flow rate control system second order plus dead time model april 20, 2006 u.t.c engineering 329

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