Using MPC to control middle-vessel continuous distillation columns

The use of model predictive control (MPC) in middle-vessel continuous distillation column (MVCC) is discussed. It is shown that using a 5 × 5 MPC implementation (where all levels are included in MPC as integral process variables) allows using a smaller middle-vessel, particularly when disturbances can be measured: a good performance is ensured without having the middle vessel drained or overfilled. Also, it is shown that MPC practically circumvents the issue of tuning the middle-vessel level controller. Furthermore, the MVCC design makes conventional decentralised control perform comparably to MPC.     

Optimal fuzzy control to reduce energy consumption in distillation columns

Distillation columns constitute a significant fraction of the capital invested in the refineries around the world; their control requires a major part of the total operating cost of chemical processes, if the used strategy is not adequate. This article presents the application of optimal fuzzy control to reduce the energy consumption of a Benzene-Toluene distillation column. This method is based on the determination of the specific values of the fuzzy controller parameters such that certain performance criterion is minimised. Results of a simulation study are presented showing the potential improvement offered by this method.Translated from Avtomatika i Telemekhanika, No. 2, 2005, pp. 36–45.Original Russian Text Copyright © 2005 by Bouyahiaoui, Grigoriev, Laaouad, Khelassi.     

A stable control structure for binary distillation columns

A Lyapunov-based controller for the composition control of binary distillation columns has been developed. It takes into account physical constraints on the inputs and ensures the global asymptotic stability of the closed-loop system with robustness to modelling errors and with the capability of performing set-point tracking and (approximate) disturbance rejection. This controller requires the knowledge of the internal state of the model and this leads to the design of an exponentially converging 'high-grain' observer. We arrive at the global asymptotic stability of the whole control structure (the controller+ the observer) by proving a somewhat general nonlinear separation principle.     

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.     

Multivariable control of ill-conditioned distillation columns utilizing process knowledge

In distillation, a reliable model of the column is generally considered as a prerequisite for the design of efficient two-product control by multivariable methods. However, such models are often very hard to obtain. In fact, even very small identification errors may introduce features which are in conflict with physical knowledge, and which make the model useless. Instead of focusing on the development of consistent models, this work is concerned with the utilization of physical process knowledge directly for multivariable control, even if a reliable input-output model is lacking. Such knowledge is, for example, the sign of the RGA-values and an estimate of the input-directionality. It is shown that such structural information of the process can form an entity of control-relevant knowledge that is sufficiently rich for the design of a multivariable SVD controller.     

Elementary nonlinear decoupling control of composition in binary distillation columns

Elementary nonlinear decoupling (END) is a model based control algorithm intended to decouple and linearize a nonlinear multivariable process in order to achieve better control than can be obtained by conventional decentralized linear feedback control. The application of END to the composition control of a theoretical binary distillation column illustrates that the quality achievable is very high.     

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.     

Reduced models and control of distillation columns with sharp temperature profiles

Distillation columns with sharp temperature profiles exhibit a characteristic dynamic behavior which is used in this correspondence to deduce a considerably simplified low-order dynamic model. Based on this model, linear state-space methods are employed in the design of the control of an extractive distillation column with a vapor side stream.     

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.     

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.     

Robust control of distillation columns: μ- vs H∞-synthesis

High-purity distillation columns are known to be difficult to control due to their ill-conditioned and non-linear behaviour. Two approaches for the design of robust controllers yielding high performance are presented. For the first approach, first principles are used to develop an uncertainty model describing the nonlinear dynamics within the entire operating range of an industrial distillation column. This structured uncertainty model is used for μ-synthesis. In a second approach which is based on loop shaping ideas, an H_∞-controller is designed. This controller performs as well as the μ-controller. The H_∞-approach offers the advantage that the burden for uncertainty modelling and computation is greatly reduced. However, the GS/T augmentation scheme, which is developed in this paper, must be used for the design of the H_∞-controller to avoid the inversion of the plant in the controller. The paper concludes with a comparison of the H_∞- and μ-synthesis methods.     

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.     

Application of predictive control techniques to a distillation column

Model-based predictive control techniques are widely recognized as having useful application to control problems characterized by complex dynamics and severe time delay. The establishment of a representative process model is the key step in the procedure and for anything other than trivially simple systems is a major hurdle. This paper describes the application of predictive control techniques to a distillation problem which embodies a pure time delay of 2–3 h and time constants of 3–4 h. A sampled-data process model is identified from monitored input/output data and from this a predictive control algorithm is designed. The application of the controller has resulted in very effective closed-loop control of the base composition of the distillation column, where previously only manual supervision was possible.     

A new approach to inversion-based feedforward control design for nonlinear systems

The finite-time transition between stationary setpoints of nonlinear SISO systems is considered as a scenario for the presentation of a new design approach for inversion-based feedforward control. Design techniques which are based on a stable system inversion result in input trajectories with pre- and/or post-actuation intervals. The presented approach treats the considered transition task as a two-point boundary value problem (BVP) and yields causal feedforward trajectories, which are constant outside the transition interval. The main idea of this approach is to provide free parameters in the desired output trajectory to solve the BVP of the internal dynamics. Thereby, a standard MATLAB function can be used for the numerical solution of the BVP. Feedforward control design techniques are illustrated by simulation results for a simple example.     

Correspondences between input estimation and feedforward control

A correspondence between input estimation (deconvolution) and feedforward is discussed from a polynomial point of view. Optimal estimation and feedforward control filters are derived from a spectral factorization and a polynomial equation. Simple loop transformations are used for transforming one problem into the other. The close relationship cannot be explained by the well-known duality between optimal state estimation and feedback control. Instead, it rests on the fact that both the problems discussed are open loop. They can be seen as two interpretations of one underlying design problem. Several other open-loop problems can be described in this framework.     

Generalized bang-bang control for feedforward constrained regulation

In the behavioral framework for continuous-time linear scalar systems, simple sufficient conditions for the solution of the minimum-time rest-to-rest feedforward constrained control problem are provided. The investigation of the time-optimal input-output pair reveals that the input or the output saturates on the assigned constraints at all times except for a set of zero measure. The resulting optimal input is composed of sequences of bang-bang functions and linear combinations of the modes associated to the zero dynamics. This signal behavior constitutes a generalized bang-bang control that can be fruitfully exploited for feedforward constrained regulation. Using discretization, an arbitrarily good approximation of the optimal generalized bang-bang control is found by solving a sequence of linear programming problems. Numerical examples are included.     

The feedforward control of linear multivariable time-invariant systems

Necessary and sufficient conditions are derived for a stable feedforward control system to exist for a multivariable linear time-invariant system so that: (1) any measurable disturbances occurring in the system are asymptotically rejected, and (2) the outputs of the system asymptotically become equal to preassigned functions of a given class of outputs. The result may be interpretated as being a generalization of the single-input, single-output feedforward servo problem to multivariable systems or as being a solution to the asymptotic decoupling problem. Some numerical examples varying from 2nd to 9th order are included to illustrate the result.     

Nonlinear control of feedforward systems with bounded signals

The stabilization problem for a class of nonlinear feedforward systems is solved using bounded control. It is shown that when the lower subsystem of the cascade is input-to-state stable and the upper subsystem not exponentially unstable, global asymptotic stability can be achieved via a simple static feedback having bounded amplitude that requires knowledge of the "upper" part of the state only. This is made possible by invoking the bounded real lemma and a generalization of the small gain theorem. Thus, stabilization is achieved with typical saturation functions, saturations of constant sign, or quantized control. Moreover, the problem of asymptotic stabilization of a stable linear system with bounded outputs is solved by means of dynamic feedback. Finally, a new class of stabilizing control laws for a chain of integrators with input saturation is proposed. Some robustness issues are also addressed and the theory is illustrated with examples on the stabilization of physical systems.     

Neural control of a batch distillation

The purpose of the work reported here was to investigate the application of neural control to a common industrial process. The chosen problem was the control of a batch distillation. In the first phase towards deployment, a complex software simulation of the process was controlled. Initially, the plant was modelled with a neural emulator. The neural emulator was used to train a neural controller using the back propagation through time algorithm. A high accuracy was achieved with the emulator after a large number of training epochs. The controller converged more rapidly, but its performance varied more widely over its operating range. However, the controlled system was relatively robust to changes in ambient conditions.     

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.