A simultaneous approach for singular optimal control based on partial moving grid

Singular optimal control plays an important role in process engineering, including optimal operation of batch and semi-batch reactions. However, for many practical applications, accurate solution of singular optimal control profiles is still an open issue. In particular, numerical optimization must deal with an ill-conditioned problem that often leads to very slow convergence or failure. Starting from the nested approach in our previous work in 2016, this study develops a more efficient strategy for singular control through a heuristic approach for the outer problem. The approach includes three stages. Starting from a coarse distribution of finite elements, sufficiently many finite elements are inserted where control profiles are steep and fixed gridpoints are inserted on the basis of error estimation of state profiles. Then, moving gridpoints are inserted where the modified switching function is violated. Initial junctions are obtained by moving the latest inserted gridpoints. Moreover, further mesh refinements are considered based on switching point detection and a moving grid point update strategy, until modified switching conditions are satisfied over the whole-time span. A key feature of this approach is that only a subset of finite elements needs to move during optimization. Complexity of the optimization formulation is considerably decreased compared to our previous work. This approach is demonstrated on eight classical singular control problems with known solutions, as well as six complex singular control problems drawn from the chemical engineering literature.     

Bang‐Bang solution of nonlinear time‐optimal control problems using a semi‐exhaustivesearch

At times, the objective is to seek a bang‐bang control policy for nonlinear time‐optimal control problems. The usefulness of iterative dynamic programming (IDP) has been shown in the literature for solving such problems. However, the convergence to the optimal solution has been obtained from about 50% of the guessed values near the optimum. In this paper, we present a semiexhaustive search method for seeking such solutions and a comparison is made with the IDP. The results show that the convergence can be obtained from a significantly higher number of guessed values chosen over a much wider region around the optimum.     

带有中间储罐的间歇精馏工艺动态控制模拟优化

甲酸甲酯-甲醇-水是化工生产过程中最常见的三元混合物之一。目前,间歇精馏工艺分离该三元混合物的研究较少,在动态控制方面也少有报道。本文研究了分离甲酸甲酯-甲醇-水的带有中间储罐的间歇精馏工艺动态控制模拟优化。利用Aspen Plus和Aspen Plus Dynamics软件,在稳态模拟的基础上,分别考察了液位控制结构和组分控制结构两种控制方案。结果表明,液位控制结构控制性能较差,达到稳定后甲醇和水的纯度较低。组分控制结构虽能提高产品纯度,但出现了较为严重的振荡现象。根据对组分控制结构的动态响应分析,本文提出了一种改进的组分控制结构,该控制结构能实现带有中间储罐的间歇精馏工艺的稳健控制,使各产品纯度得到提高。     

Optimal operation and tracking control of vapor-recompressed batch distillation

Vapor recompressed batch distillation (VRBD) is an energy-integrated configuration which works on the principle of a heat pump. Operation of such a column is challenging due to unsteady, nonlinear dynamics and strong interplay between separation and energy efficiency. In this paper, a two-step approach is proposed for optimal operation and control of such a column. Initially, an openloop optimal operation policy is generated for maximization of an overall performance index using offline optimization. To this end, three performance indices are proposed to capture interplay between separation and energy efficiency. Subsequently, a model-based output feedback controller is designed to track this optimal performance trajectory. The effectiveness of the proposed approach is demonstrated using a benzene-toluene separation case study wherein it is shown that the proposed approach helps to achieve optimal operation in the presence of operational disturbances.     

基于结构逼近式神经网络的间歇反应器优化控制

利用结构逼近式混合神经网络（SAHNN）建立了一类典型放热液相二级平行间歇反应的数学模型。基于主产物浓度和反应温度的递归神经网络（RNN）模型,使用混合PSO-SQP算法求解该间歇反应主产物产率最大化问题,进而得到反应温度优化曲线。鉴于反应温度实时可测,提出扩展的EISE指标,该指标把实时计算的模型误差引入控制策略,为基于模型的控制增加了反馈通道,增强了控制方法的鲁棒性和抗干扰性能。利用 原理对所提出的一步超前预测控制做了稳定性分析,证明了算法的正确性。研究的结果充分证明了基于SAHNN混合神经网络模型的优化控制策略的有效性。     

Smooth penalty function method for rigorous optimization of distillation processes

Integer decisions on stage numbers and feed locations, and global optimality are still challenging for rigorous optimization of distillation processes. In the present article, we propose a smooth penalty function method to address both these problems. The proposed method is based on the relaxation of the integer decision problem into continuous nonlinear programming (NLP) problem by adopting the bypass efficiency model developed by Dowling and Biegler. A smooth penalty term (SPT) is proposed and added to the total annual cost (TAC) function to form a new objective function, namely, the smooth penalty function. Using the new objective function, the problem is initially solved with negative weight coefficients for the SPTs regarding each column section to get an optimum near the global optimum of the SPT. Then, starting from this solution, the problem is solved again iteratively by increasing the values of the weight coefficients until all the stage numbers become integers. The performance of the method is validated by an illustrating problem and in three case studies, including a reactive distillation optimization problem.     

Solving power-constrained gas transportation problems using an MIP-based alternating direction method

We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to difficult nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the nonlinearities and a tailored alternating direction method. Most other publications in the field of gas transport optimization only consider pressure and flow as main physical quantities. In this work, we additionally incorporate heat power supplies and demands as well as a mixing model for different gas qualities. We demonstrate the capabilities of our method on Germany's largest transport networks and hereby present numerical results on the largest instances that were ever reported in the literature for this problem class.     

A novel analytical second-order sensitivity calculation approach using the finite element method for chemical engineering problems

This paper presents an effective orthogonal collocation approach to approximate dynamic optimization problems into nonlinear programming problems, where the resulting problems can then be usually solved by first-order sensitivity based algorithms. However, the results obtained fail to satisfy the timeliness and accuracy requirements of some dynamic optimization problems. A novel collocation approach with second-order sensitivity information is therefore first proposed to improve the efficiency of the method. The resulting nonlinear programming problem is obtained through the orthogonal collocation on finite element combined with a single shooting approach. Three benchmark optimal control problems are considered to demonstrate the performance of the presented approach. Comparisons among the proposed approach, the BFGS method, and other literature solutions are also carried out in detail. Numerical results validate the effectiveness of the proposed method and the time saving benefit.     

无累积罐循环全回流间歇精馏三温控制操作

提出了通过塔顶、塔中上以及塔中3个温度控制进行操作状态转换的无累积罐循环全回流间歇精馏控制方法,并以理想物系--乙醇-正丙醇混合物为分离物系进行了实验研究。通过实验确定了温度控制条件为当塔顶温度稳定后且塔顶和塔中上温差为0.3 ℃时变全回流为全采出操作,当塔中温度升高1.0 ℃时停止全采出转为全回流操作。同时还考察了在不同乙醇投料浓度条件下这种操作的运行情况,发现不同投料浓度对塔顶产品平均纯度的影响并不显著,基本能保持在0.99。最后在相同的投料浓度和操作条件下,对比了这种新型控制方式和双温度控制方式,结果表明三温度控制方式比双温度控制方式操作时间减少了23.3 min,分离效率提高了23.95%,产品浓度提高了1.06%,产品收率提高了1.08%。     

基于均匀分布NSGAII算法的污水处理多目标优化控制

针对污水处理过程控制中能耗过大、出水水质超标严重等问题，提出了一种基于均匀分布的NSGAII(non-dominated sorting genetic algorithm II based on uniform distribution, UDNSGAII)多目标优化智能控制系统。首先，该方法以污水处理能耗和出水水质作为优化目标，建立多目标优化模型。其次，为了获得溶解氧和硝态氮的优化设定值，提高Pareto解的性能，该算法将种群映射到目标函数对应的超平面, 并在该平面上进行聚类以增加解的多样性。此外，加入分布性判断模块和分布性加强模块提高解的分布性。最后，采用比例积分微分(proportional integral derivative, PID)控制器对溶解氧和硝态氮的优化设定值进行底层跟踪控制。为了验证该算法的有效性，采用国际基准的污水处理仿真平台(benchmark simulation model No.1, BSM1)来进行实验。结果显示，所提出的UDNSGAII多目标优化控制方法能够在满足出水水质达标的同时，有效地降低污水处理过程能耗。     

Mixed integer optimal control of an intermittently aerated sequencing batch reactor for wastewater treatment

Optimal aeration control strategies for sequencing batch reactors in WWT with bypass nitrification are hereby studied. The operation is defined alternating aerobic and anoxic phases with high frequency. The controlled variable, the aeration, can only adopt fixed values, on and off, leading to a discrete trajectory of bang–bang type. The problem is to compute the number of switches and individual length of each aerobic and anoxic stage. This leads to a mixed integer nonlinear optimal control problem (MINTOC). The solution is challenging, since both integer and continuous variables ought to be considered in the optimization. In contrast to previous work, where optimization is performed based on the separation and independent solution of the integer and continuous problem, we apply an algorithm originally proposed by Sager (2005). The optimization program minimizes operation time and energy consumption. Effluent concentrations are considered as nonlinear constraints in accordance to environmental regulations.     

Design and control of acetonitrile/N-propanol separation system via extractive distillation using N-methyl pyrrolidone as entrainer

The extractive distillation process for separating a binary azeotrope of acetonitrile and n-propanol is investigated using N-methyl pyrrolidone as entrainer. On the basis of multiparameter optimization, a design with optimized operation conditions for the process is presented. Two dynamic control structures are proposed. Feed disturbances are used to evaluate the dynamic performance. The response results reveal that the control structure CS1 with temperature–composition cascade control loop can handle all the disturbances and maintain product purities, except one large transient deviation, while the improved control structure CS2 with average temperature control loop can overcome this obstacle and handle disturbances effectively.     

On solving optimal control problems with free initial condition using iterative dynamic programming

For solving optimal control problems where the initial conditions of some of the state variables are not specified, a procedure based on iterative dynamic programming (IDP) is presented. In this procedure, the free initial conditions are taken to be additional control variables for the first time stage only; then the search for the optimal initial conditions and also the optimal control policy is carried out simultaneously using IDP. The procedure is straightforward, and as illustrated with two nonlinear optimal control problems, for each case the optimum performance index is readily obtained.     

A thermal‐flywheel approach to distributed temperature control in microchannel reactors

Microchannel reactors are a promising route for monetizing distributed natural gas resources. However, intensification and miniaturization represent a significant challenge for reactor control. Focusing on autothermal methane‐steam reforming reactors, a novel microchannel reactor temperature control strategy based on confining a layer of phase‐change material (PCM) between the reactor plates is introduced. Melting‐solidification cycles, which occur with latent heat exchange at constant temperature, allow the PCM layer to act as an energy storage buffer—a “thermal flywheel”—constituting a distributed controller that mitigates temperature excursions caused by fluctuations in feedstock quality. A novel stochastic optimization algorithm for selecting the PCM layer thickness (i.e., distributed controller “tuning”) is introduced. Furthermore, a hierarchical control structure, whereby the PCM layer is complemented by a supervisory controller that addresses persistent disturbances, is proposed. The proposed concepts are illustrated in a comprehensive case study using a detailed two‐dimensional reactor model. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2051–2061, 2013     

CO2 methanation: Optimal start‐up control of a fixed‐bed reactor for power‐to‐gas applications

Utilizing volatile renewable energy sources (e.g., solar, wind) for chemical production systems requires a deeper understanding of their dynamic operation modes. Taking the example of a methanation reactor in the context of power‐to‐gas applications, a dynamic optimization approach is used to identify control trajectories for a time optimal reactor start‐up avoiding distinct hot spot formation. For the optimization, we develop a dynamic, two‐dimensional model of a fixed‐bed tube reactor for carbon dioxide methanation which is based on the reaction scheme of the underlying exothermic Sabatier reaction mechanism. While controlling dynamic hot spot formation inside the catalyst bed, we prove the applicability of our methodology and investigate the feasibility of dynamic carbon dioxide methanation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 23–31, 2017     

基于多目标分层的预测控制定态优化技术

多目标分层优化要求是从复杂工业过程的现场实际应用背景出发而提出的.详细阐述了复杂工业过程的多目标分层优化要求的含义,在预测控制两级分层结构的基础上提出了基于二次规划的定态优化有效求解方法.通过Shell控制问题等仿真结果,说明所提出的定态优化技术具有良好的控制性能,能够适应生产过程的需要.     

氨法碳捕集过程中氨逃逸控制

本研究致力于解决再生氨法碳捕集过程中氨的逃逸问题。根据实验室前期研究结果,分别选取抑制效果较好的丙三醇和Co（Ⅱ）进行实验研究。详细分析了其抑制氨逃逸机制,并通过IR、XRD等对物种进行分析。同时探究其对再生氨法碳捕集过程CO₂脱除效率和解吸效果的影响。实验结果表明,丙三醇和Co（Ⅱ）对氨逃逸均有较好的抑制效果,平均抑氨效率在40%以上。二者的引入对吸收过程均无显著影响,且Co（Ⅱ）能使CO₂解吸比例提高。