Nonlinear Predictive Control of Fed‐Batch Cultures of Escherichia coli

A strategy for controlling a fed‐batch Escherichia coli culture is described to maintain the culture at the boundary between oxidative and oxido‐fermentative regimes. A nonlinear predictive controller is designed to regulate the acetate concentration, constraining the feed rate to follow an optimal reference profile which maximizes the biomass growth. For the sake of simplicity and efficiency, the original problem is converted into an unconstrained nonlinear programming problem, solved by control vector parameterization techniques. The robustness of the structure is further improved by explicitly including the difference between system and model prediction. A robustness study based on a Monte Carlo approach is used to evaluate the performance of the proposed controller. This control law is finally compared to the generic model control strategy.     

一种可变时间节点的控制向量参数化方法

控制向量参数化方法是求解最优控制的一种常用方法,其时间网格通常是固定的。在每个时间段上,控制向量表示为由一组参数确定的时间的函数。时间网格的划分会影响到数值求解最优控制问题时最优化算法的准确性和效率。为了同时优化控制参数和时间网格的节点,提出了一种可变时间节点控制向量参数化方法,通过带有时间参数的S型函数来近似分段常数参数化方法中的切换过程。推导出了最优控制性能指标对时间参数的导数,并提出了处理时间节点约束的算法。利用所提出方法求解带有两个控制的最优控制实例,对于两个控制获得了不同的时间网格划分,从而能够更好地近似最优控制轨迹。     

Control Vector Parameterization‐Based Adaptive Invasive Weed Optimization for Dynamic Processes

A novel optimal approach named invasive weed optimization‐control vector parameterization (IWO‐CVP) for chemical dynamic optimization problems is proposed where CVP is used to transform the problem into a nonlinear programming (NLP) problem and an IWO algorithm is then applied to tackle the NLP problem. To improve efficiency, a new adaptive dispersion IWO‐based approach (ADIWO‐CVP) is further suggested to maintain the exploration ability of the algorithm throughout the entire searching procedure. Several classic chemical dynamic optimization problems are tested and detailed comparisons are carried out among ADIWO‐CVP, IWO‐CVP, and other methods. The research results demonstrate that ADIWO‐CVP not only is efficient, but also outperforms IWO‐CVP in terms of both accuracy and convergence speed.     

A mathematical programming approach for cyclic production and cleaning scheduling of multistage continuous plants

The objective of this paper is to address the cyclic scheduling of cleaning and production operations in multiproduct multistage plants with performance decay. A mixed-integer nonlinear programming (MINLP) model based on continuous time representation is proposed that can simultaneously optimize the production and cleaning scheduling. The resulting mathematical model has a linear objective function to be maximized over a convex solution space thus allowing globally optimal solutions to be obtained with an outer approximation algorithm. Case studies demonstrate the applicability of the model and its potential benefits in comparison with a hierarchical procedure for the production and cleaning scheduling problem.     

二次求解具有控制切换结构的动态优化问题

基于多级表述策略,提出了二次求解具有控制切换结构动态优化问题的数值方法。基于常用的优化方法获得初始控制结构。动态优化问题根据控制结构进行分级,每一级对应一个特定的控制弧段,进而将原问题表述为一个多级动态优化问题。基于控制向量参数化(CVP),多级动态优化问题转化为一个非线性规划(NLP)问题进行求解。控制参数和级长作为优化变量。基于Pontryagin极大值原理,构造多级伴随系统,进而获得NLP求解器所需的梯度信息。仿真实例验证了方法的有效性。     

基于PSO-控制变量参数化混合策略的间歇化工过程优化控制

控制变量参数化方法作为一种化工过程动态优化的梯度搜索算法，其求解效率过于依赖初始给定轨迹。目前初始轨迹一般都是设定在边界值或中间值，缺乏科学依据，从而大大影响了算法的收敛速度。针对这一问题，提出了一种粒子群优化(PSO)与控制变量参数化方法混合的策略，首先利用粒子群优化对间歇化工过程最优控制量进行求解，结果作为控制变量参数化方法初始给定轨迹，进行二次优化。双层优化的混合策略提高了控制变量参数化方法的收敛速度和粒子群优化算法的求解精度。将混合策略应用于两个间歇化工过程优化控制实例，仿真结果表明了该算法对求解化工过程动态优化问题具有可行性和有效性。     

一种求解化工动态优化问题的迭代自适应粒子群方法

智能优化方法因其简单、易实现且具有良好的全局搜索能力,在动态优化中的应用越来越广泛,但传统的智能方法收敛速度相对较慢。提出了一种迭代自适应粒子群优化方法（IAPSO）来求解一般的化工动态优化问题。首先通过控制变量参数化将原动态优化问题转化为非线性规划问题,再利用所提出的迭代自适应粒子群优化方法进行求解。相比传统的粒子群优化方法,该种迭代自适应粒子群优化方法具有收敛速度更快的优点,主要原因是：该算法根据粒子种群分布特性自适应调整参数;该算法通过缩减搜索空间并迭代使用粒子群算法搜索最优解。将提出的迭代自适应粒子群方法应用到多个经典动态优化问题中,测试结果表明,该方法简单、有效,精度高,且收敛速度比传统粒子群算法有显著提升。     

Control of pH neutralization process using simulation based dynamic programming

The pH neutralization process has long been taken as a representative benchmark problem of nonlinear chemical process control due to its nonlinearity and time-varying nature. For general nonlinear processes, it is difficult to control with a linear model-based control method so nonlinear controls must be considered. Among the numerous approaches suggested, the most rigorous approach is the dynamic optimization. However, as the size of the problem grows, the dynamic programming approach suffers from the curse of dimensionality. In order to avoid this problem, the Neuro-Dynamic Programming (NDP) approach was proposed by Bertsekas and Tsitsiklis [1996]. The NDP approach is to utilize all the data collected to generate an approximation of optimal cost-to-go function which was used to find the optimal input movement in real time control. The approximation could be any type of function such as polynomials, neural networks, etc. In this study, an algorithm using NDP approach was applied to a pH neutralization process to investigate the feasibility of the NDP algorithm and to deepen the understanding of the basic characteristics of this algorithm. As the approximator, the neural network which requires training and the k-nearest neighbor method which requires querying instead of training are investigated. The approximator has to use data from the optimal control strategy. If the optimal control strategy is not readily available, a suboptimal control strategy can be used instead. However, the laborious Bellman iterations are necessary in this case. For pH neutralization process it is rather easy to devise an optimal control strategy. Thus, we used an optimal control strategy and did not perform the Bellman iteration. Also, the effects of constraints on control moves are studied. From the simulations, the NDP method outperforms the conventional PID control.     

三元复合驱采出水处理研究进展

随着三元复合驱采油技术在油田的广泛应用,三元复合驱采出水产量不断增加。三元复合驱采出水水质复杂,具有矿化度高、黏度大、含油乳化程度高、小油滴含量高、油水分离困难等特点,对油田生产和环境的影响日益严重。因此,开展三元复合驱采出水高效处理方法的研究成为一项重要的任务。本文分析了影响三元复合驱采出水油水分离特性的各种因素,介绍了目前国内应用于三元采出水处理的先进技术,如膜分离法、气浮选分离法、高级氧化法、微生物法等,阐述了这些处理技术的优势及存在的问题,重点介绍了气浮选分离法和微生物法在三元采出水处理中的应用情况,并对大庆油田三元复合驱采出水现场处理工艺进行了介绍,最后对今后的研究工作提出了一些展望。     

A quadratic approximation‐based algorithm for the solution of multiparametric mixed‐integer nonlinear programming problems

An algorithm for the solution of convex multiparametric mixed‐integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed‐integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp‐QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed‐integer outer approximation (mp‐MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers AIChE J, 59: 483–495, 2013     

A formulation methodology for multicomponent distillation sequences based on stochastic optimization

Based on stochastic optimization strategy, a formulation methodology is proposed for synthesizing distillation column sequences, allowing more than one middle component as the distributing components between a pair of key components in the non-sharp split. In order to represent and manipulate the distillation configuration structures, a new coding procedure is proposed in the form of one-dimensional array. Theoretically, an array can represent any kind of split (non-sharp and sharp).With the application of a binary sort tree approach, a robust flow sheet encoding and decoding procedure is developed so that the problem formulation and solution becomes tractable. In this paper, the synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem and an improved simulated annealing approach is adopted to solve the optimization problem. Besides, a shortcut method is applied to the evaluation of all required design parameters as well as the total function.     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

一种基于伪Wigner-Ville分析的动态优化问题网格重构策略

为了解决控制向量参数化方法逼近精度和计算时间之间的矛盾，提出了一种基于伪Wigner-Ville时频分析的控制向量参数化方法。该方法首先给定较少的网格进行第一次优化迭代，快速获得控制变量的大致轨迹。然后通过伪Wigner-Ville分析得出不同时间网格节点瞬时频率变化对性能指标的影响，籍此对原有网格节点进行重构，包括对时间节点的消除、细化。并且结合变时间节点控制向量参数化方法的思想，将瞬时频率为极大值时对应的时间节点作为待优化参数，与控制变量一同进行求解优化，从而找到准确的最优时间切换点。三个经典的化工反应实例用于验证所提方法，计算结果表明：与传统的控制向量参数化方法和文献结果相比，所提方法可以更有效地重构时间网格，找到准确的时间切换点，不仅计算成本低，而且计算精度更出色。     

Inferential Control of Reactive Destillation Columns – An Algorithmic Approach

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed‐integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed‐integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.     

Optimizing inventory policies in process networks under uncertainty

We address the inventory planning problem in process networks under uncertainty through stochastic programming models. Inventory planning requires the formulation of multiperiod models to represent the time-varying conditions of industrial process, but multistage stochastic programming formulations are often too large to solve. We propose a policy-based approximation of the multistage stochastic model that avoids anticipativity by enforcing the same decision rule for all scenarios. The proposed formulation includes the logic that models inventory policies, and it is used to find the parameters that offer the best expected performance. We propose policies for inventory planning in process networks with arrangements of inventories in parallel and in series. We compare the inventory planning strategies obtained from the policy-based formulation and the analogous two-stage approximation of the multistage stochastic program. Sequential implementation of the planning strategies in receding horizon simulations shows the advantages of the policy-based model, despite the increase in computational complexity.     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

基于粒子群优化算法的球磨机制粉系统PID-ANN解耦控制器

球团厂钢球磨煤制粉系统是多变量强耦合、时滞、非线性以及生产工况变化大的复杂对象,其自动控制问题一直是控制界关注的热点。基于粒子群算法具有对整个参数空间进行高效并行搜索的特点以及PID神经网络的自调节和自适应特性,设计了具有PID结构的多变量自适应神经网络控制器。PID神经网络解耦控制方法被用来消除回路之间的耦合,神经网络连接权值由粒子群算法进行学习优化。仿真研究表明所建模型和所提控制方法具有较好的控制品质、良好的自适应解耦能力和自学习功能。该控制策略可在大范围内克服系统的非线性和强耦合问题,具有很高的工程实用价值。     

A self-tuning control method for Wiener nonlinear systems and its application to process control problems

Many chemical processes can be modeled as Wiener models, which consist of a linear dynamic subsystem follow-ed by a static nonlinear block. In this paper, an effective discrete-time adaptive control method is proposed for Wiener nonlinear systems with uncertainties. The parameterization model is derived based on the inverse of the nonlinear function block. The adaptive control method is motivated by self-tuning control and is derived from a modified Clarke criterion function, which considers both tracking properties and control efforts. The un-certain parameters are updated by a recursive least squares algorithm and the control law exhibits an explicit form. The closed-loop system stability properties are discussed. To demonstrate the effectiveness of the obtained results, two groups of simulation examples including an application to composition control in a continuously stirred tank reactor (CSTR) system are studied.     

一种求解最优控制问题的变时间节点控制向量参数化方法

控制向量参数化方法是求解最优控制问题的一种常用数值方法。它通过离散化控制时域,将控制向量近似地表示成一组参数化的函数。离散化后的时间网格通常是固定的,其划分会影响到最优控制问题数值求解的精度和效率。为了同时优化控制参数和时间网格节点,提出了一种时间节点可变的控制向量参数化方法。推导出了最优控制性能指标对时间参数的导数与对时间分段长度导数之间的关系,得到了性能指标的梯度表达式。用两个经典最优控制实例对所提出的方法进行了测试,结果表明所提出方法能够更好地逼近最优控制轨迹。