Fast and reliable computational strategy for developing a rigorous model-driven soft sensor of dynamic molecular weight distribution

Key polymer properties are substantially directly related to the polymer molecular weight distribution (MWD). On-line monitoring and prediction of dynamic MWD profiles are highly important for on-line quality control of polymerization processes. In this study, a fast and reliable computational strategy for an equation-oriented model-based soft sensor for the high-density polyethylene grade transition process is developed. The simultaneous collocation approach is adopted to discretize the dynamic model. A novel moving finite element method is proposed to improve the on-line performance of the derived large-scale nonlinear equation systems. The sensitivity information of the nonlinear equation systems contributes to a convergence enhancement strategy for the sensor. The prediction accuracy and computational efficiency are demonstrated using industrial data. A potential application to extend the polymerization process with changeable flowsheet is also tested through simulation.     

Modeling and control of an LDPE autoclave reactor

A two-compartment four-cell model is developed for the adiabetic slim type autoclave reactor for free radical polymerization of low density polyethylene (LDPE). It is possible to determine not only the reactor performance represented by the monomer conversion and the reaction temperature but also the properties of the polymer product characterized by the average molecular weight and the polydispersity. It turns out that the reactor performance predicted is in good agreement with the plant data and the properties of the polymer product are estimated within reasonable ranges of actual values. The steady state multiplicity is found to exist and is examined by constructing the bifurcation diagram. The effects of various operation parameters on the reactor performance and the polymer properties are investigated systematically to show that the temperature distribution plays the central role for the properties of the polymer products. Therefore, it is essential to establish a good control strategy for the temperature in each compartment. The adaptive pole-placement control algorithm is applied to the temperature control of the adiabatic slim type autoclave reactor. The recursive least square method is used for the model identification. To accomplish a satisfactory control, the estimator and controller are initialized during the period of start-up. It is shown that the reactor system can be adaptively controlled by the pole-placement control algorithm, especially when the reactor temperature distribution is changed.     

Realization of online optimizing control in an industrial semi-batch polymerization

In this work, the realization of an online optimizing control scheme for an industrial semi-batch polymerization reactor is discussed in detail. The goal of the work is the automatic minimization of the duration of the batch without violating the tight constraints for the product specification which translate into stringent temperature control requirements for a highly exothermic reaction. Crucial factors for a successful industrial implementation of the control scheme are the development and the validation of a process model that is suitable for process optimization purposes and the estimation of unmeasured process states and the online compensation of model uncertainties. Two implementations are proposed, a direct online optimizing control scheme and a simplified scheme that combines a model-predictive temperature controller and a monomer feed controller that steers the cooling power to a predefined value in a cascaded fashion. We show by simulation results with a validated process model that both schemes achieve the goals of tight temperature control and reduction of the batch time. The performance of the NMPC controller is superior, on the other hand the cascaded scheme could be directly implemented into the DCS of the plant and is in daily operation while the online optimizing scheme requires an additional computer and is currently in the test phase.     

Control of industrial gas phase propylene polymerization in fluidized bed reactors

The control of a gas phase propylene polymerization model in a fluidized bed reactor was studied, where the rigorous two phase dynamic model takes into account the polymerization reactions occurring in the bubble and emulsion phases. Due to the nonlinearity of the process, the employment of an advanced control scheme for efficient regulation of the process variables is justified. In this case, the Adaptive Predictive Model-Based Control (APMBC) strategy (an integration of the Recursive Least Squares algorithm, RLS and the Generalized Predictive Control algorithm, GPC) was employed to control the polypropylene production rate and emulsion phase temperature by manipulating the catalyst feed rate and reactor cooling water flow, respectively. Closed loop simulations revealed the superiority of the APMBC in setpoint tracking as compared to the conventional PI controllers tuned using the Internal Model Control (IMC) method and the standard Ziegler–Nichols (Z–N) method. Moreover, the APMBC was able to efficiently arrest the effects of superficial gas velocity, hydrogen concentration and monomer concentration on the process variables, thus exhibiting excellent regulatory control properties.     

Product property and production rate control of styrene polymerization

A multivariable multi-rate nonlinear model predictive control (NMPC) strategy is applied to styrene polymerization. The NMPC algorithm incorporates a multi-rate Extended Kalman Filter (EKF) to handle state variable and parameter estimation. A fundamental model is developed for the styrene polymerization CSTR, and control of polymer properties such as number average molecular weight (NAMW) and polydispersity is considered. These properties characterize the final polymer distribution and are strong indicators of the polymer qualities of interest. Production rate control is also demonstrated. Temperature measurements are available frequently while laboratory measurements of concentration and molecular weight distribution are available infrequently with substantial time delays between sampling and analysis. Observability analysis of the augmented system provides guidelines for the design of the augmented disturbance model for use in estimation using the multi-rate EKF. The observability analysis links measurement sets and corresponding observable disturbance models, and shows that measurements of moments of the polymer distribution are essential for good estimation and control. The CSTR is operated at an open-loop unstable steady state. Control simulations are performed under conditions of plant-model structural mismatch and in the presence of parameter uncertainty and disturbances, and the proposed multi-rate NMPC algorithm is shown to provide superior performance compared to linear multi-rate and nonlinear single-rate MPC algorithms. The major contributions of this work are the development of the multi-rate estimator and the measurement design study based on the observability analysis.     

Latent variable MPC for trajectory tracking in batch processes

A novel multivariate empirical model predictive control strategy (LV-MPC) for trajectory tracking and disturbance rejection for batch processes is presented. The strategy is based on dynamic principal component analysis (PCA) models of the batch process. The solution to the control problem is computed in the low dimensional latent variable space of the PCA model. The trajectories of all variables over the future horizon are then computed from the latent variable solution of the controller. The excellent control performance and the modest closed-loop data requirements for identification are illustrated for the temperature tracking in simulations of an emulsion polymerization process, an exothermic chemical reaction system and for MIMO temperature and pressure tracking in a nylon polymerization autoclave.     

Model predictive control for continuous lactide ring‐opening polymerization processes

Polylactic acid (PLA) is an attractive environment‐friendly thermoplastic that is bio‐sourced and biodegradable. PLA is industrially produced by the ring‐opening polymerization of lactide. This reaction is sensitive to drifts in the operating conditions and impurities in the raw materials that may affect the reaction rate as well as the polymer properties, which can be very costly in continuous processes. It is therefore crucial to employ a control strategy that allows recovering the nominal conditions and maintaining the desired properties and conversion level in case of drift. Three control strategies are discussed in this paper: proportional‐integral (PI) controller, dynamic optimization, and model predictive control (MPC). The proposed approaches are validated by simulation of a continuous PLA process constituted of three cascade reactors including one loop reactor in the middle. Besides the coupling of inputs and outputs, the process model is highly nonlinear, and the control is done only on the boundaries. The results show that the open‐loop optimization strategy provides better performance compared to the PI controller if the disturbance is assumed to be measured. The MPC also shows superior performances provided that the disturbance is first estimated. A polynomial model is developed to predict the nonmeasured disturbance based on the measured outputs.     

丙烯间歇液相本体聚合模拟

从聚合反应动力学出发,对丙烯间歇液相本体聚合工业装置建立数学模型,采用PR状态方程进行汽液平衡计算。链增长速率常数k_p、链转移速率常数K_t由质均分子量为20万及30万2个品牌的生产条件及产品性质去拟合得到。应用拟合出的参数,对质均分子量为40万的产品的生产工艺条件进行模拟,模拟结果与实际相比为:聚合物的产量误差0.66%,质均分子量误差2.07%,模拟结果与实际较为吻合。并对反应过程中变量随时间变化情况进行分析,得出聚合物质量、氢气浓度、液相体积等随时间的变化规律,对实际生产工艺的开发与改进具有指导意义。     

Control of a LDPE reactive extrusion process

A constrained model predictive control strategy is implemented to control the weight-average molecular weight and the high molecular weight end of the molecular weight distribution of a low-density polyethylene (LDPE) in a reactive extrusion process. To achieve simultaneous regulation of these properties, the amplitude and width of square wave-shaped pulses of a peroxide solution injected to the extruder are independently manipulated. The two polymer properties are inferred on-line from consistency and power-law index measurements obtained with an in-line wedge rheometer. Simulations and experimental results show that independent control of the polymer properties is feasible by this method, but only in a narrow range of operating conditions.     

Gray-box modeling and control of polymer molecular weight distribution using orthogonal polynomial neural networks

A method of modeling and control on polymer molecular weight distribution (MWD) is presented in this paper. An orthogonal polynomial feedforward neural network (OPFNN) and a recurrent neural network (RNN) are combined to model the shape of MWD. In this combined neural networks, the weights of OPFNN are equivalent to moments of MWD through a linear transformation, when the polynomial used as the basis function of OPFNN satisfies some requirements. So the weights are given practical feature, and terms the neural network model a gray-box model. Then the requirements of polynomial are deduced. After modeling, an optimal control scheme is discussed on tracking the desired MWD during the polymerization process. The modeling error is added into the performance function to improve the control effect. The modeling and control method is tested on styrene polymerization reacted in CSTR, and simulation results proved the effectiveness of the method.     

低密度聚乙烯(LDPE)聚合工艺模拟与分析

本文利用Aspen Tech Inc.的Polymer Plus建立了低密度聚乙烯聚合反应过程模型,利用其灵敏度分析方法对影响产品产量和分子量的引发剂浓度、反应温度等因素进行了分析,得出了引发剂量的增加可以提高产量同时分子量下降;随着温度的升高数均分子量降低,聚合物产量PE上升;聚合物的分子量,聚合物产量随着聚合压力的升高而不断增大.     

基于Kriging函数的聚合反应过程分子量分布的回归建模与优化

以分子量分布作为聚合物产品的质量指标越来越受到关注,针对分子量分布机理建模较复杂的问题,提出了利用克里金插值方法获得了基于数据的分子量分布模型。首先,建立了分子量分布的离散化模型,可以较为准确地估计特定链长处的分子量,从而实现对分子量分布曲线的离散化表征。进一步,提出了一种多维插值建模方法实现了对分子量分布的整体建模,可以对于任意链长处的分子量进行估计。最后将基于数据的分子量分布模型替代机理模型,实现了对分子量分布的静态优化,获得了较好的效果。     

Borstar双峰聚合反应产品性质分析及模型建立

通过对Borstar双峰聚合反应过程产品性质实验分析,Borstar双峰聚乙烯技术超临界环管反应器生产聚合物熔融指数相对于分子量呈指数规律变化,气相反应器生产的聚合物熔融指数随分子量增加而呈一定规律的减少,聚合物分子量继续增加聚合物熔融指数减少趋势缓慢;在实验分析的基础上,基于聚合反应机理应用MATLAB软件建立工业装置聚合过程聚乙烯熔融指数及密度等产品性质计算模型和确定模型参数,通过模型拟合值和实际值的比较,模型能够准确预测熔融指数和密度的变化趋势,有关聚乙烯在环管中的熔融指数、在流化床内的熔融指数和密度的质量模型相对平均误差分别为2.4%,0.5%和0.3%。通过产品质量预测模型的推导和分析,环管部分熔融指数主要受温度、[H2]/[C2H4]影响;而气相部分熔融指数既受环管聚合物来料性质影响,又受气相反应器温度和[H2]/[C2H4]和[C4H8]/[C2H4]的影响     

在线场景更新的多阶段非线性模型预测聚合反应控制

针对聚合过程中时不变不确定性参数不能直接估计的情况,导致的多阶段非线性模型预测控制中场景树生成的合理性问题,提出一种基于贝叶斯概率加权的在线场景更新算法.该方法利用前一时间步中每个场景的模型预测信息和过程状态测量信息计算对应场景的概率权重,然后通过合适的自适应步长在线更新场景树中不确定性的离散实现场景.所提方法在保证过程约束满足的同时,逐渐缩小不确定性集合逼近不确定性的真实值,从而降低保守性,提升控制器性能.通过多个批次的半间歇聚合反应过程实例仿真结果表明,所提出的方法可以有效降低批次反应时间,提高生产效率.     

分子量分布的广义状态反馈跟踪控制

针对化工过程中分子量分布的跟踪控制问题, 提出了一种简单的广义状态反馈控制方法, 实现给定分子量分布的跟踪. 该方法充分利用复合动态支持向量机模型, 实现分子量分布函数在时间域和空间域上的分离, 从而将分布函数的跟踪问题转化为动态权值向量的时间域跟踪问题, 并设计了状态反馈与积分器相结合的控制结构, 采用线性矩阵不等式技术对闭环系统稳定性和跟踪性能进行分析. 仿真结果表明该方法的可行性.     

蚁群算法在乳液聚合单体配比优化中的应用

以乳液聚合单体配料成本最低为目标函数,建立乳液聚合单体优化配料数学模型。运用蚁群算法和MATLAB语言,以丙烯酸酯共聚乳液中单体配比为例,对该数学模型作仿真优化计算,结果表明:在保证玻璃化的温度满足控制要求的条件下.其吨乳液成本比原手工配比方法节约52.78元,实现了乳液聚合单体配料的优化,表明蚁群算法应用于乳液聚合生产单体配料是可行的。     

多模型预测控制在苯乙烯聚合反应中的应用

针对苯乙烯聚合反应过程的非线性特性,将预测控制方法与多模型建模和控制原理结合起来,提出了一种基于性能指标的切换多模型非线性预测控制方法,针对聚合反应过程进行的仿真实验结果表明,该方法对类似非线性对象具有适用性,控制性能相比较普通预测控制算法也有了很明显的改进和提高.     

Polymer property prediction and optimization using neural networks

Prediction and optimization of polymer properties is a complex and highly nonlinear problem with no easy method to predict polymer properties directly and accurately. The problem is especially complicated with high molecular weight polymers such as engineering plastics which have the greatest use in industry. The effect of modifying a monomer (polymer repeat unit) on polymerization and the resulting polymer properties is not easy to investigate experimentally given the large number of possible changes. This severely curtails the design of new polymers with specific end-use properties. In this paper, we show how properties of modified monomers can be predicted using neural networks. We utilize a database of polymer properties and employ a variety of networks ranging from backpropagation networks to unsupervised self-associating maps. We select particular networks that accurately predict specific polymer properties. These networks are classified into groups that range from those that provide quick training to those that provide excellent generalization. We also show how the available polymer database can be used to accurately predict and optimize polymer properties.     

Parametric optimization and control for a smart Proton Exchange Membrane Water Electrolysis (PEMWE) system

Hydrogen production from Proton Exchange Membrane Water Electrolysis (PEMWE) system is attracting attention due to its ability to circumvent the effect of the intermittent nature of variable renewal energy. However, the relatively high operating temperatures of the PEMWE system exacerbates the degradation of polymer membranes in PEMWE system. This paper describes the development of an optimal thermal management strategy for a PEMWE system that can attenuate the long-term effects of high operating temperatures or rapid temperature changes on the polymer membranes. The thermal management strategy is tested on a laboratory scale smart PEMWE system. First, a high fidelity mathematical model of the smart PEMWE is developed and validated based on which the application of the PARameteric Optimization and Control (PAROC) framework results in the design of an explicit model predictive controller which is deployed into the laboratory PEMWE system. It is shown that the smart PEMWE prototype system empowered with the embedded control policy achieves effective temperature control across the electrolyzer maintaining the integrity of the membrane electrode assembly.     

Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.