复杂非线性系统的子系统分解方法

利用社区发现算法研究了一种复杂非线性化工系统的子系统分解方法,并进行了分布式模型预测控制设计。引入信息图论的节点表示系统的状态、输入和输出变量,构建非线性过程系统的加权有向图,节点通过加权边连接,加权反映了节点间连接的强度,因而能够同时反映系统内部的连通性和连接强度。利用社区结构发现算法将所有变量分成子系统的群组,使得每个组内的关联比不同组间的相互作用强,从而得到复杂化工过程系统的子系统分解。针对连续搅拌反应釜过程,实施子系统分解,并设计分布式模型预测控制算法,结果表明,所提出的子系统分解方法更能考虑子系统之间的连接权重,得到更有利于分布式模型预测控制的子系统划分,提升系统控制的性能。     

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.     

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.     

Decomposition strategy for the global optimization of flexible energy polygeneration systems

The optimal design and operation of flexible energy polygeneration systems using coal and biomass to coproduce power, liquid fuels, and chemicals are investigated. This problem is formulated as a multiperiod optimization problem, which is a potentially large‐scale nonconvex mixed‐integer nonlinear program (MINLP) and cannot be solved to global optimality by state‐of‐the‐art global optimization solvers, such as BARON, within a reasonable time. A duality‐based decomposition method, which can exploit the special structure of this problem, is applied. In this work, the decomposition method is enhanced by the introduction of additional dual information for faster convergence. The enhanced decomposition algorithm (EDA) guarantees to find an ε‐optimal solution in a finite time. The case study results show that the EDA achieves much faster convergence than both BARON and the original decomposition algorithm, and it solved the large‐scale nonconvex MINLPs to ε‐optimality in practical times. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3080–3095, 2012     

Synthesis of industrial systems based on value analysis

In this contribution, we present a novel methodology for flexible design of industrial systems based on their detailed differential value analysis. Evolving from graph theory, this methodology devises a mechanism for systematic structural decomposition of large-scale industrial systems into basic processing elements (paths and trees), combination of elements into subsystems and evaluation of individual elements/subsystems to correlate with the overall system margin. This helps to reduce the size of the large combinatorial problems and comprehensively analyse the multiple objectives and the sets of optimal operating states, capital investments and marginal contributions at elemental/subsystems levels that are critical for flexible designs. The approach generates the whole set of optimal solutions compared to the one point solution of the deterministic approaches (MINLP) while allowing additional complexity of process level models in the site-wide integration due to the systematic structural decomposition of a system into its basic elements/subsystems. A recent industrial application on oil upgrading system design is used to illustrate the methodology.     

一类非线性动态系统的一致性分散可靠性预测

针对一类带有隐含退化过程的非线性动态系统,提出了一种基于粒子滤波的一致性分散可靠性预测方法。该方法将原系统重叠分解为若干个相互关联的子系统,每个子系统利用其局部测量信息以及子系统间通信得到的信息,估计出原系统的状态和参数,进而预测原系统的可靠性。同时,该方法通过一致性策略使得所有子系统的估计和预测结果保持一致。五容水箱模型的仿真实验结果表明,该方法能够很好地预测系统的可靠性,同时该方法能够使得所有子系统的估计和预测结果保持一致。     

Evaluation and improvement of dynamic optimality in electrochemical reactors

A systematic approach for the dynamic optimization problem statement to improve the dynamic optimality in electrochemical reactors is presented in this paper. The formulation takes an account of the diffusion phenomenon in the electrode/electrolyte interface. To demonstrate the present methodology, the optimal time-varying electrode potential for a coupled chemical-electrochemical reaction scheme, that maximizes the production of the desired product in a batch electrochemical reactor with/without recirculation are determined. The dynamic optimization problem statement, based upon this approach, is a nonlinear differential algebraic system, and its solution provides information about the optimal policy. Optimal control policy at different conditions is evaluated using the best-known Pontryagin's maximum principle. The two-point boundary value problem resulting from the application of the maximum principle is then solved using the control vector iteration technique. These optimal time-varying profiles of electrode potential are then compared to the best uniform operation through the relative improvements of the performance index. The application of the proposed approach to two electrochemical systems, described by ordinary differential equations, shows that the existing electrochemical process control strategy could be improved considerably when the proposed method is incorporated.     

基于子系统关联变量轮换的大系统在线协调优化

化工过程复杂大系统的在线优化过程中,存在流程前后的关联导致优化时间过长或得不到优化解的问题,需要按子系统优化并协调的优化方法来解决,而协调优化方法存在关联变量寻优方向不一致的问题。提出了一种基于子系统间关联变量轮换思想的分解协调优化方法,对大系统分解得到的子系统以轮换的方式进行优化,子系统中包含的多个优化问题分别在固定关联变量优化独立变量和固定独立变量优化关联变量的条件下求解,此轮换过程迭代进行,直至满足优化终止条件。将提出的方法应用在催化裂化装置仿真实例中与整体优化方法的结果作比较,证明了方法的有效性。最后,将基于关联变量轮换的协调优化方法应用在化工过程的在线优化中,结果表明本方法在在线优化应用中是可行的。     

基于随机优化的热耦合复杂精馏系统的综合(Ⅰ)模型化方法

基于随机型最优化策略,针对包含简单塔、带有侧线蒸出及侧线汽提塔的复杂塔、全热耦合（或Petlyuk）塔的热耦合复杂精馏塔系统的综合问题,提出一种模型化方法.针对热耦合复杂精馏流程系统所需塔段数目以及冷凝器和再沸器数目的不确定性,提出了一种分解求解策略,将原问题分解成一系列具有不同塔段数的子问题分别求解;针对流程结构的优化提出一种流程结构的编码表达法,该方法将问题的分离序列结构和热耦合方式分别用两组编码表示,对分离序列的编码采用了数据结构理论中的二叉树排序方法,使流程结构的描述变得更加简便;最后以预分馏塔组分回收率及回流比为连续变量,建立了热耦合复杂精馏系统优化的[JP+1]混合整数非线性规划（MINLP）模型,该模型用改进的模拟退火算法求解,可同时得到优化的流程结构和操作参数.     

A systematic approach for synthesizing a low-temperature distillation system

In this paper, by combining a stochastic optimization method with a refrigeration shaft work targeting method, an approach for the synthesis of a heat integrated complex distillation system in a low-temperature process is presented. The synthesis problem is formulated as a mixed-integer nonlinear programming (MINLP) problem, which is solved by simulated annealing algorithm under a random procedure to explore the optimal operating parameters and the distillation sequence structure. The shaft work targeting method is used to evaluate the minimum energy cost of the corresponding separation system during the optimization without any need for a detailed design for the heat exchanger network (HEN) and the refrigeration system (RS). The method presented in the paper can dramatical y reduce the scale and complexity of the problem. A case study of ethylene cold-end separation is used to il ustrate the application of the approach. Compared with the original industrial scheme, the result is encouraging.     

Optimization and nonlinear control of a batch crystallization process

Crystallization process has been widely used for separation in many chemical industries due to its capability to provide high purity product. To obtain the desired quality of crystal product, an optimal cooling control strategy is studied in the present work. Within the proposed control strategy, a dynamic optimization is first preformed with the objective to obtain the optimal cooling temperature policy of a batch crystallizer, maximizing the total volume of seeded crystals. Two different optimization problems are formulated and solved by using a sequential optimization approach. Owing to the complex and nonlinear behavior of the batch crystallizer, the nonlinear control strategy which is based on a generic model control (GMC) algorithm is implemented to track the resulting optimal temperature profile. The optimization integrated with nonlinear control strategy is demonstrated on a seeded batch crystallizer for the production of potassium sulfate.     

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.     

On constrained infinite-time nonlinear optimal control

In this work, we consider the infinite-time optimal control of input affine nonlinear systems subject to point-wise in time inequality constraints on both the process inputs and outputs. Fundamental to solving this constrained infinite-time nonlinear optimal control (CITNOC) problem is the ability to calculate the value function of it's unconstrained counterpart, the infinite-time nonlinear optimal control (ITNOC) problem. Unfortunately, the traditional ITNOC solution procedure of specifying an objective function and then solving for the optimal control policy and corresponding value function is computationally intractable in all but the simplest of examples. However, in many cases one can easily identify a stabilizing feedback for near operating point regulation. Building from this local policy, the proposed method is to construct a meaningful optimal control objective function as well as its corresponding value function. These functions are then used to analyze the closed-loop stability of the proposed policy. Upon return to the constrained case the constructed objective and value functions are again used to develop a self-consistent constrained finite-time scheme that will, for the first time, provide an exact solution to the CITNOC problem. The mechanics of the proposed method are then illustrated by an example from chemical reactor control.     

一类面向多级过程系统的实时进化方法

针对传统的实时优化执行前需要达到稳态、系统整体优化时间长、难以实时调整控制参数等问题提出一类面向多级过程系统的实时进化方法。把多级过程系统分成多个相互关联的子系统，当发生扰动时将系统等待稳态的过程分为若干个“拟稳态”。在每个拟稳态区间内，应用粒子群算法依次优化每一个子系统，其他各子系统设为静态，对子系统间的共享变量和内部变量进行协调，最终得到系统的最优解，把优化操作解送入控制器，连续改变系统设定值。给出了算法的详细步骤以两级串联反应器为对象进行了实例研究，验证了方法的有效性。     

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time-scale multiplicity

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.     

A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: Applications to particulate processes and discrete dynamic systems

The solution of optimal control problems (OCPs) becomes a challenging task when the analyzed system includes non-convex, non-differentiable, or equation-free models in the set of constraints. To solve OCPs under such conditions, a new procedure, LARES-PR, is proposed. The procedure is based on integrating the LARES algorithm with a generalized representation of the control function. LARES is a global stochastic optimization algorithm based on the artificial chemical process paradigm. The generalized representation of the control function consists of variable-length segments, which permits the use of a combination of different types of finite elements (linear, quadratic, etc.) and/or specialized functions. The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem. The element size is also determined as part of the solution of the optimization problem, using a novel two-step encoding strategy. These building blocks result in an algorithm that is flexible and robust in solving optimal control problems. Furthermore, implementation is very simple.The algorithm's performance is studied with a challenging set of benchmark problems. Then LARES-PR is utilized to solve optimal control problems of systems described by population balance equations, including crystallization, nano-particle formation by nucleation/coalescence mechanism, and competitive reactions in a disperse system modeled by the Monte Carlo method. The algorithm is also applied to solving the DICE model of global warming, a complex discrete-time model.     

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。     

Integrated design and control of semicontinuous distillation systems utilizing mixed integer dynamic optimization

Semicontinuous distillation systems are notoriously difficult to design and optimize because the structural parameters, operational parameters, and control system must all be determined simultaneously. In the past 15 years of research into semicontinuous systems, studies of the optimal design of these systems have all been limited in scope to small subsets of the parameters, which yields suboptimal and often unsatisfactory results. In this work, for the first time, the problem of integrated design and control of semicontinuous distillation processes is studied by using a mixed integer dynamic optimization (MIDO) problem formulation to optimize both the structural and control tuning parameters of the system. The public model library (PML) of gPROMS is used to simulate the process and the built-in optimization package of gPROMS is used to solve the MIDO via the deterministic outer approximation method. The optimization results are then compared to the heuristic particle swarm optimization (PSO) method.     

强制循环蒸发系统线性自抗扰解耦控制的鲁棒设计

针对强制循环蒸发系统液位与出料密度两个回路的非线性耦合问题,提出了一种基于粒子群算法的线性定常自抗扰解耦控制设计。首先通过引入虚拟控制量,将对象解耦配置为两个单输入单输出子系统,并对每个回路设计降维线性扩张状态观测器。随后,对观测器动态线性化得到的近似积分器环节进行比例控制。最后,在可能的大工况内通过粒子群算法优化控制增益耦合矩阵和比例增益。该算法使用观测器估计并补偿动态耦合部分,降低了控制器对数学模型的依赖程度;使用粒子群算法优化定常控制增益矩阵,避免了实时测量出料温度,降低了对传感测量的要求,提高了可靠性并降低了实施难度。数学仿真结果表明该算法能有效地消除液位回路和出料密度回路的耦合作用,在大工况内具有很强的鲁棒性。     

Improving scenario decomposition algorithms for robust nonlinear model predictive control

This paper deals with the efficient computation of solutions of robust nonlinear model predictive control problems that are formulated using multi-stage stochastic programming via the generation of a scenario tree. Such a formulation makes it possible to consider explicitly the concept of recourse, which is inherent to any receding horizon approach, but it results in large-scale optimization problems. One possibility to solve these problems in an efficient manner is to decompose the large-scale optimization problem into several subproblems that are iteratively modified and repeatedly solved until a solution to the original problem is achieved. In this paper we review the most common methods used for such decomposition and apply them to solve robust nonlinear model predictive control problems in a distributed fashion. We also propose a novel method to reduce the number of iterations of the coordination algorithm needed for the decomposition methods to converge. The performance of the different approaches is evaluated in extensive simulation studies of two nonlinear case studies.