Efficient deterministic multiple objective optimal control of (bio)chemical processes

In practical optimal control problems multiple and conflicting objectives are often present, giving rise to a set of Pareto optimal solutions. Although combining the different objectives into a convex weighted sum and varying the weights is the most common approach to generate the Pareto front (when deterministic optimisation routines are exploited), it suffers from several intrinsic drawbacks. A uniform variation of the weights does not necessarily lead to an even spread on the Pareto front, and points in non-convex parts of the Pareto front cannot be obtained [Das, I., Dennis, J.E., 1997. A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems. Structural Optimization 14, 63-69]. Therefore, this paper investigates alternative approaches based on novel methods as normal boundary intersection [Das, I., Dennis, J.E., 1998. Normal-boundary intersection: a new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM Journal on Optimization 8, 631-657] and normalised normal constraint [Messac, A., Ismail-Yahaya, A., Mattson, C.A., 2003. The normalized normal constraint method for generating the Pareto frontier. Structural and Multidisciplinary Optimization 25, 86-98] to mitigate these drawbacks. The resulting multiple objective optimal control procedures are successfully used in (i) the design of a chemical reactor with conflicting conversion and energy costs, and (ii) the control of a bioreactor with a conflict between yield and productivity.     

Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

A wide range of problems arising from real world applications present multiple and conflicting objectives to be simultaneously optimized. However, this multi-objective nature is too often neglected. Multi-objective optimization proved to be a powerful tool to correctly describe the trade-offs among conflicting objectives in a set of optimal solutions known as the Pareto set. This paper introduces an interactive method to solve multi-objective problems based on geometric considerations. The method returns a wider Pareto set, at a negligible computational cost, when compared to existing methods. The interactivity also allows the decision-maker to explore only relevant parts of the Pareto set. The extreme solutions yield insightful considerations on the generation of the scalarization parameters for the Normal Boundary Intersection and the Enhanced Normalized Normal Constraints methods. The proposed method is applied to: (i) three scalar multi-objective problems and (ii) the multi-objective optimal control of a tubular and a fed-batch reactor.     

Robust temperature control for batch chemical reactors

Since batch chemical reactors exhibit an integrating response, temperature control for these systems can be a real problem for conventional PID controllers. Tuning can be extremely difficult due to the reduced stability margins proved for this type of processes. In this work, a simple robust control strategy for temperature regulation in batch and semi-batch chemical reactors is proposed. The feedback controller is composed by an approximate I/O linearizing feedback equipped with a calorimetric balance estimator. Based on standard results from singular perturbations, it is proven that the proposed feedback controller (i) can track a bounded temperature trajectory as close as desired (i.e., practical stability) by adjusting a single estimation parameter, and (ii) after a short transient, the performance of the exact I/O linearizing feedback can be recovered as the calorimetric balance estimation rate is increased.     

Robust discrete control of nonlinear processes: Application to chemical reactors

Trajectory tracking or rejecting persistent disturbances with digital controllers in nonlinear processes is a class of problems where classical control methods breakdown since it is very difficult to describe the dynamic behavior over the entire trajectory. In this paper, a model-based robust control scheme is proposed as a potential solution approach for these systems. The proposed control algorithm is a robust error feedback controller that allows us to track predetermined operation profiles while attenuating the disturbances and maintaining the stability conditions of the nonlinear processes. Various numerical simulation examples demonstrate the effectiveness of this robust scheme. Two examples deal with effective trajectory tracking in chemical reactors over a wide range of operating conditions. The third example analyses the attenuation of periodic load in a biological reactor. All examples illustrate the ability of the robust control scheme to provide good control in the face of parameter uncertainties and load disturbances.     

Robust feed-back control of distributed chemical reaction systems

There are many distributed processes in the chemical industry as it is the case of tubular reactors in which the parameters or the structure of the reaction terms are only a rough approximation of reality. In order to efficiently control this kind of systems, it is important to take into account this lack of detailed information (robustness). In this work, we make use of the classical theory on the robust nonlinear control for finite dimensional systems and extend it to distributed process systems by taking advantage of the special nature of dissipative systems. In this way, theoretical issues related to the nonlinearity of the diffusion terms and inhomogeneous boundary conditions are handled by means of the Kirchhoff and state transformations, respectively. In addition, and for practical reasons, the problem of controller saturation is considered. The different aspects of the methodology will be illustrated through a number of computational experiments concerning non-isothermal tubular reactors with convection and/or diffusion terms.     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Integrated design and control under uncertainty: Embedded control optimization for plantwide processes

High performance processes should operate close to design boundaries and specification limits, while still guaranteeing robust performance without design constraint violations. Since design chemical process is operating close to tighter boundaries safely; much attention has been devoted to integrating design and control, in which the design decisions, dynamics, and control performance are considered simultaneously in some optimal fashion. However, rigorous methods for solving design and control simultaneously lead to challenging mathematical formulations which easily become computationally intractable. In an earlier paper of our group, a new mathematical methodology to reduce the combinatorial complexity of integrating design and control was introduced (Malcolm et al., 2007). We showed that substantial problem size reduction can be achieved by embedding control for specific process designs. In this paper, we extend the embedded control methodologies to plantwide flowsheet. The case study for the reactor-column flowsheet will demonstrate the current capabilities of the methodology for integrating design and control under uncertainty.     

Optimization of a plate-fin heat exchanger design through an improved multi-objective teaching-learning based optimization (MO-ITLBO) algorithm

Teaching-learning-based optimization (TLBO) is a recently developed heuristic algorithm based on the natural phenomenon of teaching-learning process. In the present work, multi-objective improved teaching-learning-based optimization (MO-ITLBO) algorithm is introduced and applied for the multi-objective optimization of plate-fin heat exchangers. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions maintained in an external archive. Minimizing total annual cost and the total weight of heat exchanger as well as minimization of total pressure drop and maximization of heat exchanger effectiveness for specific heat duty requirement are considered as objective functions. Two application examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm.     

化工过程大范围工况变化的工况迁移控制策略判定

化工过程出现大范围的工况变化时，复杂的迁移控制策略会带来一定的操作不确定性，因此需要对控制策略进行选择判定。考虑到直接估计工况变化过程生产指标变化量带来的判定误差，引入了中间变量，提出了基于中间变量的控制策略选择判定方法，并分析给出了构建中间变量的基本准则。进而通过对某实际乙烯精馏塔工况变化过程的仿真研究，说明了中间变量的引入能够很大程度地降低对生产指标的估计误差，验证了基于中间变量的控制策略选择判定方法的可用性。     

Economic model predictive control of chemical processes with parameter uncertainty

This work proposes an EMPC (Economic Model Predictive Control) algorithm that integrates RTO (Real Time Optimization) and EMPC objectives within a single optimization calculation. Robust stability conditions are enforced on line through a set of constraints within the optimization problem.A particular feature of this algorithm is that it constantly calculates a set point with respect to which stability is ensured by the aforementioned constraints while searching for economic optimality over the horizon. In contrast to other algorithms reported in the literature, the proposed algorithm does not require terminal constraints or penalty terms on deviations from fixed set points that may lead to conservatism.Changes in model parameters over time are also compensated for through parameter updating. The latter is accomplished by including the parameters’ values as additional decision variables within the optimization problem.Several case studies are presented to demonstrate the algorithm’s performance.     

Plantwide control for optimal operation of industrial-scale crude distillation unit processes

In this article, a combination of the wavelet neural network framework and the line-up competition algorithm is used to solve the economic optimization algorithm for an industrial-scale atmospheric distillation column (ADC) process. Compared to the relevant measuring data from Sinopec Wuhan Petroleum Group Company, China, the first optimal operating conditions show that the increments of the duties of furnace and pump-arounds of the ADC can effectively improve oil production. In our approach, the preflash column (PFC) coupled with ADC is denoted as an industrial-scale crude distillation unit (CDU) process. Since the PFC can produce light naphtha and reduce the furnace duty and steam consumption of ADC, it is verified that the CDU process provides the higher economic potential than ADC. Based on the second optimal operating conditions, the plantwide control strategy is employed to operate the system safely as well as regulate the outputs of the plant in the presence of inlet perturbations. Within the plantwide control framework, the inventory control aims to keep the controlled variables close to the desired operating condition and the quality control loops use a combination of inferential predictions and feedforward ratios to effectively suppress the temperature spikes of trays and furnaces. Finally, the simulations show that the product quality is guaranteed due to no offset ASTM D86 distillation temperature responses.     

Energy shaping plus damping injection control for a class of chemical reactors

Traditionally, stabilization of chemical reacting systems has been achieved with linear P or PD compensation schemes. Practical and numerical results have showed that classical linear compensation can yield acceptable performance. On the other hand, recent years have witnessed the emergence of systematic feedback control strategies based on energy and port-interconnected systems. These approaches exploit the physical structure of the chemical reactor to construct compensation schemes with physical appealing. The aim of this work is to show that traditional PD compensation for CSTRs can be interpreted in terms of mechanical system analogies. In the line of energy shaping plus damping injection for robotic systems, it is shown that proportional feedback is a type of potential energy shaping to accommodate a unique equilibrium point. On the other hand, derivative control acts as a damping injector for the energy balance within the chemical reactor. The stability proof uses a novel approach to convert the temperature dynamics into a second-order systems where the mechanical analogies become more evident. In this way, the stability analysis can be performed with singular perturbation methods with a Lyapunov function for the energy balance derived from a “potential plus kinetics” energy construction.     

化工过程约束优化控制的可行性分析及约束处理

在化工领域过程控制中,普遍存在着各种对输出变量、输入变量甚至中间变量的约束。不同约束条件之间的矛盾会造成约束条件无法全部满足,优化控制器无可行解,给实际生产造成负面影响。从凸体几何角度,将化工生产过程中约束优化控制的可行性判定转化为凸多面体是否相交的问题,将不可行时合理的约束处理方案转化为一系列线性规划或非线性规划问题,提出无需人为参与的自动进行约束优化控制可行性分析和约束调整的算法。Shell公司提供的重油分馏塔典型案例实验证明,该算法能够在约束优化控制不可行时自动有效地进行合理的约束调整,超调量小,控制作用变化平缓,且有一定控制裕量。     

Integration of scheduling,design, and control of multiproduct chemical processes under uncertainty

The development of a methodology that addresses the simultaneous design, scheduling, and control of multiproduct processes is focused. The proposed methodology takes into account the influence of disturbances by the identification of their critical frequency, which is used to quantify the worst‐case variability in the controlled variables via frequency response analysis. The uncertainty in the demands of products has also been addressed by creating critical demand scenarios with different probabilities of occurrence, while the nominal stability of the system has been ensured. Two case studies have been developed as applications of the methodology. The first case study focuses on the comparison of classical semisequential approach against the simultaneous methodology developed, while the second case study demonstrates the capability of the methodology in application to a large‐scale nonlinear system. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2456–2470, 2015     

A feedback control framework for safe and economically‐optimal operation of nonlinear processes

Maintaining safe operation of chemical processes and meeting environmental constraints are issues of paramount importance in the area of process systems and control engineering, and are ideally achieved while maximizing economic profit. It has long been argued that process safety is fundamentally a process control problem, yet few research efforts have been directed toward integrating the rather disparate domains of process safety and process control. Economic model predictive control (EMPC) has attracted significant attention recently due to its ability to optimize process operation accounting directly for process economics considerations. However, there is very limited work on the problem of integrating safety considerations in EMPC to ensure simultaneous safe operation and maximization of process profit. Motivated by the above considerations, this work develops three EMPC schemes that adjust in real‐time the size of the safety sets in which the process state should reside to ensure safe process operation and feedback control of the process state while optimizing economics via time‐varying process operation. Recursive feasibility and closed‐loop stability are established for a sufficiently small EMPC sampling period. The proposed schemes, which effectively integrate feedback control, process economics, and safety considerations, are demonstrated with a chemical process example. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2391–2409, 2016     

Addressing the control problem of algae growth in water reservoirs with advanced dynamic optimization approaches

In this work, we develop a lake eutrophication model to determine restoration policies for water quality improvement. This hybrid biogeochemical model has been formulated within a simultaneous dynamic optimization framework as an optimal control problem, whose solution provides limiting nutrient inflow profiles to the lake, as well as in-lake biomanipulation profiles. The water quality model comprises a set of partial differential algebraic equations in time and space, which result from dynamic mass balances on main phytoplankton groups, nutrients, dissolved oxygen and biochemical demand of oxygen. Spatial discretization has been performed in two layers. The simultaneous approach proceeds by discretizing control and state variables by collocation over finite elements and solving the large scale nonlinear program with an interior point method with successive quadratic programming techniques.     

C60有机化学反应研究概述

Ｃ６０有机化学反应介当前化学领域一个研究热点之一，已有许多具有应用前景的Ｃ６０衍生物被相继合成出来，从有机反应的角度，概述了Ｃ６０衍生物合成中的几个主要反应类型。     

An input/output approach to the optimal transition control of a class of distributed chemical reactors

An input/output approach to the optimal concentration transition control problem of a certain type of distributed chemical reactors is proposed based on the concept of residence time distribution, which can be determined in practice by using data from experimental measurements or computer simulations. The main assumptions for the proposed control method to apply are that the thermal and fluid flow fields in the reactor are at pseudo-steady-state during transition and that the component whose concentration is to be controlled participates only in first-order reactions. Using the concept of cumulative residence time distribution, the output variable is expressed as the weighted sum of discretized inputs or input gradients in order to construct an input/output model, on the basis of which a constrained optimal control problem, penalizing a quadratic control energy functional in the presence of input constraints, is formulated and solved as a standard least squares problem with inequality constraints. The effectiveness of the proposed optimal control scheme is demonstrated through a continuous-stirred-tank-reactor (CSTR) network and a tubular reactor with axial dispersion and a first-order reaction. It is demonstrated through computer simulations that the proposed control method is advantageous over linear quadratic regulator (LQR) and proportional-integral (PI) control in terms of control cost minimization and input constraint satisfaction.