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.     

Identification of multi-model LPV models with two scheduling variables

In order to model complex industrial processes, this work studies the identification of linear parameter varying (LPV) models with two scheduling variables. The LPV model is parameterized as blended linear models, which is also called multi-model structure. Several weighting functions, linear, polynomial and Gaussian functions, are used and compared. The usefulness of the method is tested using a high purity distillation column model in a case study. The case study shows that a good fit of identification data is not enough to verify model quality and can even be misleading in nonlinear process identification; other measures related to process knowledge should be used in model validation. The case study also shows that commonly used LPV model based on parameter interpolation can fail for the high purity distillation column. Finally, several pitfalls in nonlinear process identification are pointed out.     

High-purity control of internal thermally coupled distillation columns based on nonlinear wave model

Internal thermally coupled distillation column (ITCDIC) is a frontier of energy saving distillation researches, which is a great improvement on conventional distillation column (CDIC). However its high degree thermal coupling makes the control design a bottleneck problem, where data-driven model leads to obvious mismatch with the real plant in the high-purity control processes, and a first-principle model which is comprised of complex mass balance relations and thermally coupled relations could not be directly used as control model for the bad online computing efficiency. In the present work, wave theory is extended to the control design of ITCDIC with variable molar flow rates, where a general nonlinear wave model of ITCDIC processes based on the profile trial function of the component concentration distribution is proposed firstly; combined with the thermally coupled relations, a novel wave model based generic model controller (WGMC) of ITCDIC processes is developed. The benzene-toluene system for ITCDIC is studied as illustration, where WGMC is compared with another generic model controller based on a data-driven model (TGMC) and an internal model controller (IMC). In the servo control and regulatory control, WGMC exhibits the greatest performances. Detailed research results confirm the efficiency of the proposed wave model and the advantage of the proposed WGMC control strategy.     

The nonlinear model-predictive control of a chemical plant using multiple neural networks

A combination of multiple neural networks (NNs) is selected and used to model nonlinear multi-input multi-output (MIMO) processes with time delays. An optimisation procedure for a nonlinear model-predictive control (MPC) algorithm based on this model is then developed. The proposed scheme has been applied and evaluated for two example problems, including the MPC of a multi-component distillation column.     

Reparametrized ARX models for predictive control of staged and packed bed distillation columns

This work is aimed at the development of reparametrized ARX type models for high dimensional and distributed parameter systems. To keep data length small while identifying a model with ARX structure, the feasibility of reparametrizing ARX models using the fractional order differential operators and orthonormal basis filters is explored. The identified noise model is further used for developing a novel observer based MPC scheme, which explicitly uses the identified unmeasured disturbance model for the future trajectory predictions. The efficacy of the proposed modeling technique and the MPC scheme is demonstrated by conducting (a) simulation studies on a staged distillation column and (b) experimental evaluations on a laboratory scale packed bed distillation column.     

Multi-variable nonlinear MPC of an ill-conditioned distillation column

A quasi-ARMAX modelling scheme is studied for the purpose of modelling and control of multi-variable ill-conditioned and nonlinear processes. A distillation column is used as a case-study. The modelling technique is in this paper extended for use in the multi-variable case. Also, the nonlinear directionality of the distillation column is analyzed and illustrated. The nonlinear MPC formulation with the quasi-ARMAX model used for prediction is studied for control of the distillation column at different operating regions.     

Adaptive dynamic matrix control of a distillation column with closed-loop online identification

This paper presents an online identification technique where a process is identified in terms of pseudo impulse response coefficients and subsequently used to update convolution type models to accommodate process-model mismatch. As an example, dynamic matrix control has been applied adaptively to control the top product composition of a distillation column for both servo and regulatory problems. The algorithm automatically detects a large step-like disturbance requiring fresh identification of the process and subsequently adapts the controller to the new model. Simulation studies using an analytical dynamic full order model of a distillation column demonstrated the usefulness of the adaptation scheme. Experimentation on a pilot scale distillation unit vindicated the simulation results.     

Nolinear model predictive control using Hammerstein models

Nonlinear models that are composed of a linear dynamic element in series with a nonlinear static element prove to be very attractive in describing the behaviour of many chemical processes. In this paper, a model predictive control scheme is proposed using the Hammerstein model structure. Two simulation examples, a pH neutralization process and a binary distillation column, are used to demonstrate the effectiveness of the method.     

Application of Wiener model predictive control (WMPC) to an industrial C2-splitter

Dual composition control of a high-purity distillation column is recognized as an industrially important, yet notoriously difficult control problem. It is proposed, however, that Wiener models, consisting of a linear dynamic element followed in series by a static nonlinear element, are ideal for representing this and several other nonlinear processes. They are relatively simple models requiring little more effort in development than a standard linear step response model, yet offer superior characterization of systems with highly nonlinear gains. Wiener models may be incorporated into MPC schemes in a unique way that effectively removes the nonlinearity from the control problem, preserving many of the favorable properties of linear MPC, especially in the analysis of stability. In this paper, Wiener model predictive control is applied to an industrial C2-splitter at the Orica Olefines plant with promising results.     

Nonlinear model-based control of a batch reactive distillation column

The inherent trade off between model accuracy and computational tractability for model-based control applications is addressed in this article by the development of reduced order nonlinear models. Traveling wave phenomena is used to develop low order models for multicomponent reactive distillation columns. A motivational example of batch esterification column is used to demonstrate the synthesis procedure. Tight control of the column is obtained with the use of reduced model in a model predictive control algorithm.     

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.     

A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study

Model-based control strategies are widely used for optimal operation of chemical processes to respond to the increasing performance demands in the chemical industry. Yet, obtaining accurate models to describe the inherently nonlinear, time-varying dynamics of chemical processes remains a challenge in most model-based control applications. This paper reviews data-driven, Linear Parameter-Varying (LPV) modeling approaches for process systems by exploring and comparing various identification methods on a high-purity distillation column case study. Several LPV identification methods that utilize input–output and series expansion model structures are explored. Two LPV identification perspectives are adopted: (i) the local approach, which corresponds to the interpolation of Linear Time-Invariant (LTI) models identified at different steady-state operating points of the system and (ii) the global approach, where a parametrized LPV model structure is identified directly using a global data set with varying operating points. For the local approach, various model interpolation schemes are studied under an Output Error (OE) noise setting, whereas in the global case, a polynomial parametrization based OE prediction error minimization approach, an Orthonormal Basis Functions (OBFs) based model estimator and a Least-Square Support Vector Machine (LS-SVM) based non-parametric approach are investigated. Through extensive simulation studies, the aforementioned LPV identification approaches are analyzed in terms of the attainable model accuracy and local frequency response behavior of the obtained models. Recommendations are provided to achieve adequate choice between the methods for a particular process system at hand.     

精馏过程动态机理模型建立

为了实现精馏过程的动态优化和先进控制,必须解决精确的动态数学模型的建立问题.本文介绍了精馏过程动态机理建模的方法,该模型的特点是考虑每块塔板温度、压力、汽相流量、液相流量、汽相浓度、液相浓度和持液量的动态特性,并且,利用正交配置方法离散模型方程,利用牛顿一拉夫逊方法解模型方程,研究结果表明该模型精度高,误差小于3%,适合于精馏过程的动态优化和先进控制策略研究.     

Supervisory multiple regime control

The objective of this work is to identify a control algorithm that is capable of handling nonlinear behaviour (operating point dependent) witnessed in most industrial processes. To this end, the proposed solution is that of a supervisory multiple model control scheme, SMMC. This work demonstrates that the multiple model methodology can be recast into a Supervisory approach, whereby the supervisor is employed as a selector. This selector (supervisor) identifies the appropriate local-controller from a fixed family set. Unlike other supervisory techniques a multiple model observer (MMO) is proposed for the selection mechanism. Switching between local-controllers is accomplished bumplessly through a multiple model bumpless transfer scheme. Consequently, producing a continuous control signal as the process transverses between different operating regimes. The key issue in this application is the unique interaction between the local-controllers and the supervisor. This interaction is necessary to ensure global stability is maintained at all times, especially during switching. In short, the SMMC scheme enables the implementation of linear control theory, which is well accepted in industry, to standard nonlinear processes. The SMMC approach warrants the control design to extend beyond normal operating conditions that breakdown when standard linear control techniques are applied. The above notion is applied to a pilot-scale binary distillation column. In this example the column's distinct operating points describe the nonlinear behaviour. The results illustrate that as the distillation column shifted between different operating points the SMMC self-regulates accordingly. This self-regulation ensures that global stability and performance are maintained at an optimum. The entire SMMC design was implemented within a PC Windows-NT environment that was interfaced to an industrial DCS system.     

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.     

Reduction of stable differential–algebraic equation systems via projections and system identification

Most large-scale process models derived from first principles are represented by nonlinear differential–algebraic equation (DAE) systems. Since such models are often computationally too expensive for real-time control, techniques for model reduction of these systems need to be investigated. However, models of DAE type have received little attention in the literature on nonlinear model reduction. In order to address this, a new technique for reducing nonlinear DAE systems is presented in this work. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feedforward neural network. This last property is important insofar as the reduced model does not require a DAE solver for its solution but system trajectories can instead be computed with regular ODE solvers. This technique is illustrated with a case study where responses of several different reduced-order models of a distillation column with 32 differential equations and 32 algebraic equations are compared.     

Optimal selection of sensors for state estimation in a reactive distillation process

The success of state estimation in a high dimensional system like multicomponent reactive distillation depends on the rigorous evaluation of the observability and appropriate selection of measurements that adequately characterize the process behavior. In this work, the dynamic state sensitive measurement information extracted from the nonlinear reactive distillation process is employed to configure the gramian covariance matrices which are then subjected to various scalar quantification measures to find the degree of observability in order to select the temperature sensors for state estimation in the process. These optimally configured process measurements are then incorporated in a process model based composition estimation scheme. The validity of the sensors that are selected by the gramian quantification measures are further ascertained through the evaluation of the estimator performance for various nonoptimal measurement combinations. The results on application to a metathesis reactive distillation column exhibit the usefulness of the empirical observability gramian based sensor selection strategy for inferential state estimation of reactive distillation process.     

A harmonic balance approach to robust neural control of MIMO nonlinear processes applied to a distillation column

Robust stability and performance are the two most basic features of feedback control process. The harmonic balance analysis based on the describing function technique enables to analyze the stability of limit cycles arising from a closed loop control process operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural network controller in series with a dynamic multivariable nonlinear plant under generic Lur’e configuration. The neural controller is replaced by its sinusoidal input describing function while a linearized model is derived to represent the nonlinear plant dynamics. The uncertainty induced by the high harmonics effect for the neural controller, together with the neglected nonlinear dynamics due to plant linearization are incorporated in the robustness analysis as structured norm bounded uncertainties. Stability and robustness conditions for the neural closed loop control system are discussed using the harmonic balance equation together with the structured singular values of the uncertainty. The application to a multivariable binary distillation column under feedback neurocontrol illustrates the usefulness of the robustness approach here developed to predict the absence of limit cycles, which of course is subject to the usual restrictions of the describing function method.     

Multi-output process identification

In model based control of multivariate processes, it has been common practice to identify a multi-input single-output (MISO) model for each output separately and then combine the individual models into a final MIMO model. If models for all outputs are independently parameterized then this approach is optimal. However, if there are common or correlated parameters among models for different output variables and/or correlated noise, then performing identification on all outputs simultaneously can lead to better and more robust models. In this paper, theoretical justifications for using multi-output identification for a multivariate process are presented and the potential benefits from using them are investigated via simulations on two process examples: a quality control example and an extractive distillation column. The identification of both the parsimonious transfer function models using multivariate prediction error methods, and of non-parsimonious finite impulse response (FIR) models using multivariate statistical regression methods such as partial least squares (PLS2), canonical correlation regression (CCR) and reduced rank regression (RRR) are considered. The multi-output identification results are compared to traditional single-output identification from several points of view: best predictions, closeness of the model to the true process, the precision of the identified models in frequency domain, stability robustness of the resulting model based control system, and multivariate control performance. The multi-output identification methods are shown to be superior to the single-output methods on the basis of almost all the criteria. Improvements in the prediction of individual outputs and in the closeness of the model to the true process are only marginal. The major benefits are in the stability and performance robustness of controllers based on the identified models. In this sense the multi-output identification methods are more ‘control relevant’.