FLOW RATE CONTROL SYSTEM SECOND ORDER PLUS DEAD TIME MODEL April 20, 2006 U.T.C Engineering 329.
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Transcript of 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