Yellow TeamYellow TeamSpray-Booth Pressure StationSpray-Booth Pressure Station
Steady, Step Behavior and Step Steady, Step Behavior and Step ModelingModeling
Jamie WestJay BakerJoel Wood
10/10/11UTC ENGR 3280L
OverviewOverview
Schematic of the systemResults of Steady State Operating CurveResults of Step FunctionFOPDT TheoryModel TheoryFOPDT ResultsFrequency Response Frequency Response Modeling Conclusions
Pressure SchematicPressure Schematic
Input M(t) - Specified by user Input M(t) - Specified by user Output - Air pressure resulting from motors Output - Air pressure resulting from motors
response. response.
Experiment Data at a Specified InputExperiment Data at a Specified Input
Graphical ResultsGraphical Results
Step Up Function (Range 15-30 cm-HStep Up Function (Range 15-30 cm-H22O)O)
0
10
20
30
40
50
60
70
14 15 16 17 18 19 20 21 22Time (sec)
Inpu
t % P
ower
0
5
10
15
20
25
30
35
Out
put (
cm-H
2O)
Input Value(%)Output(cm-H20)
Delta M=20
Delta C=15
K=15/20=0.75 cm H2O/%
To=0.1sec
Tau=1.5 sec .632*15=9.48
Step Down Function Step Down Function (Range 30-15 cm-H(Range 30-15 cm-H22O)O)
Average to Values Per Range
0.000.050.100.150.200.250.300.350.400.45
1 2 3
Separate Ranges
Tim
e (s
)
Step Up
Step Down
Average Tau Values Per Range
-1.00
-0.50
0.00
0.50
1.00
1.50
2.00
2.50
1 2 3
Seperate Ranges
Tim
e (s
)Step Up
Step Down
Average k Values per Range
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1 2 3
Separate Ranges
cm-H
2O/%
Step Up
Step Down
FOPDTFOPDT
Model Equation
C(t)= A*u(t-td-t0)*K*(1-e-(t-td-to/tau))
For the given output range of 15-30 cm-H2O, the following parameters were used:
Td=15 sec.A=20 %K=0.75 cm-H2O/% t0=0.4 sec.Tau=1.5 sec.
Inbl=45% PowerOutbl=15 cm-H2O
First Order Step Up Response with First Order Step Up Response with Time DelayTime Delay
K=0.76 +/-.02 cm-H2O/%Power
Tau=1.5 +/-0.3 sec. To= 0.1 sec.
First Order Step Down Response First Order Step Down Response with Time Delaywith Time Delay
Experimental and Model inputs
K=0.74 +/-0.15 cm-H2O/%Power
To=0.1 sec.
Tau= 2.1+/-0.2 sec.
Average To Values Per Range
0.00
0.04
0.08
0.12
0.16
0.20
Exp Model
Separate Ranges
Tim
e (s
)
Step Up
Step Down
Average Tau Values Per Range
0.00
0.50
1.00
1.50
2.00
2.50
Exp Model
Seperate Ranges
Tim
e (s
)
Step Up
Step Down
Average k Values per Range
0.690.700.710.720.730.740.750.760.770.780.79
Exp Model
Separate Ranges
cm-H
2O/%
Step Up
Step Down
Experimental Increasing Step Function Data
Steady State Gain K= .76 +/- .02 cm H20 / % Power
Dead Time to = 0.1 sec.
Time Constant Tau = 1.5 +/- .3 sec.
Model Increasing Step Function Data
Steady State Gain K = .75 cm H20 / % Power
Dead Time to = 0.4 sec.
Time Constant Tau = 1.5 sec.
First Order Step Up Response First Order Step Up Response ResultsResults
Experimental Decreasing Step Function Data
Steady State Gain K= .74 +/- .015 cm H20 / % Power
Dead Time to = 0.1 sec.
Time Constant Tau = 2.1 +/- .2 sec.
Model Decreasing Step Function Data
Steady State Gain K = .75 cm H20 / % Power
Dead Time to = 0.4 sec.
Time Constant Tau = 1.5 sec.
First Order Step Down Response First Order Step Down Response ResultsResults
Sine Wave at .2 Frequency Sine Wave at .2 Frequency
Lissajous @ .2 FrequencyLissajous @ .2 Frequency
Bode Plot for range 2Bode Plot for range 2
Phase angle vs. FrequencyPhase angle vs. Frequency
What we find with Bode What we find with Bode
Range 1 Range 2 Range 3
FU 0.46 cycles/sec .44 cycles /sec 0.4 cycles/sec
k 1 cm-H20/% 1 cm-H20/% 1 cm-H20/%
order 0.82 0.85 0.8
1/kcu 0.34 cm-H20/% 0.34 cm-H20/% 0.35 cm-H20/%
Modeling – Frequency vs. ARModeling – Frequency vs. AR
Modeling – Frequency vs. PAModeling – Frequency vs. PA
Conclusion Part 1Conclusion Part 1
Understanding the Steady State Operating Range of the system allows the user to predict Output pressures
Operating range of the motor was 5-45 cm-H2OFOPDT transfer functions are important to approximate
the response of dynamic processesFOPDT Model Graph and Experimental Graph are
consistentPressure System has a quick response time of To=0.1sec. Differential of Tau: Step Up 1.5+/-.3sec. Step Down
2.1+/-.2 sec.
Conclusion Part 2Conclusion Part 2
Sine Wave ExperimentBode Graph –AR vs. Frequency Bode Graph – PA vs. Frequency Yellow team 1/kcu – k – order – FU calcsFrequency Response Modeling