team flow eric parker jason gunn nathan funk. outline zbackground zprevious work zmodeling zresults...
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Team Flow
Eric Parker Jason Gunn Nathan Funk
Outline
BackgroundPrevious WorkModelingResults and ConclusionsQuestions
FLOW SYSTEM
Flow Background
Storage Tank
Pump
Flow Meter
Flow Background
Input = % motor speed
Output = mass flow rate (lbs/min)
SSOC Operating Range 10% - 90%
SSOC vs. COC
y = 0.64x - 1.12
0
10
20
30
40
50
60
0 20 40 60 80 100
Input (% motor speed)
Ou
tpu
t (l
b/m
in)
Controller Operating Curve
21 lb/min
30 lb/min
Previous Work
Modeling Step InputFOPDT ModelTransfer Function Parameters
tau=0.4sec K=0.66 (lbs/min)/% to=0.3 sec where
G=(Ke^(to*s))/(tau*s+1)
First Order Step Response
0
10
20
30
40
50
60
70
80
90
100
15 17 19 21 23 25 27
Time (sec)
% M
oto
r In
pu
t
0
10
20
30
40
50
60
70
Flo
w R
ate
(lbs/
min
)
Input
Experimental Output
Model Output
Previous WorkModeling Sine InputFOPDT ModelTransfer Function Parameters
tau=0.4sec K=0.7 (lbs/min)/% to=0.3 sec
Bode Plots
Frequency response
35
40
45
50
55
60
65
25 30 35 40 45 50
Time (sec)
% IN
PU
T
10
15
20
25
30
35
40
45
OU
TP
UT
(lb
s/m
in)Delta Y
Delta M
Input
Exp. Output
Model Output
Bode Plots
Two Types
Phase Angle vs Frequency
AR vs Frequency
Bode Plot
-360
-270
-180
-90
0
0.01 0.1 1 10
Frequency (Hz)
Ph
ase
An
gle
Fu
Model
Experimental
Bode Plot
0.1
1
0.01 0.1 1 10
Frequency (HZ)
AR
1/Kcu
Fu
-m = order
ExperimentalModel
Bode Results
Apparent Order is 1.8
Kcu = 2.6 (lbs/min)/%
Fu = 0.8 Hz
Modeling
Root Locus
ROOT LOCUS PLOT
-10
-8
-6
-4
-2
0
2
4
6
8
10
-7 -6 -5 -4 -3 -2 -1 0
REAL AXIS
IMA
GIN
AR
Y A
XIS
Ultimate
Critical
Quarter Decay
Theoretical Results
K cd= .22
K qd=3.4
K cu=5.2
Experimental Results
K cd=<.1
K qd=1.6
K cu=2.3
Kcd=.1
17
17.5
18
18.5
19
19.5
20
20.5
21
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30
Time (sec)
Lb
/min
Kqd=1.6
20
22
24
26
28
30
32
34
36
38
40
29 29.5 30 30.5 31 31.5 32 32.5 33 33.5 34
Time (sec)
Lb
/min
4.0
1
Verification
1st peak = 4.02nd peak = 1.01/4 = .25 decay
Frequency1/(31.7-
30.5)=.83hz
Kcu=2.3
18
23
28
33
38
57 58 59 60 61 62 63 64 65
Time (sec)
lb/m
in
5 3.5
Calculations
1st peak=37.5 - 32.5=52nd peak=36-32.5=35Decay=(3.5/5)= .70
Frequency1/(59.2-57.9)
= .77hz
Experimental Results
K cd=<.1
K qd=1.6
K cu=2.3
Discussion
Theory ExperimentalKcd=.22 Kcd<.1
Kqd=3.4 Kqd=1.6
Kcu=5.2 Kcu=2.3
Conclusions
Critical damped Kc value .1
Quarter decay Kc value 1.6
Ultimate Kc value 2.3
QUESTIONS ?