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Root Locus PlottingRed Squad
Flow SystemBen Gordon, Ben Klingler, Dianah Dugan
October 31, 2007
University of Tennessee ChattanoogaENGR 329
Introduction
Flow system background Previous work: Transfer function Root Locus Theory Modeling Results Conclusions
Background
Waste Water Treatment Plant
Background Block Diagram of Filter Wash Flow
System
Background
Steady-State Operating Curve
0
5
10
15
20
25
10 20 30 40 50 60 70 80 90 100
Power Input (%)
Ave
rag
e O
utp
ut
(lb
/min
)
Lower
Middle
Upper
Background: FOPDT Parameters
1
0
s
Ke st
C (s)M (s)
Power Input (%) Flow Output (lb/min)
Previous Parameters
Step Response K (lb/min%)=0.32, to (s)=1.1, tau (s)=1.4
Step Modeling K (lb/min%)=0.24, to (s)=0.73, tau (s)=0.58
Sine Response Modeling K (lb/min%)=0.29, to (s)=0.61, tau (s)=0.57
Feedback Control
Root Locus Theory Quadratic Formula
a
acbbx
2
42
Gives real and complex roots for root locus
Root Locus Lower Region
ROOT LOCUS PLOT
-6
-4
-2
0
2
4
6
-4 -3 -2 -1 0 1
REAL AXIS
IMA
GIN
AR
Y A
XIS
KCD
K500
K10
KQD
KCU
Lower Region Results
K = 0.26 lb/min%, t0 = 0.53 s, tau = 0.7 s
Critical Damping (KCD) 0.6
1/500th Decay (K500) 2.6
1/10th Decay (K10) 6.9
Quarter Decay (KQD) 8.9
Ultimate (KCU) 14
Root Locus Middle Region
ROOT LOCUS PLOT
-8
-6
-4
-2
0
2
4
6
8
-5 -4 -3 -2 -1 0 1 2
REAL AXIS
IMA
GIN
AR
Y A
XIS
KCD
K500
K10
KQDKCU
Middle Region Results
K=0.32 lb/min%, t0=0.49 s, tau=0.61 s
Critical Damping (KCD) 0.42
1/500th Decay (K500) 2
1/10th Decay (K10) 5.4
Quarter Decay (KQD) 6.9
Ultimate (KCU) 11
Root Locus Upper Region
ROOT LOCUS PLOT
-6
-4
-2
0
2
4
6
-4 -3 -2 -1 0 1
REAL AXIS
IMA
GIN
AR
Y A
XIS
KCD
K500
K10
KQD
KCU
Results for Upper Region K= 0.29 lb/min%, t0= 0.58 s, Tau=
0.50 sCritical Damping (KCD) 0.16
1/500th Decay (K500) 1.6
1/10th Decay (K10) 4.6
Quarter Decay (KQD) 6
Ultimate (KCU) 9.4
Conclusions
Know how the system responds to different controller inputs
Starting to know how to control the response from the system, by using different Kc values for the controller
