BASIC ECONOMIC OPTIMIZATION MODEL FOR A CONTINUOUS EXTRACTION PROCESS*

A basic mathematical model, mainly focused on economic assessment is directly applied to a counter-current, stage-wise, solvent-selective extraction system. A standard extraction model, based on the modeling of a mixer-settler process, is used as point of departure. This system is used to extract a dissolved compound in a process stream. Thereafter sensible operating and economic parameters are integrated into it. An adequate handling of these parameters allows a practical preliminary optimization process modeling. The economic assessment model can be applied from one to "ri" stages in any industrial stage-wise process unit. An optimum number of stages are determined based on solvent extraction and economic assessment.     

全局自优化控制策略及其测量变量子集选择

针对过程系统的优化运行问题,介绍一种基于Monte Carlo模拟的全局自优化控制策略。利用非线性模型计算整个操作空间内的平均经济损失,通过对某些条件进行合理假设,得到全局被控变量的解析表达形式。为了平衡传感器成本和系统性能,在全局自优化控制策略的基础上,引入混合整数约束,对测量变量子集进行选择。通过求解混合整数规划问题,能够同时获得最优的测量变量子集以及由其构成的全局被控变量,此外上述子集选择方法还可以处理附加的结构性约束问题。通过对蒸发过程的研究表明,该方法可以更加高效地处理测量变量子集选择问题,通过对精馏塔案例的研究,进一步验证了该方法在处理结构性约束问题中的优势。     

Adaptive Linear Dynamic Matrix Control applied to an integrating process

Dynamic Matrix Control (DMC) has proven to be a powerful tool for optimal regulation of chemical processes under constrained conditions. It is based on a linear convolution model derived from step-response measurements. A model predictive control algorithm optimises closed-loop performance for a nominal operating point. However, as the process moves away from this point, control usually becomes sub-optimal due to process non-linearity. As seen in this work, the DMC algorithm can be made adaptive, to establish a new local model, by recursive estimation of the local step response parameters from normal plant variations. However, when used for control of plants containing integrating process units, steady-state offsets occur for sustained changes. Thus, a novel Adaptive Linear Dynamic Matrix Control (ALDMC) algorithm has been developed and used to control a 2-input/2-output system with an integrating behaviour. Comparisons of model control and plant control with and without these features demonstrated the importance of integral compensation for integrating processes, and model adaptation in the case of plant/model mismatch. Some cross-compensation of integration by the adaptive feature was also noted. An holistic technique is demonstrated which simultaneously recognises residual integration disturbances and matrix parameter variations, whereas previous techniques which recognise only one of these will fail in the presence of the other.     

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。     

QUADRATIC PROGRAMMING SOLUTION OF DYNAMIC MATRIX CONTROL (QDMC)

QDMC is an improved version of Shell's Dynamic Matrix Control (DMC) multivariable algorithm which provides a direct and efficient method for handling process constraints. The algorithm utilizes a quadratic program to compute moves on process manipulated variables which keep controlled variables close to their targets while preventing violations of process constraints. Several on-line applications have demonstrated its excellent constraint handling properties, transparent tuning and robustness, while requiring minimal on-line computational load.     

Optimization of a Process for the Solvent Fractionation of Palm Oil Using a Model Based on Interpolation of Experimental Data

This work deals with the problem of finding the optimum operating conditions of a process for which a large amount of experimental data has been obtained from a pilot plant. A computer simulation model based on direct linear interpolation on the experimental data was developed and incorporated in an optimization routine able to deal with constraints. A sensitivity analysis around the maximum and a brief analysis of the effects of increasing the capacity of the main pieces of equipment were carried out. The results show that a substantial increment in the production can be achieved when operating at the optimum conditions and that good control of some variables should be observed to prevent deviations from that maximum.     

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.     

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.     

催化裂化装置裕量评价与瓶颈分析

考虑实际过程中存在着各种不确定因素,在化工过程设计时有必要对设计变量留出足够的裕量,使操作点位于过程约束边界内。基于过程稳态最优设计的一阶灵敏度分析,设计变量的局部裕量造成过程有效约束存在边界距离,操作变量进行操作优化所能获得的最大潜在经济效益是由有效约束的边界距离决定的。因此,采用操作优化得到的装置潜在经济效益可以用于对装置总体裕量进行评价。以催化裂化装置为主要研究对象,采用操作优化的方法计算装置的潜在经济效益,以此对装置的总体裕量进行评价。考虑过程的动态变化过程,结合动态优化的方法,利用稳态优化的经济效益和动态优化的经济效益对装置的总体裕量进行划分,分清保证操作控制可实现性的控制裕量和可以提升装置潜在经济效益的工艺裕量。通过分析各设计变量的局部裕量对装置总体裕量的影响确定设计瓶颈的所在,找到消除设计瓶颈的途径。     

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     

A safe-parking framework for plant-wide fault-tolerant control

This work addresses the problem of handling actuator faults in a chemical plant. We consider a multi-unit nonlinear process system subject to input constraints and actuator faults in one unit that preclude the possibility of operating the unit at its nominal equilibrium point. The interconnected nature of the units in a plant brings forth unique opportunities as well as challenges that simply do not exist when handling faults in isolated units. In particular, the fact that the outlet streams from a faulty unit go through subsequent (well functioning) units raises the possibility of better restricting the effects of the fault to the faulty unit. At the same time, handling a fault in a unit may necessitate appropriate action in the downstream unit, which is not a result of a fault in the downstream unit. To address such issues that arise when handling faults in chemical plants, in this work we present a safe-parking framework (we define, in a previous work on handling faults in isolated units, a safe-park point as an operating point where in the event of a fault, a unit can be operated in a way that prevents onset of hazardous situation and allows smooth resumption of nominal operation) for plant-wide fault-tolerant control. We first consider the case where there exists a safe-park point for the faulty unit such that the effect of safe-parking can be completely rejected (via changing the nominal values of the manipulated variables) in the downstream unit. Steady-state as well as dynamic considerations (including the presence of input constraints) is used in determining the necessary conditions for safe-parking the multi-unit system. We next consider the problem where no viable safe-park point for the faulty unit exists such that its effect can be completely rejected in the subsequent unit. A methodology is presented to simultaneously safe-park the consecutive units. Finally, we incorporate performance considerations in the safe-parking framework and illustrate the implementation of the safe-parking framework using a multi-unit chemical reactor system.     

催化裂化反应再生系统的先进控制策略

催化裂化装置具有复杂的过程动态特性,操作约束与经济目标之间存在矛盾,从而为自动控制提出了深入的研究课题.从过程控制的角度讨论了催化裂化反应再生系统的过程特点,并在此基础上提出预测控制与协调决策一体化的先进控制策略.实际工业对象的应用结果表明,这样的控制方案是切实可行的.     

A cognitive approach to develop dynamic models: Application to polymerization systems

An alternative procedure based on cognitive approach is applied to develop dynamic models. The solution copolymerization of methyl methacrylate and vinyl acetate in a continuous stirred tank reactor is analyzed to illustrate the cognitive model development. Factorial planning was used to discriminate the process variables with higher impact on the process performance (effects) and they are used to built‐up a dynamic model based on the functional fuzzy relationship of Takagi–Sugeno type. Gaussian membership functions are considered for the cognitive sets and subtractive clustering method supplied the parameters of the premises of the model. Consequence functions are obtained through an optimization problem solved by a least square based algorithm. The kinetic parameters and reactor operating conditions are obtained from the literature and a mathematical model is considered as plant for identification data generation. Dynamic cognitive models showed satisfactory predictive capabilities and may be an interesting alternative to attack problems of modeling in chemical processes. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

设计余量对运行优化和化学过程控制性能的影响简

Operation optimization is an effective method to explore potential economic benefits for existing plants. The m.aximum potential benefit from operationoptimization is determined by the distances between current operating point and process constraints, which is related to the margins of design variables. Because of various ciisturbances in chemical processes, some distances must be reserved for fluctuations of process variables and the optimum operating point is not on some process constraints. Thus the benefit of steady-state optimization can not be fully achied（ed while that of dynamic optimization can be really achieved. In this study, the steady-state optimizationand dynamic optimization are used, and the potential benefit-is divided into achievable benefit for profit and unachievable benefit for control. The fluid catalytic cracking unit （FCCU） is used for case study. With the analysis on how the margins of design variables influence the economic benefit and control performance, the bottlenecks of process design are found and appropriate control structure can be selected.     

Nonlinear model predictive control: current status and future directions

Linear model predictive control (LMPC) is well established as the industry standard for controlling constrained multivariable processes. A major limitation of LMPC is that plant behavior is described by linear dynamic models. As a result, LMPC is inadequate for highly nonlinear processes and moderately nonlinear processes which have large operating regimes. This shortcoming coupled with increasingly stringent demands on throughput and product quality has spurred the development of nonlinear model predictive control (NMPC). NMPC is conceptually similar to its linear counterpart except that nonlinear dynamic models are used for process prediction and optimization. The purpose of this paper is to provide an overview of current NMPC technology and applications, as well as to propose topics for future research and development. The review demonstrates that NMPC is well suited for controlling multivariable nonlinear processes with constraints, but several theoretical and practical issues must be resolved before widespread industrial acceptance is achieved.     

Optimization of an operating domestic wastewater treatment plant using elitist non-dominated sorting genetic algorithm

Multi-objective optimization of an operating domestic wastewater treatment plant is carried out using binary coded elitist non-dominated sorting genetic algorithm. Activated sludge model with extended aeration is used for optimization. For optimal plant operation, two different optimization problems are formulated and solved. The first optimization problem involves single-objective function to estimate kinetic parameters in activated sludge model using available plant data by minimizing the weighted sum-of-square errors between computed and plant values. The second optimization problem involves single-, two- and three-objective functions for efficient plant monitoring. In second category problem, objective functions are based on plant performance criteria (i.e., maximizing the influent flow rate of wastewater and minimizing the exit effluent concentration) and economic criteria (i.e., minimizing the plant operating cost). The important decision variables are: mean cell-residence time, mixed liquor suspended solid concentration in the reactor and underflow sludge concentration. Unique solution is obtained for the single-objective function optimization problem whereas a set of non-dominated solutions are obtained for the multi-objective optimization problems. A set of optimal operating conditions are proposed based on the present optimization study, which enhances the plant performance without affecting the discharge effluent quality. Finally, sensitivity analyses of the model results to the kinetic parameters and the kinetic parameters to the GA parameters are carried out to know the sensitivity of the obtained results with changes in the input parameter space.     

An emphasis on optimum fuel production for Indian coal preparation plants treating multiple coal sources

Optimization of operating parameters of integrated coal washing plants for achieving maximum clean coal yield at any desired clean coal ash level is a major problem. The problem is largely associated with processing of raw coal obtained from different seams/collieries with frequent variations in proportions and characteristics of individual coals. For large number of source coals or washing different size fractions there are no simple methods of optimization. This paper presents a numerical solution to the constrained non-linear optimization of a multivariable objective function utilizing Excel^® spreadsheet. The method is capable of handling any number of source coals with different size fractions. Here the yield is optimized subject to constraints on both ash and specific gravity. It is shown that the operational constraints of different washeries in the integrated plant utilizing gravity separation methods can also be overcome. The method offers the plant operators an easy and straightforward way for determining the optimum cut points of separation for blended coals to produce a maximum overall product yield at specified level of ash content.     

Optimum design of integrated liquid recovery plants by variable population size genetic algorithm

Increase in the price of energy sources as well as economic problems have caused cryogenic natural gas plants to become more complex and efficient. After selecting the process configuration, the flow rate, pressure, and temperature of the process fluid streams are determining factors which should be tuned in order to find the optimum condition. Products specification and operating costs of the plant are two significant parameters which should be considered in an optimal design. Moreover, process design limitations contribute to the problem being more difficult. This paper shows how the optimal operating point in an integrated NGL recovery plant can be found through solving a complex constrained optimization problem. A Variable Population size Genetic Algorithm (VPGA) was used for optimization. As well, the role of VPGA algorithm parameters in solving the process design problems is investigated in this study. The analysis showed that the VPGA method has better performance compared to the general GA methods. The plant‐wide net profit increases 12493360 $/year only by changing the selected operating conditions to its optimal value.     

平衡分解率模拟分解炉工艺特性

应用高温、悬浮态气固反应试验台测得的碳酸钙平衡分解率，建立了分解炉的数学模型，并针对某水泥厂的物料及工艺参数进行了分解炉工艺特性模拟实验，提出了用平衡因子评价实际分解炉状态的概念，其模拟结果与实际情况有很好的可比性。这种模型可用于各种类型分解炉的工艺特性研究、工业设计和生产控制。     

Model predictive control for the self-optimized operation in wastewater treatment plants: Analysis of dynamic issues

This paper describes a procedure to find the best controlled variables in an economic sense for the activated sludge process in a wastewater treatment plant, despite the large load disturbances. A novel dynamic analysis of the closed loop control of these variables has been performed, considering a nonlinear model predictive controller (NMPC) and a particular distributed NMPC-PI control structure where the PI is devoted to control the process active constraints and the NMPC the self-optimizing variables. The well-known self-optimizing control methodology has been applied, considering the most important measurements of the process. This methodology provides the optimum combination of measurements to keep constant with minimum economic loss. In order to avoid nonfeasible dynamic operation, a preselection of the measurements has been performed, based on the nonlinear model of the process and evaluating the possibility of keeping their values constant in the presence of typical disturbances.