Team Green

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Team Green
Speed Control Root Locus Plotting

• John Barker
• Keith Skiles
• John Beverly

UTC ENG 329 March 22, 2006
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Presentation Purpose

• Root Locus Plotting
• Determine various Kc Values for system controller
• Determine Offsets for Different Kc Values

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Steady State Operating Curve (SSOC) and FOPDT
Parameters Review

• System Background Review
• (Description, SSOC, Step Response)
• Step Response (Experiment Model)
• Sine Response (Experiment Model)
• Bode Plots

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Aerator Mixer Speed Control System
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Block Diagram of System
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SSOC Graph
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First Order Plus Dead Time(FOPDT) Theory
-t0s

• System Transfer Function
• G(s) Ke-to /ts1
• Parameters
• t0Dead Time
• K System Gain
• t Time Constant

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Step Response Results
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Step Response Averages
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Frequency Response PlotSine Response Freq.
0.3 Amplitude 15
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Frequency Response Model Conclusions
Frequency Response
Step Response
K 17.3 rpm/ to .2s t .17s
K 17.1 rpm/ to0.14s t 0.19s
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Bode Plot Model
Baseline Modeling Variables
t00.14s K 17.1 rpm/ t 0.19s
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Bode Plot AR
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Bode Plot Phase Angle
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System Conclusions
Order 1 fu 2.3 Hz Kcu 0.2 ( / RPM)
K 17.1 rpm/ to0.14s t 0.19s
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Feedback Control
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Root Locus Parameters

• KCD Critically Damped
• KQD Value of KC that produces one-quarter
  oscillating decay
• KCU Ultimate Controller Gain

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z Locations
All Kc Units are / RPM
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Results from Root Locus

• Ultimate KCU 0.16
• Quarter Decay KQD 0.10
• Critically Damping KCD 0.002
• Underdamped 0.002ltKClt0.16
• Overdamped 0ltKClt0.002
• Ultimate Frequency fu 2.3 Hz
• All Units unless noted are ( / RPM)

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Offset

• Steady State Error
• Steady state deviation of controlled variable
  from the set point

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Offset for KCD
Mbar 81
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Offset for Decay Ratio of 1/500
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Offset for Decay Ratio of 1/10
?r -400 RPM
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Offset for Decay Ratio of 1/4
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Offset for KCU
?r -400 RPM
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Offsets for Different Kc Values
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Final Values for Set Point of 1400 RPM
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Final Values for a Set Point of 1400 RPM
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Conclusions

• For KC Needed
• Overdamped 0ltKClt0.002
• Critically Damped KC 0.002
• 1/500 Decay KC 0.03
• 1/10 Decay KC 0.08
• 1/4 Decay KC 0.10
• All Units are ( / RPM)