(434h) Low-Hanging Fruit in High-Purity Distillation Control

It has been estimated that distillation stands for up to 10-15% of the world's energy consumption. Improved control of distillation columns can reduce the amount of energy needed to operate the column and bring huge savings. Sometimes model-based control, like Model-Predictive Control (MPC) is used to improve control, but it comes with a rather high cost of installation and maintenance. On the other hand, simple extensions to elementary PI control can also bring improvements, with a lower degree of complexity, and lower cost of installation and maintenance. The purpose of this presentation is to draw attention to some low-hanging fruit concepts, i.e. distillation control concepts with maximal improvement compared to installation and maintenance costs.

The dynamics of distillation columns is well known for its complexity. Distillation columns are ill-conditioned systems, which makes them difficult to control. They also demonstrate directionality, i.e. we get different speeds of responses in different directions [4]. Different speed in different directions means that at least a second order model is needed for a 2x2 system, and the high number of parameters makes it difficult to identify a good dynamic process model [7].

In this presentation we consider two simple extensions of PI control, namely 1) static decoupling and 2) SVD control, which can be considered as a static input/output decoupling concept [5]. Static decoupling has not traditionally been recommended for high-purity distillation, but these recommendations were made on experiments that failed because the decouplers were designed on models that did not consider the directionality of distillation [8]. With a good model, which accurately models the different speeds in different gain directions, it is straightforward to design static decouplers also for high-purity distillation control [3].

When Copernicus modeled the solar system, all attention was on the fact that Earth was a planet among others, orbiting the Sun [1]. Now 500 year later it is time to credit the modeling concept itself, namely the brilliant idea that uses coordinate system's transformations as a part of the model, and simple models in the target coordinate system. Despite very simple models, which basically included the planet's orbital period and distance to sun, Copernicus was able to accurately predict the planet's future positions. It turns out that this modeling approach is well suited also for modeling and identification of ill-conditioned processes, including distillation columns. If we assume that ill-conditioned processes are built from independent phenomena, we can model the process in phenomena coordinates, usually with first-order dynamics without interaction, and use rotation matrices as interfaces between inputs/outputs and phenomena. This approach can be seen as a generalization of the well known ”Mixing Tank Model'' of distillation columns [4, p 1857]. For distillation, the suggested modeling concept means that we identify a gain and a "dominant time constant" to describe mass transfer phenomenon, and a smaller gain and a smaller "internal time constant" to describe the impact on concentration due to mixing.

The advantages when distillation columns are modeled in "column coordinates”' are that we can considerably simplify the models (in terms of number of parameters and state variables), and that the identification is done in directions important for control [2]. The resulting model is called the SVD model, because it uses the same input/output rotation matrices as we obtain with singular-value decomposition. The SVD model is identified in two steps: first we identify the coordinate transformations (two static rotation matrices) and after that we do the actual identification experiments, which identify the phenomena using simple ARX models with least-squares regression. A practical advantage is that model fit in the transformed coordinates much better describe model goodness than model fit in the outputs [2].

Experiments on a well known distillation benchmark "Column A" [6] suggest that simple extensions of PI control can bring large improvements. If decentralized PI control is our baseline, and MPC control performance is defined as the best achievable performance, we found that static decoupling can take us roughly half way, and SVD Control provides control performance that is close to MPC control [3]. It was also found that the low-state and low-parameter SVD model structure is well suited for MPC control of high-purity distillation control.

REFERENCES

[1] N. Copernici Torinensis. De revolutionibus orbium coelestium. Norimbergae. 1543.
[2] M. Friman, “Identification of ill-conditioned systems using output rotation,” The 21st World Congress, The International Federation of Automatic Control, Accepted for publication, 2020.
[3] M. Friman. High-Purity Distillation Control: Should We Keep It Simple? CDC2021, 60th IEEE conference on Decision and Control, Austin Texas, USA, 2021, Submitted.
[4] S. Skogestad and M. Morari, “Understanding the dynamic behavior of distillation columns,” Ind. & Eng. Chem. Research, 27, 10, pp. 1848–1862, 1988.
[5] S. Skogestad and I. Postlethwaite, MULTIVARIABLE FEEDBACK CONTROL, Analysis and Design (2nd Edition). Wiley, 2007.
[6] S. Skogestad, “Matlab distillation column model (”Column A”),”1997, online, accessed: 2019-10-20. [Online]. Available: ”folk.ntnu.no / skoge / book / matlab m / cola / cola.html”
[7] E. Jacobsen and S. Skogestad, “Inconsistencies in dynamic models for ill-conditioned plants: Applications to low-order models of distillation columns.” Ind. & Eng. Chem. Research, 33, pp. 631–640, 1994
[8] K. Weischedel and T. J. McAvoy, “Feasibility of decoupling in conventionally controlled distillation columns,” Ind. Eng. Chem. Fundam., 19, pp. 379–384, 1980.