Integrated scheduling and dynamic optimization of batch processes using state equipment networks

A systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Data‐driven model predictive quality control of batch processes

The problem of driving a batch process to a specified product quality using data‐driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this “missing data” problem by integrating a previously developed data‐driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed‐loop simulations of a nylon‐6,6 batch polymerization process with limited measurements. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2852–2861, 2013     

Moving horizon approach of integrating scheduling and control for sequential batch processes

Online integration of scheduling and control is crucial to cope with process uncertainties. We propose a new online integrated method for sequential batch processes, where the integrated problem is solved to determine controller references rather than process inputs. Under a two‐level feedback loop structure, the integrated problem is solved in a frequency lower than that of the control loops. To achieve the goal of computational efficiency and rescheduling stability, a moving horizon approach is developed. A reduced integrated problem in a resolving horizon is formulated, which can be solved efficiently online. Solving the reduced problem only changes a small part of the initial solution, guaranteeing rescheduling stability. The integrated method is demonstrated in a simulated case study. Under uncertainties of the control system disruption and the processing unit breakdown, the integrated method prevents a large loss in the production profit compared with the simple shifted rescheduling solution. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1654–1671, 2014     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

Nonlinear quality prediction for multiphase batch processes

Typically, a multiphase batch process comprises several steady phases and transition periods. In steady phases, the data characteristics remain similar during the phase and have a significant repeatability from batch to batch; thus most data nonlinearities can be removed through the batch normalization step. In contrast, in each transition period, process observations vary with time and from batch to batch, so nonlinearities in the data may not be eliminated through batch normalization. To improve quality prediction performance, an efficient nonlinear modeling method—relevance vector machine (RVM) was introduced. RVMs were formulated for each transition period of the batch process, and for combining the results of different process phases. For process analysis, a phase contribution index and a variable contribution index are defined. Furthermore, detailed performance analyses on the prediction uncertainty and variation were also provided. The effectiveness of the proposed method is confirmed by an industrial example. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1778–1787, 2012     

Deterministic vs. stochastic performance assessment of iterative learning control for batch processes

The performance assessment of linear time‐invariant batch processes when iterative learning control (ILC) is implemented has been discussed. Previous literatures show that conventional performance assessment cannot be directly applied to batch processes due to the nature of batch operations. Chen and Kong have suggested a new method to assess the control performance of batch processes using optimal ILC as the benchmark. In their work, ILC controllers are assumed to affect either stochastic or deterministic performance but without considering their interaction. This work elaborates the controllers effects on both stochastic and deterministic control performance of batch processes. It is shown that the optimal solution based on the minimum variance control law has a trade‐off between deterministic and stochastic performance, which can be shown by a trade‐off curve. Furthermore, a method is proposed to estimate this curve from routine operating data, against which the performance of ILC controllers can be assessed. Simulation studies are conducted to verify the proposed method. © 2012 American Institute of Chemical Engineers AIChE J, 59: 457–464, 2013     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Continuous-time approaches for short-term scheduling of network batch processes: Small-scale and medium-scale problems

Two time representation approaches, discrete-time and continuous-time approaches, have been developed for short-term scheduling of batch process in small-scale and medium-scale during the last two decades. As usually establishing advantages over discrete-time approaches in the scheduling problems, continuous-time approaches have gained increasing attention in the last 10 years. The reported continuous-time approaches can be divided into four categories: global event-based, unit-specific event-based, slot-based and precedence-based models. In this paper, more complex processes, network batch processes in small and medium scales, are considered. Six models based on different continuous-time representations are compared in several benchmark examples from the literature. The compared items include problem size, computational times and model convergence. Moreover, two intermediate storage policies (limited and unlimited intermediate storage) and two objective functions (maximization of profit and minimization of makespan) are addressed.     

A two-stage approach for the synthesis of inter-plant water networks involving continuous and batch units

This paper presents a mathematical optimization model for inter-plant water network (IPWN) synthesis, where process units operate in mixed continuous and batch modes. The current developed model consists of a two-stage approach, and is dedicated to the special case where there are more continuous than batch units. In the first stage, all batch units are treated as continuous units by using auxiliary water storage tanks, and a continuously operated IPWN is synthesized to minimize the fresh water consumption. Subject to the determined IPWN flow rates, the water storage policy for the batch units is determined in the second stage to minimize the total storage capacity. Alternatively, the formulations of both stages can be combined and solved simultaneously to minimize the IPWN cost. Two modified literature examples are used to illustrate the proposed approach.     

Complex integration of processes

Pinch analysis is nowadays a practical tool for designing heat exchanger networks in chemical and process industries. Rules for integrating process units have also been worked out in the last decade or two. Process units can be described as different types of energy unit operations, donors and acceptors. Yet, heat integration alone is not sufficient for process integration. The largest savings are achieved when simultaneously optimizing enthalpy and mass flows — energy and material recycling is required to save the natural resources and protect the nature. Mathematical programming is increasingly used to optimize the problems both in continuous and batch operations. Task integration is spreading out: multifunctional units lower the capital investment, thus, the total annual cost Recent development of the complex integration with examples and reasonable forecast of the future development is presented in the paper.     

Robust model predictive control and fault handling of batch processes

This work considers the control of batch processes subject to input constraints and model uncertainty with the objective of achieving a desired product quality. First, a computationally efficient nonlinear robust Model Predictive Control (MPC) is designed. The robust MPC scheme uses robust reverse‐time reachability regions (RTRRs), which we define as the set of process states that can be driven to a desired neighborhood of the target end‐point subject to input constraints and model uncertainty. A multilevel optimization‐based algorithm to generate robust RTRRs for specified uncertainty bounds is presented. We then consider the problem of uncertain batch processes subject to finite duration faults in the control actuators. Using the robust RTRR‐based MPC as the main tool, a robust safe‐steering framework is developed to address the problem of how to operate the functioning inputs during the fault repair period to ensure that the desired end‐point neighborhood can be reached upon recovery of the full control effort. The applicability of the proposed robust RTRR‐based controller and safe‐steering framework subject to limited availability of measurements and sensor noise are illustrated using a fed‐batch reactor system. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Enhanced process comprehension and quality analysis based on subspace separation for multiphase batch processes

Phase‐based subpartial least squares (subPLS) modeling algorithm has been used for online quality prediction in multiphase batches. It strictly assumes that the X – Y correlations are identical within the same phase so that they can be defined by a uniform regression model. However, the accuracy of this precondition has not been theoretically checked when put into practical application. Actually it does not always agree well with the real case and may have to be rejected for some practical processes. In the present work, it corrects the “absolute similarity” of subPLS modeling by a more general recognition that only one part of the underlying correlations are time‐wise common within the same phase while the other part are time‐specific, which is referred to as “partial similarity” here. Correspondingly, a two‐step phase division strategy is developed, which separates the original phase measurement space into two different parts, the common subspace and uncommon subspace. It is only in the common subspace where the underlying X – Y correlations are similar, a phase‐unified regression model can be extracted for online quality prediction. Moreover, based on the subspace separation, offline quality analyses are conducted in both subspaces to explore their respective cumulative manner and contribution in quality prediction. The strength and efficiency of the proposed algorithm are verified on a typical multiphase batch process, injection molding. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A survey on applications of optimization-based integrating process design and control for chemical processes

Process design and control are closely related to each other in chemical engineering activities. Traditionally, process design and control system design are carried out in sequence. However, the integration of process design and control (IPDC) can bring greater economic benefits and process dynamic performance than traditional sequential design methods. This is true, particularly for modern chemical processes, in which various process units become more interacting and compact owing to the widespread use of heat integration and recycled streams, and the resulted impacts between process design and control begin to significantly influence both the capital and operational costs. Recently, considerable studies about the IPDC for chemical processes have been reported in published literature. The purpose of the paper is to survey the applications of optimization-based integrating process design and control for chemical processes. Firstly, attention has been focused on the applications of IPDC to different process units, for example, chemical reactors and separation columns. Then, the survey is extended to the applications of IPDC to plant-wide chemical processes. Finally, the future research challenges in the application of IPDC to chemical processes have been briefly discussed.     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016     

Quality‐relevant fault diagnosis with concurrent phase partition and analysis of relative changes for multiphase batch processes

Multiplicity of phases as indicated by changes of process characteristics is an inherent nature of many batch processes for both normal and fault cases. To more efficiently perform online fault diagnosis via reconstruction for multiphase batch processes, the phase nature and the relationship between normal and fault cases within each phase should be deeply addressed. This article proposes a quality‐relevant fault diagnosis strategy with concurrent phase partition and analysis of relative changes for multiphase batch processes. First, a concurrent phase partition algorithm is developed. The basic idea is to track the changes of process characteristics at normal and fault statuses jointly so that multiple sequential modeling phases are identified simultaneously for both normal and fault cases. Then, the relative changes from the normal status to each fault case are analyzed in each phase to reveal the specific fault effects more efficiently. The fault effects are decomposed in two different monitoring subspaces, principal subspace, and residual subspace, by capturing their different roles in removing out‐of‐control signals. The significant increases relative to the normal case are judged to be responsible for the concerned alarm monitoring statistics in each phase. The others are composed of general variations that are deemed to still follow normal rules and thus insignificant to remove alarm monitoring statistics. Those alarm‐responsible fault deviations are then used to develop reconstruction models which can more efficiently recover the fault‐free part for online fault diagnosis. The proposed algorithm is illustrated with a typical multiphase batch process with one normal case and three fault cases. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2048–2062, 2014     

An in silico evaluation of data‐driven optimization of biopharmaceutical processes

Two methodological improvements of the design of dynamic experiments (C. Georgakis, Ind Eng Chem Res. 2013) for the modeling and optimization of (semi‐) batch processes are proposed. Their effectiveness is evaluated in two representative classes of biopharmaceutical processes. First, we incorporate prior process knowledge in the design of the experiments. Many batch processes and, in particular, biopharmaceutical processes are usually not understood completely to enable the development of an accurate knowledge‐driven model. However, partial process knowledge is often available and should not be ignored. We demonstrate here how to incorporate such knowledge. Second, we introduce an evolutionary modeling and optimization approach to minimize the initial number of experiments in the face of budgetary and time constraints. The proposed approach starts with the estimation of only a linear Response Surface Model, which requires the minimum number of experiments. Accounting for the model's uncertainty, the proposed approach calculates a process optimum that meets a maximum uncertainty constraint. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2796–2805, 2017     

Greedy algorithm for scheduling batch plants with sequence‐dependent changeovers

This article presents a new algorithm for scheduling multistage batch plants with a large number of orders and sequence‐dependent changeovers. Such problems are either intractable when solved with full‐space approaches or poor solutions result. We use decomposition on the entire set of orders and derive the complete schedule in several iterations, by inserting a couple of orders at a time. The key idea is to allow for partial rescheduling without altering the main decisions in terms of unit assignments and sequencing (linked to the binary variables) so that the combinatorial complexity is kept at a manageable level. The algorithm has been implemented for three alternative continuous‐time mixed integer linear programing models and tested through the solution of 10 example problems for different decomposition settings. The results show that an industrial‐size scheduling problem with 50 orders, 17 units distributed over six stages can effectively be solved in roughly 6 min of computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Delay‐range‐dependent guaranteed cost control for batch processes with state delay

A guaranteed cost control scheme is proposed for batch processes described by a two‐dimensional (2‐D) system with uncertainties and interval time‐varying delay. First, a 2‐D controller, which includes a robust feedback control to ensure performances over time and an iterative learning control to improve the tracking performance from cycle to cycle, is formulated. The guaranteed cost law concept of the proposed 2‐D controller is then introduced. Subsequently, by introducing the Lyapunov–Krasovskii function and adding a differential inequality to the Lyapunov function for the 2‐D system, sufficient conditions for the existence of the robust guaranteed cost controller are derived in terms of matrix inequalities. A design procedure for the controller is also presented. Furthermore, a convex optimization problem with linear matrix inequality (LMI) constraints is formulated to design the optimal guaranteed cost controller that minimizes the upper bound of the closed‐loop system cost. The proposed control law can stabilize the closed‐loop system as well as guarantee H_∞ performance level and a cost function with upper bounds for all admissible uncertainties. The results can be easily extended to the constant delay case. Finally, an illustrative example is given to demonstrate the effectiveness and advantages of the proposed 2‐D design approach. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2033–2045, 2013