-Pressure System- Root Locus Cory Richardson Dennis To Jamison Linden 6/14/2015, UTC, ENGR-329

Contents  Background Description, SSOC, Input/Output  Transfer Function  Step Response/Frequency Response  Root Locus  Modeling  Results  Conclusions

Background - System Figure 1. Schematic diagram of the Dunlap Plant Spray-Paint Booths

Background - Block Diagram Figure 2. Block diagram of paint booth system

Background - SSOC Operating Range for Output Operating Range for Input

Transfer Function Transfer Function m(s) Input c(s) Output

Background – Step Response

Background – Step Response Results ExperimentModel Gain cm- H2O/% Dead Time0.5 s0.48 s Time Constant1.7 s1.75 s

Frequency Response - Example c (1.45) T (25.3) m (15) t (-1.8)

Frequency Response – Bode Plots f u =0.85 Hz

Frequency Response – Bode Plots K= 0.35 cm-H 2 O/% 2 nd Orderfu=0.85 AR=.024

Modeling Approach – Bode Plots

Results Comparison  Experimental Results: K = 0.1 – 0.35(cm-H 2 0/%) t 0 = 0.6 s  = 1.7 s 2 nd Order system Ultimate Frequency = 0.85 Hz Ultimate Controller Gain = 42 – 204 (%/cm-H 2 O)

Results Comparison  Model Results: K = 0.1 – 0.35 (cm-H 2 O/%) t 0 = 0.85 s  = 1.7 s

System  2 nd order system  f u = 0.85 Hz  From the model: K = 0.1 – 0.35 (cm-H 2 O/%) t 0 = 0.85 s  = 1.7 s  K cu = 18.2 – 55.6 (%/cm-H 2 O)

Feedback Control

 Locations

Kc Locations 45-60%

Kc Locations 60-75%

Kc Locations 75-90%

Root Locus Results (45-60%)  Ultimate K cu =55  1/500 th Decay K c =11  1/10 th Decay K c =27  Quarter Decay K c =36  Critically Damping K c = 4.4  Underdamped 4.4< K c < 55  Overdamped 0 < K c < 4.4 *all units are %/cm H 2 O

Root Locus Results (60-75%)  Ultimate K cu =28  1/500 th Decay K c =5.9  1/10 th Decay K c =16  Quarter Decay K c =18  Critically Damping K c = 2.2  Underdamped 2.2< K c < 28  Overdamped 0 < K c < 2.2 *all units are %/cm H 2 O

Root Locus Results (75-90%)  Ultimate K cu =14  1/500 th Decay K c =2.8  1/10 th Decay K c =7.9  Quarter Decay K c =8.6  Critically Damping K c = 1.0  Underdamped 1.0< K c < 14  Overdamped 0 < K c < 1.0 *all units are %/cm H 2 O

Conclusions For 45-60% K c needed Overdamped 0 < K c < 4.4 Critically Damped K c = 4.4 Underdamped 4.4< K c < 55 Quarter Decay K c = 36 *all units are % / cm H 2 O

Conclusions For 60-75% K c needed Overdamped 0 < K c < 2.2 Critically Damped K c = 2.2 Underdamped 2.2< K c < 28 Quarter Decay K c = 18 *all units are % / cm H 2 O

Conclusions For 75-90% K c needed Overdamped 0 < K c < 1.0 Critically Damped K c = 1.0 Underdamped 1.0< K c < 14 Quarter Decay K c = 8.6 *all units are % / cm H 2 O

Conclusions Offset=