitoring using asynchronous inter‐sample output predictions

In this article, the problem of observer design in linear multi‐output systems with asynchronous sampling is addressed. The proposed multi‐rate observer is based on a continuous‐time Luenberger observer design coupled with an inter‐sample predictor for each sampled measurement, which generates an estimate of the output in between consecutive measurements. The sampling times are not necessarily uniformly spaced, but there exists a maximum sampling period among all the sensors. Sufficient and explicit conditions are derived to guarantee exponential stability of the multi‐rate observer. The proposed framework of multi‐rate observer design is examined through a mathematical example and a gas‐phase polyethylene reactor. In the latter case, the amount of active catalyst sites is estimated, with a convergence rate that is comparable to the case of continuous measurements. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3384–3394, 2017     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes

In the present work, we consider the problem of variable duration economic model predictive control of batch processes subject to multi‐rate and missing data. To this end, we first generalize a recently developed subspace‐based model identification approach for batch processes to handle multi‐rate and missing data by utilizing the incremental singular value decomposition technique. Exploiting the fact that the proposed identification approach is capable of handling inconsistent batch lengths, the resulting dynamic model is integrated into a tiered EMPC formulation that optimizes process economics (including batch duration). Simulation case studies involving application to the energy intensive electric arc furnace process demonstrate the efficacy of the proposed approach compared to a traditional trajectory tracking approach subject to limited availability of process measurements, missing data, measurement noise, and constraints. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2705–2718, 2017     

Stem cell biomanufacturing under uncertainty: A case study in optimizing red blood cell production

As breakthrough cellular therapy discoveries are translated into reliable, commercializable applications, effective stem cell biomanufacturing requires systematically developing and optimizing bioprocess design and operation. This article proposes a rigorous computational framework for stem cell biomanufacturing under uncertainty. Our mathematical tool kit incorporates: high‐fidelity modeling, single variate and multivariate sensitivity analysis, global topological superstructure optimization, and robust optimization. The advantages of the proposed bioprocess optimization framework using, as a case study, a dual hollow fiber bioreactor producing red blood cells from progenitor cells were quantitatively demonstrated. The optimization phase reduces the cost by a factor of 4, and the price of insuring process performance against uncertainty is approximately 15% over the nominal optimal solution. Mathematical modeling and optimization can guide decision making; the possible commercial impact of this cellular therapy using the disruptive technology paradigm was quantitatively evaluated. © 2017 American Institute of Chemical Engineers AIChE J, 64: 3011–3022, 2018     

Multi‐objective optimization superimposed model‐based process design of an enzymatic hydrolysis process

The concepts of green process engineering and rigorous model‐based approaches have proven to be highly beneficial in process engineering. Although a combination of these two principles thus appears extremely promising, it is not found very commonly in literature. The very high complexity resulting from this combination poses great challenges for the process design and design engineers. Therefore, this work presents an innovative methodology for the model‐based process design with superimposed multi‐objective optimization for an exemplary process. This process for the enzymatic hydrolysis of fatty acid methyl ester combines several aspects of green process engineering and represents an exemplary process with an enzymatic liquid‐liquid‐solid reaction system. The optimization results based on operating and investment costs reveal important insights on the exemplary process and highlight the great advantages of the developed methodology as a profound basis for academic and industrial process design purposes. © 2017 American Institute of Chemical Engineers AIChE J, 63: 1974–1988, 2017     

An optimization framework to combine operable space maximization with design of experiments

The introduction of Quality by Design in the pharmaceutical industry stimulates practitioners to better understand the relationship of materials, processes and products. One way to achieve this is through the use of targeted experimentation. In this study, an optimization framework to design experiments that effectively leverage parameterized process models is presented to maximize the space covered in the output variables while also obtaining an orthogonal bracketing study in the process input factors. The framework considers both multi‐objective and bilevel optimization methods for relating the two maximization objectives. Results are presented for two case studies—a spray coating process and a continuously stirred reactor cascade—demonstrating the ability to generate and identify efficient designs with fit‐for‐purpose trade‐offs between bracketed orthogonality in the input factors and volume explored in the process output space. The proposed approach allows a more complete understanding of the process to emerge from a small set of experiments. © 2018 The Authors. AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers. AIChE J, 64: 3944–3957, 2018     

A framework for ammonia supply chain optimization incorporating conventional and renewable generation

Ammonia is an essential nutrient for global food production brought to farmers by a well‐established supply chain. This article introduces a supply chain optimization framework which incorporates new renewable ammonia plants into the conventional ammonia supply chain. Both economic and environmental objectives are considered. The framework is then applied to two separate case studies analyzing the supply chains of Minnesota and Iowa, respectively. The base case results present an expected trade‐off between cost, which favors purchasing ammonia from conventional plants, and emissions, which favor building distributed renewable ammonia plants. Further analysis of this trade‐off shows that a carbon tax above $25/t will reduce emissions in the optimal supply chain through building large renewable plants. The importance of scale is emphasized through a Monte Carlo sensitivity analysis, as the largest scale renewable plants are selected most often in the optimal supply chain. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4390–4402, 2017     

Multistream heat exchangers: Equation‐oriented modeling and flowsheet optimization

Multistream heat exchangers (MHEXs), typically of the plate‐fin or spiral‐wound type, are a key enabler of heat integration in cryogenic processes. Equation‐oriented modeling of MHEXs for flowsheet optimization purposes is challenging, especially when streams undergo phase transformations. Boolean variables are typically used to capture the effect of phase changes, adding considerable difficulty to solving the flowsheet optimization problem. A novel optimization‐oriented MHEX modeling approach that uses a pseudo‐transient approach to rapidly compute stream temperatures without requiring Boolean variables is presented. The model also computes an approximate required heat exchange area to determine the optimal tradeoff between operating and capital expenses. Subsequently, this model is seamlessly integrated in a previously‐introduced pseudo‐transient process modeling and flowsheet optimization framework. Our developments are illustrated with two optimal design case studies, an MHEX representative of air separation operation and a natural gas liquefaction process. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1856–1866, 2015