Modeling and Identification for Quench Column Bottom Temperature Control

Copyright 1(;) IFAC System Identification, Kitak yushu , Fukuoka, Japan. 1997

MODELING AND IDENTIFICATION FOR QUENCH COLUMN BOTTOM TEMPERATURE CONTROL Genichi Emoto, Randy M. Miller and Seiji Ebara Mitsubishi Chemical Corporation , 3-10 Ushiodori, Kurashiki, Okayama 712 Japan

Abstract: Simplified process models such as first-order plus time-delay models are often used for IMC-based PID controller tuning. This paper shows that such a simplified assumption is not always appropriate through a case study of an ethylene plant quench column bottom temperature control loop. It is important to understand the physical meaning of the process behavior in modeling of complicated processes. This practical experience shows that when a high-order model was decomposed to several low order models based on physical meaning and appropriate simplification of the high-order model, a better control result was obtained. Further, this physically explained transfer function model could be used to estimate a reasonable model uncertainty. Keywords. Identification, Process Models, Process Control, Chemical Industry

1.

assumed to be first-order or second-order. Through the application of IMC-based PID controller tuning to a quench column bottom temperature controller, it was found that the open loop step response is rather complicated and consequently straightforward simplification of the process produced an unsatisfactory result.

INTRODUCTION

IMC-based PID controller tuning methods are widely applied in the process industry. The IMC design method is based on an assumed process model and relates the controller tuning to the model parameters in a straightforward manner. The IMC approach is based on the simplified block diagram shown in Fig. 1. The transfer function G denotes the actual process plus related control instrumentation. A process model G and controller output P are used to calculate a model response C.

2.

PROCESS DESCRIPTION

A quench column immediately follows the primary fractionator in an ethylene plant. Cracked hydrocarbon gas, which contains water, is fed to the quench column after the heavy components are separated in the primary fractionator. This cracked gas is cooled by water (quench water) in an upper and a lower packed section. In the bottom section, cooled cracked gas condenses and is separated into gasoline and water. Bottom's water, used as the heat medium for other process reboilers, is about 80t. After heat recovery in several process reboilers, cooled water is recycled to the quench column as a upper reflux with a temperature of about 30"C and a lower reflux with temperature of about 60"C. The process flow diagram is shown in Fig. 2.

Fig.1 Block diagram of internal model control In a practical application of IMC-based PID controller tuning, the process modelG is usually

537

r--------------------~ Charge Gas

Compressor Sea Water

Sea Water

-f3-~

~/'...r~----IoE~E---'

.

Reboilers

~---,I

. .. @ uu nuunumuuunuuu nnnUn.n.._

Primary Fractionator

Gasoline Stripper Primary Fractionator

Fig. 2

:

~L:==~~==~~~~~ ) Process Water Stripper

Simplified Process Diagram of Quench Column

3.

CONTROL PROBLEM

filtered step response test data. DMI® is used here only as an intermediate for future modeling. The input-output FIR model is given by ;

In the current system, the bottom temperature PID controller manipulates the bypass flow rate of the reflux cooler (E-121). This control loop is called "TC105". This loop had shown poor performance especially following a big disturbance such as a furnace swap. PID controller parameters were set based on trial and error. Consequently it was decided to apply IMC-based PID controller tuning.

4.

M

O(k + 1):= I>;M(k -i + 1) + 00 + d(k + 1)

(1)

;=1

where k denotes discrete time; 0 0 is the output initial condition; M(k)is a change in input (or manipulated variable) at different time intervals k; d(k) accounts for un-modelled factors that affect O(k); a,. are the unit step response coefficients of the system; and M is the number of time intervals required for the system to reach steady state. Therefore, a,. = aM for i;::: M . DMI® calculates the unit step response coefficients a,. . The step response of the high-order HR model is shown in FigA. In this model, k and M are selected as 1 minute and 60 minutes, respectively.

STEP TEST

In order to identify the process model G, an open loop step test was performed. Test data are shown in Fig.3.

~5~

0 . 141-~--~--~--_=:::::==='1

~8~

0.12

0.1 80.50

100

200

300

400

500

~ :~E='~--'--,~I o

100

200

300

400

SOD

10

min

30

40

50

60

min

Fig. 3 TC105 Step Test Data

5.

20

Fig. 4 High-order FIR model of TC105 FigA shows bottom temperature's dynamic behavior

IDENTIFICATION

when the MV (E-121 bypass flow) is changed stepwise 1%. The resultant model indicates that the bottom temperature's dynamics are composed of a quick response and slow response and furthermore the quick response seems to be a second order

At first, a process model was made using DMI® software. DMI® creates a high-order input-output FIR model based on a least squares estimation from

538

flow was assumed to be first-order, it is reasonable to assume the effect on bottom temperature is secondorder.

system.

6.

INTERPRET ATION MODEL

OF

HIGH

ORDER 6.2 Approximated high-order model decomposition

Process dynamics behavior shown in FigA seems strange and complicated. By utilizing knowledge of the process mechanics, the complicated high-order model can be approximately decomposed into several simple models.

Based on the above knowledge, a high-order FIR model was approximated as a composite model composed of a second-order system plus time-delay (A+B) and a first-order system plus long time-delay (C). In this approximation, the time-delay {} AB was decided as one minute based on the step test. Other parameters, such as process gain, time constant were adjusted in order to fit the step response curve of the high order FIR model in the time domain.

6.1 Physical explanation

The hypothesis that explains the complicated dynamics of bottom temperature is summarized as follows;

Second-order system plus time-delay (A +B); KAB e-9AlJs 2 0 .AB s-+2.AB~ABs+l

(A) Quick response

First-order system plus time-delay; When E-121 (Reflux cooler, see Fig.2) bypass flow rate is increased, temperature of lower reflux rises immediately and the bottom temperature rises shortly thereafter.

(3)

K AB =0.08 CC/%), • AB =0.949 (min), ~AB =0.664, {} AB =l(min)

First-order system plus long time-delay (C);

~e-9cs

(B) Relatively quick response First-order system plus time-delay with negative gain; When E-121 bypass flow rate is increased, E-121 outlet temperature goes down because the heat duty of E-121is constant. Temperature of the upper reflux goes down, followed by the bottom temperature. The absolute gain is smaller than in (A). The time-delay is assumed to be longer than in (A) because of the heat exchanger thermal holdup.

(4)

.cs+ 1 Kc =0.06 tC/%), .c =14 (min), {}c =9 (min)

(C) Slow response

First-order system plus long time-delay; When E-121 bypass flow rate is increased, the bottom temperature rises as a consequence of (A) plus (B). The bottom fluid (quench water) is recycled to E-121 after heat recovery in several process reboilers. This causes a gradual increase in the bottom temperature. ·0 . 02L----'---~-~--~--~---'

o

The quench column behaves like a mixer rather than a distillation column especially for liquid flow. So, the dynamics of the quick response (A+B) can be written as follows,

10

20

30

40

50

60

min

Fig. 5 High-order model vs. Composite model

(2)

6.3 Approximate decomposition

second-order

model

Further, the second-order model in (3) can be decomposed approximately to first order models based on the Laplace transformation of equation (2). In this transformation we assumed that the terms related to column feed and gas exit from top are constant.

where V denotes liquid hold up at column's bottom; T denotes temperature; C p denotes heat capacity; f denotes flow rate; Subscripts are denoted by the following streams, a :lower reflux, b :upper reflux, o :bottom exit flow, f: column feed, g :exit gas from top, respectively. Because the response of the reflux temperature from a change in E-121 bypass

539

PID parameters can be obtained through the simplifIcation of high-order model based on IMCbased tuning rule. However, simulation shows that an inappropriate simplification leads to an unsatisfactory result.

Therefore, transfer functions of upper reflux and lower reflux can be expressed as fIrst-order plus timedelay models.

7.1 Model simplification

Ta(s) =~e-8Qs, 1/,(s) =~e-8bS fa(S) 't'a s + 1 fb(s) 't'b s + 1

(6)

In order to calculate PID controller tuning, a highorder FIR model must be simplified as a first-order system or second-order model. Both model approximations are described below.

Bb > Ba As it is clear that (V / fo»> ra' 'Cb' To (s) can be expressed as a combination of two fIrst-order plus time-delay models. Their time constant is V / fo and its value is calculated from an energy balance. To this end, the second-order system (3) is decomposed based on the above physical meaning and step response curve fitting.

Model ( I) : First-order system plus time-delay model; Approximate overall high-order FIR model and transfer function model (10) are shown in Fig. 7.

~e-8Ds

(10)

'C DS + 1

First-order system plus time-delay (A);

~e-(JAS

K D =0.1382("C/%),

'CA

=9.6 (min), 8 D =1 (m in)

(7)

The time constant was selected to minimize the sum of square of the error between the response curve of high order model and the first-order model.

'C A s+l

K A =0.11 CC/%),

'CD

=2.5 (min), 8 A =1 (min)

First-order system plus time-delay, negative gain (B);

~e-(JBS

0.141-~--~-~==:::;;;;;;====-=='

(8)

0.12

'C B s+l KB

=-0.03 CC/%),

'CB

0.1

=2.5 (min), 8 B =5 (min)

0.091r--~--_~ Second..irder model (3) 0.08

t

0.07

0.04

COlJ1>OSile JIDdeI (7)+(8)

0.02

0.06 0.05

OU-_~--~-~--~-~-~

o

(.)

fil

c

0.04

10

20

30

40

50

60

mm

Fig. 7 High-order vs. approximated first-order model

0.03 0.02

Model (IT) : Second-order system plus time-delay model, which is the result of previous section (3), is shown in Fig. 6. This model represents quick part of the overall response.

0.01

o

I

·0.01L--~--~-~--~-~--

o

Fig. 6

5

10

15 min

20

25

30

Second-order model vs. Composite Model 7.2 1MC-based PlD controller tuning

Finally, the high-order model can be approximately expressed as a combination of three fIrst-order elements.

PID parameters, kc, 'Cl ' r D are calculated based on IMC-based tuning rules. PID controller 1

k c (1+-+rDs)

(11)

'Cls

where Gp denotes process model; IMC-based PID controller tuning are defmed in following formula. 7.

PID TUNING 540

For first-order system plus time-delay process

1)

model) leads to sluggish servo and regulatory performance while PID controller tuning based on model (11) (quick dynamics of this process) leads to satisfactory performance.

7.4 Control result

2)

PID parameters based on the model (11) were implemented in the actual TC105 controller. Excellent performance is demonstrated for a setpoint change and a furnace swap (main disturbance). Compared to the previous controller. this represents a signiftcant improvement.

For second-order system plus time-delay model

"'1::£:"1 o s~

where -r f denotes desired closed-loop time constant. Time-delay is approximated expansion; e -8s = 1- es

by

Taylor

60.5

series

80

"

Cooai>ION

o

50

100

150

200

250

300

350

400

Disturbanre

83

~J-~~~~t=~~'l ()82

7.3 Simulation PID parameters. shown in Table 1. were obtained for process model ( I ) and (11 ) respectively.

o

Fig. 9

50

100

150

200

TC105 control performance

Table 1 PID parameters Case

P

I (min)

D (m in)

Tuning ( I)

11.67

10.10

0.48

10.00

1.26

0.71

8.

Frequency domain characteristics are compared for the step test data. composite model (high-order model). model ( I ). model (11). Bode plots of the composite model and model (11) are similar to the step test data.(Fig.IO&12) Conversely. significant discrepancies in the gain and phase of model ( I ) and the data at the dominant frequency of the system as can be seen in Fig. 11.

Model ( I ) base Tuning (11) Model ( 11 ) base

rV?---~/-_n--~ : I .Q.S

o

10

20

30

40

50

AMPLITUDE PLOT. input. 1 output #

::"1

60

10'

I:~lJJ;; - -;- - -;- --- - I .Q.02

o

10

20

30

40

50

VALIDATION

10.3 ID·'

~I 10'

10'

10'

60

min

Fig. 8

Control Simulation ;Solid line (Tuning 11).

Dashed line (Tuning I) Substantial differences in control performance are shown in Fig. 8 for the PID controllers in Table 1 applied to the FIR model. PID controller tuning based on model ( I ) (ftrst-order plus time-delay

Fig. 10 Bode plot ;Solid line (Composite model). Dashed line (Step test data)

541

~

::':[

10"L-_ _ _ _

~

10·'

_____

10·'

~

quench column bottom temperature and K B is proportional to reflux cooler's duty. Both bottom temperature and reflux cooler's duty are proportional to sea water temperature.

1

_ _ __ . J

10' p

mechanism that K A and Kc are proportional to

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~P""

I~t ~---:-------;/''- I pHAS" PI

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a=y=

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---------

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~

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,"",,,or ,,.,w ."''', ,

I~l

------<~/'<

I

k

10·'

10°

equation (13), kc

j

(18)

'

G

denotes generalized control gain.

Through practical experience in an industrial chemical process, the importance of physical phenomenon in plant identification was demonstrated. Especially for IMC-based PID controller tuning, misdirected simplification of high-order systems can lead to unsatisfactory control performance.

10 '

MODEL UNCERTAINTY ESTIMATION

REFERENCES

By physical interpretation of a high-order model, model uncertainty can be approximately estimated. As mentioned, the quench column bottom temperature process model can be expressed as a composite model (9). In this process, the coolant used in the reflux cooler is sea water. So, the heat duty changes from summer to winter. As the identification shown in this paper was done in summer, we can estimate the process gain change in winter as a function of sea water based on the heat balance . The winter model can be expressed as following equation

Gp _w denotes

f(T)

10. CONCLUSION

Fig. 12 Bode plot ;Solid line (Model n), Dashed line (Step test data)

where

kc ---

C G -

kc denotes nominal control gain calculated from

to'

frequency (rad/sec)

9.

(17)

where K A_G denotes generalized process gain of K A

_~oL------~------~~-~-~ 10.2

{3 = max(Q) min(Q)

Further gain scheduling can be introduced by exploiting the dominant part of composite model (first term of (16».

_ _ __ . J

10'

,

where TB denotes bottom temperature; Q denotes

Fig. 11 Bode plot ;Solid line (Model I), Dashed line (Step test data)

: :': [

min(TB )

reflux cooler's duty; a, {3, r can be estimated from historical data.

~

frequency (rad/sec)

AMPLITUDE PLOT, input # 1 output #

max(TB )

Garcia, C. E., A. M. Morshedi (1986), Quadratic programming solution of dynamic matrix control (QDMC), Chem. Eng. Commun., 46, 73-87. Rivera, D. E., M. Morari and S. Skogestad (1986), Internal Model Control, 4. PID Controller design, Ind. Eng . Process Design Dev. 25 252 Seborg, D. E., T. F. Edgar and D. A. Mellichamp (1989) , Process Dynamics and Control, John WHey & Sons, New York

winter model (worst case

model), K A' K B , Kc denote nominal process gain, denotes sea water temperature, a, {3, r are appropriate multipliers calculated based on process T

542