FLOW RATE CONTROL SYSTEM

SECOND ORDER PLUS DEAD TIME MODEL

April 20, 2006

U.T.C

Engineering 329

Yellow Team

• Jimy George

• Jeff Lawrence

• Taylor Murphy

• Jennifer Potter

Outline

• Flow System Background

• SOPDT System Theory

• Model Results

Outline

• Proportional Controller

• Comparison of FOPDT & SOPDT results

• Conclusion

Flow System Setup

Block Diagram

Laplace Domain

R(s) C(s)

Time Domain

1)()(

1

12

2)(

1

12

10

02

01

tttt

eettUAKtc

Modeling ObservationsExperimental Versus Model For Step Up Response

66

70

74

78

82

86

90

24 25 26 27 28Time (s)

Inp

ut (

%)

15

16

17

18

19

20

21

Output (lb/min)

Experimental Input

Model InputExperimental Output

Model Output

Parameters involved

A = 15Input Baseline = 70

Output Baseline = 16K = 0.24t0 = 0.4

tau1 = 0.22tau2 = 0.18

Modeling Observations RecapExperimental Versus Model For Step Up Response

66

70

74

78

82

86

90

24 25 26 27 28Time (s)

Inp

ut (

%)

15

16

17

18

19

20

21

Output (lb/min)

Experimental Input

Model InputExperimental Output

Model Output

tau1 = 0.22tau2 = 0.18

Negative Feedback Loop

Kc

R(s) M(s) C(s)

Closed Loop Transfer Function

111

11

21

21

0

0

ss

eKK

ss

eKK

CLTFst

c

st

c

Characteristic Equation

01222220

2102

210

20

130

21

KKs

tKK

ts

tts

tcc

Characteristic Equation

For

024.01048.06.012.00079.0 23 cc KsKss

K = 0.24t0 = 0.4

tau1 = 0.22tau2 = 0.18

Solving CE for Kc

Direct Substitution

Set s = iωU

Set like terms equal to zero

Imaginary part:

[0.0079 ωU3-(0.6 +0.048Kcu) ωU]i=0i

Direct Substitution (cont’d)

Real part:

0.24Kcu - 0.12 ωU2 + 1 = 0

ωU = 5 => fu = 0.8

Kcu = 8.3 %/(lb/min)

Corresponding Frequency Experiment

Response at 0.8Hz frequency

65

70

75

80

85

90

95

10 11 12 13 14 15

Time(sec)

Inpu

t(%

)

15

16

17

18

19

20

21

Out

put

Input Value(%)

Output(lb/min)

Observations

• Phase Angle = -1800

• Amplitude Ratio = 0.12

• Kcu calculated = 8.3

Comparison of fu

SOPDT

Bode Plots Luyben MethodRouth/Direct

Substitution MethodsDirect Substitution

Method

0.87 0.67 1.2 0.8

fu HzFOPDT

Comparison of Kc

SOPDT

Bode Plots Luyben MethodRouth/Direct

Substitution MethodsDirect Substitution

Method

10 9.6 10 8.3

FOPDTKc (%/(lb/min))

Conclusion

• Kc = 8.3 %/(lb/min)

• SOPDT more accurate than FOPDT

• Always scope for improved results