1. Jamie West Jay Baker Joel Wood 11/2/11 UTC ENGR 3280L
Yellow Team Spray-Booth Pressure Station Steady, Step Behavior and Step Modeling, Sine Wave , Modeling
Jamie West
Jay Baker
Joel Wood
11/2/11
UTC ENGR 3280L

2. Overview Schematic of the system
Results of Steady State Operating Curve
Results of Step Function
FOPDT Theory
Model Theory
FOPDT Results
Frequency Response
Frequency Response Modeling
Root Locus Theory
Root Locus Modeling
Conclusions
Overview

3. Pressure Schematic

4. Input M(t) - Specified by user Output - Air pressure resulting from motors response.

5. Experiment Data at a Specified Input

6. Graphical Results

7. Step Up Function (Range 15-30 cm-H2O)

8. Step Down Function (Range 30-15 cm-H2O)

12. FOPDT Model Equation C(t)= A*u(t-td-t0)*K*(1-e-(t-td-to/tau))
For the given output range of 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% Power
Outbl=15 cm-H2O
FOPDT

13. First Order Step Up Response with Time Delay
K=0.76 +/-.02 cm-H2O/%Power
Tau=1.5 +/-0.3 sec.
To= 0.1 sec.
First Order Step Up Response with Time Delay

14. First Order Step Down Response with Time Delay
Experimental and Model inputs
To=0.1 sec.
K=0.74 +/-0.15 cm-H2O/%Power
Tau= 2.1+/-0.2 sec.
First Order Step Down Response with Time Delay

18. First Order Step Up Response Results
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 Results

19. First Order Step Down Response Results
Experimental Decreasing Step Function Data
Steady State Gain K= .74 +/ 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 Results

20. Input Sine .2 Hz

21. Output Sin .2 Hz

22. Plain Bode Range 1

23. PA vs. Frequency Range 1

24. Bode Plot for range 2

25. Phase angle vs. Frequency

26. Bode – Range 3

27. PA vs. Frequency – Range 3

28. FU,k,order,1/Kcu per Range

29. Modeling – Frequency vs. AR

30. Modeling – Frequency vs. PA

31. Root Locus Theory Equation to find the roots of the system
In this equation z stands for the damping ratio
Once the damping ratio has been determined this equation is used to find the decay ratio

32. Different Effects of the Damping Ratio (z )
For The response is z ≥1 overdamped = monotonic and stable 0 < z < 1 underdamped = oscillatory and stable z = 0 undamped = sustained oscillations -1 < z < 0 unstable = growing oscillations z ≤ -1 runaway = monotonic unstable
Different Effects of the Damping Ratio (z )

33. Root Locus Background
Kcd- The value where kc is the highest while still having a stable and monotonic output
Kqd- Value of kc where one quarter of the oscillation is produced
Kcu-The value where kc is the highest and produces an oscillatory and stable output.

34. Kcd -(Critical Damping)can be found where the plot of the root locus crosses the x-axis
Kqd -(Quarter Decay)is found where a ratio of 4.5 is present between the real root and imaginary root
Kcu -(Ultimate) is found where the real portion of the root changes from negative to positive.

35. Kc Values Per Range

36. Modeling Results 1-15 cm-h2o 15-30 cm-h2o 30-45 cm-h2o Ultimate 78.5
1-15 cm-h2o
15-30 cm-h2o
30-45 cm-h2o
Ultimate
78.5
5.94 30
Quarter Decay
51.7
3.9
20.5
Critically Damping 12
0.38
4.7
Underdamped
12 < Kc < 78.5
.38 < Kc < 5.94
4.7 < Kc < 30
Overdamped
0 < Kc < 12
0 < Kc < .38
0 < Kc < 4.7
Modeling Results

37. 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-H2O
FOPDT transfer functions are important to approximate the response of dynamic processes
Conclusion 1

38. Conclusion 2 FOPDT Model Graph and Experimental Graph are consistent
Pressure 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 2

39. Conclusion 3 Sine Wave Experiment Bode Graph –AR vs. Frequency
Bode Graph – PA vs. Frequency
Yellow team
1/Kcu = .35 cm-H20/%
k = 1 cm – H20/%
FU = .43 cycles/second
Order = .8
Conclusion 3

40. Conclusions