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A Discrete Time Model of Boiler Drum and Heat Exchanger QAD Model BDT 921

Carlos Iván Mesa M.

Cód.: 45121608

Control Digital

Ing. Automatización

Unisalle 22-Febrero-2012

Faculty of electrical and electronic engineeringUniversiti Tun Hussein Onn Malaysia (uthm)October 20-22, 2009, Bandung, Indonesia, IEEE

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ABSTRACTThe document discusses the

procedure followed to control a system discreetly heat exchanger and a drum-boiler control laboratory of the university which were are controlled analogously.

PID is chosen as a control discreetly.The plant behavior is analyzed

using the simulation tool Matlab.

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INTRODUCTIONBoiler drum and heat exchanger are

commonly used in industries in almost all process and power plants to generate steam for the main purpose of electricity generation via steam turbines.

Figure 1 – The boiler drum and heat exchanger QAD Model BDT 921

Figure 2 - The front panel control of boiler drum and heat exchanger QAD

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BOILER DRUM

Figure 3 - The real system of boiler drum

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BOILER DRUM MODEL(Schematic)

Figure 4 - The P&ID of boiler drum and heat exchanger

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BLOCK DIAGRAM

Figure 5 – Block Diagram for boiler drum control system

Table 1 – Parameter gain values for boiler drum model

Parameter gain Value

Boiler tank transfer function, GP 1/500s

Current to pressure converter, GI/P 0.0527

Level transmitter, Gt 0.16

Level set to voltage converter, GHV 0.04

Voltage to current converter, GVI 4

level control valve, GV 1144

Gain of PID controller, GC variable

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TRANSFER FUNCTION

Transfer function for single loop

Proportional controller (P)

Proportional plus integral controller (PI) 𝑃𝐼 (𝑠)=𝐺𝑐 ¿

𝐺𝑐=¿ 100

𝑃𝐵¿

𝐶 (𝑠)𝑅(𝑠)

=0,019𝐺𝑐

𝑠+0,019𝐺𝑐

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FUNCION DE TRANSFERENCIA

Proportional plus integral controller (PI)

Replace Ti = 30:

Discrete time Transfer function:

𝐶 (𝑠)  𝑅(𝑠)

=0,019𝐺𝑐 𝑠+

0,019𝐺𝑐

𝑇 𝑖

𝑠2+0,019𝐺𝑐 𝑠+0,019𝐺𝑐

𝑇 𝑖

𝐶 (𝑧)𝑅(𝑧)

= 0,3259 𝑧−0,305𝑧 2−1,663 𝑧+0,6839

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HEAT EXCHANGER MODEL

Figure 6 - The real system of heat exchanger

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THE P&ID OF HEAT EXCHANGER

Figure 7 – The P&ID of heat exchanger

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BLOCK DIAGRAM

Figure 8 – Block Diagram for heat exchanger control System

Table 2 - Parameter gain values for heat exchanger model

Parameter gain Value Gain of temperature to voltage values

converter, GHV x Gain of voltage to current values converter, GVI

0.000053

Gain of PID controller, GC variable Gain of temperature to voltage values

converter, GHV x Gain of voltage to

9022.28 2.55s

Gain of temperature transmitter, GT 0.076

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Transfer function for single loop

Proportional controller (P)

Proportional plus integral controller (PI)

𝐺𝑐=¿

100𝑃𝐵 (1+ 1

𝑇1 𝑠+𝑇 𝑑𝑠)¿

𝐺𝑐=¿

100𝑃𝐵 (1+ 1

𝑇1 𝑠 )¿

TRANSFER FUNCTION

𝐶 (𝑠)𝑅(𝑠)

=𝐺𝑐

𝐺𝑐+53,13 𝑠+20,83

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Proportional plus integral controller (PI)

Replace Ti = 30:

Discrete time Transfer function:

𝐶 (𝑠)  𝑅(𝑠)

=0,019𝐺𝑐 𝑠+

0,019𝐺𝑐

𝑇 𝑖

𝑠2+0,019𝐺𝑐 𝑠+0,019𝐺𝑐

𝑇 𝑖

TRANSFER FUNCTION

𝐶 (𝑠)  𝑅(𝑠)

=0,5453 𝑧2−1,045 𝑧+0,5011

𝑧 2−1,955 𝑧+0,9555

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BOILER DRUM RESULT

Table 3 - Comparison data obtained from experiment and with simulated

Signal Types

 

Time (s)

Rise TimeTr

Peak TimeTp

Settling Time

Ts

Experiment 10s 20s 65s

Simulated 8s 10s 60s

Difference 2s 10s 5s

Figure 9 – Comparison simulation using z-domain transfer function with 2s sampling time and measured response of experiment to step change in boiler drum for PB = 10 and Ti = 30s

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BOILER DRUM RESULT

Table 4 - Comparison data obtained from experiment and with simulated

Signal Types 

Time (s)

Rise TimeTr

Peak TimeTp

Settling Time

Ts

Experiment 65s 60s 65s

Simulated 60s 65s 70s

Difference 5s 5s 5s

Figure 10 – Comparison simulation using z-domain transfer function with 0,5s sampling time and measured response of experiment to step change in boiler drum for PB = 20 , Ti = 24s, and Td = 6s

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SIMULATION ON MATLABMATLAB CODEclear all

close all

clc

gvi=0.000053

ts=2;

gt=0.076

num= [0.5453 -1.045 0.5011]

den=[1 -1.955 0.9555]

gc=tf(num,den,ts)

num2=[9022.28]

den2=[2.55 1]

gp=tf(num2,den2)

gpz=c2d(gp,ts)

w=series(gc,gpz)

f=feedback(w,1)

final=series(f,gvi)

%

step(gpz)

figure

step(gc)

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TRANSFER FUNCTION

Para la función de transferencia

𝐶 (𝑠)  𝑅(𝑠)

=0,5453 𝑧2−1,045 𝑧+0,5011

𝑧 2−1,955 𝑧+0,9555

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CONCLUSIONMathematical model for a process control plant

is important because it provides key information as to the nature and characteristic of the system which is vital for the investigation and prediction of the system operation

The set of equations that make up that model is an approximation of the true process.

The model of boiler drum and heat exchanger process control training system QAD Model BDT921 from the transfer function result has second order.