Supervisory Fuzzy Adaptive Control of a Binary Distillation Column

Srinivasan Santhanam, Gruduute Student Reza Langari, Assistant Professor

I. ABSTRACT Distillation column i s widely used in the chemical industry for separation and has been studied exten- sively for improvements an composition control by using multivariable control straiegies. The avail- ability of process computers with higher processing power at a lower price has led t o greater interests in the application of advanced control techniques. Al- most all of the advanced control techniques rely on an accurate model of the process t o be controlled. If an accurate process model is not available, then satisfactory control cannot be achieved. Here we present a new fuzzy adaptive technique t o adapt the feedforward model and decoupling model in a bina y distillation column in order to reject the feedflow dis- turbances affecting the distillate composition.

11. INTRODUCTION Some of the different advanced control techniques used in distillation column control include internal model control (I.M.C), optimal control, dynamic ma- trix control (D.M.C), feedforward control and de- coupling control [l]. All of the above control tech- niques need an accurate model of the process to be controlled. For a complex, non-linear, interacting process like the distillation column, such a process model does not exist [2] [3] [4]. If the process cannot be usefully modeled within the framework assumed by the theory, then satisfactory control cannot be achieved. In addition to the model deficiency, a dif- ficult process may also be characterized as having a considerable amount of essential a priori information available only in a qualitative form. These features are a form of imprecision which prevent the the- ory from being used [5]. Huang and Tomizuka [SI have used an implicit fuzzy model of the plant to derive the control rules when an accurate model of the plant is not available, based on the concept of inverting the plant model. Cartwright and Thom- son [7] have used a similar fuzzy model for composi- tion control in a binary distillation column. Langari and Tomizuka [SI have proposed a fuzzy linguistic

The authola are with the Department of Mechanical Engineer- ing, Texas A&M University, College Station, TX 77843, USA.

model based feedforward control to compensate for measurable disturbances affecting the manufactur- ing processes.

In this paper, we explore a binary distillation col- umn control system in which the reflux flow is used to control the distillate composition and the vapor boil up rate is used to control the bottoms composi- tion(Fig.1). Our objective is to control the distillate composition in the presence of measurable changes in the feedflow and interaction between the distillate and bottom controllers. We propose a fuzzy adap- tation scheme based on linguistic adaptive rules and discuss the issues related to the design of these rules. Next, we present the application of this technique to a benzene-toluene binary distillation column and review the results. We conclude the paper with an overview of the research issues that need further ex- ploration.

111. FEEDFORWARD AND DECOUPLING CONTROL The feedforward model shown in Fig.1 predicts the change in the reflux flow required to keep the distil- late composition at its setpoint after a disturbance in the feedflow. A feedforward calculation accurate to *lo%, for example, will reduce the sensitivity of product quality to those measured disturbances by a factor of 10 - a substantial reward for modest accuracy [9]. Because of the presence of large con- trol interactions, a decoupler model is also shown in Fig.1. The decoupler cancels the effect of the bottoms controller on the distillate composition by predicting the change in the reflux flow.

A typical transfer function for a binary distillation column is shown in Fig.:! [lo]. Because of the pres- ence of large delays in the process, Smith predictor dead-time compensator is used for the distillate and bottoms composition controllers(Fig.3).

If the feedforward and decoupling models are not accurate, then the dist;llate controller will be de- pended on to take the control action whenever the disturbance enters the column in the form of a change in the feedflow. Because the distillate controller

0-7803-1896-X/94 $4.00 01994 IEEE 1063

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cannot take control action until error is introduced in the control loop and because of the presence of large time delays in the loop, the control perfor- mance deteriorates significantly, resulting in poor composition control. In practice, the plant is dif- ferent from the model and there is uncertainty in the plant gain [l l] . Hence, some form of supervi- sory control is required for adapting these models to achieve tight composition control.

Simple adaptation schemes do not exist for MIMO systems. For example, in the system shown in Fig.4, if we decide to use the output of the controller 1 for adapting the gain of the feedforward models, there is no simple adaptation scheme that can be used to decide which of the feedforward model gains has to be changed. Here, we propose a simple and powerful supervisory fuzzy adaptation scheme based on fuzzy linguistic adaptive rules. The fuzzy supervisor mon- itors the process continuously and decides changes to the feedforward and decoupler model gains, if any, after every change in the feedflow. In the next sec- tion, we discuss the technical issues associated with the design of the linguistic adaptive rules and show how the fuzzy adaptive scheme can be used to effec- tively adapt the feedforward and decoupler models and reject the feedflow disturbances.

I v . FUZZY ADAPTATION

In the distillation column considered here( Fig. l), we have used the top tray temperature controller for in- directly controlling the distillate composition. The objective of the fuzzy adaptive supervisor is to mon- itor the top tray temperature continuously and de- cide if the gain of the feedforward model or decou- pler model has to be changed. If the temperature goes above or below a control band around the set- point after a step change in the feedflow, then a gain change is needed. But, to decide which model gain has to be changed, the fuzzy supervisor also needs to know the response of the feedforward model and decoupler model during the time (or a dead-time before when there is a delay in the loop) of the tem- perature overshoot or undershoot.

Suppose, for example, after a feed flow increase, there is an overshoot in top tray temperature T2 which starts at t imet = t l and ends at t ime t = t2. The fuzzy supervisor calculates the output of the feedforward model in terms of the change in mag- nitude a refluz dead-time (reflux dead-time denotes the time delay between a change in the reflux flow and the effect of this change in the top tray temper- ature) before time t l and for a time equal to t2 - t l . Similarly, it calculates the output of the decou-

pler model a reflux dead-time before time t l and for a time equal to t2 - tl . Having found out the re- sponses of both the models during the time of the overshoot, the fuzzy supervisor has to calculate how much the gain of each model has to be changed. The calculation of the change in model gain is based on the following facts:

1. If there is an overshoot in temperature, then the gain of the model which decreased the re- flux has to be decreased and the gain of the model which increased the reflux has to be in- creased.

2. If there is an undershoot in temperature, then the gain of the model which decreased the reflux has to be increased and the gain of the model which increased the reflux has to be decreased.

3. The amount of change depends on the extent of the temperature overshoot or undershoot and the response of the models during this time.

For the example of increase in feedflow and over- shoot in temperature, it is easy to see that the feed- flow feedforward signal should have increased during the time of the overshoot. Hence, the decrease in the feedforward model gain can be calculated using the fuzzy rule table shown in Fig.5.

Zero, small, medium, ... are linguistic terms which are represented as fuzzy subsets of the universe of discourse that corresponds to the particular variable of interest. Using fact 3 above, it is easy to see that for a large increase in the feedforward signal and a small overshoot in temperature, only a very very small decrease in feedforward model gain is required.

It is possible that the decoupler model may also have contributed to the reflux change during the time of the temperature overshoot. However, in most of the industrial distillation columns, the time taken by the liquid flowing from the feed tray to the col- umn bottom represents the dominant dead-time in the column. Hence, after a feedflow change, the top tray temperature changes first followed by a delayed change in the bottom tray temperature. Also, there may be a time delay associated with the reboiler in the bottom temperature controller loop. This means that the contribution from the feedforward model after a feedflow change comes first followed by a delayed contribution from the decoupler model.

Nevertheless, considering that there exists an over- lap, for the above example, the fuzzy supervisor will propose a decrease in the feedforward model gain

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and an increase in the decoupler model gain at the same time. Noting that each of these gain changes, if applied independently, is capable of bringing the overshoot within the control band (assuming one of the two models is accurate), we devise a gain scal- ing method(Fig.6) that uses the contribution of each model towards the reflux change to decide the ac- tual change in the model gains.

One fuzzy meta rule (a meta rule refers to a gen- eral description based on which a number of specific rules may be derived) for the fuzzy adaptive super- visor can be summarized as follows.

.If there is a smal l overshoot after a large increase in feed flow,

there should be a very very small decrease in the gain of the signal that decreased the reflux a repuz dead-time before the overshoot

there should be a very very small increase in the gain of the signal that increased the reflux a refiuz dead-time before the overshoot

if both signals are present, calculate the gains as above and apply after suitable scaling.

(or)

(or)

V. RESULTS

We implemented the supervisory fuzzy adaptation scheme on a benzene-toluene binary distillation col- umn simulation program (Fig.7). Feed composition, temperature and column pressure are assumed to be a constant. The initial tray composition were chosen from an industrial distillation column [12]. Initially, arbitrary values for the feedforward gain and decoupler gain were chosen as 1.0 & 0.2 respec- tively. The response of top tray temperature T2 for a step increase of 10% in the feedflow (from 100 mole/minute to 110 mole/minute) at time t = t l is shown in Fig.8. We made the fuzzy computed changes to the feedforward model gain and the de- coupler model gain and again applied a step increase of 10% in the feedflow at time t = t2. From Fig.8, we note that the response of the tray temperature is improved significantly. The above steps were re- peated until time t = t5, when no overshoot in the tray temperature is observed. Fig.9 and Fig.10 show the feedforward gain changes and the decoupler gain changes proposed by the fuzzy scheme.

VI. CONCLUSION

In this paper we showed that a simple supervisory fuzzy adaptation scheme based on fuzzy linguistic adaptive rules can adapt the feedforward model and

decoupler model in a binary distillation column to achieve tight composition control in the presence of feedflow disturbances. It is clear that if the pro- cess cannot be usefully modeled within the frame- work assumed by the theory, then satisfactory con- trol cannot be achieved. By using a linguistic adap- tation scheme, we showed that qualitative informa- tion about the process can be used to achieve signifi- cant improvements in control performance. The ap- plication of this technique can be extended to distil- lation columns with feed composition and feed tem- perature variations and to multiproduct distillation columns.

REFERENCES

[l] M. N. Karim and G. K. F. Lee, Study of Ro- bustness in Multivariable Control System De- sign for Distillation Columns, Advances in In- strumentation Vol. 38, pp. 695-705, 1983.

[2] A. E. Nisenfeld and R. C. Seeman, Distillation Column. North Carolina: Instrument Society of America, 1987.

[3] K. E. Haggblom and K. V. Waller, Practical Distillation Control Edited by William L. Luy- ben. New York: Van Nostrand Reinhold, pp. 193, 1992.

[4] D. A. Hokanson and J . G. Gerstle, Practical Distillation Control Edited by William L. Luy- ben. New York: Van Nostrand Reinhold, pp. 253, 1992.

[5] R. M. Tong, A control engineering review of fuzzy systems, Automatica, vol. 13, pp. 559- 569, 1977.

[6] L. J . Huang and M. Tomizuka, A self paced fuzzy tracking controller for two dimensional motion control. IEEE Transactions on Sys- tems, Man, and Cybernetics, 1990.

[7] P. Cartwright and M. Thomson, Knowledge based control of a binary distillation column, IEE colloquium on knowledge based control: principles and applications (Digest No. 091), London, 1991.

[8] G. Langari and M. Tomizuka, Fuzzy linguis- tic model based control, IEEE International Symposium on Intelligent Control, Philadel- phia, 1990.

[9] F. G. Shinskey, Distillation Control for Pro- ductivity and Energy Conservation. New York: McGraw-Hill, 1971.

[IO] K. V. Waller, Practical Distillation Control Edited by William L. Luyben. New York: Van Nostrand Reinhold, pp. 318, 1992.

[I11 S. Skogestad, Practical Distillation Control Edited by William L . Luyben. New York: Van Nostrand Reinhold, pp. 291-309, 1992.

W. L. Luyben, Process Modeling Simulation and Control for Chemical Engineers. New York: McGraw- Hill, 1990.

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