Pressure Control System: Root Locus Plotting

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 Controlled Variable M System C % Motor Speed Pressure in cm-H2O

5. Background: SSOC Output: 1.3 –3.8 cm H2O Operating Range: 30 – 70%

6. K = 0.061 cm of H2O / % to = 0.25 sec t = 0.4 sec Background: FOPDT Parameters

7. Feedback Control

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

9. ³ 1 < z < 1 = 0 -1 < z < 0 z £ -1 Overdamped = monotonic and stable Underdamped = oscillatory and stable Undamped = sustained oscillations Unstable = growing oscillations Run-away = monotonic and unstable Effects of z

10. Four Possible Responses

11. Root Locus Parameters • KCD = highest value of KC that provides monotonic and stable output (critically damped) • KQD = value of KC that produces one- quarter oscillating decay • KCU = highest value of KC that causes oscillatory and stable output (marginally stable)

12. Root Locus Parameters • KCD is found where the roots go from real to complex • KQD is found where the ratio of the imaginary root to the real root is 4.5 • KCU is found where the real portion of the root goes from negative to positive.

13. Parameter Locations Dr Henry’s Suggestion: Put the VALUES of the Kc’s for the different choices you have on this graph KQD KCU KCD

14. z Locations

15. Results from Root Locus • Ultimate Kcu= 37 • Quarter Decay Kc = 24. • Critically Damping Kc = 0.1 • Underdamped 0.1< Kc < 37 • Overdamped 0 < Kc < 0.1 *all units are % / cm H2O

16. Conclusions ForKc needed Overdamped 0 < Kc < 0.1 Critically Damped Kc = 0.1 Underdamped 0.1< Kc < 36.9 Quarter Decay Kc = 24.2 *all units are % / cm H2O

17. Questions?