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Green Team Speed System Proportional Only Controller Design and Experimental 11-09-05 Dustin Fraley DeAndre Strong Stephanie Wilson
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Outline Description of Speed System Previous work Step Response Frequency Response Root Locus Proportional only controller response curves Model Experimental Results Conclusions
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Speed System Diagram SRC 1 ST 1 Motor / Generator SCZ 1
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SSOC Input-Output Relationship Speed System M(t) Input (%) C(t) Output (RPM)
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Step Response Input-Output Relationship Ke -t 0 M(t) Input (%) C(t) Output (RPM) τ – Time Constant (s) = 0.2 t 0 – Dead Time (s) = 0.1 K – Gain (RPM/%) = 17
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Frequency Response Input-Output Relationship Ke -t 0 M(t) Input (%) C(t) Output (RPM) τ – Time Constant (s) t 0 – Dead Time (s) K – Gain (RPM/%)
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tau - t 0 - tau -0.2 s t 0 – 0.1 s
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Step and Frequency Response Experiments Conclusions FOPDT Parameters = 0.2 s t o = 0.1 s K = 17 RPM/% order about 1st f u = 3.5 Hz K cu = 0.3%/RPM
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Feedback Controller
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Characteristic Equation (CE) Padés Approximation
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Control Gain Locations K C-CD =0.02 %/RPM K CU =0.3 %/RPM K QD =0.19 %/RPM Over-damped Under-dampedUnstable f u = 24/2 Π = 3.82 Hz
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Root Locus Conclusions Ultimate K cu = 0.3 Quarter Decay K c = 0.19 Critically Damping K CD = 0.02 Underdamped 0.02<K c <0.3 Overdamped 0<K c <0.02 *all units are % / RPM
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Determination of f u Bode plots f u = 3.5 Hz Characteristic Equation (CE) f u = 4 Hz Root Locus f u = 3.8 Hz
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P-only Controller Analysis Model FOPDT Parameters = 0.2 s t o = 0.1 s K = 17 RPM/% Values found for Ultimate (Marginal Stability) Quarter Decay Critical Damping Overdamped
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Decay Ratio – 1 Oscillatory Settling Time – Never Offset - CBD Set Point Output
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Decay Ratio – 0.25 Oscillatory Settling Time – 1.25 s Offset – 71 RPM Set Point Output
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Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 219 RPM Set Point Output
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Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 230 RPM Set Point Output
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Controller Operating Curve for Model m bar = 63% r(t) = 1100 RPM delta r = 300 RPM
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P-only Controller Analysis Experimental FOPDT Parameters = 0.2 s t o = 0.1 s K = 17 RPM/% Values found for Ultimate (Marginal Stability) Quarter Decay Critical Damping Overdamped
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Set Point Output SIW 11-5-05
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RPM Set Point Output SIW 11-5-05
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RPM Set Point Output SIW 11-5-05
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Set Point Output SIW 11-5-05
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could not be determined
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Model vs. Experimental Decay Ratio Settling Offset
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FVT = delta R*(1-K C K/(1+K C K))
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Conclusions Low K c values Model and experimental responses are analogous Higher K c values Experimental responses never settle Recommended K c = 0.19 (%/RPM) High offset (75 RPM)
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Proportional-Integral Feedback Controller
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