Model predictive control for the reactant concentration control of a reactor

The reactant concentration control of a reactor using Model Predictive Control (MPC) is presented in this paper. Two major difficulties in the control of reactant concentration are that the measurement of concentration is not available for the control point of view and it is not possible to control the concentration without considering the reactor temperature. Therefore, MIMO control techniques and state and parameter estimation are needed. One of the MIMO control techniques widely studied recently is MPC. The basic concept of MPC is that it computes a control trajectory for a whole horizon time minimising a cost function of a plant subject to a dynamic plant model and an end point constraint. However, only the initial value of controls is then applied. Feedback is incorporated by using the measurements/estimates to reconstruct the calculation for the next time step. Since MPC is a model based controller, it requires the measurement of the states of an appropriate process model. However, in most industrial processes, the state variables are not all measurable. Therefore, an extended Kalman filter (EKF), one of estimation techniques, is also utilised to estimate unknown/uncertain parameters of the system. Simulation results have demonstrated that without the reactor temperature constraint, the MPC with EKF can control the reactant concentration at a desired set point but the reactor temperator is raised over a maximum allowable value. On the other hand, when the maximun allowable value is added as a constraint, the MPC with EKF can control the reactant concentration at the desired set point with less drastic control action and within the reactor temperature constraint. This shows that the MPC with EKF is applicable to control the reactant concentration of chemical reactors.     

Model-based control strategies for a chemical batch reactor with exothermic reactions

Batch reactor control provides a very challenging problem for the process control engineer. This is because a characteristic of its dynamic behavior shows a high nonlinearity. Since applicability of the batch reactor is quite limited to the effectiveness of an applied control strategy, the use of advanced control techniques is often beneficial. This work presents the implementation and comparison of two advanced nonlinear control strategies, model predictive control (MPC) and generic model control (GMC), for controlling the temperature of a batch reactor involving a complex exothermic reaction scheme. An extended Kalman filter is incorporated in both controllers as an on-line estimator. Simulation studies demonstrate that the performance of the MPC is slightly better than that of the GMC control in nominal case. For model mismatch cases, the MPC still gives better control performance than the GMC does in the presence of plant/model mismatch in reaction rate and heat transfer coefficient.     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

Machine learning-based predictive control of nonlinear processes. Part I: Theory

This article focuses on the design of model predictive control (MPC) systems for nonlinear processes that utilize an ensemble of recurrent neural network (RNN) models to predict nonlinear dynamics. Specifically, RNN models are initially developed based on a data set generated from extensive open-loop simulations within a desired process operation region to capture process dynamics with a sufficiently small modeling error between the RNN model and the actual nonlinear process model. Subsequently, Lyapunov-based MPC (LMPC) that utilizes RNN models as the prediction model is developed to achieve closed-loop state boundedness and convergence to the origin. Additionally, machine learning ensemble regression modeling tools are employed in the formulation of LMPC to improve prediction accuracy of RNN models and overall closed-loop performance while parallel computing is utilized to reduce computation time. Computational implementation of the method and application to a chemical reactor example is discussed in the second article of this series.     

Dynamic recurrent radial basis function network model predictive control of unstable nonlinear processes

A multistep model predictive control (MPC) strategy based on dynamically recurrent radial basis function networks (RBFNs) is proposed for single-input single-output (SISO) control of uncertain nonlinear processes. The control system consists of two automatically configured RBFNs, a trained network representing the plant model and a network with on-line learning to function as controller. The automatic configuration and learning of the networks is carried out by using a hierarchically self-organizing learning algorithm. This control strategy is structurally simple and computationally efficient since a single output node of each RBFN is configured to provide multistep predictions for plant output and controller. The performance of the proposed RBFNMPC strategy is evaluated by applying to two unstable nonlinear chemical processes, a chemical reactor and a biochemical reactor, and also a stable polymerization reactor. Further, the results of the RBFNMPC is compared with similar RBFN model based control strategies and also with well tuned PID/PI controller. The results show the better performance of the proposed RBFNMPC for the control of open-loop unstable nonlinear processes that exhibit multiple steady-state behavior.     

Polymer property control in a continuous styrene polymerization reactor using model-on-demand predictive controller

The model-on-demand (MoD) framework was extended to the model predictive control (MPC) to design a multiple variable model-on-demand predictive controller (MoD-PC). This control algorithm was applied to the property control of polymer product in a continuous styrene polymerization reactor. For this purpose, a local auto-regressive exogenous input (ARX) model was constructed with a small portion of data located in the region of interest at every sample time. With this model an output prediction equation was formulated to calculate the optimal control input sequence. Jacket inlet temperature and conversion were chosen as the elements of regressor state vector in data searching step. Simulation studies were conducted by applying the MoD-PC to MIMO control problems associated with the continuous styrene polymerization reactor. The control performance of the MoD-PC was then compared with that of a nonlinear MPC based on the polynomial auto-regressive moving average (ARMA) model for disturbance rejection as well as for setpoint-tracking. As a result, the MoD-PC was found to be an effective strategy for the production of polymers with desired properties.     

A robustly stabilizing fault-tolerant MPC: A performance improvement-based approach

In terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost-contracting formulation-based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision-making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.     

Some manifold learning considerations toward explicit model predictive control

Model predictive control (MPC) is a de facto standard control algorithm across the process industries. There remain, however, applications where MPC is impractical because an optimization problem is solved at each time step. We present a link between explicit MPC formulations and manifold learning to enable facilitated prediction of the MPC policy. Our method uses a similarity measure informed by control policies and system state variables, to “learn” an intrinsic parametrization of the MPC controller using a diffusion maps algorithm, which will also discover a low-dimensional control law when it exists as a smooth, nonlinear combination of the state variables. We use function approximation algorithms to project points from state space to the intrinsic space, and from the intrinsic space to policy space. The approach is illustrated first by “learning” the intrinsic variables for MPC control of constrained linear systems, and then by designing controllers for an unstable nonlinear reactor.     

Online estimation and control of polymer quality in a copolymerization reactor

The validity of an online state estimator for a semi-batch MMA/MA solution copolymerization reactor was established using online densitometer and viscometer. Using the conventional extended Kalman filter (EKF) as the state estimator, the experiment was conducted under both isothermal and nonisothermal conditions for application to the control of copolymer properties. Further analysis was made by using ofline measurement data for the mol fraction of MMA in the remaining monomers and the solid content. The EKF was found to provide a good estimate for the state of the copolymerization system. A model predictive controller was designed and implemented to obtain copolymers with uniform copolymer composition and the desired weight average molecular weight by adopting the feed flow rate of MMA and the reaction temperature as control inputs. The controller was proven effective with a satisfactory performance for the control of polymer properties in the semi-batch copolymerization reactor.     

Increased Reactor Performance versus Reactor Safety Aspects in Acrylate Copolymerization

The aim of reducing cycle times of semibatch‐polymerization processes requires systematic investigations of the kinetics, careful adjustment of the desired polymer properties, proper thermal reactor design and reliable reactor safety assessment [1]. As a concrete example, a semibatch‐copolymerization was carefully examined with respect to four different aspects. Thermo‐kinetics of the reaction were investigated with isoperibolic reaction calorimetry and GC. In order to obtain reliable values for the overall heat transfer coefficient of the production scale reactor, cooling experiments were carried out with solvent and final copolymer solution as reactor content. For consistent reactor safety assessment additional investigations are necessary including case studies of breakdown incidences. These simulations were performed with a mathematical model based on the GC data and experimental vapor pressure curves. As a result of these calculations, a reduction of reaction time from 10 to 6 hours was possible. To convert into practice, it must be ensured that even in this shortened time a product of the same quality is produced.     

模型预测控制在钠氨合成工艺上的应用研究

基于钠氨合成连续化生产工艺,从化学反应机理出发,建立钠氨塔式反应器动态机理模型。并对模型进行动态分析,对多变量非线性模型进行集总化、线性化处理。推广单变量模型预测控制到多变量模型预测控制,对反应器温度进行控制。通过仿真比较,验证了MPC控制算法比PID控制具有更好的控制效果。     

EXTENDED KALMAN FILTER CONTROLLER: FIRST PRINCIPLES MODELS TO NEURAL NETWORKS

Extended Kalman filters (EKF) have been widely employed for state and parameter estimation in chemical engineering systems. Gao et al. [Gao, F., Wang, F. and Li, M. (1999). Ind. Eng. Chem. Res., 38, 2345-2349] have proposed the use of EKF for control computation using a neural network representation of the system in a discrete-time framework. In the present study, an EKF controller is proposed in a continuous time framework with models incorporating different levels of process knowledge. The problem of process-model mismatch is handled by incorporating EKF-based state and/or parameter estimation along with control computation. A batch reactor temperature control problem for a highly exothermic reaction between maleic anhydride and hexanol to form hexyl monoester of maleic acid is considered as a test bed to evaluate the performance of the proposed control schemes. Three different models are considered, namely the first principles model, a reduced-order process model, and an artificial neural network (ANN) model for formulation of the control schemes. The performance of the proposed control scheme using first principles model is compared to that of generic model control, and a similar performance is achieved. The present study illustrates the usefulness of the proposed control schemes and can be easily extended to general chemical engineering systems.     

Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor

This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open-loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection.     

Fault detection by using the innovation signal: application to an exothermic reaction

Plants in the chemical and biochemical industries are becoming larger and more complex. The growing safety and environmental demands are forcing industry to look for new and more powerful techniques for the detection of process faults. In this paper, we present a method for detecting faults that can appear in some parts of a chemical plant. This method is based on statistical information generated by the extended Kalman filter (EKF) and is intended to reveal any drift from the normal behavior of the process. The work done in this paper is an application of the EKF to a nonlinear system such as stirred reactors in the presence of exothermic chemical reactions. We examine the abnormal behavior of a chemical reactor due to two different faults in its control parameters. The chosen reaction is a very exothermic oxido-reduction one; the oxidation of sodium thiosulfate by hydrogen peroxide.     

Economic model predictive control of nonlinear process systems using Lyapunov techniques

In this work, we develop model predictive control (MPC) designs, which are capable of optimizing closed‐loop performance with respect to general economic considerations for a broad class of nonlinear process systems. Specifically, in the proposed designs, the economic MPC optimizes a cost function, which is related directly to desired economic considerations and is not necessarily dependent on a steady‐state—unlike conventional MPC designs. First, we consider nonlinear systems with synchronous measurement sampling and uncertain variables. The proposed economic MPC is designed via Lyapunov‐based techniques and has two different operation modes. The first operation mode corresponds to the period in which the cost function should be optimized (e.g., normal production period); and in this operation mode, the MPC maintains the closed‐loop system state within a predefined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the economic MPC to an appropriate steady‐state. In this operation mode, suitable Lyapunov‐based constraints are incorporated in the economic MPC design to guarantee that the closed‐loop system state is always bounded in the predefined stability region and is ultimately bounded in a small region containing the origin. Subsequently, we extend the results to nonlinear systems subject to asynchronous and delayed measurements and uncertain variables. Under the assumptions that there exist an upper bound on the interval between two consecutive asynchronous measurements and an upper bound on the maximum measurement delay, an economic MPC design which takes explicitly into account asynchronous and delayed measurements and enforces closed‐loop stability is proposed. All the proposed economic MPC designs are illustrated through a chemical process example and their performance and robustness are evaluated through simulations. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Composition estimation of multicomponent reactive batch distillation with optimal sensor configuration

An inferential state estimation scheme based on extended Kalman filter (EKF) with optimal selection of sensor locations using principal component analysis (PCA) is presented for composition estimation in multicomponent reactive batch distillation. The properties of PCA are exploited to provide the most sensitive dynamic temperature measurement information of the process to the estimator for accurate estimation of compositions. The state estimator is supported by a simplified dynamic model of reactive batch distillation that includes component balance equations together with thermodynamic relations and reaction kinetics. The performance of the proposed scheme is evaluated by applying it for composition estimation on all trays, reboiler, reflux drum and products of a reactive batch distillation column, in which ethyl acetate is produced through an esterification reaction between acetic acid and ethanol. This quaternary system with azeotropism is highly nonlinear and typically suited for implementation of the proposed scheme. The results demonstrate that the proposed EKF estimation scheme with optimal temperature sensor configuration is effective for inferential estimation of compositions in multicomponent reactive batch distillation.     

Optimal reaction conditions for the minimization of energy consumption and by‐product formation in a poly(ethylene terephthalate) process

We determined the optimal reaction conditions to minimize the energy cost and the quantities of by‐products for a poly(ethylene terephthalate) process by using the iterative dynamic programming (IDP) algorithm. Here, we employed a sequence of three reactor models: the semibatch transesterification reactor model, the semibatch prepolymerization reactor model, and the rotating‐disc‐type polycondensation reactor model. We selectively chose or developed the reactor models by incorporating experimentally verified kinetic models reported in the literature. We established the model for the entire reactor system by connecting the three reactor models in series and by resolving some joint problems arising when different types of reactor models were interconnected. On the basis of the simulation results of the reactor system, we scrutinized the cause and effect between the reaction conditions and the final quality of the polymer product. Here, we set up the optimization strategy by using IDP on the basis of the integrated reactor model, and the process variables with significant influence on the properties of polymer were selected as control variables with the help of a simulation study. With this method, we could refine the reaction conditions at the end of each iteration step by contracting the spectra of control regions, and the iteration process finally stopped when the profile of the optimal trajectory converged. We also took the constraints on the control variables into account to guarantee polymer quality and to suppress side reactions. Constituting six different strategies by setting weighting vectors differently, we examined the differences in optimal trajectories, the trend of optimality, and the quality of the final polymer product. For each of the strategies, we conducted the optimization to examine whether the number‐average degree of polymerization approached the desired value. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 993–1008, 2002     

On-line monitoring of a CSTR polymerization reactor using multivariable filters

Three multivariable filters are evaluated for on-line monitoring of a CSTR polymerization reactor. The first filtering algorithm is the Kaiman filter. This linear filter is simple to implementation, but cannot exactly estimate the dynamic behavior of the polymerization reactor. To compensate the state model inadequacies, nonlinear models can be considered in the filtering algorithm. The precise state estimation can be guaranteed by the extended Kaiman filter (EKF). Finally, the auto-regressive exogenous inputs model based filter (ARXF) is developed to reduce the modeling cost. These different filters are applied to the continuous solution polymerization of a MMA-AIBN-EA system as a case study. The ARXF is easy to implement and shows satisfactory results.     

Enhanced model predictive control of a catalytic flow reversal reactor

The combustion of lean methane air mixtures in a catalytic flow reversal reactor (CFRR) is studied using a two dimensional heterogeneous continuum model, based on mole and energy balance equations for the solid (the inert and catalytic sections of the reactor) and the fluid phases. Following a design of experiments (DOE), many simulations were carried out to investigate the reactor performance. The results show the impact on the methane conversion and the maximum temperature in the reactor of key process parameters such as the methane inlet concentration, the superficial gas velocity, the switching time, and the mass extraction rate. A simple empirical model is deduced to predict the maximum temperature and conversion of methane in the reactor at stationary state. This model is combined with a model predictive control (MPC) strategy in the form of a terminal constraint to improve the controller performance. Results show that the control of the reactor is improved.     

Robust Integrated Design of processes with terminal penalty model predictive controllers

In this work, a novel methodology for the Integrated Design (ID) of processes with linear Model Predictive Control (MPC) is addressed, providing simultaneously the plant dimensions, the control system parameters and a steady state working point. The MPC chosen operates over infinite horizon in order to guarantee stability and it is implemented with a terminal penalty. The ID methodology considers norm based indexes for controllability, as well as robust performance conditions by using a multi-model approach. Mathematically, the ID is stated as a multiobjective nonlinear constrained optimization problem, tackled in different ways. Particularly, objective functions include investment, operating costs, and dynamical indexes based on the weighted sum of some norms of different closed loop transfer functions of the system. The paper illustrates the application of the proposed methodology with the ID of the activated sludge process of a wastewater treatment plant (WWTP).