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

2. Yellow Team
Jimy George
Jeff Lawrence
Taylor Murphy
Jennifer Potter

3. 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

4. Flow System Setup

5. Block Diagram

6. Steady State Operation

7. SSOC

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

9. Frequency Response Experiment

10. 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

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

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

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

14. Closed Loop Transfer Function

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

16. Root Locus Parameters
KCD
KQD
KCU

17. 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

18. 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

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

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

21. 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