고순도 증류탑의 제어를 위한 단온도를 이용한 프로파일 위치 추정기

신 준호*, 서 호동, 한 명완**, 박 선원

한국과학기술원 화학공학과, (주) 선경건설*, 충남대학교 화학공학과**

Profile Position Observer Using Tray Temperatures

for Control of High-Purity Distillation Column

Joonho Shin*, Hodong Seo, Myungwan Han**, and Sunwon Park

Dept. of Chemical Engineering, KAIST, SKEC*

Dept. of Chemical Engineering, ChungNam National University**

Introduction

High-purity distillation columns have been well known to pose a formidable controller design problem, resulting from unique characteristics, such as complex dynamics, high nonlinearity and interaction between the control loops. Tight control of high-purity distillation columns has been a subject of research for many years.

Han and Park (1993) proposed a model-based controller design that deals with both nonlinear and multivariable characteristics of high-purity distillation columns. The controller was developed by incorporating Hwang's (1991) nonlinear wave model of high-purity distillation column into the generic model control (GMC) framework by Lee and Sullivan (1988).

The objective of this article is to present a new, concise profile position observer using tray temperatures, which can be easily measured instead of tray compositions.

The performance of the control system using this observer has been tested in dynamic simulation and compared with that of Han and Park (1993).

The simulation model used in this work is a high-purity (yD = 0.99, xB = 0.01) distillation column model, referred to as column at operating point A by Skogestad and Morari (1998). This model is shown in Table 1. in detail.

Theory

The model-based profile position controller using nonlinear wave theory was described in the paper written by Han and Park (1993) in detail.

Simulation and Results

Simulation Examples

It is important to examine the robustness aspects of the controller about input uncertainty and temperature measurement noise for applications to real distillation columns.

The tuning parameters for the profile position controllers and PI composition controllers can be determined by using GMC and DCLR (Desired Closed-Loop Response) tuning rule, respectively. The tuning parameters and the parameters for the proposed profile observer are listed in Table 2.

Input Uncertainty

Skogestad and Morari (1988) showed that the closed-loop system may be extremely sensitive to input uncertainty when the LV configuration is used. For testing the performance of the proposed control scheme in the presence of input uncertainties, the following uncertainties used by Skogestad and Morari (1988) have been chosen.

Fig. 2 shows the closed-loop transient response to a step change in the feed composition for different values of input uncertainty.

Temperature Measurement Noise

In measuring the temperatures of real distillation columns, there can be measurement noise, which may deteriorate the performance of the control system. To examine the performance of the observer when the temperature measurement is noisy, arbitrary noise from -0.5 to 0.5℃ is given to every measurement tray. Fig. 3 shows good performance of the control system even with noisy temperature measurement (± 0.5℃) and unmeasured feed composition disturbance (from 0.5 to 0.2) because the proposed profile position observer uses the multiple tray temperature measurements.

Comparison of the Proposed Controller with Other Control Strategies

Skogestad and Morari (1988) studied a high-purity distillation column of which the details are shown in Table 2. Fig. 4 shows the closed-loop response to small setpoint change in xB at operating C and a transition from operating point A to operating point C using logarithmic compositions as controlled outputs.

Fig. 4 shows that our results are very similar to that of Han and Park's (1993).

Conclusions

A new nonlinear profile position observer which uses tray temperatures instead of tray compositions is developed in order to overcome the measurement problem related to the online composition measurement.

The performance of the proposed control scheme is as good as that of Han and Park. Since the proposed profile position observer is concise, requires only tray temperature measurements, and is insensitive to measurement noise, it can be directly applicable to the real high-purity distillation columns.

Acknowledgment

This work was supported (in part) by the Korean Science and Engineering Foundation (KOSEF) through the Automation Research Center at POSTECH.

References

1. M. Han and S. Park, "Control of High-Purity Distillation Columns Using a Nonlinear Wave Theory", AIChE Journal, 39, 787-796, 1993

2. Y. Hwang, "Nonlinear Wave Theory for Dynamics of Binary Distillation Columns", AIChE Journal, 37, 705-723, 1991

3. J. Shin, M. Lee, and S. Park, "Design of Composition Estimator for Inferential Control of High-Purity Distillation Columns", Chemical Process Control-V, 1996

4. P. Lee and G. Sullivan, "Generic Model Control", Computers and Chemical Engineering, 12(6), 573-580, 1988

5. Lee, Y., M. Lee, and S. Park, "PID Controller Tuning to Obtain Desired Closed-Loop Responses for Multiple-Input Multiple-Output System", KIChE Meeting, Fall, 1996

Table 1. Steady-State Data for Distillation Column at Operating Points A and C

Column Data
Number of theoretical trays				N = 40
Feed tray (1 = reboiler)				NF = 21
Feed compositions				zF = 0.5
Antoine coefficient		A1 = 15.83660, B1 = 2697.55, C1 = -48.78
		A2 = 15.43113, B2 = 2697.55, C2 = -48.78
Operating Data
			A	C
	yD		0.99	0.90
	xB		0.01	0.002
	D/F		0.5	0.555
	L/F		2.706	2.737
Measurement trays : 10, 12, 14, 16, 18, 22, 24, 26, 28, 30

Table 2. Parameters for the Controllers

and the Proposed Observer

GMC tuning
K11 = 1.50	K12 = 0.03
K21 = 1.50	K22 = 0.03
PI tuning
without logarithmic transformation	with logarithmic transformation
KC,1 = -60.0, □I,1 = 14.0	KC,1 = -0.1, □I,1 = 12.0
KC,2 = -60.0, □I,2 = 14.0	KC,2 = -0.1, □I,2 = 12.0
Constants for profile position observer
rectifying section	stripping section
k0 = 0.1, k2 = -18.0, b = 0.03	k0 = 0.1, k2 = -22.5, b = 0.03

Figure 2. Closed-loop transient responses for different values of input uncertainty.

Figure 1. Schematic procedure of determining representative temperatures and profile positions.

Figure 4. Comparison of control performances (logarithmic compositions as controlled outputs) : (a) closed-loop response to a small setpoint change in xB of column C from 0.002 to 0.0021 ; (b) transition from operation point A to C

Figure 3. Closed-loop transient response with noisy temperature measurement (±0.5℃)