Dynamic real‐time optimization with closed‐loop prediction

Process plants are operating in an increasingly global and dynamic environment, motivating the development of dynamic real‐time optimization (DRTO) systems to account for transient behavior in the determination of economically optimal operating policies. This article considers optimization of closed‐loop response dynamics at the DRTO level in a two‐layer architecture, with constrained model predictive control (MPC) applied at the regulatory control level. A simultaneous solution approach is applied to the multilevel DRTO optimization problem, in which the convex MPC optimization subproblems are replaced by their necessary and sufficient Karush–Kuhn–Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints. The performance of the closed‐loop DRTO strategy is compared to that of the open‐loop prediction counterpart through a multi‐part case study that considers linear dynamic systems with different characteristics. The performance of the proposed strategy is further demonstrated through application to a nonlinear polymerization reactor grade transition problem. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3896–3911, 2017     

Closed-loop dynamic real-time optimization with stabilizing model predictive control

Dynamic real-time optimization (DRTO) is a supervisory strategy at the upper level of the industrial process automation architecture that computes economically optimal set-point trajectories that are in turn passed on to the lower-level model predictive control (MPC) for tracking. The economically optimal solution, in several process industries, could lead to operating the plant at or around an unstable steady state. The present article accounts for this by developing a closed-loop DRTO (CL-DRTO) formulation that enables handling unstable operating points via an underlying MPC with stability constraints. To this end, a stabilizing MPC that handles trajectory tracking for unstable systems is embedded within the upper-level DRTO. The resulting CL-DRTO problem is reformulated by applying a simultaneous solution approach. The economic benefits realized by the proposed strategy are illustrated through applications to both linearized and nonlinear dynamic models for single-input single-output and multi-input multi-output continuous stirred tank reactor case studies.     

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     

Multi-rate observer design and optimal control to maximize productivity of an industry-scale fermentation process

Chemical industries focus primarily on profitable operations, resulting in growing attention and advances in the field of digital twins and optimal control algorithms. However, most industries still struggle due to a lack of physical sensors, infrequent measurements, and asynchronous sampling. Thus, in this work, we have designed a multi-rate state observer for state estimation from plant measurements and developed a model predictive controller (MPC) that maximized the profitability of an industry-scale fermentation process (fermenter volume < 378,500 L). Additionally, as the fermentation process is complex due to the use of microorganisms, which cannot be accurately captured using a first-principles model, we utilize a previously developed hybrid model in the proposed MPC formulation. The MPC uses a GAMS-MATLAB framework to determine the optimal input profiles while considering practical process constraints. It is shown using multiple datasets, that the MPC can increase productivity while also decreasing the plant operating cost.     

分批补料反应过程的非固定终端经济优化控制

针对批次生产周期不确定问题,提出一种非固定终端的经济优化控制方法。首先采用经济模型预测控制方法,用收益最大化的经济型目标函数代替终端约束,并将批次生产周期纳入被优化变量,建立动态经济优化问题,并通过对每个控制变量进行有差异的参数化,将动态优化问题转化为非线性规划（NLP）问题;然后使用内点罚函数法求解含非线性约束的优化问题,得到的最优控制序列和最佳批次生产周期,可将不确定扰动带来的损失降低到最小。其次采用非固定预测时域的滚动时域控制方法,不仅提高多变量系统的协同控制能力,而且根据实时预测终端产品产量不断优化更新关键操纵变量的控制分段函数的分割数及控制序列,从而可灵活优化操纵变量和操作时间的轨迹。最后在苯胺加氢过程上进行了批次优化控制性能测试,测试结果表明,非固定终端的经济优化控制从批次的总生产效益角度来优化每个批次生产的操作条件,实现批次反应过程生产时间与经济效益的最优化管理。     

基于动态代谢通量分析的发酵过程多目标优化

通过动态代谢通量分析方法建立发酵过程模型,提出了一种基于微观代谢信息的发酵过程多目标优化策略,该策略基于所建微观模型,根据动态特性将发酵过程分为菌体生长和产物合成两个阶段,进行特征分析并从微观通量层面分别设计优化目标与约束条件,采用多目标粒子群算法求得最优解。该方法用于青霉素发酵过程底物流加速率和pH的操作轨迹优化,仿真实验结果表明,采用基于微观通量的多目标优化策略能够提高产物终端浓度,表明优化策略的有效性。     

A property‐based approach to the synthesis of material conservation networks with economic and environmental objectives

This article presents a multiobjective optimization model for the recycle and reuse networks based on properties while accounting for the environmental implications of the discharged wastes using life‐cycle assessment. The economic objective function considers fresh sources and treatment costs, whereas the environmental objective function is measured through the eco‐indicator 99. The model considers constraints in the process sinks as well as in the environment based on stream properties such as pH, chemical oxygen demand, toxicity, density, and color, in addition to the composition of the waste streams. A global optimization procedure is developed by indirectly tackling properties through property operators and by segregating the process streams before treatment. Three examples are included, and the results show that it is possible to consider simultaneously the trade‐offs between the total annual costs and the overall environmental impact using the proposed methodology. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

化工过程预测控制的在线优化实现机制

多层结构的预测控制已逐渐成为工业过程控制领域的主流控制方案。在此控制架构基础上,根据操作工或工艺优化所给定期望值的不同,将稳态优化问题具体化为两种基本情况,并对此提出基于复合目标函数的优化问题,可针对不同过程要求退化为线性、二次或二者兼有的优化问题形式。为保证最优目标的可行性并在一定程度上避免关键变量饱和,对不可行的期望值适当调整。将所得最优目标增量化处理后送入模型预测控制动态控制层,确保了上下层之间变量传递的一致性。包含约束的全混槽反应器系统仿真实例表明,流程的优化实现层可针对不同的过程要求有效给出最优目标以便动态控制,说明了该优化流程的可行性。     

动态实时优化策略下的分层式预测控制及其在化工过程中的应用

针对化工过程中那些因存在批处理、含有物料回流环节而很难达到稳态的过程以及一些因扰动的存在而很难精确地操作在一个设定点处的非线性过程,采用常规的稳态优化会产生低效或失效优化解的问题,提出一种动态实时优化策略。即在多层控制结构中的RTO层采用动态优化而非常规的稳态优化,依照过程的优化操作信息在满足过程动态规律和物料、产品市场价格变化的条件下实现生产的经济利润最优,事例仿真结果表明该方法的可行性和有效性。     

稳态目标优化的稳定MIMO约束预测控制

A two-stage multi-objective optimization model-predictive control algorithms(MPC) strategy is presented. A domain MPC controller with input constraints is used to increase freedom for steady-state objective and enhance stabilization of the controller. A steady-state objective optimization algorithm oriented to transient process is adopted to realize optimization of objectives else than dynamic control. It is proved that .the stabilization for both dynamic control and steady-state objective optimization can be guaranteed. The theoretical results are demonstrated and discussed using a distillation tower as the model. Theoretical analysis and simulation results show that this control stratek--v is efl$cient and provides a good strategic solution to uractical urocess control.     

Economic model predictive control with time‐varying objective function for nonlinear process systems

Economic model predictive control (EMPC) is a control scheme that combines real‐time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time‐varying process economics). In the present work, we focus on the development of a Lyapunov‐based EMPC (LEMPC) scheme that is formulated with an explicitly time‐varying economic cost function. First, the formulation of the proposed two‐mode LEMPC is given. Second, closed‐loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed‐loop simulations of a chemical process that the proposed LEMPC can achieve stability with time‐varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. © 2013 American Institute of Chemical Engineers AIChE J 60: 507–519, 2014     

不确定性间歇过程的一种实时优化控制方法

针对不确定性间歇过程的实时优化问题,提出了一种集成批间和批内优化的新实时优化控制方法。首先求解标称模型得到最优输入轨迹的结构,然后将输入轨迹参数化为若干标量决策变量及子输入轨迹。对最优性条件中的终端约束部分,使用批间优化满足约束条件;对梯度轨迹部分,提出一种回归法近似最优输入轨迹,以解决不确定扰动的在线不可测问题,实现梯度轨迹的批内优化。对一个间歇反应器的仿真研究表明了新方法的有效性。     

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     

A new framework and a simpler method for the development of batch crystallization recipes

We use a new generalized dimensionless model of a seeded batch crystallization process to compare results from four crystal growth rate/concentration trajectories: a numerically‐computed optimal trajectory, a constant growth rate trajectory, a trajectory proposed by Mullin and Nyvlt [Chem Eng Sci. 1971;26:369–377] that can be calculated without a kinetic model, and a linear concentration‐time trajectory. Because the model is generalized and dimensionless it is not specific to any particular solute–solvent system. We show that if seed properties are good, all trajectories achieve a good result, whereas if seed properties are poor all trajectories achieve a poor result. If seed properties are intermediate, the linear concentration trajectory performs much worse than the other trajectories. On the basis of this, we conclude: (1) Linear trajectories and natural cooling trajectories are poor and should be avoided. When evaluating the benefit derived from an optimization of a temperature/saturation concentration trajectory, the appropriate benchmark should be the Mullin‐Nyvlt trajectory, which typically performs much better than the linear trajectory and can be calculated knowing only the mass of seeds at the beginning of the batch. (2) Changing seed properties is more likely to improve batch crystallizer performance than optimizing the growth/saturation concentration trajectory. (3) For rapid process development, the most reasonable approach is to use the Mullin‐Nyvlt trajectory and seek to improve process performance by adjusting seed properties. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Optimal process operation for the production of linear polyethylene resins with tailored molecular weight distribution

An optimization model is presented to determine optimal operating policies for tailoring high density polyethylene in a continuous polymerization process. Shaping the whole molecular weight distribution (MWD) by adopting an appropriate choice of operating conditions is of great interest when designing new polymers or when improving quality. The continuous tubular and stirred tank reactors are modeled in steady state by a set of differential‐algebraic equations with the spatial coordinate as independent variable. A novel formulation of the optimization problem is introduced. It comprises a multi‐stage optimization model with differential‐algebraic equality constraints along the process path and inequality end‐point constraints on product quality. The resulting optimal control problem is solved at high computational efficiency by means of a shooting method. The results show the efficiency of the proposed approach and the benefit of predicting and controlling the complete MWD as well as the interplay between operating conditions and polymer properties. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

An integrated framework for scheduling and control using fast model predictive control

Integration of scheduling and control involves extensive information exchange and simultaneous decision making in industrial practice (Engell and Harjunkoski, Comput Chem Eng. 2012;47:121–133; Baldea and Harjunkoski I, Comput Chem Eng. 2014;71:377–390). Modeling the integration of scheduling and dynamic optimization (DO) at control level using mathematical programming results in a Mixed Integer Dynamic Optimization which is computationally expensive (Flores‐Tlacuahuac and Grossmann, Ind Eng Chem Res. 2006;45(20):6698–6712). In this study, we propose a framework for the integration of scheduling and control to reduce the model complexity and computation time. We identify a piece‐wise affine model from the first principle model and integrate it with the scheduling level leading to a new integration. At the control level, we use fast Model Predictive Control (fast MPC) to track a dynamic reference. Fast MPC also overcomes the increasing dimensionality of multiparametric MPC in our previous study (Zhuge and Ierapetritou, AIChE J. 2014;60(9):3169–3183). Results of CSTR case studies prove that the proposed approach reduces the computing time by at least two orders of magnitude compared to the integrated solution using mp‐MPC. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3304–3319, 2015     

基于模型预测控制及智能寻优的水泥粉磨优化控制

本文提出一种基于运行状态软测量和成本软约束的多变量模型预测控制(MPC)。MPC控制与传统的专家经验控制和模糊控制相比,通过模型对系统工艺参数的预测,不断地学习更新模型,更符合水泥粉磨大时延、多工况的特性。应用中通过对水泥粉磨装置的阶跃响应实验,建立多变量预测控制模型,解决水泥粉磨系统生产过程的不确定性。在此基础上,通过增量学习和机器学习找到最优运行参数,使水泥粉磨的MPC控制一直保持在最优工况。     

Discrete-time contraction constrained nonlinear model predictive control using graph-based geodesic computation

Modern chemical processes need to operate around time-varying operating conditions to optimize plant economy, in response to dynamic supply chains (e.g., time-varying specifications of product and energy costs). As such, the process control system needs to handle a wide range of operating conditions whilst optimizing system performance and ensuring stability during transitions. This article presents a reference-flexible nonlinear model predictive control approach using contraction based constraints. Firstly, a contraction condition that ensures convergence to any feasible state trajectories or setpoints is constructed. This condition is then imposed as a constraint on the optimization problem for model predictive control with a general (typically economic) cost function, utilizing Riemannian weighted graphs and shortest path techniques. The result is a reference flexible and fast optimal controller that can trade-off between the rate of target trajectory convergence and economic benefit (away from the desired process objective). The proposed approach is illustrated by a simulation study on a CSTR control problem.     

Actuator stiction compensation via model predictive control for nonlinear processes

The problem of valve stiction is addressed, which is a nonlinear friction phenomenon that causes poor performance of control loops in the process industries. A model predictive control (MPC) stiction compensation formulation is developed including detailed dynamics for a sticky valve and additional constraints on the input rate of change and actuation magnitude to reduce control loop performance degradation and to prevent the MPC from requesting physically unrealistic control actions due to stiction. Although developed with a focus on stiction, the MPC‐based compensation method presented is general and has potential to compensate for other nonlinear valve dynamics which have some similarities to those caused by stiction. Feasibility and closed‐loop stability of the proposed MPC formulation are proven for a sufficiently small sampling period when Lyapunov‐based constraints are incorporated. Using a chemical process example with an economic model predictive controller (EMPC), the selection of appropriate constraints for the proposed method is demonstrated. The example verified the incorporation of the stiction dynamics and actuation magnitude constraints in the EMPC causes it to select set‐points that the valve output can reach and causes the operating constraints to be met. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2004–2023, 2016     

Optimal reaction conditions for the minimization of energy consumption and by‐product formation in a poly(ethylene terephthalate) process

We determined the optimal reaction conditions to minimize the energy cost and the quantities of by‐products for a poly(ethylene terephthalate) process by using the iterative dynamic programming (IDP) algorithm. Here, we employed a sequence of three reactor models: the semibatch transesterification reactor model, the semibatch prepolymerization reactor model, and the rotating‐disc‐type polycondensation reactor model. We selectively chose or developed the reactor models by incorporating experimentally verified kinetic models reported in the literature. We established the model for the entire reactor system by connecting the three reactor models in series and by resolving some joint problems arising when different types of reactor models were interconnected. On the basis of the simulation results of the reactor system, we scrutinized the cause and effect between the reaction conditions and the final quality of the polymer product. Here, we set up the optimization strategy by using IDP on the basis of the integrated reactor model, and the process variables with significant influence on the properties of polymer were selected as control variables with the help of a simulation study. With this method, we could refine the reaction conditions at the end of each iteration step by contracting the spectra of control regions, and the iteration process finally stopped when the profile of the optimal trajectory converged. We also took the constraints on the control variables into account to guarantee polymer quality and to suppress side reactions. Constituting six different strategies by setting weighting vectors differently, we examined the differences in optimal trajectories, the trend of optimality, and the quality of the final polymer product. For each of the strategies, we conducted the optimization to examine whether the number‐average degree of polymerization approached the desired value. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 993–1008, 2002