Nonlinear model predictive control of biodiesel production via transesterification of used vegetable oils

The economic performance of an industrial scale semi-batch reactor for biodiesel production via transesterification of used vegetable oils is investigated by simulation using nonlinear model predictive control (NMPC) technology. The objective is to produce biodiesel compliant to the biodiesel standards at the minimum costs. A first-principle model is formulated to describe the dynamics of the reactor mixture temperature and composition. The feed oil and mixture composition are characterized using a pseudo-component approach, and the thermodynamic properties are estimated from group contribution methods. The dynamic model is used by the NMPC framework to predict the optimal control profiles, where a multiple shooting based dynamic optimization problem is solved at every sampling time. Simulation results with the economic performance of an industrial scale semi-batch reactor are presented for control configurations manipulating the methanol feed flow rate and the heat duty.     

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.     

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.     

Predictive functional control based on an adaptive fuzzy model of a hybrid semi-batch reactor

In this paper a new approach to the control of a nonlinear, time-varying process is proposed. It is based on a recursive version of the fuzzy identification method and predictive functional control. First, the recursive fuzzy identification method is derived, after which it is used in connection with fuzzy predictive functional control to construct an adaptive fuzzy predictive functional controller. The adaptive FPFC is then tested on a nonlinear, time-varying, semi-batch reactor process and compared with the standard FPFC, which uses non-adaptive fuzzy model. The simulation results are promising; they indicate that the control of time-varying, nonlinear processes with the FPFC can be improved with the use of an adaptive fuzzy model. An improvement in reference tracking and disturbance rejection can be observed, but the main advantage is the reduced number of switchings between hot and cold water. This is an important improvement in the case of real applications.     

Sensitivity compensating nonlinear control: Exact model based approach

A novel sensitivity compensating nonlinear control (SCNC) approach is proposed within generic model control (GMC) framework for processes exhibiting input sensitivity. The proposed approach consists of defining a new process, control law and set point such that the determined control action drives the original process to its desired set point. External reset feedback (ERF), used to compensate for input saturation, is extended to higher relative degree systems as extended ERF (EERF), and is incorporated in the context of SCNC approach. The proposed control algorithms are evaluated by application to an open-loop unstable CSTR control problem and a multi-product semi-batch polymerization reactor temperature control problem. The present study illustrates the versatility of the proposed SCGMC schemes compared to the basic GMC schemes in terms of output tracking and smoother input profiles. SCNC can be extended to other nonlinear model based controllers where the control law can be expressed analytically.     

Design of observer based nonlinear model predictive controller for a continuous stirred tank reactor

Model predictive control (MPC) schemes are now widely used in process industries for the control of key unit operations. Linear model predictive control (LMPC) schemes which make use of linear dynamic model for prediction, limit their applicability to a narrow range of operation (or) to systems which exhibit mildly nonlinear dynamics.

In this paper, a nonlinear observer based model predictive controller (NMPC) for nonlinear system has been proposed. An approach to design NMPC based on fuzzy Kalman filter (FKF) and augmented state fuzzy Kalman filter (ASFKF) has been presented. The efficacy of the proposed NMPC schemes have been demonstrated by conducting simulation studies on the continuous stirred tank reactor (CSTR). The analysis of the extensive dynamic simulation studies revealed that, the NMPC schemes formulated produces satisfactory performance for both servo and regulatory problems. Simulation results also include an inferential control case, where the reactor concentration is not measured but estimated from temperature measurement and used in the NMPC based on FKF and ASFKF formulations.     

LFT modelling and identification of anaerobic digestion

In this paper, a reduced order model of anaerobic digestion is first proposed, with the main goal to develop an efficient tool for process monitoring and control. Then, in order to perform parameter estimation, the model has been rewritten in a linear fractional transformation (LFT) formulation, using a symbolic tool originally developed for linear models and modified for the processing of nonlinear models. Two different test cases have been considered. In a first case, the data used for parameter identification have been generated by simulating the well known and more complex ADM1 model, considering waste activated sludge as substrate. In a second case, experimental data were collected on a laboratory scale equipment, operated in a semi-batch experiment, performing the anaerobic digestion of ultra-filtered cheese-whey.     

Optimal iterative learning control for end-point product qualities in semi-batch process based on neural network model

An optimal iterative learning control (ILC) strategy of improving endpoint products in semi-batch processes is presented by combining a neural network model. Control affine feed-forward neural network (CAFNN) is proposed to build a model of semi-batch process. The main advantage of CAFNN is to obtain analytically its gradient of endpoint products with respect to input. Therefore, an optimal ILC law with direct error feedback is obtained explicitly, and the convergence of tracking error can be analyzed theoretically. It has been proved that the tracking errors may converge to small values. The proposed modeling and control strategy is illustrated on a simulated isothermal semi-batch reactor, and the results show that the endpoint products can be improved gradually from batch to batch. Supported by the National Natural Science Foundation of China (Grant Nos. 60404012, 60874049), the National High-Tech Research & Development Program of China (Grant No. 2007AA041402), the New Star of Science and Technology of Beijing City (Grant No. 2006A62), and the IBM China Research Lab 2008 UR-Program     

Robust end-point optimizing feedback for nonlinear dynamic processes

The paper suggests two novel approaches to the synthesis of robust end-point optimizing feedback for nonlinear dynamic processes. Classically, end-point optimization is performed only for the nominal process model using optimal control methods, and the question of performance robustness to disturbances and model-plant mismatch remains unaddressed. The present contribution addresses the end-point optimization problem for nonlinear affine systems with fixed final time through robust optimal feedback methods. In the first approach, a nonlinear state feedback is derived that robustly optimizes the final process state. This solution is obtained through series expansion of the Hamilton-Jacobi-Bellman PDE with an active opponent disturbance. As reliable measurements or estimates of all states may not always be available, the second approach also robustly optimizes the process end-point, but uses output rather than state information. This direct use of measurement information is preferred since the choice of a state estimator for robust state feedback is non-trivial even when the observability issue is addressed. A linear time-variant output corrector is obtained by feedback parametrization and numerical optimization of a nonlinear H _∞ cost functional. A number of possible variations and alternatives to both approaches are also discussed. As model-plant mismatch is particularly common with chemical batch processes, the suitability of the robust optimizing feedback is demonstrated on a semi-batch reactor simulation example, where robustness to several realistic mismatches is investigated and the results are compared against those for the optimal open-loop policy and the optimal feedback designed for the nominal model.     

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.     

Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.     

Non-parametric confidence bounds for process performance monitoring charts

Statistical Process Control (SPC) provides a tool for achieving and maintaining product quality. In today's climate of major data monitoring campaigns there has been an increase in interest in the multivariate statistical projection techniques of principal components analysis and projection to latent structures for process performance monitoring. Within univariate SPC, techniques for identifying when a process is moving out of control are well established. Similar guidelines are required for multivariate statistical process control (MSPC). Two approaches will be discussed - Hotelling's T² statistic and a new approach, the M² statistic. Both approaches will be illustrated by application to a high pressure low density polyethylene tubular reactor and to a batch methyl methacrylate polymerisation reactor.     

Control of integrated processes: A case study on reactive distillation in a medium-scale pilot plant

This paper deals with the systematic design of a multivariable controller for a medium-scale reactive distillation column that is operated in semi-batch mode. This is a challenging problem because of the time-varying and strongly nonlinear dynamics of the process and considerable deviations of the behaviour of the real plant from the rigorous model used for process design. The design procedure consists of three steps: first, a suitable control structure that enables the operation of the column near the economically optimal operating point is determined based upon the rigorous nonlinear process model. In a second step, a linear model of the column is identified from experiments and used to compute the best attainable control performance for the chosen control structure. In this step, actuator limitations and model uncertainties described by confidence intervals that were obtained in the identification procedure are considered. In the third step, the resulting high-order controller is approximated by a low-order controller that gives nearly the same performance and preserves robust stability for the computed uncertainty bounds. The controller performance is demonstrated in a series of experiments that were performed at the real reactive distillation column.     

Fuzzy Predictive Functional Control in the State Space Domain

In the paper, a well-known predictive functional control strategy is extended to nonlinear processes. In our approach the predictive functional control is combined with a fuzzy model of the process and formulated in the state space domain. The prediction is based on a global linear model in the state space domain. The global linear model is obtained by the fuzzy model in Takagi–Sugeno form and actually represents a model with changeable parameters. A simulation of the system, which exhibits a strong nonlinear behaviour together with underdamped dynamics, has evaluated the proposed fuzzy predictive control. In the case of underdamped dynamics, the classical formulation of predictive functional control is no longer possible. That was the main reason to extend the algorithm into the state space domain. It has been shown that, in the case of nonlinear processes, the approach using the fuzzy predictive control gives very promising results.     

Robust iterative learning control of an exothermic semi-batch chemical reactor

This work focuses on the temperature control of a semi-batch chemical reactor used for flue chemicals production. Such reactor is equipped with a heating/cooling system composed of different thermal fluids. In order to ensure the tracking performance of the desired temperature profile, an iterative learning control (ILC) named batch model predictive control (BMPC) has been adopted. The synthesis of the considered strategy is illustrated and improvements of the algorithm scheme are proposed. Firstly, a guaranteed convergence of the algorithm is illustrated. Secondly, in presence of high frequency disturbance effects, an off-line filtering is adopted for enhancing the achieved performances. Third, a robust supervisory control procedure is employed to choose the right fluid and to reduce the superfluous fluid changeovers, mainly where fluids are of different nature. Finally, the incidence of repetitive disturbances, on line low frequency disturbances and model mismatch are investigated through simulation runs.     

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.     

重介质选煤过程模型与数据混合驱动的自适应运行反馈控制

重介质悬浮液密度是决定重介质选煤产品质量的重要影响因素,但由于重介质选煤运行过程是一个时变的强非线性过程,导致根据实时工况的变化在线调整重介质悬浮液密度异常困难.为此,本文针对重介质选煤过程特性,提出一种模型与数据混合驱动的自适应运行反馈控制方法,用于在线调整重介质悬浮液密度设定值.所提方法首先将重介质选煤过程分解为低阶线性模型和未建模动态非线性项两部分;进而针对线性部分,将PI控制与一步最优控制相结合,设计了模型驱动的自适应PI控制器;并利用随机向量函数链接网络设计了数据驱动的虚拟未建模动态补偿器;最后分析了闭环系统稳定性,并在基于MATLAB和Unity3D的虚拟现实仿真平台上进行了对比仿真实验,验证了所提方法的有效性.     

高速公路匝道非线性反馈控制器的设计与仿真

提出了一种非线性方法设计高速公路入口匝道反馈控制器,非线性反馈控制器由高速公路交通流模型和比例积分调节器组成。阐述了入口匝道控制原理,建立了高速公路交通流模型,模型的流量—密度关系是非线性的,设计了高速公路匝道非线性反馈控制器模型。仿真结果表明非线性反馈控制器性能优越,它能使高速公路主线交通流密度保持为设定的期望密度,同时又能维持可接受的匝道服务水平。     

LPV model development and control of a solution copolymerization reactor

In this paper, linear parameter-varying (LPV) control is considered for a solution copolymerization reactor, which takes into account the time-varying nature of the parameters of the process. The nonlinear model of the process is first converted to an exact LPV model representation in the state-space form that has a large number of scheduling variables and hence is not appropriate for control design purposes due to the complexity of the LPV control synthesis problem. To reduce such complexity, two approaches are proposed in this paper. First, an approximate LPV representation with only one scheduling variable is obtained by means of a parameter set mapping (PSM). The second approach is based on reformulating the nonlinear model so that it provides an LPV model with a fewer number of scheduling parameters but preserves the same input–output behavior. Moreover, in the implementation of the LPV controllers synthesized with the derived models, the unmeasurable scheduling variables are estimated by an extended Kalman filter. Simulation results using the nonlinear model of the copolymerization reactor are provided in order to illustrate the performance of the proposed controllers in reducing the convergence time and the control effort.     

工业流化床乙烯气相聚合中的在线测量与模型分析(I)

工业流化床乙烯气相聚合过程是一类典型的多变量复杂非线性系统。我们首先分析了若干主要过程变量(反应器温度等)对两个质量变量(树脂熔融指数和密度)的影响趋势，给出了两组变量间的非线性函数结构形式．然后运用多元统计投影原理和非线性函数的Taylor逼近原理建立了流化床乙烯气相聚合过程变量和质量变量之间的主元多项式非线性偏最小二乘软测量(Nonlinear PLS)模型，并对理论结果进行了推证。基于实际工业运行装置的采样数据对Nonlinear PLS模型进行了求取和验证，利用所求模型进行了树脂熔融指数和密度预测并将预测结果和误差分析结果与线性PLS及机理模型进行了比较。最后运用所建立的模型进行流化床乙烯气相聚合过程操作条件的模型预测分析.全文分为两部分，这是第一部分。