Flow Rate Control System
description
Transcript of Flow Rate Control System
Flow Rate Control System
“Frequency Response”
By: Taylor Murphy
March 1, 2006
U.T.C.
Engineering 329
Yellow Team
Jimy GeorgeJeff LawrenceTaylor MurphyJennifer Potter
Outline
System Background– Description, SSOC, Step Response
Frequency Response Experiment Frequency Response Model Results Conclusions
Flow System Setup
Block Diagram
Steady State Operation
Flow Rate Versus Time @ 80% Input
7576777879808182838485
0 10 20 30 40
Time (s)
Power Input
(%)
0
5
10
15
20
25
Flow Rate (lb/min)
Input
Output
Steady Operation
SSOCTeam Steady-State Operating
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80 90 100
Power (%)
Output (lbs/min)Operating Range for Input
Operating Range for Output
SSOC with Step RangesTeam Steady-State Operating
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80 90 100
Power (%)
Output (lbs/min)
Operating Range for Output
LowMid-Low
Mid-High
High
Low - 45-55%Mid-Low - 55-70%Mid-High - 70-85%High - 85-100%
Experimental and Model Results
Experimental and Model Results
70
72
74
76
78
80
82
84
86
24 24.5 25 25.5 26 26.5 27 27.5 28
Time (s)
Input (%)
14
15
16
17
18
19
20
21
22
Output (lb/min)
Excel Model of FOPDT
Experimental
Values
K (lb/min/%) = 0.26
Tau (sec) = 0.46
t0 (sec) = 0.42
Step Results; K
Week 6 Values of K
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 3 4 5 6 7 8
Trial
K (lb/min/%)
45%-55% 55% -70% 70% -85% 85%-100%
Week 6 Values of K
Ste p down
Ste p Up Ste p Up
Ste p Down
Ste p Up
Ste p Down
Ste p Up
Ste p Down0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1 2 3 4 5 6 7 8
Trial
K (lb/min/%)
45%-55% 55% -70% 70% -85% 85%-100%
Step Results; Tau
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (sec)
45%-55% 55%-70% 70%-85% 85%-100%
Week 6 Values of Tau
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
1 2 3 4 5 6 7 8
Trial
Tau (sec)
45%-55% 55%-70% 70%-85% 85%-100%
Step Results; t0
Week 6 Values of t 0
Step down
Step Up Step Up
Step Down
Step Up
Step Down
Step Up
Step Down
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 2 3 4 5 6 7 8
Trial
t0 (sec)
45%-55% 55% -70% 70%-85% 85% -100%
Week 6 Values of t 0
Ste p down
Ste p Up Ste p Up
Ste p Down
Ste p Up
Ste p Down
Ste p Up
Ste p Down
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 2 3 4 5 6 7 8
Trial
t0 (sec)
45%-55% 55% -70% 70%-85% 85% -100%
Week 6 Values of t 0
Ste p down
Ste p Up Ste p Up
Ste p Down
Ste p Up
Ste p Down
Ste p Up
Ste p Down
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 2 3 4 5 6 7 8
Trial
t0 (sec)
45%-55% 55% -70% 70%-85% 85% -100%
Frequency Response Experiment
Operate with alternating frequencies Amplitude equal to 5% or 7.5% Base Power equal to center of region. Starting Frequency of 1/(tau*2*pi) Vary frequency up and down to the
limits - when output is in phase with input or there is no perceptible oscillation
Sample Sine PlotInput and Output for Flow System at a 0.3 Hz Frequency
0
10
20
30
40
50
60
0 5 10 15 20 25 30
Time (seconds)
Input (%)
-1
1
3
5
7
9
11
13
15
17
Output (lbs/min)
Input
Output
TM2-20-06
(Transients)
Sample Sine PlotInput and Output for Flow System at a 0.3 Hz Frequency
0
10
20
30
40
50
60
40 41 42 43 44 45 46 47
Time (seconds)
Input (%)
8
9
10
11
12
13
14
15
Output (lbs/min)
Input
Output
T=3.4 Sec
t=0.6 sec
Phase Angle = (t/T)*360 = 64
dC=2.2dM=10dC/dM= 0.22 lbs/min/%
TM2-20-06
Bode Graph of Phase Angle vs Frequency
-360
-330
-300
-270
-240
-210
-180
-150
-120
-90
-60
-30
00.01 0.1 1
Frequency (Hz)
Phase Angle (degrees)
Bode Graph of Amplitude Ratio vs. Frequency
0.01
0.1
1
0.01 0.1 1Frequency (Hz)
Amplitude Ratio (lbs/mim/%)
fu=0.85 (cycles/time) K=0.24
lbs/min/%
1/Kcu=0.1% min/lbs
K=0.24 (lbs/min/%)Order=1fu=0.85 HzKcu=10 (%/lbs/min)tau=0.33 (sec)to=0.42 (sec)
Example Experimental Bode Plots
Modeling Approach
Output Function
Used Excel to Model
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Model Bode Plots 45%-55%Bode Plot of Frequency vs Phase Angle
-400
-350
-300
-250
-200
-150
-100
-50
0
0.01 0.1 1 10
Frequency (Hz)
Phase Angle (degrees)
Experimental
Model
TM2-20-06Bode Plot of Frequency vs Amplitude Ratio
0.01
0.1
1
0.01 0.1 1 10
Frequency (Hz)Amplitude Ratio (lbs/min/%)
Experimental
Model
TM2-20-06
Model Bode Plots 55%-70%Bode - Amplitude Ratio
0.01
0.1
1
0.01 0.1 1
Frequency (cycles/sec)
Amplitude Ratio (lb/min/%)
Experimental
Model
JP2-20-06 Bode - Phase Angle
-360
-180
0
0.01 0.1 1
Frequency (cycles/sec)
Phase Angle (degrees)
Experimental
Model
JP2-20-06
Model Bode Plots 70%-85%
Experimental Data Versus Model for PA
-270
-180
-90
0
0.01 0.1 1
Frequency (cycles/sec)
Phase Angle (degrees)
PA
Model PA
JL2-20-06
Experimental Data Versus Model for AR
0.01
0.1
1
0.01 0.1 1
Frequency (cycles/sec)
Amplitude Ratio (lb/min/%)
AR
Model AR
JL2-20-06
Model Bode Plots 85%-100%Frequency vs Amplitude ratio
0.01
0.1
1
0.01 0.1 1 10Frequency (Hz)
Amplitude Ratio (lb/min/%)Experiment
Model
JG2-20-06
Frequency vs. Phase Angle
-240
-220
-200
-180
-160
-140
-120
-100
-80
-60
-40
-20
00.01 0.1 1Frequency (Hz)
Phase Angle (degrees)
Experiment Model
JG2-20-06
Comparison of Results: GainExperiment and Model Values for K
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8
K (lbs/min/%)
Model Model Model Model
Lab Lab Lab Lab
45-55% 55-70% 70-85% 85-100%
Comparison of Results: Time ConstantExperiment and Model Values for Tau
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
1 2 3 4 5 6 7 8
Tau (seconds)Lab
Model
Lab Lab Lab
Model Model Model
45-55% 55-70% 70-85% 85-100%
Comparison of Results: Dead TimeExperiment and Model Values for to
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6 7 8
to (seconds)
Model Model Model Model
Lab Lab Lab Lab
45-55% 55-70% 70-85% 85-100%
Comparison of Results: Ultimate Frequency
Experimental Values for Ultimate Frequency
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 2 3 4
Frequency (Hz)
45-55% 55-70% 70-85% 85-100%
Comparison of Results: Ultimate Controller Gain
Experimental Values for Ultimate Controller Gain
0
2
4
6
8
10
12
14
1 2 3 4
Kcu (%/lbs/min)
45-55% 55-70% 70-85% 85-100%
Comparison of Results: OrderExperimental Order of System
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4
Order
45-55% 55-70% 70-85% 85-100%
Conclusion
FOPDT parameters from the model:
K = 0.22 lbs/min/%
Tau = 0.3 sec
to = 0.37 sec
Other values from experiment:
Kcu = 10 %/(lbs/min)
fu = 0.87 Hz
Order = 1