Jamie West Jay Baker Joel Wood 10/10/11 UTC ENGR 3280L Yellow Team Spray-Booth Pressure Station Steady, Step Behavior and Step Modeling Jamie West Jay Baker Joel Wood 10/10/11 UTC ENGR 3280L

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 Conclusions

Pressure Schematic

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

Experiment Data at a Specified Input

Graphical Results

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

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

FOPDT 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% Power Outbl=15 cm-H2O FOPDT

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

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

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

First Order Step Down Response Results 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 Results

Sine Wave at .2 Frequency

Lissajous @ .2 Frequency

Bode Plot for range 2

Phase angle vs. Frequency

What we find with Bode Range 1 Range 2 Range 3 FU 0.46 cycles/sec k 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. AR

Modeling – Frequency vs. PA

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 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 Part 1

Conclusion Part 2 Sine Wave Experiment Bode Graph –AR vs. Frequency Bode Graph – PA vs. Frequency Yellow team 1/kcu – k – order – FU calcs Frequency Response Modeling Conclusion Part 2