Optimal control of batch processes using particle swam optimisation with stacked neural network models

An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural network models are developed form historical process operation data. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalize wide model prediction confidence bounds. The optimisation problem is solved using PSO, which can cope with multiple local minima and could generally find the global minimum. Application to a simulated fed-batch process demonstrates that the proposed technique is very effective.     

ANNSA: a hybrid artificial neural network/simulated annealing algorithm for optimal control problems

This paper introduces a numerical technique for solving nonlinear optimal control problems. The universal function approximation capability of a three-layer feedforward neural network has been combined with a simulated annealing algorithm to develop a simple yet efficient hybrid optimisation algorithm to determine optimal control profiles. The applicability of the technique is illustrated by solving various optimal control problems including multivariable nonlinear problems and free final time problems. Results obtained for the different case studies considered agree well with those reported in the literature.     

Iterative learning control for the systematic design of supersaturation controlled batch cooling crystallisation processes

The paper presents an approach to improve the product quality from batch-to-batch by exploiting the repetitive nature of batch processes to update the operating trajectories using process knowledge obtained from previous runs. The data based methodology is focused on using the linear time varying (LTV) perturbation model in an iterative learning control (ILC) framework to provide a convergent batch-to-batch improvement of the process performance indicator. The major contribution of this work is the development of a novel hierarchical ILC (HILC) scheme for systematic design of the supersaturation controller (SSC) of seeded batch cooling crystallizers. The HILC is used to determine the required supersaturation setpoint for the SSC and the corresponding temperature trajectory required to produce crystals with desired end-point property. The performance and robustness of these approaches are evaluated through simulation case studies. These results demonstrate the potential of the ILC approaches for controlling batch processes without rigorous process models.     

Robustness of reinforced gradient-type iterative learning control for batch processes with Gaussian noise☆

In this paper, a reinforced gradient-type iterative learning control profile is proposed by making use of system matrices and a proper learning step to improve the tracking performance of batch processes disturbed by exter-nal Gaussian white noise. The robustness is analyzed and the range of the step is specified by means of statistical technique and matrix theory. Compared with the conventional one, the proposed algorithm is more efficient to resist external noise. Numerical simulations of an injection molding process il ustrate that the proposed scheme is feasible and effective.     

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.     

Evaluation of optimisation techniques and control variable formulations for a batch cooling crystallization process

The mathematical optimisation of a batch cooling crystallization process is considered in this work. The objective is to minimize the standard deviation of the final crystal size distribution (CSD), which is an important feature in many industrial processes. The results with the problem written as a nonlinear programming and solved with the successive quadratic programming (SQP) coupled with the discretization of the control variable are compared with those obtained when SQP coupled with the parameterisation of the control variable is applied. Also it is proposed the implementation of the genetic algorithm (GA) coupled with parameterisation of the control variable. Extensive evaluations show that the SQP method is sensitive both to the parameterisation formulation and to the initial estimate. The solution with GA provided the control variable profile that leads to the minimum standard deviation of the final CSD. Nevertheless, it is a very time-consuming technique, which hampers its utilization in real time applications. However, its feature of global searching suggests its suitability in solving offline problems, in order to provide initial setup profiles. Bearing this in mind, it is proposed an algorithm which allows for the implementation of GA solution in a real time fashion, taking advantage of its robustness to find out the optimal solution.     

基于MKPLS和SQP方法的间歇过程迭代优化控制

采用多向核偏最小二乘（MKPLS）方法建立间歇过程的模型并进行操作条件的优化。由于存在模型失配和未知扰动，基于MKPLS模型的最优控制轨迹在实际对象上往往难以实现最优的产品质量指标。本文利用间歇过程批次间的重复特性与序贯二次规划（SQP）优化算法中迭代计算的相似特点，提出了一种基于MKPLS模型的批次间优化调整策略，使得经过逐步优化调整得到的控制轨迹作用于实际对象时，可以得到更优的质量指标。该方法的有效性在苯乙烯聚合反应器和乙醇流加发酵过程的仿真对象上得到了验证。     

On-line optimal control of a seeded batch cooling crystallizer

In this paper, an on-line optimal control methodology is developed for the optimal quality control of a seeded batch cooling crystallizer process. An extended Kalman filter is successfully implemented to predict seven unmeasured state variables based on three measurements in the batch process. A PI controller is used in a feedback control system to implement the optimal path. It is found that the PI controller can ensure tracking of the optimal path. The simulation results show that on-line optimal control strategy leads to a substantial improvement of the end product quality expressed in terms of the mean size and the width of the distribution. The effects of the plant/model mismatch and disturbances are also tested and discussed.     

Spatial batch optimal design based on self-learning Gaussian process models for LPCVD processes

Low pressure chemical vapor deposition (LPCVD) is one of themost important processes during semiconductor manufacturing. However, the spatial distribution of internal temperature and extremely few samples makes it hard to build a good-quality model of this batch process. Besides, due to the properties of this process, the reliability of the model must be taken into consideration when optimizing the MVs. In this work, an optimal design strategy based on the self-learning Gaussian processmodel (GPM)is proposed to control this kind of spatial batch process. The GPMis utilized as the internalmodel to predict the thicknesses of thin films on all spatial-distributed wafers using the limited data. Unlike the conventional model based design, the uncertainties of predictions provided by GPM are taken into consideration to guide the optimal design of manipulated variables so that the designing can be more prudent. Besides, the GPM is also actively enhanced using as little data as possible based on the predictive uncertainties. The effectiveness of the proposed strategy is successfully demonstrated in an LPCVD process.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

Trajectory tracking of a batch polymerization reactor based on input–output-linearization of a neural process model

Input–output-linearization via state feedback offers the potential to serve as a practical and systematic design methodology for nonlinear control systems. Nevertheless, its widespread use is delayed due to the fact that developing an accurate plant model based on physical principles is often too costly and time consuming. Data-based modeling of dynamic systems using neural networks offers a cost-effective alternative. This work describes the methodology of input–output-linearization using neural process models and gives an extended simulative case study of its application to trajectory tracking of a batch polymerization reactor.     

Iterative learning reliable control of batch processes with sensor faults

An iterative learning reliable control (ILRC) scheme is developed in this paper for batch processes with unknown disturbances and sensor faults. The batch process is transformed into and treated as a two-dimensional Fornasini-Marchesini (2D-FM) model. Under the proposed control law, the closed-loop system with unknown disturbances and sensor faults not only converges along both the time and the cycle directions, but also satisfies certain H_∞ performance. For performance comparison, a traditional reliable control (TRC) law based on dynamic output feedback is also developed by considering the batch process in each cycle as a continuous process. Conditions for the existence of ILRC scheme are given as biaffine and linear matrix inequalities. Algorithms are given to solve these matrix inequalities and to optimize performance indices. Applications to injection packing pressure control show that the proposed scheme can achieve the design objectives well, with performance improvement along both time and cycle directions, and also has good robustness to uncertain initialization and measurement disturbances.     

基于输入轨迹参数化的间歇过程迭代学习控制

针对间歇过程的迭代学习控制问题,提出了一种基于输入轨迹参数化的迭代学习控制策略。根据最优输入轨迹的主要形态特征,将其参数化为较少量的决策变量,降低传统迭代学习控制复杂性的同时维持良好的优化控制效果。基于输入轨迹参数化的迭代学习控制策略能保持算法的简洁性和易实现性,在不确定扰动影响下逐步改善产品质量。对一个间歇反应器的仿真研究验证了本文方法的有效性。     

The control of MSF desalination plants based on inverse model control by neural network

In this paper, a nonlinear inverse model control strategy based on neural network is proposed for MSF desalination plant. Artificial neural networks (ANNs) can handle complex and nonlinear process relationships, and are robust to noisy data. The designed neural networks consist of three layers identified from input–output data and trained with a descent gradient algorithm. The set point tracking performance of the proposed method was studied when the disturbance is present in the MSF system. Three controllers are designed for controlling the top brine temperature, the level of last stage and salinity. These results show that a neural network inverse model control strategy (NNINVMC) is robust and highly promising to be implemented in such nonlinear systems. Also the comparison between the top brine temperature of the proposed model and NN predicted data from the literature supports the accuracy of the model.     

Recursive data-based prediction and control of product quality for a PMMA batch process

In many batch processes, frequent process/feedstock disturbances and unavailability of direct on-line quality measurements make it very difficult to achieve tight control of product quality. Motivated by this, we present a simple data-based method in which measurements of other process variables are related to end product quality using a historical data base. The developed correlation model is used to make on-line predictions of end quality, which can serve as a basis for adjusting the batch condition/time so that desired product quality may be achieved. This strategy is applied to a methyl methacrylate (MMA) polymerization process. Important end quality variables, the weight average molecular weight and the polydispersity, are predicted recursively based on the measurements of reactor cooling rate. Subsequently, a shrinking-horizon model predictive control approach is used to manipulate the reaction temperature. The results in this study show promise for the proposed inferential control method.     

Evaluation of neural network models and quality forecasting based on process time-series data

Complex industrial process modelling is critically important within the context of industrial intelligence. In recent years, soft sensor techniques based on neural networks have become increasingly popular for modelling nonlinear industrial processes. This paper proposes an integrated framework of neural network modelling and evaluation for nonlinear dynamic processes. This framework achieves an integrated solution for modelling, prediction, evaluation, and network structure parameter selection. It can be applied to noisy sensors and dense data in the time domain. The framework's proposed evaluation mechanism employs two novel evaluation metrics, the variational auto-encoder (VAE)-based Kullback–Leibler (KL) divergence metric and the maximum likelihood estimation-based J metric, which both evaluate the model by mining the statistical properties of the residuals. The framework models the dynamic process with a model order based-gated recurrent units (MOb-GRU) neural network and a modified transformer model. Numerical experiments demonstrate that the evaluation mechanism functions properly in scenarios with multiple signal-to-noise ratios and multiple noise statistical properties and that the framework produces accurate modelling results.     

污水处理过程的模糊神经网络控制

模糊神经网络(FNN)技术的迅速发展及其理论的不断完善为其在各个领域的应用奠定了基础。分析了FNN用于污水处理系统过程控制的可行性和必要性。简述了模糊系统和神经网络在污水处理中应用的现状。指出针对不同污水处理工艺建立不同综合(集成)智能控制系统是污水生物处理过程控制的主要研究方向,同时应加强对污水处理的活性污泥数学模型、通用性预测与故障分析系统、“软测量”技术及在线生物传感器等相关理论与技术的研究。     

Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor

In this paper we describe the design of hybrid fuzzy predictive control based on a genetic algorithm (GA). We also present a simulation test of the proposed algorithm and a comparison with two hybrid predictive control methods: Explicit Enumeration and Branch and Bound (BB). The experiments involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve. The GA-hybrid predictive control strategy proved to be a suitable method for the control of hybrid systems, giving similar performance to that of typical hybrid predictive control strategies and a significant saving with respect to the computation time.     

一种基于聚类方法的多阶段间歇过程监控方法

针对阶段不等长的多阶段间歇过程,提出了一种基于k-均值聚类方法的阶段分段策略,可以将不等长的阶段准确分类。首先,将间歇过程的三维训练数据按变量方向展开成二维矩阵,再通过k-均值聚类的方法按照相关性将数据聚成多类并运用主元分析（PCA）方法分别对每一类建立模型。在线监控时,通过计算样本与模型之间的相似系数以选择最合适的模型进行在线监控。此方法可以将不同批次在同一采样时刻的过程数据按照相关性分到多个阶段,更符合生产过程中常见的过程数据阶段不等长的情况。最后利用青霉素仿真验证了该方法的有效性。     

基于SOTSFNN的溶解氧浓度控制方法

针对污水处理过程溶解氧浓度难以控制的问题,提出了一种基于自组织T-S模糊神经网络的控制方法。其实质是采用模糊规则层激活强度的方法,根据实际环境自适应的对神经元进行调整,构造合适的控制结构,从而提高控制精度。同时采用梯度下降法对控制器的各个参数进行实时调整。该控制器运用在污水处理基准仿真模型中进行实验,结果表明,提出的SO-TSFNN控制方法能够较好地实现对溶解氧浓度的控制,具有较好的自适应性。