Pressure Control System:Root Locus Plotting

Team Green:

X

Y

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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-H2O

Background: SSOC

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 10 20 30 40 50 60 70 80 90 100

% Motor

Operating Range: 30 – 70%

Ou

tpu

t: 1.3 –3.8 cm

H2O

Background: FOPDT Parameters

K = 0.061 cm of H2O / %

to = 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

Stable, Monotonic

Unstable, Oscillatory Unstable, Monotonic

Stable, Oscillatory

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)

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.

Parameter Locations

ROOT LOCUS PLOT

-10

-8

-6

-4

-2

0

2

4

6

8

10

-6 -5 -4 -3 -2 -1 0 1

REAL AXIS

IMA

GIN

AR

Y A

XIS

KCD

KCUKQD

Dr Henry’s Suggestion:Put the VALUES of the Kc’sfor the different choices you have on this graph

Locations ROOT LOCUS PLOT

-10

-8

-6

-4

-2

0

2

4

6

8

10

-6 -5 -4 -3 -2 -1 0 1

REAL AXIS

IMA

GIN

AR

Y A

XIS

DR=0

DR=1/500

DR=1/10

DR=1/4

DR=1/1

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

Conclusions

For Kc 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

Questions?