Flow Rate Control System “Root Locus Plotting” March 22, 2006 U.T.C. Engineering 329

Yellow Team Jimy George Jeff Lawrence Taylor Murphy Jennifer Potter

Outline Flow System Background Previous Work Root Locus Theory Modeling Results Conclusions First, I will provide a brief background in the Level II System Followed by FOPDT Theory & Model Theory Then I will discuss our results and colclude the presentation

Flow System Setup

Block Diagram

Steady State Operation

SSOC

Experimental and Model Results K (lb/min/%) = 0.26 Tau (sec) = 0.46 t0 (sec) = 0.42

Frequency Response Experiment

Bode Plots Kcu (%*min/lb) = 10.00 K (lb/min/%) = 0.24 Tau (sec) = 0.27 t0 (sec) = 0.35 m (order) = 1.14 fu (Hz) = 0.95 Bode Plots

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

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

FOPDT Parameters K = 0.24 lb/min/% Tau = 0.28 sec t0 = 0.4 sec

Closed Loop Transfer Function

Root Locus Theory Use Pade’s Approximation Find Roots of Denominator

Root Locus Parameters KCD KQD KCU

Response to Step Change in Set Point Symbol Average Critical Damping KCD 0.08 1/500th Decay KC500 1.8 1/10 Decay KC10 4.8 Quarter Decay KQD 6.6 Ultimate KCU 10 ζ Locations

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

Conclusions (cont.) For: Overdamped Kc needed: 0 < Kc < 0.08 For: Critically Damped Kc needed: Kc = 0.08 *all units are %*min / lb

Conclusions (cont.) For: Underdamped Kc needed: 0.08 < Kc < 10 For: Quarter Decay Kc needed: Kc = 6.6 *all units are %*min / lb

Response to Step Change in Set Point Conclusions (cont.) Response to Step Change in Set Point KC (%*min/lb) Offset (lb/min) Critical Damping 0.08 4.9 1/500th Decay 1.8 3.5 1/10 Decay 4.8 2.3 Quarter Decay 6.6 1.9 Ultimate 10 1.5