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 cm-H 2 O)

Step Down Function (Range cm-H 2 O)

FOPDT Model Equation C(t)= A*u(t-t d -t 0 )*K*(1-e -(t-td-to/tau ) ) For the given output range of cm-H 2 O, the following parameters were used: Td=15 sec. A=20 % K=0.75 cm-H 2 O/% t 0 =0.4 sec. Tau=1.5 sec. Inbl=45% Power Outbl=15 cm-H 2 O

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

Experimental Increasing Step Function Data Steady State Gain K=.76 +/-.02 cm H 2 0 / % Power Dead Time t o = 0.1 sec. Time Constant Tau = 1.5 +/-.3 sec. Model Increasing Step Function Data Steady State Gain K =.75 cm H 2 0 / % Power Dead Time t o = 0.4 sec. Time Constant Tau = 1.5 sec. First Order Step Up Response Results

Experimental Decreasing Step Function Data Steady State Gain K=.74 +/-.015 cm H 2 0 / % Power Dead Time t o = 0.1 sec. Time Constant Tau = 2.1 +/-.2 sec. Model Decreasing Step Function Data Steady State Gain K =.75 cm H 2 0 / % Power Dead Time t o = 0.4 sec. Time Constant Tau = 1.5 sec. First Order Step Down Response Results

Sine Wave at.2 Frequency

Frequency

Bode Plot for range 2

Phase angle vs. Frequency

What we find with Bode Range 1Range 2Range 3 FU0.46 cycles/sec.44 cycles /sec0.4 cycles/sec k1 cm-H20/% order /kcu0.34 cm-H20/% 0.35 cm-H20/%

Modeling – Frequency vs. AR

Modeling – Frequency vs. PA

Conclusion 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-H 2 O 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 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