Henrik Weisberg Andersen

Dynamics and identification of a binary distillation column

Abstract Recent work in the area of control design has shown that the degree of gain directionality has a significant impact in achievable robust performance. Thus, it is important to obtain process models which give a satisfactory description of gain directionality. In this paper a parametric identification algorithm is applied to a case study of binary distillation. When the actuators are perturbed simultaneously this approach yields models which give a satisfactory description of the high-and low-gain directions. However, a common practical approach for modeling of distillation columns is to perturb the inputs separately and then combine the models into an overall description of the plant dynamics. It is shown that this method might have the drawback that the obtained model yields a poor description of the low-gain direction in the distillation plant. This indicates that modelling of multivariable processes can be improved by application of multivariable identification algorithm.

Evaluating estimation of gain directionality: Part 1: Methodology

For multivariable systems the input-output gain depends on the directionality of the inputs. This is denoted gain directionality, and explicit bounds on the possible gain of a system are obtained from singular value decomposition. In order to obtain high performance of multivariable control schemes it is mandatory that the dynamic model describes the gain directionality with sufficient accuracy. Based on this we pose the questions: with what accuracy can the gain directionality be estimated for a given system? Given an identified model what is the quality of the estimate of the gain directionality? This leads to an analysis in which a model set is defined based on a linear reference model, a relative output uncertainty description and the experimental design. The experimental design may include feedback, i.e. closed-loop identification. The error in the estimate of the gain in a given direction is then formulated as an H∞-norm problem. Given this representation the uncertainty on the estimated gain can be obtained by the structured singular value.

Evaluating estimation of gain directionality: Part 2: A case study of binary distillation

Abstract The analysis method presented in part 1 of this paper is applied to case studies of binary distillation using the LV and DV control configurations. Based on this we conclude that insufficient estimation of the maximum and minimum process gains for multivariable systems, i.e. gain directionality, is caused by misalignment of inputs and outputs with the corresponding input and output singular vectors, together with a high condition number. This uncertainty has a significant impact on the achievable control performance of multivariable controllers designed from the identified model. For these classes of MIMO systems we show that the uncertainty in the estimate of gain directionality can be reduced by using multi-input perturbations or preferably closed-loop identification as opposed to single-input perturbations. In the case of closed-loop identification it is sufficient to use simple single-loop proportional control, designed from limited qualitative knowledge about the plant. For standard parametric identification commonly used model evaluation techniques, such as degrees of explanation and the quality of the estimated individual transfer functions, are compared to the methodology presented in part 1. As shown, these standard evaluation techniques cannot be used to conclude whether the gain directionality has been adequately estimated. However, using the proposed method tight bounds are obtained on the quality of the estimated gain directionality. Furthermore, we illustrate that the quality of the estimate of gain directionality has a strong impact on achievable control performance, i.e. a significant error in the estimate of the low-gain direction in the plant will cause significant deterioration of the control performance whenever control action is required in this direction. Thus, by using proper scaling of the plant inputs and outputs the method presented analyses the model quality with respect to the control problem at hand.

Controller adjustment for improved nominal performance and robustness—II. Robust geometric control of a distillation column

Abstract In Part I of this paper a general frequency domain method to adjust multivariable controllers with respect to both nominal performance and robustness are presented. In Part II this method is used to examine and improve the control of a binary distillation column. The selected control strategies are conventional PI control and geometric control. The PI controller is adjusted in order to obtain satisfactory robustness properties. The basic geometric controller is extended with feedback from state variables which do not alter the nominal disturbance rejection. Both constant gain feedback and integration are examined. The included control parameters are adjusted for improved nominal performance and for robustness. The major result is that the adjusted geometric controller has a robustness which equals that of the adjusted conventional PI controller. However, the nominal performance of the geometric controller is superior to that of conventional PI control. Thus we expect the adjusted geometric controller to have improved performance on a real column compared to that of conventional PI control.

Controller adjustment for improved nominal performance and robustness—I. A frequency domain approach

Abstract A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, minimum stability margin, steady-state sensitivity and maximum sensitivity to modelling errors. For a given control structure the parameters are found which minimize an objective function consisting of a weighted sum of deviations between desired and obtained values of these objectives.

Tuning of dual-composition distillation column control

Abstract A frequency domain approach is used to compare the nominal performance and robustness of dual-composition distillation column control tuned according to Ziegler—Nichols (ZN) and Biggest Log Modulus Tuning (BLT) for three binary distillation columns. The scope of this paper is to examine whether ZN and BLT design yield satisfactory control of distillation columns. Further, PI controllers are tuned according to a proposed multivariable frequency domain method. A result is that the ZN-tuned controllers yield an undesired overshoot and oscillation and poor stability robustness properties, whereas BLT tuning removes the overshoot and oscillation, but at the expense of a more sluggish response. It is concluded that, if a simple control design is to be used, the BLT method should be preferred compared to the ZN method. The frequency domain design approach presented yields a more proper trade off between oscillation, response time and stability robustness. However, this method is more complicated to use than the ZN and BLT methods. Moreover, it is shown that properly tuned diagonal PI controllers can provide performance and robustness properties which equal well-tuned PI controllers extended with decoupling. It is also illustrated how servo filtering can be used to yield a proper trade off between performance and high-frequency control effort. The properties of the different controllers are illustrated by transient simulations.

Discrete-time control of a binary distillation column

Abstract A discrete-time model a binary distillation column, obtained by parametric identification, is used for discrete-time control design. The design is performed by a discrete-time, multivariable frequency domain method in which the main idea is to trade-off nominal performance, control effort and robustness. The case study of binary distillation column control is used to illustrate the elements in the design approach. The process model used for control design is based on a multivariable parametric identification method and represents a type of model which is relevant from a practical point of view. In the first part of the case study a simple diagonal PI controller is designed and compared with a standard Ziegler—Nichols tuned controller. As shown the frequency domain design technique yields controller settings which significantly reduce the overshoot and oscillation which compared to ZN design. In this part of the case study the nominal disturbance rejection is improved by inclusion of feedback from internal tray concentrations and feedforward from disturbances in the feed-flow rate. This controller yields ideal nominal performance, i.e. the disturbances are decoupled from the product concentrations. In order to improve the setpoint tracking and robustness properties of this controller it is extended with PI feedback from the product concentrations and the control parameters are adjusted by means of the proposed frequency domain method. The resulting controller yields improved nominal disturbance rejection and equivalent robustness properties when compared to conventional diagonal PI control. This illustrates some main features in practical control design, i.e. the type of model used is of practical importance, the number of measurements included in the controller is adjusted in order to achieve the desired performance and the control parameters are tuned in order to trade-off no minal performance, control effort and robustness.

Robust Geometric Control of a Distillation Column

A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, minimum stability margin, steady-state sensitivity and maximum sensitivity to modelling errors. For a given control structure the parameters are found which minimize an objective function consisting of the weighted sum of deviations between desired and obtained values of these objectives. This method is used to examine and improve geometric control of a binary distillation column.