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     

Reference Trajectory Optimization Under Constrained Predictive Control

Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.     

基于证据网络的多变量MPC经济性能评估

MPC控制系统作为先进控制策略,已经被广泛地应用于工业生产中。但在实际工业中,MPC控制系统的变量的软约束往往设定得比较保守,使系统无法达到最优经济性能。针对有约束的MPC控制系统,采用二次型经济性能指标函数来评价系统的经济性能,将最优工作点的求解问题转化为一个典型的有约束的线性规划问题。进而根据历史数据和二次型经济性能指标函数所得最优运行结果建立多变量MPC的证据网络模型,通过证据网络的反向推理和决策,得到造成MPC控制系统性能下降的可能原因,并提出改善控制系统性能的策略。最后通过仿真实验,验证了基于证据网络的经济性能评估的有效性。     

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     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

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.     

Optimal operation of integrated processing systems: Part II: Closed-loop on-line optimizing control

A method for tracking the economically optimal operating conditions of a chemical process in the presence of constraints is developed. The technique is based on an on-line search rather than a fundamental model. The most profitable operating point is found by fitting a dynamic model of the process based on data obtained from experimental moves on the plant. This model is used to compute gradients of the economic objective and of the constraints so that a direction of economic improvement inside the allowed operating region of the plant is always obtained. Constraint violations during the transients are prevented by a multivariable regulator. A new regulation method (Internal Model Control) is used which permits explicit handling of constraints and which can be made robust against modelling errors. This combined optimization/regulation approach is tested in a demonstrative simulation example and shown to be reliable for following a moving optimum and safely handling complex constraint moves.     

Design and Analysis of Integrated Predictive Iterative Learning Control for Batch Process Based on Two-dimensional System Theory

Based on the two-dimensional (2D) systemtheory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model predictions along the batch index can be calculated analytically due to the 2D Roesser model of the batch process. Then, an integrated framework of combining iterative learning control (ILC) andmodel predictive control(MPC) is formed reasonably. The output of feedforward ILC is estimated on the basis of the predefined process 2D model. By minimizing a quadratic objective function, the feedback MPC is introduced to obtain better control performance for tracking problem of batch processes. Simulations on a typical batch reactor demonstrate that the satisfactory tracking performance as well as faster convergence speed can be achieved than traditional proportion type (Ptype) ILC despite the model error and disturbances.     

Design of multi-parametric NCO tracking controllers for linear dynamic systems

A methodology for combining multi-parametric programming and NCO tracking is presented in the case of linear dynamic systems. The resulting parametric controllers consist of (potentially nonlinear) feedback laws for tracking optimality conditions by exploiting the underlying optimal control switching structure. Compared to the classical multi-parametric MPC controller, this approach leads to a reduction in the number of critical regions. It calls for the solution of more difficult parametric optimization problems with linear differential equations embedded, whose critical regions are potentially nonconvex. Examples of constrained linear quadratic optimal control problems with parametric uncertainty are presented to illustrate the approach.     

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。     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

一种新的生产计划与催化裂化装置过程操作集成的闭环策略

Production planning models generated by common modeling systems do not involve constraints for process operations, and a solution optimized by these models is called a quasi-optimal plan. The quasi-optimal plan cannot be executed in practice some time for no corresponding operating conditions. In order to determine a practi- cally feasible optimal plan and corresponding operating conditions of fluidized catalytic cracking unit （FCCU）, a novel close-loop integrated strategy, including determination of a quasi-optimal plan, search of operating conditions of FCCU and revision of the production planning model, was proposed in this article. In the strategy, a generalized genetic algorithm （GA） coupled with a sequential process simulator of FCCU was applied to search operating conditions implementing the quasi-optimal plan of FCCU and output the optimal individual in the GA search as a final genetic individual. When no corresponding operating conditions were found, the final genetic individual based correction （FGIC） method was presented to revise the production planning model, and then a new quasi-optimal production plan was determined. The above steps were repeated until a practically feasible optimal plan and corresponding operating conditions of FCCU were obtained. The close-loop integrated strategy was validated by two cases, and it was indicated that the strategy was efficient in determining a practically executed optimal plan and corresponding operating conditions of FCCU.     

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.     

Model Predictive Control with Feedforward Strategy for Gas Collectors of Coke Ovens

In coking process, the production quality, equipment life, energy consumption, and process safety are all influenced by the pressure in gas collector pipe of coke oven, which is frequently influenced by disturbances. The main control objectives for the gas collector pressure system are keeping the pressures in collector pipes at appropriate operating point. In this paper, model predictive control (MPC) strategy is introduced to control the collector pressure system due to its ability to handle constraint and good control performance. Based on a method proposed to simplify the system model, an extended state space model predictive control is designed, which combines the feedforward strategy to eliminate the disturbance. The simulation results in a system with two coke ovens show the feasibility and effectiveness of the control scheme.     

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.     

On-line optimization control for a time-varying process using multiple models: A laboratory scale fermenter application

The aim of this work is to present a technique which is able to deal with discontinuous time varying systems based on the identification of local linear models at different operating conditions. The ideal process trajectory is predicted through an optimizing algorithm using a Model Predictive Control Scheme (MPC) in cascade with conventional PID controllers which are responsible for driving the system along at the optimal conditions. A laboratory scale reactor for the production of gluconic acid is studied in order to assess the reliability and performance of this control strategy.     

Explicit Nonlinear Predictive Control of a Distillation Column Based on Neural Models

A nonlinear Model Predictive Control (MPC) algorithm and its application to a distillation column are described. The algorithm uses a neural model of the process that is linearized online around the current operating point. The algorithm is computationally efficient because the control policy is calculated explicitly without any optimization. The algorithm requires online repetition of a matrix decomposition task and the solution of linear equations. The obtained solution is projected onto the admissible set of constraints imposed on the magnitude and the increment of the manipulated variables. For the distillation column considered, the control accuracy is comparable not only to that obtained in MPC with online linearization and quadratic programming but also to that obtained in nonlinear MPC, which is based on full nonlinear optimization repeated at each sampling instant.     

Model predictive control for multivariable unstable processes with constraints on manipulated variables

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.