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 ?