Root Locus Plotting Red Squad Flow System Ben Gordon, Ben Klingler, Dianah Dugan October 31, 2007...

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