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

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

Background: Schematic Diagram

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

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

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

Feedback Control

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

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

Four Possible Responses

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)

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.

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

 Locations

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

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

Questions?