Cascade closed-loop optimization and control of batch reactors

In this paper, a cascade closed-loop optimization and control strategy for batch reactors is proposed. Based on the reduction of a physical conservation model a cascade system is developed, which can effectively combine optimization and control to achieve good on-line optimization and tracking performance under the common condition where incomplete knowledge of the reaction system exists. A two-tier estimation scheme using a nonlinear observer for heat production rate and reaction rates is also developed. In the reaction rate estimation, calorimetric information is used. The on-line closed-loop optimization strategy uses a descending horizon dynamic optimization algorithm based on nonlinear programming and an additive unknown disturbance for feedback. A simple adaptive nonlinear tracking system is designed based on the generic model control concept. The efficiency of this strategy is demonstrated through simulations on a batch reactor under various operation conditions, such as noisy measurements, varying initial states and model mismatch.     

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.     

Measurement and control of polymerization reactors

The measurement and control of polymerization reactors is very challenging due to the complexity of the physical mechanisms and polymerization kinetics. In these reactors many important variables, which are related to end-use polymer properties, cannot be measured on-line or can only be measured at low sampling frequencies. Furthermore, end-use polymer properties are related to the entire molecular weight, copolymer composition, sequence length, and branching distributions. This paper surveys the instrumentation technologies, which are of particular interest in polymerization reactors with emphasis on, for example, measurement of viscosity, composition, molecular weight, and particle size. This paper presents a hierarchical approach to the control system design and reviews traditional regulatory techniques as well as advanced control strategies for batch, semibatch, and continuous reactors. These approaches are illustrated by focusing on the control of a commercial multiproduct continuous emulsion polymerization reactor. Finally, the paper captures some of the trends in the polymer industry, which may impact future development in measurement and reactor control.     

Design and optimisation of batch and semi-batch reactors

This paper addresses a systematic methodology for batch and semi-batch reactor design and optimisation for both ideal and non-ideal mixing. It can be applied to non-isothermal and multiphase systems. The method starts from a general representation in the form of a temporal superstructure based on the similarity of between plug flow reactors and ideal batch reactors. The temporal superstructure of a batch reactor exists in both the space and time dimensions. For non-ideal mixing, this paper addresses a mixing compartment network model to represent mixing inside reactors. The mixing compartment network is then included into the temporal superstructure to model non-ideally mixed batch reactors and the mixing pattern optimised with the other variables. Besides the operation variables for batch reactors, this method can also suggest the optimum mixing pattern and promising reactor configurations for mechanical design. A profile-based approach is proposed to make a search of the profiles for temperature, pressure and feed addition. This approach starts from a set of initial profiles of temperature, pressure and feed addition. Then the performance of the batch reactor is evaluated against the objective function under different profiles. An optimal set of profiles is then found by this profile searching process. A stochastic optimisation technique based on simulated annealing is employed to obtain optimal solutions. This method is also extended to multiphase reaction systems based on the concept of shadow reactor compartments. A number of case studies are presented to illustrate the use of the proposed methodology.     

Nonlinear model predictive control of an industrial polymerization process

Nonlinear model predictive control (NMPC) is used to maintain and control polymer quality at specified production rates because the polymer quality measures have strong interacting nonlinearities with different temperatures and feed rates. Polymer quality measures that are available from the laboratory infrequently are controlled in closed-loop using a NMPC to set the temperature profile of the reactors. NMPC results in better control of polymer quality measures at different production rates as compared to using the nonlinear process model with reaction kinetics to implement offline targets for reactor temperatures.     

Nonlinear adaptive control algorithm for a multicomponent batch distillation column

In this article, a nonlinear adaptive control strategy is proposed for a multicomponent batch distillation column. The hybrid control scheme consists of a generic model controller (GMC) and a nonlinear adaptive state estimator (ASE). In the first part of the study, an adaptive observer is designed aiming to estimate the partially known parameters based on the measured compositions in the presence of process/predictor mismatch. The open-loop dynamic behavior of the developed ASE estimator is investigated under initialization error, disturbance, and uncertain parameters. In the subsequent part, the adaptive GMC-ASE controller (GMC control structure in conjunction with ASE estimator) has been synthesized for the example distillation column. A simulation-based comparative study has been conducted between the derived nonlinear GMC-ASE control algorithm and a gain-scheduled proportional integral (GSPI) law in terms of constant composition control. The proposed adaptive control scheme is shown to be quite promising due to the exponential error convergence capability of the ASE estimator in addition to the high-quality performance of the GMC controller.     

Adaptive output-feedback power-level control for modular high temperature gas-cooled reactors

Smallmodular reactors (SMRs) are beneficial in providing electricity power safely and viable for specific applications such as seawater desalination and heat production. Due to its inherent safety feature, the modular high temperature gas-cooled reactor (MHTGR) is considered as one of the best candidates for SMR-based nuclear power plants. Since its dynamics presents high nonlinearity and parameter uncertainty, it is necessary to develop adaptive power-level control, which is beneficial to safe, stable, and efficient operation of MHTGR and is easy to be implemented. In this paper, based on the physically-based control design approach, an adaptive outputfeedback power-level control is proposed for MHTGRs. This control can guarantee globally bounded closedloop stability and has a simple form.Numerical simulation results showthe correctness of the theoretical analysis and satisfactory regulation performance of this control.     

An adaptive fuzzy approach for the incineration temperature control process

There are many factors affecting the combustion process in incinerators; one of them is how to control the temperature of the incineration and reduce the emissions. In this work, a second-order model of the adaptive fuzzy control strategy is adopted to stabilize the combustion temperature and the results demonstrate that the adaptive control strategy with the adaptive factors is a good method to achieve the goal of incineration temperature control.     

Temperature Control of a Bench‐Scale Batch Polymerization Reactor for Polystyrene Production

Batch polymerization reactors commonly use optimal temperature control as the strategic operation parameter. This strategy allows for better operability and a more economic process. The main objective of the batch polymerization reactor control is to obtain acceptable product quality. Direct measurement of polymer quality is rarely achievable, which makes the online control of the reactor difficult. Temperature is the most controllable operational variable in the polymer reactor, which is seen to have a direct effect on the polymer properties. Temperature is chosen as the set point by using either the isothermal temperature or optimal temperature trajectory. Online control of the optimal temperature profile of a bench‐scale batch polymerization reactor was experimentally investigated in this study. The temperature trajectory was used as the target for controllers to follow. The time‐profile temperature was obtained with the objective of obtaining the desired conversion and number‐average chain length within the minimum time. Two advanced controls of fuzzy logic control and generic model control were applied to the polymer reactor. A comparison of the controllers reveals that both performed better than conventional controllers.     

Optimal hybrid modeling approach for polymerization reactors using parameter estimation techniques

The dynamics of polymerization catalytic reactors have been investigated by many researchers during the past five decades; however, the emphasis of these studies was directed towards correlating process model parameters using empirical investigation based on small scale experimental setup and not on real process conditions. The resulting correlations are of limited practical use for industrial scale operations. A statistical study for the relative correlation of each of the effective process parameters revealed the best combination of parameters that could be used for optimizing the process model performance. Parameter estimation techniques are then utilized to find the values of these parameters that minimize a predefined objective function. Published real industrial scale data for the process was used as a basis for validating the process model. To generalize the model, an artificial neural network approach is used to capture the functional relationship of the selected parameters with the process operating conditions. The developed ANN-based correlation was used in a conventional fluidized catalytic bed reactor (FCR) model and simulated under industrial operating conditions. The new hybrid model predictions of the melt-flow index and the emulsion temperature were compared to industrial measurements as well as published models. The predictive quality of the hybrid model was superior to other models. The suggested parameter estimation and modeling approach can be used for process analysis and possible control system design and optimization investigations.     

Nonlinear adaptive switching control for a class of non-affine nonlinear systems

An improved nonlinear adaptive switching control method is presented to relax the assumption on the higher order nonlinear terms of a class of discrete-time non-affine nonlinear systems. The proposed control strategy is composed of a linear adaptive controller, a neural network (NN) based nonlinear adaptive controller and a switching mechanism. An incremental model is derived to represent the considered system and an improved robust adaptive law is chosen to update the parameters of the linear adaptive controller. A new performance criterion of the switching mechanism is designed to select the proper controller. Using this control scheme, all the signals in the system are proved to be bounded. Numerical examples verify the effectiveness of the proposed algorithm.     

State estimation for continuous emulsion polymerization

Various aspects of the use of extended Kalman Filters for tracking the states of continuous emulsion polymerization reactors are investigated. The importance of introducing meaningful nonstationary stochastic states to account for unknown impurities, initiator efficiencies, modelling errors, etc. is illustrated. The robustness of these state estimators to unmodelled and unmeasured disturbances, to modelling errors, and to input errors is evaluated. A procedure for selecting an optimal set of on-line sensors is presented. The emulsion polymerization of styrene-butadiene rubber (SBR) is used as the example system.     

Effect of monomer feed and production rate on the control of molecular weight distribution of polyethylene in gas phase reactors

The control of the polymer molecular weight distribution via altering the monomer to hydrogen molar ratio in fluidized bed reactors is examined. The molar ratio is altered by manipulating the monomer and hydrogen feed rates using nonlinear model predictive controller. The simulation revealed promising results however a trade-off between utilizing both the monomer and hydrogen flows simultaneously and the hydrogen flow exclusively exists. Utilization of the monomer and hydrogen flows together favors the rapid transition to the required MWD but at the expense of higher purge and inconsistent production rate. Exclusive use of the hydrogen intake leads to steady production rate and less consumption of the purge. However, longer time is needed to achieve the desired MWD. The same phenomena are observed when discrete mechanism for product withdrawal is implemented.     

Application of recurrent neural networks in batch reactors: Part I. NARMA modelling of the dynamic behaviour of the heat transfer fluid temperature

This paper is focused on the development of nonlinear models, using artificial neural networks, able to provide appropriate predictions when acting as process simulators. The dynamic behaviour of the heat transfer fluid temperature in a jacketed chemical reactor has been selected as a case study. Different structures of NARMA (Non-linear ARMA) models have been studied. The experimental results have allowed to carry out a comparison between the different neural approaches and a first-principles model. The best neural results are obtained using a parallel model structure based on a recurrent neural network architecture, which guarantees better dynamic approximations than currently employed neural models. The results suggest that parallel models built up with recurrent networks can be seen as an alternative to phenomenological models for simulating the dynamic behaviour of the heating/cooling circuits which change from batch installation to installation.     

Nonlinear control of the dissolved oxygen concentration integrated with a biomass estimator for production of Bacillus thuringiensis δ-endotoxins

Bacillus thuringiensis is a microorganism that allows the biosynthesis of δ-endotoxins with toxic properties against some insect larvae, being often used for the production of biological insecticides. A key issue for the bioprocess design consists in adequately tracking a pre-specified optimal profile of the dissolved oxygen concentration. To this effect, this paper aims at developing a novel control law based on a nonlinear dynamic inversion method. The closed-loop strategy includes an observer based on a Bayesian Regression with Gaussian Process, which is used for on-line estimating the biomass present in the bioreactor. Unlike other approaches, the proposed controller leads to an improved response time with effective disturbance rejection properties, while simultaneously prevents undesired oscillations of the dissolved oxygen concentration. Simulation results based on available experimental data were used to show the effectiveness of the proposal.     

Two observer-based nonlinear control approaches for temperature control of a class of continuous stirred tank reactors

In this paper, two nonlinear observer based controllers for temperature control of a continuous stirred tank reactor in which a special class of parallel exothermic reactions take place are proposed. A reduced order nonlinear observer is constructed to estimate the concentration in the reactor. The observer is coupled with two nonlinear controllers, designed based on two well-known techniques, namely input-output linearization and backstepping for controlling the reactor temperature. For dampening the effect of observer error dynamics, a compensating term is used in each control law. The asymptotical stability of the closed-loop system is shown by the Lyapunov's stability theorem. The effectiveness of the proposed controllers has been demonstrated through computer simulations.     

An experimental study for property control in a continuous styrene polymerization reactor using a polynomial ARMA model

By using a multivariable nonlinear model predictive controller (NLMPC), the control experiments for the monomer conversion and the weight-average molecular weight are conducted in a continuous styrene polymerization reactor. Instead of a complex first-principles model, a polynomial auto-regressive moving average model (ARMA) is used to describe the nonlinear behavior of the polymerization reactor. The pseudorandom multilevel input signals mounted on the jacket inlet temperature and the feed flow rate are applied to the polymerization reaction system to identify a polynomial ARMA model. In the experiments of identification and control, the monomer conversion and the weight-average molecular weight are measured by on-line densitometer and viscometer with appropriate correlations. The on-line measurements are found to be in good agreement with the off-line analysis by the gravimetry and the gel permeation chromatography. Since a polynomial ARMA model is expected to give a higher order objective function of input variables, we employ the extended Kalman filter based NLMPC scheme to reduce the computational requirement in the control experiments. The NLMPC based on the polynomial ARMA model is found to perform satisfactorily for the control of the polymer properties during a grade-transition period as well as under the steady-state operation.     

Dynamics and stability of ethylene polymerization in multizone circulating reactors

Multizone circulating bed reactors (MZCR) have the exclusive characteristics of producing polymers of different molecular weights in a single particle. Traditional fluidized bed reactors, on the other hand, can produce only one kind of molecular weight with relatively narrow distribution. A dynamic model for the MZCR is used to illustrate the basic dynamic behavior of the new reactor design used for polyethylene production. The model is used to study the copolymerization of ethylene with butene. Several parameter sensitivity analyses are performed to show the computer-simulated time responses for reactor temperature, number-average molecular weight, weight-average molecular weight, catalyst feed rate and the monomer/comonomer concentration along the reactor length. At certain operating conditions dynamic instability is observed and the results for the effect of cooling water temperature, catalyst feed rate, monomer and comonomer initial feed concentration on the reactor temperature and polymer molecular weight reveal that the system is very sensitive to disturbances in the heat exchanger coolant temperature. Also, at some operating conditions, the reactor temperature oscillates above the polymer melting temperature. Temperature runaway above polymer softening point is a serious problem which may cause polymer melting and hence reactor shutdown. The oscillatory behavior of the reactor temperature necessitates a suitable temperature control scheme to be installed.     

Generalized delta rule (GDR) algorithm with generalized predictive control (GPC) for optimum temperature tracking of batch polymerization

The generalized delta rule (GDR) algorithm with generalized predictive control (GPC) control was implemented experimentally to track the temperature on a set point in a batch, jacketed polymerization reactor. An equation for optimal temperature was obtained by using co-state Hamiltonian and model equations. To track the calculated optimal temperature profiles, controller used should act smoothly and precisely as much as possible. Experimental application was achieved to obtain the desired comparison. In the design of this control system, the reactor filled with styrene-toluene mixture is considered as a heat exchanger. When the reactor is heated by means of an immersed heater, cooling water is passed through the reactor-cooling jacket. So the cooling water absorbs the heat given out by the heater. If this is taken into consideration, this reactor can be considered to be continuous in terms of energy. When such a mixing chamber was used as a polymer reactor with defined values of heat input and cooling flow rate, system can reach the steady-state condition. The heat released during the reaction was accepted as a disturbance for the heat exchanger. Heat input from the immersed heater is chosen as a manipulated variable. The neural network model based on the relation between the reactor temperature and heat input to the reactor is used. The performance results of GDR with GPC were compared with the results obtained by using nonlinear GPC with NARMAX model.The reactor temperature closely follows the optimal trajectory. And then molecular weight, experimental conversion and chain lengths are obtained for GDR with GPC.     

Nonlinear temperature control of a batch suspension polymerization reactor

This paper concerns nonlinear temperature control of a batch polymerization reactor where suspension polymerization of methyl methacrylate (MMA) takes place. For this purpose, four control algorithms, namely, a fix proportional‐integral (PI) controller, an adaptive proportional‐integral‐derivative (PID) controller and two globally linearizing control (GLC) schemes, one for known kinetic model (GLC‐I) and the other for unknown kinetic model (GLC‐II), are selected. The performances of these controllers are compared through simulation and real‐time studies in the presence of different levels of parameter uncertainty. The results indicate that GLCI and GLC‐II have better performances than fix PI and adaptive PID, especially in case of strong gel effect. The worst performance belongs to adaptive PID because of rapid model changes in gel effect region. GLC‐II has a simpler structure than GLC‐I and can be used without requiring the kinetic model. In implementation of GLC‐I the closed loop observer should be used because of model uncertainties.