1. Root Locus Plotting Red Squad Flow System Ben Gordon, Ben Klingler, Dianah Dugan October 31, 2007 University of Tennessee Chattanooga ENGR 329

2. Introduction Flow system background Previous work: Transfer function Root Locus Theory Modeling Results Conclusions

3. Background Waste Water Treatment Plant

4. Background Block Diagram of Filter Wash Flow System

5. Background Lower Middle Upper

6. Background: FOPDT Parameters C (s)M (s) Power Input (%)Flow Output (lb/min)

7. 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

8. Feedback Control

9. Root Locus Theory Quadratic Formula Gives real and complex roots for root locus

10. Root Locus Lower Region K CD K 500 K 10 K QD K CU

11. Lower Region Results K = 0.26 lb/min%, t 0 = 0.53 s, tau = 0.7 s Critical Damping (K CD )0.6 1/500th Decay (K 500 )2.6 1/10th Decay (K 10 )6.9 Quarter Decay (K QD )8.9 Ultimate (K CU )14

12. Root Locus Middle Region K CD K 500 K 10 K QD K CU

13. Middle Region Results K=0.32 lb/min%, t 0 =0.49 s, tau=0.61 s Critical Damping (K CD )0.42 1/500th Decay (K 500 )2 1/10th Decay (K 10 )5.4 Quarter Decay (K QD )6.9 Ultimate (K CU )11

14. Root Locus Upper Region K CD K 500 K 10 K QD K CU

15. Results for Upper Region K= 0.29 lb/min%, t 0 = 0.58 s, Tau= 0.50 s Critical Damping (K CD )0.16 1/500th Decay (K 500 )1.6 1/10th Decay (K 10 )4.6 Quarter Decay (K QD )6 Ultimate (K CU )9.4

16. 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