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.     

Iterative learning control of heat-up phase for a batch polymerization reactor

This paper describes a novel method for heat-up phase control of an industrial batch polymerization reactor where heat transfer characteristics change with batches due to fouling of the polymer products on the reactor wall. The main objective of the control is to settle the reactor temperature on a target value within ± 0.1°C in a minimum possible time. To achieve this goal utilizing the repetitive nature of batch operation, the control problem was defined as a tracking problem and feedback-assisted iterative learning control (FBALC) was employed as the underlying control technique. The proposed control method was applied to an industrial batch reactor polymerizing ABS resin. After on-site evaluation for an extended period of time, it was found that the proposed method gives a pronounced improvement in heat-up phase operation. Consistent heat-up profiles with a minimized settling time are obtained.     

Post analysis on different operating time processes using orthonormal function approximation and multiway principal component analysis

In most batch process operations, operators often need to adjust the different operating time in each batch run to get the desired product quality since the input specifications provided are different. The proposed method is the combination of the orthonormal function approximation and the multiway principal component analysis (MPCA). It is used to analyze and monitor batch processes at the different operating time. Like the philosophy of statistical process control in the traditional MPCA, this method leads to simple monitoring charts, easy tracking of the progress on each batch run and monitoring the occurrence of observable upsets. The only information needed to exploit the procedure is the historical data collected from the past successful batches. The methodology has been applied to two examples, a batch chemical reactor and a wafer plasma etching process, to illustrate the general use of this proposed method.     

Experimental investigations on fuzzy logic for process control

The present work is concerned with the design and experimental testing of fuzzy algorithms for the on-line control of a few processes: temperature of a methyl methacrylate batch polymerization reactor, evaporating and condensing temperatures of a refrigeration system and the overhead composition of a batch distillation column. PID-fuzzy algorithms were developed and compared to conventional PID controllers, proving to be more suitable and reliable for the polymerization process. For the batch distillation column, fuzzy control reduced the batch time and the energy consumption. The PID-fuzzy also outperformed the conventional PID in terms of energy savings for the refrigeration system.     

Productivity optimization of an industrial semi-batch polymerization reactor under safety constraints

In this work the operation of an industrial semi-batch reactor is optimized. In the reactor a strongly exothermic polymerization reaction takes place and the objective is to minimize the duration of the batch time. Various operational as well as quality and safety related constraints have to be met during the batch and at its final time. In particular, a cooling system failure is taken into account explicitly since the temperature rise in this case must not exceed a corresponding limit. The optimization is based on a detailed process model derived from first principles. A reduced model is developed for optimization and trajectories for the operational variables feed flowrate and reactor temperature are calculated. The results show that significant reductions of the batch time are possible and that their extent depend on the formulated safety constraints. For a selected case the obtained optimal trajectories are verified experimentally in laboratory and production scale.     

Modelling and simulation of semi-batch polymerisation reactor for improved reactants dosing control

This paper presents a temperature model of an industrial, semi-batch, emulsion-polymerisation reactor, which together with the already designed chemical reactions model is able to predict the temperature in the reactor as a result of varying operating conditions. The model was derived from the energy balance equations and validated on real-plant data. The model was used to analyse the influence of reactants dosing during the batch on the reactor temperature. The analysis shows that during the batch dosing of the two reactants, initiator and monomer, needs to be mutually balanced and adjusted to the current process situation, otherwise, the temperature in the reactor may become oscillatory and unstable towards the end of the batch because of the limited heat removal capacity of the condenser. To keep the reactor temperature in a narrow region also the control strategy was proposed that adjusts the monomer flow and initiator addition, using reactor temperature as a controlled variable. Simulation results show that the proposed reactants dosing control significantly reduces the variations in the reactor temperature and at the same time results in more uniform final batch results.     

Design and control of an ethyl acetate process: coupled reactor/column configuration

In this paper, design and control of a realistic coupled reactor/column process to produce ethyl acetate is studied. The process design is more complicated because the ethyl acetate product is neither the lightest nor the heaviest component in the system. A search procedure is proposed to obtain the optimum process design and operating condition of this process. The optimum process design is the one that minimize the Total Annual Cost (TAC) of this process while satisfying the stringent product impurity specifications. The optimum overall process design includes a continuous-stirred tank reactor (CSTR) coupled with a rectifier, a decanter, another stripper, and a recycle stream. After the process design is established, the next step is to use dynamic simulation to test the appropriate control strategy for this process. Sensitivity analysis is performed to obtain the suitable temperature control points for the columns. The proposed control strategy is very simple containing only one temperature control loop in each column. This recommended simpler control strategy uses the ratio of acetic acid feed rate to ethanol feed rate to control the 5th stage temperature of the rectifier and uses the stripper reboiler duty to control the 5th stage temperature of the stripper. The proposed control strategy does not need any on-line composition measurements and can properly hold product purity in spite of feed flow rate and feed composition disturbances. For small deviations of the product impurity compositions during disturbances, a slow cascade outer composition loop structure can be implemented using off-line composition measurements from the quality lab.     

精馏塔多通道对角矩阵解耦控制仿真

在化工生产中,许多单元操作的控制涉及至少2个被控变量,因此产生至少2个以上的控制回路。在该类具有多个控制回路的多变量控制系统中,同一被控对象上的多个控制回路,在实现其各自的控制目标时,将发生相互作用和相互影响。精馏塔是化工等行业中广泛使用的高耗能分离设备,为满足工艺要求和节能,需将塔顶和塔底产品流控制在设计值,即双成分控制。通常,利用回流量和加热量作操纵变量分别控制塔顶和塔底产品的组成。不过,回流量的变化也会影响塔底产品的组成,加热量的改变也会影响塔顶产品的组成。当采用温度作为反映产品组成的间接指标时,塔顶和塔底温度控制回路具有强烈的耦合作用,会导致系统不稳定。一个简单有效的方法就是解出耦合,因此,本文先介绍了一种基于对角矩阵的温度解耦控制方案,并在MATLAB/Simulink平台进行了控制仿真。结果显示:与两个独立PID回路控制相比,对角矩阵解耦控制不仅能达到更优的控制效果,还具有极强的对象特性鲁棒性。     

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.     

Plant-wide design and control of acetic acid dehydration system via heterogeneous azeotropic distillation and divided wall distillation

Energy-saving plant-wide design and plant-wide control of an acetic acid dehydration system with the feed containing methyl acetate and p-xylene are investigated in the study. A heterogeneous azeotropic distillation using isobutyl acetate as an entrainer is designed to obtain high-purity acetic acid at the column bottom and to keep a small acetic acid loss through the top aqueous draw. The accumulation of p-xylene in the column is avoided by adding a side product stream. The mixture in the aqueous phase of decanter, containing mostly water, methyl acetate, and isobutyl acetate is separated using a divided wall distillation column. The whole acetic acid dehydration system includes a heterogeneous azeotropic distillation column and a divided wall distillation column.The control strategies using temperature loops are proposed for this acetic acid dehydration system. For the heterogeneous azeotropic distillation column, the requirements for acetic acid compositions in both the aqueous phase of the decanter and the column bottom can be satisfied by designing entrainer inventory temperature control and cascade temperature control simultaneously. The stages of controlled temperatures are chosen by singular value decomposition and closed-loop analysis methods based on the criteria of minimum entrainer makeup. For the divided wall distillation column, steady-state analysis methods are used for the selection of proper controlled and manipulated variables and the determination of their pairings. Dynamic simulation results demonstrate that the proposed plant-wide control strategy can maintain product purities and reject external disturbances in feed flow and composition changes as well as internal disturbances such as changes in liquid and vapor splits.     

Plant-wide hierarchical optimization and control of an industrial hydrocracking process

Hydrocracking is a crucial refinery process in which heavy hydrocarbons are converted to more valuable, low-molecular weight products. Hydrocracking plants operate with large throughputs and varying feedstocks. In addition the product specifications change due to varying economic and market conditions. In such a dynamic operating environment, the potential gains of real-time optimization (RTO) and control are quite high. At the same time, real-time optimization of hydrocracking plants is a challenging task. A complex network of reactions, which are difficult to characterize, takes place in the hydrocracker. The reactor effluent affects the operation of the fractionator downstream and the properties of the final products. In this paper, a lumped first-principles reactor model and an empirical fractionation model are used to predict the product distribution and properties on-line. Both models have been built and validated using industrial data. A cascaded model predictive control (MPC) structure is developed in order to operate both the reactor and fractionation column at maximum profit. In this cascade structure, reactor and fractionation units are controlled by local decentralized MPC controllers whose set-points are manipulated by a supervisory MPC controller. The coordinating action of the supervisory MPC controller accomplishes the transition between different optimum operating conditions and helps to reject disturbances without violating any constraints. Simulations illustrate the applicability of the proposed method on the industrial process.     

Inferential control system of distillation compositions using dynamic partial least squares regression

In order to control product compositions in a multicomponent distillation column, the distillate and bottom compositions are estimated from on-line measured process variables. In this paper, inferential models for estimating product compositions are constructed using dynamic Partial Least Squares (PLS) regression, on the basis of simulated time series data. It is found that the use of past measurements is effective for improving the accuracy of the estimation. The influence of selection of measurements and sampling intervals on the performance is also investigated. From the detailed dynamic simulation results, it is found that the cascade control system based on the proposed dynamic PLS model works much better than the usual tray temperature control system.     

Effect of interaction multiplicity on control system design for a MTBE reactive distillation column

The control strategy of a reactive distillation for synthesis of MTBE is investigated. Although steady state multiplicities occur in the column, a linear control is still possible since a controlled and manipulated variable-pairing scheme that exhibits a sufficiently large range of near linear relations can be found, if we operate at constant reflux ratio. Reboiler duty is used to control the temperature of a stage just below the reaction section and near the top of the stripping section. Stoichiometric balance is controlled by a feed ratio plus internal composition control scheme, using a control valve installed on the C4 feed-line as the manipulated variable. Such a scheme is capable of maintaining the desirable steady state that achieves high product purity and reactant conversion. However, a similar scheme that uses a control valve installed on the methanol feed-line as the manipulated variable shows severe oscillation. It is caused by multiplicity in the interaction between the temperature and stoichiometric control loops.     

A one-point quadrature eight-node brick element with hourglass control

An efficient and accurate eight-node brick element is developed for linear static and dynamic structural analyses. In the element formulation, one-point quadrature is used so that computational time is substantially reduced without adversely effecting the accuracy. Hourglass control is provided to suppress spurious modes, and the stabilization parameters which must be specified by users in many other one-point quadrature elements are not required. An effective procedure to eliminate volumetric and shear locking is also developed. Several examples are presented to demonstrate the performance of this element.     

Optimization of a catalytic reactor subject to temperature constraints

The optimal design for maximum yield of SO₃ in the oxidation of SO₂ over a commercial vanadium pentoxide catalyst is considered. The control variables are the wall heat flux and the reactor radius, both as functions of axial distance. The volume and length of the reactor are both specified, as well as the maximum radial-average temperature. The problem is attacked by a partial averaging technique, whereby the full set of state partial differential equations are integrated forward, but a set of ordinary functional-differential adjoint equations are integrated on the backward pass in order to determine the new estimate of the optimal control. It is found that the optimal design consists of two approximately constant-radius adiabatic sections separated by a small intercooler, which is fairly close to existing commercial designs.     

Optimal control of dilute acid pretreatment and enzymatic hydrolysis for processing lignocellulosic feedstock

Lignocellulosic feedstock is one of the potential renewable sources for producing ethanol for transportation. The process steps viz., acid pretreatment and enzymatic hydrolysis in bio-chemical process route are intended to produce fermentable sugars, which can be readily fermented for producing ethanol. However, the dilute acid pre-treatment and enzymatic hydrolysis process steps are found to be economically inefficient. The present work aims at optimizing these process steps for improving the process performance. Such optimization is expected to increase conversion, reduce energy or material requirement, thereby improving the economics. The kinetic models of acid pretreatment and enzymatic hydrolysis for lignocellulosic feedstock processing are adapted from literature. Subsequently, these kinetic models are augmented by associated mass and energy balances, to develop a batch reactor model and fed-batch reactor model for dilute acid pretreatment and enzymatic hydrolysis processes, respectively. Optimal control with Pontryagin's maximum principle has been implemented to determine the optimal time dependent profiles of heating and cooling fluid flow rates and operating temperatures for acid pretreatment and substrate feed rate profile for enzymatic hydrolysis to optimize the respective processes performance. Different objective functions such as maximizing concentration of desired product, minimizing the batch time, and maximizing profit have been considered. The simulation results yielded an increase of 6.7% and 8.8% in final concentration of desired product; 43% and 42.5% reduction in batch processing time for pretreatment and enzymatic hydrolysis processes, respectively. Finally, the simulation results have also provided optimal operating policies which have increased the profit of pretreatment by 124% and enzymatic hydrolysis by 150%, thereby improving the techno-economic feasibility for processing lignocellulosic feedstock.     

Optimal vibration control of piezolaminated smart beams by the maximum principle

Active control of a vibrating beam using piezoelectric patch actuators is considered. The specific structure to be studied is an Euler–Bernoulli beam with piezoelectric actuators bonded to the top and bottom surfaces of the beam. The equation of motion includes Heaviside functions and their derivatives due to finite size piezo patches which provide the control force to damp out vibrations. Optimal control theory is formulated with the objective function specified as a weighted quadratic functional of the dynamic responses of the beam which is to be minimized at a specified terminal time. The expenditure of the control forces is included in the objective function as a penalty term. The optimal control law is derived using a maximum principle developed by Sadek et al. [1]. The maximum principle involves a Hamiltonian expressed in terms of an adjoint variable with the state and adjoint variables linked by terminal conditions leading to a boundary-initial-terminal value problem. The explicit solution of the problem is developed using eigenfunction expansions of the state and adjoint variables. The numerical results are given to assess the effectiveness and the capabilities of piezo actuation to damp out the vibrations.     

一种间歇反应过程迭代动态规划方法

随着工业过程对降低产品成本、改进产品质量、满足安全要求和环境规范,间歇反应过程的优化变得越来越重要.本文因此给出了一种有效的基于随机选点的间歇反应过程迭代动态规划算法,并给出了算法实现的详细步骤,能够有效实现间歇反应过程中温度、浓度等变量的动态优化问题.所述的迭代动态规划算法通过调节分段数P和离散点数(N和M)可以有效的避免计算量激增的问题,具有稳定可靠、易寻找到全局最优解的优点.以典型的间歇反应动态优化问题作为实例进行了研究,并与国际上公开报道结果进行了详细的比较研究,结果表明了所述方法的可靠有效性.     

Online switching of entrainers for acetic acid dehydration by heterogeneous azeotropic distillation

Traditionally, a foreign chemical such as isobutyl acetate (IBA) is used as an entrainer in a heterogeneous azeotropic distillation (HAD) column to separate acetic acid (HAc) and water. However, the loss of this entrainer may contaminate the process of manufacturing terephthalic acid because of the recycle of product streams to an oxidation reactor and other parts of the process. In the study, use of p-xylene (PX), a component indigenous to the terephthalic acid process and already present in the feed to the HAc dehydration column, as the entrainer for the separation of HAc and water is investigated. Optimization results show that using the HAD process with PX as the entrainer not only overcomes the shortcomings of IBA as the entrainer but also requires less energy consumption. Moreover, we demonstrate that it is possible to dynamically transform the HAD column with IBA as the entrainer into the HAD column with PX as the entrainer, without the need of shutdown and startup. The key to successful implementation of such a dynamic transition is to maintain a proper PX inventory inside the HAD column. While simple sidedraw flow control can be used, it will create PX imbalance if there is a flow measurement bias. A temperature control scheme was found to accelerate such a transition and maintain HAc purities at their designed values.     

Trajectory tracking in batch processes using neural controllers

Optimal operation of batch processes usually involves closely following a pre-optimized batch trajectory, e.g., the temperature trajectory in an exothermic batch reactor. Controllers for trajectory tracking have previously been designed and tuned based on a physical or empirical plant model. In batch processes where it is difficult to build a sufficiently accurate model, it is attractive to tune a nonlinear parameterized controller directly on the plant data, provided the number of batch runs required for the iterative tuning remains acceptably low. In a recent work, the authors have proposed a tuning method that makes the best use of each plant run to rigorously calculate the correct gradient for the iterative tuning optimization. In this work, this method is applied to obtain a tuned neural-network controller for tracking the temperature trajectory in an exothermic batch reactor example taken from the literature. Results indicate the efficacy of the method for optimizing a neural controller without requiring an excessive number of batch runs for the trial-and-error iterations.