A reliable multi-objective control strategy for batch processes based on bootstrap aggregated neural network models

This paper presents a reliable multi-objective optimal control method for batch processes based on bootstrap aggregated neural networks. In order to overcome the difficulty in developing detailed mechanistic models, bootstrap aggregated neural networks are used to model batch processes. Apart from being able to offer enhanced model prediction accuracy, bootstrap aggregated neural networks can also provide prediction confidence bounds indicating the reliability of the corresponding model predictions. In addition to the process operation objectives, the reliability of model prediction is incorporated in multi-objective optimisation in order to improve the reliability of the obtained optimal control policy. The standard error of the individual neural network predictions is taken as the indication of model prediction reliability. The additional objective of enhancing model prediction reliability forces the calculated optimal control policies to be within the regions where the model predictions are reliable. By such a means, the resulting control policies are reliable. The proposed method is demonstrated on a simulated fed-batch reactor and a simulated batch polymerisation process. It is shown that by incorporating model prediction reliability in the optimisation criteria, reliable control policy is obtained.     

A batch-to-batch iterative optimal control strategy based on recurrent neural network models

A batch-to-batch model-based iterative optimal control strategy for batch processes is proposed. To address the difficulties in developing detailed mechanistic models, recurrent neural networks are used to model batch processes from process operational data. Due to model-plant mismatches and unmeasured disturbances, the calculated optimal control profile may not be optimal when applied to the actual process. To address this issue, model prediction errors from previous batch runs are used to improve neural network model predictions for the current batch. Since the main interest in batch process operation is on the end of batch product quality, a quadratic objective function is introduced to track the desired qualities at the end-point of a batch. Because model errors are gradually reduced from batch-to-batch, the control trajectory gradually approaches the optimal control policy. The proposed scheme is illustrated on a simulated methyl methacrylate polymerisation reactor.     

Control of polystyrene batch reactors using neural network based model predictive control (NNMPC): An experimental investigation

Controlling batch polymerization reactors imposes great operational difficulties due to the complex reaction kinetics, inherent process nonlinearities and the continuous demand for running these reactors at varying operating conditions needed to produce different polymer grades. Model predictive control (MPC) has become the leading technology of advanced nonlinear control adopted for such chemical process industries. The usual practice for operating polymerization reactors is to optimize the reactor temperature profile since the end use properties of the product polymer depend highly on temperature. This is because the end use properties of the product polymer depend highly on temperature. The reactor is then run to track the optimized temperature set-point profile. In this work, a neural network-model predictive control (NN-MPC) algorithm was implemented to control the temperature of a polystyrene (PS) batch reactors and the controller set-point tracking and load rejection performance was investigated. In this approach, a neural network model is trained to predict the future process response over the specified horizon. The predictions are passed to a numerical optimization routine which attempts to minimize a specified cost function to calculate a suitable control signal at each sample instant. The performance results of the NN-MPC were compared with a conventional PID controller. Based on the experimental results, it is concluded that the NN-MPC performance is superior to the conventional PID controller especially during process startup. The NN-MPC resulted in smoother controller moves and less variability.     

Batch Process Modelling and Optimal Control Based on Neural Network Model

This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process.     

Batch Process Modelling and Optimal Control Based on Neural Network Models

This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process.     

Design and Stability Analysis of Fuzzy Model-based Predictive Control – A Case Study

In the paper a fuzzy model based predictive control algorithm is presented. The proposed algorithm is developed in the state space and is given in analytical form, which is an advantage in comparison with optimisation based control schemes. Fuzzy model-based predictive control is potentially interesting in the case of batch reactors, heat-exchangers, furnaces and all the processes with strong nonlinear dynamics and high transport delays. In our case it is implemented to a continuous stirred-tank simulated reactor and compared to optimal PI control. Some stability and design issues of fuzzy model-based predictive control are also given.     

Optimal Process Control Using Neural Networks

Infinite time optimal controllers have been designed for a dispersion type tubular reactor model by using the framework of adaptive critic optimal control design. For the reactor control problem, which is governed by two coupled nonlinear partial differential equations, an optimal controller synthesis is presented through two sets of neural networks. One set of neural networks captures the relationship between the states and the control, whereas the other set of networks captures the relationship between the states and the costates. This innovative approach embeds the solutions to the optimal control problem for a large number of initial conditions in the domain of interest. Although the main aim of this paper is to solve a process control problem, the methodology presented here can be viewed as a practical computational tool for many problems associated with nonlinear distributed parameter systems. Numerical results demonstrate the viability of the proposed method.     

Temperature control in catalytic cracking reactors via a robust PID controller

The stabilization of fluid catalytic cracking reactors is tackled in this paper. A robust PID control law is developed in order to control the outlet reactor temperature. The suggested control is based on a reduced order model of the reactor given by a system of ordinary differential equations. The controller is synthesized using an input/output linearizing control law coupled to a proportional-derivative reduced order observer to infer on-line the unknown heat of reaction. The proposed control algorithm leads to a classical PID structure. New tuning rules are given, based on the system structure, estimations and closed-loop time constants. This control strategy turns out to be robust against model uncertainties, noisy temperature measurements and set point changes. The performance of the reaction temperature in a tubular riser reactor is numerically compared when the proposed control scheme and standard PID controllers are applied.     

Time delay integrating systems: a challenge for process control industries. A practical solution

Temperature control of processes that involve the heating and cooling of a closed batch reactor can be a real problem for conventional proportional-integral-derivative (PID) based loop controllers. This paper describes the application of a new industrial advanced process controller. This controller is designed to handle integrating type processes with long dead times and long time constants. The results demonstrate that reactors that could previously only be operated manually can be easily automated using an adaptive model predictive control technology. The barrier to automation of the reactor batch controls can be now removed resulting in tremendous improvements in batch consistency, batch cycle times, and productivity.     

An expert trajectory design for control of nuclear research reactors

In this study, an expert trajectory was proposed for control of nuclear research reactors. The trajectory being followed by the reactor power is composed of three parts. In order to calculate periods at the midpoint of each part of the trajectory, a period generator was designed based on artificial neural networks. The contribution of the expert trajectory to the reactor control system was investigated. Furthermore, the behavior of the controller with the expert trajectory was tested for various initial and desired power levels, as well as under disturbance. It was seen that the controller could control the system successfully under all conditions within the acceptable error tolerance.     

Boundary control for an industrial under-actuated tubular chemical reactor

Several control strategies are presented and studied for an industrial under-actuated tubular chemical reactor. This work presents a case-study of the performance of a decentralized versus centralized control strategy. The tubular reactor under consideration is characterized by nonlinear kinetic laws, and it has some structural constraints on the location of the heat exchangers and of the sensors. For this system, a set of PI controllers is considered and a multivariable LQR controller is constructed to optimally choose the gains. The performance of these control strategies is studied. Finally, a direct numerical treatment of optimal control of the partial differential equations is presented. Industrial results are given for the linear controllers. Simulations emphasize the possible relevance of a direct numerical treatment of the nonlinear partial differential equations.     

Development of PARS-EX pilot plant to study control strategies

A PARtially Simulated EXothermic chemical reactor (PARS-EX) pilot plant is developed in this work to carry out and evaluate various conventional and advanced control strategies. In this reactor, the heat generated from the assumed exothermic reaction was simulated through the use of a controlled steam flow rate into the reactor. Since there is no actual reaction involved, the system is defined as a ‘partially simulated’ reactor. The temperature of the reactor was regulated by an external plate heat exchanger that both cools the process fluid and recycles it back into the reactor. A software interface was also developed to exchange real online data and implement the various control strategies. The advanced control strategies used to control the temperature of the reactor in this work are the neural network-based controllers, which overcome the hassle in periodically tuning conventional controllers. An adaptive method is also incorporated to cater for changes in the process conditions. Tests involving set point tracking and various external and internal disturbance changes were carried out to evaluate and demonstrate the robustness of the neural network-based controllers on the PARS-EX plant. For all of the realistic online cases studied, the neural network-based controllers exhibit better control results compared to the conventional controllers.     

Reinforcement learning for batch process control: Review and perspectives

Batch or semi-batch processing is becoming more prevalent in industrial chemical manufacturing but it has not benefited from advanced control technologies to a same degree as continuous processing. This is due to its several unique aspects which pose challenges to implementing model-based optimal control, such as its highly nonstationary operation and significant run-to-run variabilities. While existing advanced control methods like model predictive control (MPC) have been extended to address some of the challenges, they still suffer from certain limitations which have prevented their widespread industrial adoption. Reinforcement learning (RL) where the agent learns the optimal policy by interacting with the system offers an alternative to the existing model-based methods and has potential for bringing significant improvements to industrial batch process control practice. With such motivation, this paper examines the advantages that RL offers over the traditional model-based optimal control methods and how it can be tailored to better address the characteristics of industrial batch process control problems. After a brief review of the existing batch control methods, the basic concepts and algorithms of RL are introduced and issues for applying them to batch process control problems are discussed. The nascent literature on the use of RL in batch process control is briefly reviewed, both in recipe optimization and tracking control, and our perspectives on future research directions are shared.     

Experimental application of nonlinear model predictive control: temperature control of an industrial semi-batch pilot-plant reactor

This paper describes the application of nonlinear model predictive control (NMPC) to the temperature control of a semi-batch chemical reactor equipped with a multi-fluid heating/cooling system. The strategy of the nonlinear control system is based on a constrained optimisation problem, which is solved repeatedly on-line by a step-wise integration of a nonlinear dynamic model and optimisation strategy. A supervisory control routine has been developed, based on the same nonlinear dynamic model, to handle automatically the fluid changeovers. Both NMPC and supervisory control have been implemented on a PC and applied to a 16 l batch reactor pilot plant. Experiments illustrate the feasibility of such a procedure involving predictive control and supervisory control.     

间歇过程最优迭代学习控制的发展:从基于模型到数据驱动

本文综述了间歇过程的基于模型的和数据驱动的最优迭代学习控制方法.基于模型的最优迭代学习控制方法需要已知被控对象精确的线性模型,其研究较为成熟和完善,有着系统的设计方法和分析工具.数据驱动的最优迭代学习控制系统设计和分析的关键是非线性重复系统的迭代动态线性化.本文简要综述了基于模型的最优迭代学习控制的研究进展,详细回顾了数据驱动的迭代动态线性化方法,包括其详细的推导过程和突出的特点.回顾和讨论了广义的数据驱动最优迭代学习控制方法,包括完整轨迹跟踪的数据驱动最优迭代学习控制方法,提出和讨论了多中间点跟踪的数据驱动最优点到点迭代学习控制方法,和终端输出跟踪的数据驱动最优终端迭代学习控制方法.进一步,迭代学习控制研究中的关键问题,如随机迭代变化初始条件、迭代变化参考轨迹、输入输出约束、高阶学习控制律、计算复杂性等.本文突出强调了基于模型的和数据驱动的最优迭代学习控制方法各自的特点与区别联系,以方便读者理解.最后,本文提出数据驱动的迭代学习控制方法已成为越来越复杂间歇过程控制发展的未来方向,一些开放的具有挑战性的问题还有待于进一步研究.     

An on-line batch span minimization and quality control strategy for batch and semi-batch processes

A novel strategy is proposed to minimize the operation time of batch and semi-batch processes. The proposed on-line strategy is based on linear regression models and employs a cascade control structure in which the primary controller calculates an optimal operation profile for the secondary controller to follow. A special feature of the proposed on-line strategy is that it conducts run-wise information feedback and achieves the attainable minimum operation time as the batch run is repeated despite model uncertainty. The performance of the proposed strategy is illustrated through simulation studies involving an exothermic batch reactor and a semi-batch reactor producing 2-acetoacetyl pyrrole.     

Optimal adaptive control of (bio)chemical reactors: past, present and future

In this paper an overview of optimal adaptive control of (bio)chemical reactors is presented. Following the paradigm of the Minimum Principle of Pontryagin the derivation of optimal control sequences for fed-batch production processes is briefly revisited. Next, it is illustrated how the obtained optimal profiles can be exploited in the characterization of nearly optimal control sequences in terms of the qualitative behavior of the specific growth and production rates as function of the limiting substrates. Implementing this knowledge leads in a natural way to the design of (nearly) optimal adaptive feedback controllers. Special emphasis will lie on the potential of on-line biomass measurements (obtained with the Biomass Monitor) in the estimation algorithm of the growth kinetics being the adaptive component of the controller. Extensions towards fermentation processes with (i) multiple substrates and (ii) non-monotonic kinetics are also included. Finally, perspectives towards optimal adaptive control of not perfectly mixed (bio)chemical reactor systems, such as chemical tubular reactors, are outlined.     

Adaptive friction compensation of servo mechanisms

In this paper, adaptive friction compensation is investigated using both model-based and neural network (non-model-based) parametrization techniques. After a comprehensive list of commonly used models for friction is presented, model-based and non-modelbased adaptive friction controllers are developed with guaranteed closed-loop stability. Intensive computer simulations are carried out to show the effectiveness of the proposed control techniques, and to illustrate the effects of certain system parameters on the performance of the closed-loop system. It is observed that as the friction models become complex and capture the dominate dynamic behaviours, higher feedback gains for model-based control can be used and the speed of adaptation can also be increased for better control performance. It is also found that neural networks are suitable candidate for friction modelling and adaptive controller design for friction compensation.     

Neural Network Structures for Optimal Control of LPCVD Reactors

In this paper, a new approach of LPCVD reactor modelling and control is presented, based on the use of neural networks. We first present the development of a hybrid networks model of the reactor. The objective is to provide a simulation model which can be used to compute online the film thickness on each wafer. In the second section, the thermal control of a LPCVD reactor is studied. The objective is to develop a multivariable controller to control a space- and time-varying temperature profile inside the reactor. A neural network is designed using a methodology based on process inverse dynamics modelling. Good control results have been obtained when tracking space-time temperature profiles inside the LPCVD reactor pilot plant. Finally, global software is elaborated to achieve film thickness control in an experimental LPCVD reactor pilot plant, in order to get a defined and uniform deposition thickness on the wafers all along the reactor. Experimental results are presented which confirm the efficiency of the optimal control strategy.     

Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.