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