Green Team Speed System Proportional Only Controller Design and Experimental Dustin Fraley DeAndre Strong Stephanie Wilson

Outline  Description of Speed System  Previous work Step Response Frequency Response Root Locus  Proportional only controller response curves  Model  Experimental  Results  Conclusions

Speed System Diagram SRC 1 ST 1 Motor / Generator SCZ 1

SSOC Input-Output Relationship Speed System M(t) Input (%) C(t) Output (RPM)

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

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/%)

tau - t 0 - tau -0.2 s t 0 – 0.1 s

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

Feedback Controller

Characteristic Equation (CE) Padés Approximation

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

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

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

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

Decay Ratio – 1 Oscillatory Settling Time – Never Offset - CBD Set Point Output

Decay Ratio – 0.25 Oscillatory Settling Time – 1.25 s Offset – 71 RPM Set Point Output

Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 219 RPM Set Point Output

Decay Ratio – 0 Monotonic Settling Time – 0.5 s Offset – 230 RPM Set Point Output

Controller Operating Curve for Model m bar = 63% r(t) = 1100 RPM delta r = 300 RPM

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

Set Point Output SIW

RPM Set Point Output SIW

RPM Set Point Output SIW

Set Point Output SIW

could not be determined

Model vs. Experimental  Decay Ratio  Settling  Offset

FVT = delta R*(1-K C K/(1+K C K))

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)

Proportional-Integral Feedback Controller