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

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

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

Input Sine wave @ .2 Hz

Output Sin wave @ .2 Hz

Plain Bode Range 1

PA vs. Frequency Range 1

Bode Plot for range 2

Phase angle vs. Frequency

Bode – Range 3

PA vs. Frequency – Range 3

FU,k,order,1/Kcu per Range

Modeling – Frequency vs. AR

Modeling – Frequency vs. PA

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

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 )

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.

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.

Kc Values Per Range

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

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

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

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

Conclusions