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