Decentralized Control System Design under Uncertainty Using Mixed‐Integer Optimization

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. In this contribution, the optimal control structure and the optimal controller parameters are determined simultaneously using mixed‐integer dynamic optimization (MIDO) under uncertainty, to account for nonlinear process dynamics and various disturbance scenarios. Application of the sigma point method is proposed in order to approximate the expectation and the variance of a chosen performance index with a minimum number of points to solve the MIDO problem under uncertainty. The proposed methodology is demonstrated with a benchmark problem of an inferential control for a reactive distillation column. The results are compared with established heuristic design methods and with previous deterministic approaches.     

Process design and control optimization: A simultaneous approach by multi‐parametric programming

We present a framework for the application of design and control optimization via multi‐parametric programming through four case studies. We develop design dependent multi‐parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115–138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Simultaneous mixed-integer dynamic optimization for integrated design and control

We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way.     

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.     

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.     

换热器网络设备面积与清洗时序同步优化

表面结垢会严重影响换热器的传热效率,定期清洗是解决该问题的主要方式.针对以往换热器网络清洗时序优化方法中用于决策的整型变量较多而难以求解的问题,提出以换热器清洗的最大允许污垢热阻为优化变量,取代表示换热器是否清洗的二进制变量,将混合整数非线性规划问题转化成非线性规划问题,能够有效地减小问题规模,降低求解难度.优化过程中兼顾换热器网络的设计型与操作型问题,采用遗传/模拟退火算法同步优化换热器的面积与清洗时序.将该方法用于一个实例,所得年度总费用与文献基本一致,验证了该方法的有效性.     

A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014     

Solving mixed integer nonlinear programming problems with line-up competition algorithm

Line-up competition algorithm (LCA), a global optimization algorithm proposed recently, is applied to the solution of mixed integer nonlinear programming (MINLP) problems. Through using alternative schemes to handle integer variables, the algorithm reported previously for solving NLP problems can be extended expediently to the solution of MINLP problems. The performance of the LCA is tested with several non-convex MINLP problems published in the literature, including the optimal design of multi-product batch chemical processes and the location-allocation problem. Testing shows that the LCA algorithm is efficient and robust in the solution of MINLP problems.     

基于信赖域算法的精馏塔优化

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型,为了消除整数变量,引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法,在该方法中采用结构优化中常用的信赖域优化算法进行求解,并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化,以不同初始值开始,均可得到令人满意的优化结果,表明所提优化方法具有良好的稳健性,对于较复杂的部分热耦合精馏过程仍然可以有效优化求解;信赖域算法在精馏塔优化中也表现出良好的收敛性。     

Hybrid simulation-optimization based approach for the optimal design of single-product biotechnological processes

In this work, we present a systematic method for the optimal development of bioprocesses that relies on the combined use of simulation packages and optimization tools. One of the main advantages of our method is that it allows for the simultaneous optimization of all the individual components of a bioprocess, including the main upstream and downstream units. The design task is mathematically formulated as a mixed-integer dynamic optimization (MIDO) problem, which is solved by a decomposition method that iterates between primal and master sub-problems. The primal dynamic optimization problem optimizes the operating conditions, bioreactor kinetics and equipment sizes, whereas the master levels entails the solution of a tailored mixed-integer linear programming (MILP) model that decides on the values of the integer variables (i.e., number of equipments in parallel and topological decisions). The dynamic optimization primal sub-problems are solved via a sequential approach that integrates the process simulator SuperPro Designer^® with an external NLP solver implemented in Matlab^®. The capabilities of the proposed methodology are illustrated through its application to a typical fermentation process and to the production of the amino acid L-lysine.     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

Integrated control and process design during optimal polymer grade transition operations

In this work we address the simultaneous process control and design problem of polymerization reactors during dynamic grade transition operation. The problem is cast as a Mixed-Integer Dynamic Optimization (MIDO) formulation and, by using the full discretization approach for solving dynamic optimization problems [Kameswaran, S., & Biegler, L. T. (2006). Simultaneous dynamic optimization strategies: Recent advances and challenges. Computers & Chemical Engineering, 30 (10–12), 1560–1575], is transformed into a Mixed-Integer Nonlinear Program (MINLP). The resulting MINLP is solved using a full space nonconvex optimization formulation [Flores-Tlacuahuac, A., & Biegler, L. T. (2007). Simultaneous Mixed-Integer Dynamic Optimization for integrated design and control. Computers & Chemical Engineering, 31, 588–600]. The control and design formulation has been applied to two polymerization reactors featuring highly nonlinear behavior. In both cases, the proposed MIDO formulation was capable of finding optimal solutions. This amounts to finding optimal steady states, reactor designs, as well as open-loop and closed-loop dynamic optimal trajectories, control structures and controller parameters by specifying either the polymer molecular weight distribution or monomer conversion. Because CPU solution time tends to increase with system complexity, some strategies for lowering CPU time are discussed.     

Sensor network design for maximizing process efficiency: An algorithm and its application

Sensor network design (SND) is a constrained optimization problem requiring systematic and effective solution algorithms for determining where best to locate sensors. A SND algorithm is developed for maximizing plant efficiency for an estimator‐based control system while simultaneously satisfying accuracy requirements for the desired process measurements. The SND problem formulation leads to a mixed integer nonlinear programming (MINLP) optimization that is difficult to solve for large‐scale system applications. Therefore, a sequential approach is developed to solve the MINLP problem, where the integer problem for sensor selection is solved using the genetic algorithm while the nonlinear programming problem including convergence of the “tear stream” in the estimator‐based control system is solved using the direct substitution method. The SND algorithm is then successfully applied to a large scale, highly integrated chemical process. © 2014 American Institute of Chemical Engineers AIChE J, 61: 464–476, 2015     

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。     

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。     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

Simultaneous mixed-integer dynamic optimization for environmentally benign electroplating

Hoist scheduling, especially cyclic hoist scheduling (CHS), is used to maximize the manufacturing productivity of electroplating processes. Water-reuse network design (WRND) for the electroplating rinsing system targets the optimal water allocation, such that fresh water consumption and wastewater generation are minimized. Currently, there is still a lack of studies on integrating CHS and WRND technologies for electroplating manufacturing. In this paper, a multi-objective mixed-integer dynamic optimization (MIDO) model has been developed to integrate CHS and WRND technologies for simultaneous consideration of productivity and water use efficiency for environmentally benign electroplating. The orthogonal collocation method on finite elements is employed to convert the MIDO problem into a mixed-integer nonlinear programming (MINLP) problem. The efficacy of the methodology is demonstrated by solving a real electroplating example. It demonstrates that the computational methods of production scheduling, process design, and dynamic optimization can be effectively integrated to create economic and environmental win-win situations for the electroplating industry.     

Integration of scheduling and control with online closed-loop implementation: Fast computational strategy and large-scale global optimization algorithm

In this paper, we propose a novel integration method to solve the scheduling problem and the control problem simultaneously. The integrated problem is formulated as a mixed-integer dynamic optimization (MIDO) problem which contains discrete variables in the scheduling problem and constraints of differential equations from the control problem. Because online implementation is crucial to deal with uncertainties and disturbances in operation and control of the production system, we develop a fast computational strategy to solve the integration problem efficiently and allow its online applications. In the proposed integration framework, we first generate a set of controller candidates offline for each possible transition, and then reformulate the integration problem as a simultaneous scheduling and controller selection problem. This is a mixed-integer nonlinear fractional programming problem with a non-convex nonlinear objective function and linear constraints. To solve the resulting large-scale problem within sufficiently short computational time for online implementation, we propose a global optimization method based on the model properties and the Dinkelbach's algorithm. The advantage of the proposed method is demonstrated through four case studies on an MMA polymer manufacturing process. The results show that the proposed integration framework achieves a lower cost rate than the conventional sequential method, because the proposed framework provides a better tradeoff between the conflicting factors in scheduling and control problems. Compared with the simultaneous approach based on the full discretization and reformulation of the MIDO problem, the proposed integration framework is computationally much more efficient, especially for large-scale cases. The proposed method addresses the challenges in the online implementation of the integrated scheduling and control decisions by globally optimizing the integrated problem in an efficient way. The results also show that the online solution is crucial to deal with the various uncertainties and disturbances in the production system.     

MILP-based initialization strategies for the optimal design of water-using networks

The optimal design of water-using systems involves necessarily the exploitation of all possible water reuse and recycling alternatives. The general problem can be formulated as a non-convex nonlinear program (NLP), but due to the presence of bilinear terms, it may be difficult for local optimization solvers to attain global optimal solutions. To overcome this difficulty, this paper presents two mixed integer linear programming (MILP)-based procedures to generate a few structurally different starting points for the NLP. In both, the problem is decomposed into calculation stages by assuming that the water streams progress in series through the water-using units, with the binary variables selecting which unit belongs to a certain stage. Their main difference concerns the way fixed flowrate units are handled, either separately or in conjunction with a fixed load operation, since the former comprise a linear subsystem. The two algorithms are compared to a closely related LP-based method taken from the literature and to the one employed by the global optimization solver BARON. The results from a large set of example problems confirm their effectiveness in avoiding local solutions despite the small number of starting points. In contrast to the previous method they are easily scalable and, for some of the larger problems, could find better solutions than BARON with significantly fewer computational resources. The results have also shown that the option of tackling one unit at a time is the most favorable.     

化工过程综合问题MINLP算法中整型变量的连续化

化工过程系统综合问题需要同时考虑设备结构参数和工艺操作参数,一般用整型变量表示设备的取舍,用连续变量表示操作参数,这就构成一个流程的超结构,在数学形式表现为一个混合整型非线性规划（MINLP）问题。混合整型非线性规划问题的求解成为化工过程综合优化的关键。今根据超结构中整型变量的特征,提出整型变量连续化处理的思路,将MINLP问题简化为NLP问题,然后采用罚函数法求解。最后将该算法运用于加氢脱烷基化（HDA）过程综合的实例研究,结果表明该算法克服了传统方法在处理整型变量时出现的麻烦,为有效快速地进行化工过程综合优化问题提供了一种新的途径。