Flow Rate Control System Proportional Only Controller April 2, 2006 U.T.C. Engineering 329

Yellow Team Jimy George Jeff Lawrence Taylor Murphy Jennifer Potter

Outline Flow System Background Previous Work Proportional Control Modeling Results Conclusions

Flow System Setup

Block Diagram

Steady State Operation

SSOC

Step Response Results K (lb/min/%) =0.26 τ (sec) =0.46 t 0 (sec) =0.42

Frequency Response Experiment

Bode Plots Kcu (%/(lb/min) =10.00 K ((lb/min)/%) =0.24 τ (sec) =0.27 t 0 (sec) =0.35 m (order) =1.14 fu (Hz) =0.95

Model Bode Plot K (lb/min/%) =0.22 t0 (sec) =0.35 Tau (sec)=0.25 f u =0.95

Model Bode Plot K (lb/min/%) =0.22 t0 (sec) =0.35 Tau (sec)=0.25 K cu =10

FOPDT Parameters K = 0.24 (lb/min)/% τ = 0.28 sec t 0 = 0.4 sec

Closed Loop Transfer Function

Root Locus Parameters K CD =0.08 K QD =6.6 K CU =10 f u =1.24 *all units for K are % / (lb/min)

ζ Locations Response to Step Change in Set PointSymbolAverage Critical DampingK CD /500th DecayK C /10 DecayK C Quarter DecayK QD 6.6 UltimateK CU 10

Results From Root Locus Ultimate Quarter Decay Critically Damped Underdamped Overdamped Kc = 10 Kc = 6.6 Kc = < Kc < 10 0 < Kc < 0.08 *all units are % / (lb/min)

Predicted Ultimate Frequency and Ultimate Gain Bode PlotLuyben Method Routh Method Direct Substitution K CU = 10% / (lb/min) K CU = 9.6% / (lb/min) K CU = 10% / (lb/min) F u =0.87 HzF u =0.67 Hzn/aF u = 1.24 Hz

Model Results for K CD Offset Offset = 4.9 lb/min Decay Ratio = 0 Settling Time = 0.8 s K CD = 0.10% / (lb/min) Set Point Output Settling Time

Model Results for K QD Offset Offset = 1.9 lb/min Decay Ratio = 0.25 Settling Time = 3.9 s K QD = 6.6%/ (lb/min) Settling Time Set Point Output

Model Results for K CU Offset = 1 lb/min Decay Ratio = 1 Settling Time = never K CU = 10%/ (lb/min) Output Set Point Offset

Proportional Only Model Results K C (%*min/lb)Offset (lb/min) Critical Damping /500th Decay /10 Decay Quarter Decay Ultimate101.5

Experimental Results for K CD Offset = 4.9 lb/min Decay Ratio = 0 Settling Time = 0.8 s K CD = 0.10% / (lb/min) Settling Time Offset

Experimental Results for K QD Offset = 2.4 lb/min Decay Ratio = 0.25 Settling Time = 4.5 s K QD = 0.10% / (lb/min) Offset Settling Time

Experimental Results for K CU Offset = 1.2 lb/min Decay Ratio = 1 Settling Time = never K CD = 10% / (lb/min) Offset

Proportional Only Experimental Results K C (%*min/lb)Offset (lb/min) Critical Damping /500th Decay /10 Decay Quarter Decay Ultimate101.2

Comparison of Results Critical Damping 1/500th Decay 1/10th Decay 1/4th Decay Ultimate Root Locus P-Only Model P-Only Experimental

Conclusion For Kc needed Overdamped0 < Kc < 0.10 Critically DampedKc = 0.10 Underdamped0.10< Kc < 10 Quarter Decay Kc = 5.0