High-purity Distillation Column Research Articles

Measurement selection for on-line estimation of nonlinear wave models for high purity distillation columns

Nonlinear wave models are commonly used to provide a reduced-order description of distillation column dynamics. Due to the simplified model structure, on-line parameter estimation is typically required for satisfactory prediction of column performance. In this paper an approach for selecting stage composition/temperature measurements for on-line estimation of wave model parameters is presented. We focus on high purity distillation columns which are particularly challenging due to the presence of highly pinched composition profiles. The proposed method provides a compromise between two competing effects, the sensitivity of stage composition predictions to model parameters and collinearities between these sensitivities. An iterative calculation procedure based on a scaled sensitivity matrix yields a ranking of the stage compositions according to their usefulness for parameter estimation. Two high purity column simulators are used to illustrate the measurement selection procedure and the subsequent design of nonlinear state/parameter estimators using the extended Kalman filtering approach. The proposed method is shown to be more flexible than a conventional measurement selection technique based on singular value decomposition.

CR-IDENT: A MATLAB TOOLBOX FOR MULTIVARIABLE CONTROL-RELEVANT SYSTEM IDENTIFICATION

This paper describes CR-IDENT, a Matlab-based toolbox that implements a comprehensive procedure for multivariable control-relevant system identification aimed primarily at process system applications. The toolbox consists of modules for multivariable input signal design (multisine and PRBS), frequency response estimation, and control-relevant frequency response curvefitting, leading to models whose end use is the design of high-performance control systems. An important component in the implementation of this design procedure is its reliance on a priori knowledge of the system of interest to design input signals meeting both theoretical and practical user requirements. Data from identification testing using these signals is the basis for the subsequent steps of frequency-response estimation and control-relevant parameter estimation, with the final result being a discrete-time state-space model that serves as the nominal model for Model Predictive Control. A high-purity distillation column example is presented to illustrate the benefits of the toolbox, from experiment design to closed-loop control.

A Simple Method for Modeling Process Asymmetry

Process asymmetry often introduces severe difficulties to process modeling and worsens control system performance. In this work, a simple modeling framework is proposed, which can effectively trade-off the difference between positive and negative process dynamics. It is characterized by small modeling effort in the consideration of process asymmetry. Modeling and control of a nonlinear high-purity ideal heat-integrated distillation column is conducted and the results obtained demonstrate the effectiveness of the modeling method proposed.

Compartmental modeling of high purity air separation columns

High purity distillation columns are critical unit operations in cryogenic air separation plants. The development of nonlinear control technology is motivated by the need to frequently change production rates in response to time varying utility costs. Detailed column models based on stage-by-stage balance equations are too complex to be incorporated directly into optimization-based strategies such as nonlinear model predictive control. In this paper, we develop reduced order dynamic models for the upper column of a cryogenic air separation plant by applying time scale arguments to a detailed stage-by-stage model that includes mass and energy balances and accounts for non-ideal vapor–liquid equilibrium. The column is divided into compartments according to the locations of liquid distributors and feed and withdrawal streams. The differential equations describing each compartment are placed in singularly perturbed form through the application of a physically based coordinate transformation. Application of singular perturbation theory yields a differential–algebraic equation model with significantly fewer differential variables than the original stage-by-stage model. A rigorous column simulator constructed using Aspen Dynamics (Aspen Technology) is used to access the tradeoff between reduced order model complexity and accuracy as the number of compartments is varied.

Dynamic compartmental modeling of nitrogen purification columns

The development of nonlinear control strategies for high purity distillation columns requires the availability of suitable nonlinear dynamic models. Relatively simple models are needed for the design of nonlinear model predictive controllers (NMPC) which are implemented on-line via repeated solution of a constrained nonlinear optimization problem. We utilize the compartmental modeling approach to construct control relevant dynamic models of a very high purity nitrogen purification column. Reduced-order nonlinear models are derived from a stage-by-stage balance model by partitioning the column into distinct compartments and applying time-scale arguments to convert most of the ordinary differential equations (ODE) describing each compartment into simpler algebraic equations. The compartmental models are dynamically simulated using the differential–algebraic equation (DAE) solver available in MATLAB. The stage-by-stage and compartmental models are compared to a rigorous dynamic simulator constructed in Aspen Dynamics to assess the merits of the proposed modeling strategy with regard to prediction accuracy and computational efficiency.

Effective Optimization for Fuzzy Model Predictive Control

This paper addresses the optimization in fuzzy model predictive control. When the prediction model is a nonlinear fuzzy model, nonconvex, time-consuming optimization is necessary, with no guarantee of finding an optimal solution. A possible way around this problem is to linearize the fuzzy model at the current operating point and use linear predictive control (i.e., quadratic programming). For long-range predictive control, however, the influence of the linearization error may significantly deteriorate the performance. In our approach, this is remedied by linearizing the fuzzy model along the predicted input and output trajectories. One can further improve the model prediction by iteratively applying the optimized control sequence to the fuzzy model and linearizing along the so obtained simulated trajectories. Four different methods for the construction of the optimization problem are proposed, making difference between the cases when a single linear model or a set of linear models are used. By choosing an appropriate method, the user can achieve a desired tradeoff between the control performance and the computational load. The proposed techniques have been tested and evaluated using two simulated industrial benchmarks: pH control in a continuous stirred tank reactor and a high-purity distillation column.

A Critical Comparison of Linear and Nonlinear Property Estimators in Inferential Control

In this paper, a comparison of linear and nonlinear estimators with particular emphasis to the closed-loop properties of the resulting inferential control scheme is presented. The concept of closed-loop “consistency” is introduced as an effective criterion for choosing the auxiliary variables. An estimator is consistent if it guarantees low closedloop steady-state offset in the true unmeasured controlled variables. By means of a case study of a high purity distillation column, a number of issues that can arise in inferential control are emphasized, and their implications on the closed-loop stability are discussed. It is shown that the use of some nonlinear estimators, which in general guarantee a superior precision, may be inappropriate because of the presence of zero gains and gain inversions that can lead the closed-loop system to instability. Moreover, in multi-input multi-output (MIMO) systems it is possible that the estimator requires the auxiliary variables to reach values that are not reachable by the actual plant.

Dynamic Precompensation and Output Feedback Control of Integrated Process Networks

In integrated process networks, the presence of large recycle flow rates induces a time scale separation where the individual units evolve in a fast time scale while the overall network evolves in a slow time scale. The slow dynamics of such networks is modeled by a high-index differential−algebraic equation (DAE) system which, in the case of cascaded control configurations, has a control-dependent state space. In this paper, a minimal-order dynamic extension is proposed to obtain a modified DAE system of index 2 with a control-independent state space that can be subsequently used as the basis for output feedback controller design. The application of this method is illustrated for a reactor−condenser network and for a two-point control problem in a high-purity distillation column.

Continuous‐time Hammerstein nonlinear modeling applied to distillation

Nonlinear dynamic predictive models are essential for opti-mal operation and control of many processes. This work pre-sents the predictive modeling of a simulated high purity distil-lation column using a continuous-time block-orientedmodeling methodology developed by Rollins et al. (1998). Theproposedmethodologyisbasedonaclosed-formexactsolutionto Hammerstein structure and, hence, referred to as the Ham-mersteinBlock-orientedExactSolutionTechniqueor H-BEST.The Hammerstein structure consists of a nonlinear static gainfunction that feeds a linear dynamic function. Thus, inputvector

Input design for model order determination in subspace identification

AbstractSubspace identification methods require that the inputs to the process being identified be persistently exciting. This may be inadequate for subspace identification of ill‐conditioned multivariable processes, because the process model order may be underestimated, leading to subsequent identification of poor models. To remedy the problem, it is proposed that inputs must be used that excite a process to be identified in a way that produces as uncorrelated process outputs as possible. This can be accomplished either in open or in closed‐loop fashion. Simulations on a high‐purity distillation column and on a heat exchanger illustrate the merit of the proposed approach.

Nonlinear Model Reduction and Control for High-Purity Distillation Columns

This article considers high-purity distillation columns with large recycle (and thus internal) flow rates. A singular perturbation analysis is employed to document a well-known observation for such columns, namely, the existence of fast and slow dynamics associated with internal and external flows, respectively. A nonlinear low-order model of the slow column dynamics, suitable for analysis and nonlinear feedback controller synthesis, is also derived. A two-tiered controller design procedure, which incorporates such a nonlinear controller, is finally proposed, and its performance and robustness characteristics are evaluated through simulations.

Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations

Abstract Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented.

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.

OUTPUT FEEDBACK REGULARIZATION OF NON-LINEAR DAE SYSTEMS

This work considers non-linear differential algebraic equation (DAE) systems whose state space depends on the manipulated inputs. An ODE representation of such systems cannot be derived independently of the controller design. An output feedback compensator is derived, which results in a modified DAE system whose state space does not depend on the new inputs and can be used for output feedback controller synthesis. Its application is illustrated in the context of control of a high-purity distillation column.

Wiener model identification and predictive control for dual composition control of a distillation column

The benefits of using the Wiener model based identification and control methodology presented in this paper, compared to linear techniques, are demonstrated for dual composition control of a moderate–high purity distillation column simulation model. An identification experiment design is presented which enables one to identify both the low and high gain directions of the distillation column, properties which are important for control and hard to identify in a conventional identification experiment setup as is demonstrated in the paper. Data from the proposed experiment design is used for indirect closed-loop identification of both a linear and a Wiener model, which shows the ability of the Wiener model to approximate the nonlinearity of the distillation column much closer than the linear model can. The identified Wiener model is used in a MPC algorithm in which the nonlinearity of the Wiener model is transformed into a polytopic description. In this way a convex optimisation problem is retained while the effect of the nonlinearity on the input–output behaviour of the plant is still taken into account. The performance of the proposed Wiener MPC is compared with linear MPC based on the identified linear models, and with a Wiener MPC in which the nonlinearity of the Wiener model is removed from the control problem via an inversion, a popular way to handle Wiener models in a MPC framework. The simulations demonstrate that the proposed Wiener MPC outperforms the other MPC algorithms.

Profile position control of distillation columns based on a nonlinear wave model

A nonlinear wave model captures an essential dynamic chanctcristic of a variety of distillation columns. A profile position control strategy based on the non1inear wave model is proposed for the control of a variety of distillation colunms such as high purity distillation column, complex distillation configurations, batch distillation configurations and for the startup of the columns. In this paper, we are mainly concerned with the control of batch distillation without and with chemical reaction among them. The controller has been developed by incOIpOrating nonlinear wave model into the generic model control framework. An observer based on the nonlinear wave model is also proposed to determine the profile position. Tight control of profile position, which leads to fast stabilization of product compositions. has been achieved. Since the profile position control alone produces a slight offset from the desired product concentration, the composition/profile position cascade system has been used to remove the offset.

Sensor locations and noise reduction in high-purity batch distillation control loops

The influence of the sensor locations on the composition control of high-purity batch distillation columns has been investigated. Using concepts of the nonlinear control theory, an input-output linearizing controller was implemented to keep the distillate composition constant at a desired value by varying the reflux ratio. An Extended Kalman Filter was developed to estimate the compositions required in the control algorithm using temperature measurements. In the presence of measurement noise, the control performance depended greatly on the sensor locations. Placing the sensors further from the top stages reduced the detrimental effects of noise but increased the inference error. To achieve accurate composition control, both noise reduction and composition estimate accuracy should be considered in the selection of the sensor locations.

Development and Experimental Verification of a Time-optimal Startup Strategy for a High Purity Distillation Column

The aim of this study is the development and experimental verification of a time-optimal startup strategy for binary high purity distillation columns. Simulated annealing (SA) is chosen as the optimization tool. This direct stochastic search method offers the possibility of finding global optima.

Nonlinear Identification of High Purity Distillation Columns

Multivariate high purity distillation columns present a number of challenging problems for both system identification and control due to their nonlinear and ill-conditioned nature. In this paper, we discuss the problem of identifying a nonlinear Wiener model for high purity distillation columns for the purpose of control. We first argue that such a model must be developed by performing a multivariate experiment in closed-loop, which is in stark contrast with the current industrial practice of single-input multi-output open-loop experiments. We then discuss the related design issues (e.g. the design of input reference signal) and how they may be tackled. Finally we present some identification results based on data obtained from a simulation model under realistic disturbance condition.

Real-Time Optimization and Nonlinear Model Predictive Control of Processes Governed by Differential-Algebraic Equations

Optimization problems in chemical engineering often involve complex systems of nonlinear DAE as the model equations. The direct multiple shooting method has been known for a while as a fast off-line method for optimization problems in ODE and later in DAE. Some factors crucial for its fast performance are briefly reviewed. The direct multiple shooting approach has been successfully adapted to the specific requirements of real-time optimization. Special strategies have been developed to effectively minimize the on-line computational effort, in which the progress of the optimization iterations is nested with the progress of the process. They use precalculated information as far as possible (e.g. Hessians, gradients and QP presolves for iterated reference trajectories) to minimize response time in case of perturbations. In typical real-time problems they have proven much faster than fast off-line strategies. Compared with an optimal feedback control computable upper bounds for the loss of optimality can be established that are small in practice. Numerical results for the Nonlinear Model Predictive Control (NMPC) of a high-purity distillation column subject to parameter disturbances are presented. # 2002 Published by Elsevier Science Ltd.