A wave propagation approach for reduced dynamic modeling of distillation columns: Optimization and control

Reduced models enable real-time optimization of large-scale processes. We propose a reduced model of distillation columns based on multicomponent nonlinear wave propagation (Kienle 2000). We use a nonlinear wave equation in dynamic mass and energy balances. We thus combine the ideas of compartment modeling and wave propagation. In contrast to existing reduced column models based on nonlinear wave propagation, our model deploys a hydraulic correlation. This enables the column holdup to change as load varies. The model parameters can be estimated solely based on steady-state data. The new transient wave propagation model can be used as a controller model for flexible process operation including load changes. To demonstrate this, we implement full-order and reduced dynamic models of an air separation process and multi-component distillation column in Modelica. We use the open-source framework DyOS for the dynamic optimizations and an Extended Kalman Filter for state estimation. We apply the reduced model in-silico in open-loop forward simulations as well as in several open- and closed-loop optimization and control case studies, and analyze the resulting computational speed-up compared to using full-order stage-by-stage column models. The first case study deals with tracking control of a single air separation distillation column, whereas the second one addresses economic model predictive control of an entire air separation process. The reduced model is able to adequately capture the transient column behavior. Compared to the full-order model, the reduced model achieves highly accurate profiles for the manipulated variables, while the optimizations with the reduced model are significantly faster, achieving more than 95% CPU time reduction in the closed-loop simulation and more than 96% in the open-loop optimizations. This enables the real-time capability of the reduced model in process optimization and control.     

Actuator fault monitoring and fault tolerant control in distillation columns

This paper presents, from a practical viewpoint, an investigation of real-time actuator fault detection, propagation and accommodation in distillation columns. Addressing faults in industrial processes, coupled with the growing demand for higher performance, improved safety and reliability necessitates implementation of less complex alternative control strategies in the events of malfunctions in actuators, sensors and or other system components. This work demonstrates frugality in the design and implementation of fault tolerant control system by integrating fault detection and diagnosis techniques with simple active restructurable feedback controllers and with backup feedback signals and switchable reference points to accommodate actuator fault in distillation columns based on a priori assessed control structures. A multivariate statistical process monitoring based fault detection and diagnosis technique through dynamic principal components analysis is integrated with one-point control or alternative control structure for prompt and effective fault detection, isolation and accommodation. The work also investigates effects of disturbances on fault propagation and detection. Specifically, the reflux and vapor boil-up control strategy used for a binary distillation column during normal operation is switched to one point control of the more valued product by utilizing the remaining healthy actuator. The proposed approach was implemented on two distillation processes: a simulated methanol-water separation column and the benchmark Shell standard heavy oil fractionation process to assess its effectiveness.     

基于塔板组成线的反应精馏图解设计

图解设计法,可以相对较少的已知数据快速、直观地获得反应精馏塔的结构和操作参数。本文在转换组成变量的基础上,系统地推导了反应精馏塔板组成线方程及设计可行性判据,提出了基于塔板组成线进行反应精馏图解设计的策略,并对理想反应体系进行了实例设计计算。研究结果表明：利用塔板组成线进行反应精馏设计可同时获得多组可行设计方案,比现有精馏线和剩余曲线设计方法更为有效,并有利于设计的优化和经济效益评价。     

数字DC/DC开关电源环路补偿器设计

建立了数字控制DC/DC开关电源闭环系统的s域小信号模型,采用数字重设计法针对给定的系统参数设计了数字补偿器。应用SISO Design Tool仿真平台,在伯德图分析和根轨迹法的基础上设计了连续域的模拟补偿器,并进行了离散化处理。在建立系统s域模型时引入了模数转换器和数字脉宽调制发生器产生的延迟效应,使补偿器的设计考虑了采样速率对系统的影响,改善了传统离散设计的误差。基于数字重设计法构建的数字补偿器实现了对脉宽调制信号的可编程精确控制,保证了变换器闭环工作良好的动态特性。仿真实验结果验证了所设计的数字补偿器的性能。     

Indirect adaptive structure for multivariable neural identification and control of a pilot distillation plant

This paper describes the design and implementation of an indirect adaptive controller that uses neural networks both for identification and control of an experimental pilot distillation column containing a mixture of ethanol and water. The MATLAB platform is applied both for the neural identification and control of the distillation plant using the Levenberg–Marquardt approach, enabling also optimal input/output net configuration. The neural controller performance has been analyzed and illustrated via experimental tests on the pilot distillation column monitored under the LabVIEW platform. Both platforms have been linked together by constituting an integrated process control interface. The obtained experimental results demonstrate the effectiveness of the neural indirect adaptive control scheme as compared to proportional–integrative–derivative, when real-time multivariable control is demanded, even in presence of disturbances.     

Linear controller design and performance limits of binary distillation column subject to disturbances with bounds on magnitudes and rates of change

In this paper, we present an application of linear controller design via convex optimization to a binary distillation column and determine its limits of performance. Disturbances of distillation process are characterized as input signals with bounded magnitudes and rates of change. Performance measures of top and bottom control loops are defined as the maximum deviation magnitudes of top and bottom compositions, respectively. This performance is often referred to as the worst-case norm of convolution systems under such disturbances. The convex optimization and the ellipsoid algorithm are applied to design linear controllers and, at the same time, determine the best achievable performance of the closed-loop system. Then, a series of convex optimization problems are efficiently solved to give a trade-off curve representing limits of performance between the top and bottom compositions. The trade-off curve provides a practical insight into the design specification that cannot be achieved for the distillation column control with dynamic controller configuration. To confirm the results, we undertake computer simulation using nonlinear dynamical model of the distillation column. Closed-loop responses of the chosen optimal linear controller are consistent with the trade-off curve and yields superior performance than that of a conventional decentralized PI controller.     

Multivariable control of double-effect distillation configurations

Heat-integrated double effect distillation column design is promising from the viewpoint of energy conservation. However, the control of the system is very difficult in the sense that the system is nonlinear, multivariable and interacting. A new model-based control scheme developed by Han and Park (AIChE J. 1993, 39 (5), 787) to deal with these difficulties has been applied to these heat-integrated distillation configurations (feed-split configuration, heavy-split configuration). Our simulation results indicate that the control scheme is able to overcome the severity of interactions and shows good control performance for a heat integrated double-effect distillation column with high purity specification.     

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.     

Control structure selection for energy integrated distillation column

This paper treats a case study on control structure selection for an almost binary distillation column. The column is energy integrated with a heat pump in order to transfer heat from the condenser to the reboiler. This integrated plant configuration renders the possible control structures somewhat different from what is usual for binary distillation columns. Further the heat pump enables disturbances to propagate faster through the system. The plant has six possible actuators of which three must be used to stabilize the system. Hereby three actuators are left for product purity control. An MILP screening method based on a linear state space model is used to determine economically optimal sets of controlled and manipulated variables. The generated sets of inputs and outputs are analysed with frequency dependent relative gain array (RGA), relative disturbance gain (RDG) and condition number (CN) to determine the best structure in terms disturbance rejection and setpoint tracking. The pairing and controller design are implemented and evaluated through nonlinear simulation. The suggested control structure is also qualitatively compared to a control structure applied experimentally.     

Case studies on closed-loop identification for MPC

In this work we study multivariable and closed-loop identification of industrial processes for use in model predictive control. The advantages of closed-loop identification are discussed and related problems of identification are outlined. Subsequently, two case studies are used to demonstrate the advantages of closed-loop identification. The first process is a simulated high purity distillation column; the second process is a deethanizer of an industrial scale ethylene unit.     

Two-point control of a reactive distillation column for composition and conversion

Reactive distillation is a hybrid process with dual process objectives: reactant conversion and product composition. Control schemes for reactive distillation frequently neglect the effect of the principal operating parameters on the reactant conversion, and this has a detrimental effect on the overall process profitability. An ETBE reactive distillation column has been used as a case study to show how a two-point control configuration, which recognises the importance of both composition and conversion, can be developed and implemented for a reactive distillation process. The combined composition and conversion control configuration was tested using SpeedUp dynamic simulations and proved to be effective in maintaining a high isobutylene conversion despite process disturbances. The two-point control scheme also had superior disturbance rejection capability, especially for feed rate changes, and composition set-point sensitivity compared with a one-point control scheme.     

软测量技术在DeltaV DCS上的实现和应用

针对丁二烯生产装置精馏塔塔顶控制回路存在的问题,建立了软测量模型,并设计了串级推断控制回路。利用从集散控制系统采集的大量现场数据,运用基于多元线性回归方法的软测量建模技术,建立了塔顶中丁二烯产品纯度的软测量模型,实现了产品质量闭环控制。通过DeltaV DCS系统实现控制回路的改造。实际使用证明,该软测量模型具有良好的特性,较高的估计精度和实时性;塔的控制更加平稳,节约了能耗,具有较好的经济效益。     

A tuning strategy for multivariable PI and PID controllers using differential evolution combined with chaotic Zaslavskii map

A technique for tuning of decoupled proportional-integral (PI) and proportional-integral-derivative (PID) multivariable controllers based on a chaotic differential evolution (DE) approach is presented in this paper. Due to the simple concept, easy implementation and quick convergence, nowadays DE has gained much attention and wide application in solving continuous non-linear optimization problems. However, the performance of DE greatly depends on its control parameters and it often suffers from being trapped in local optimum. The application of chaotic sequences based on chaotic Zaslavskii map instead of random sequences in DE is a powerful strategy to diversify the population and improve the DE’s performance in preventing premature convergence to local optima. The optimized PD and PID controllers shows good closed-loop responses in control of the binary Wood–Berry distillation column, a multivariable process with strong interactions between input and output pairs. Some comparison results of PD and PID tuning using chaotic DE, classical DE and genetic algorithm are presented and discussed.     

Globally convergent multivariable adaptive decoupling controller and its application to a binary distillation column

This paper describes a new multivariable adaptive decoupling controller combining a decoupling compensator with a generalized minimum variance technique. The controller can completely decouple closed-loop systems both dynamically and in the steady state. It can control an unstable and/or non-minimum phase system and it can control the process with an arbitrary time delay structure. The proof of global convergence for the algorithm is also given. Successful experimental results of the adaptive decoupling control for a pilot-scale binary distillation column demonstrate the effectiveness of the proposed adaptive decoupling algorithm.     

Nonlinear model predictive control of a reactive distillation column

This paper considers the application of nonlinear model predictive control (NLMPC) to a highly nonlinear reactive distillation column. NLMPC was applied as a nonlinear programming problem using orthogonal collocation on finite elements to approximate the ODEs that constitute the model equations for the reactive distillation column. Diagonal PI controls were used to identify that the [L/D,V] and the [L/D,V/B] configurations performed best. NLMPC was applied using the [L/D,V] configuration and found to provide a factor of 2–3 better performance than the corresponding PI controller. The effect of process/model mismatch on the performance of the NLMPC controller was also evaluated.     

Dynamics and control of totally refluxed reactive distillation columns

According to the mechanism of the reaction operation involved, reactive distillation columns are often designed to work in a totally refluxed operation mode. The totally refluxed operation mode makes the reflux drum interact solely with the reaction operation involved and retards considerably the dynamics of the latter. The resultant great difference in process dynamics between the reaction operation and the separation operation involved leads frequently to under-damped responses with the degree of under-dampness closely dependent on the inventory control of the reflux drum. With the tight inventory control of the reflux drum, the degree of under-dampness can be suppressed and this presents a favorable effect to process dynamics and controllability of the totally refluxed reactive distillation columns. Two hypothetical ideal reactive distillation columns with and without a side reaction, respectively, and a high-purity ethylene glycol reactive distillation column are employed to examine the unique dynamics and controllability of the totally refluxed reactive distillation columns. The results obtained are in good accordance with the above interpretation. The current work reveals the general behaviors of the totally refluxed reactive distillation columns and can be particularly useful in control system synthesis and design.     

Fault-tolerant control of a polyethylene reactor

This work focuses on fault-tolerant control of a gas phase polyethylene reactor. Initially, a family of candidate control configurations, characterized by different manipulated inputs, is identified. For each control configuration, a bounded nonlinear feedback controller, that enforces asymptotic closed-loop stability in the presence of constraints, is designed, and the constrained stability region associated with it is explicitly characterized using Lyapunov-based tools. Next, a fault-detection filter is designed to detect the occurrence of a fault in the control actuator by observing the deviation of the process states from the expected closed-loop behavior. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed-loop stability in the event of control system faults. Closed-loop system simulations demonstrate the effectiveness of the fault-tolerant control strategy.     

Plant and controller reduction problems for closed-loop performance

Model reduction problems which consider preserving closed-loop performance (H₂, H_∞, and μ) in the presence of reduction error are developed. These are formulated as weighted multiplicative error problems (for plant reduction) and weighted additive error problems (for controller reduction), with the weight function incorporating explicitly such control information as the desired sensitivity operator bound, the setpoint/disturbance spectrum, and the plant uncertainties. These problems are efficiently solved using the frequency-weighted balanced realization technique. The benefits of these reduction problems are illustrated with examples taken from the control of a binary distillation column     

Reduced order bilinear models for distillation columns

The distillation columns are considered as compartmental systems. Because the inputs act linearly upon the transports matter flows, it is possible to include this type of system in the class of bilinear systems. By considering as output the distillate concentration of one of the products contained in the distilled mixture, the distillation column can be assimilated to a compartmental system with three compartments each of them replacing a set of distillation plates. These considerations finally permit a characterization of a distillation column by a minimal bilinear model having only three state variables and eight structural parameters. An identification algorithm permitting the identification of such a reduced order bilinear model is presented and is based on the minimization of the output error. Simulation results obtained by using as reference a complete non-linear model of a distillation column are presented. These results illustrate the validity of the approach proposed as well as the performance of the identification method. The reduced order bilinear model obtained is robust and valid for large variations of the inputs and of the working points. The use of the resulting bilinear model for control purposes is discussed.     

考虑间壁换热的间壁塔模型的模拟仿真研究

精馏是化工生产过程中应用最广泛的分离技术。间壁塔作为一个完全热耦合精馏塔,与传统两塔精馏序列相比,不仅可以减少设备投资,减少占地面积,还能节约精馏过程中的能耗。以环己烷-环庚烷-环辛烷的分离为研究对象,建立间壁塔和传统两精馏序列的模型,分析间壁塔的间壁传热对总能耗的影响,对新工艺(间壁塔分离工艺)和旧工艺(传统两塔精馏序列分离工艺)进行仿真和优化研究。通过优化计算,在满足产品纯度要求前提下,得到了两工艺的最优工艺操作条件。比较两种工艺的塔板数和能耗,间壁塔工艺在节约成本的同时节能17.9%。