1. Pressure Control System: Root Locus Plotting Team Green: X Y Z

2. Outline Pressure System Background Previous Work: Transfer Function Root Locus Theory Modeling Results Conclusions

3. Background: Schematic Diagram

4. Background: Block Diagram Manipulated Variable M System C Controlled Variable % Motor Speed Pressure in cm-H 2 O

5. Background: SSOC Operating Range: 30 – 70% Output: 1.3 –3.8 cm H 2 O

6. Background: FOPDT Parameters K = 0.061 cm of H 2 O / % t o = 0.25 sec  = 0.4 sec

7. Feedback Control

8. Root Locus Theory Where  is the damping ratio. Decay Ratio =

9. Effects of          Overdamped = monotonic and stable Underdamped = oscillatory and stable Undamped = sustained oscillations Unstable = growing oscillations Run-away = monotonic and unstable

10. Four Possible Responses

11. Root Locus Parameters K CD = highest value of K C that provides monotonic and stable output (critically damped) K QD = value of K C that produces one-quarter oscillating decay K CU = highest value of K C that causes oscillatory and stable output (marginally stable)

12. Root Locus Parameters K CD is found where the roots go from real to complex K QD is found where the ratio of the imaginary root to the real root is 4.5 K CU is found where the real portion of the root goes from negative to positive.

13. Parameter Locations K CD K CU K QD Dr Henry’s Suggestion: Put the VALUES of the Kc’s for the different choices you have on this graph

14.  Locations

15. Results from Root Locus Ultimate K cu = 37 Quarter Decay K c = 24. Critically Damping K c = 0.1 Underdamped 0.1< K c < 37 Overdamped 0 < K c < 0.1 *all units are % / cm H 2 O

16. Conclusions For K c needed Overdamped 0 < K c < 0.1 Critically Damped K c = 0.1 Underdamped 0.1< K c < 36.9 Quarter Decay K c = 24.2 *all units are % / cm H 2 O

17. Questions?