-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=