Green TeamSpeed System

Proportional Only Controller Design and Experimental

11-09-05

Dustin FraleyDeAndre 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

SpeedSystem

M(t)

Input(%)

C(t)

Output

(RPM)

Steady State Operating Curve For Speed

C = 17.3m - 9.7

0

200

400

600

800

1000

1200

1400

1600

1800

0 10 20 30 40 50 60 70 80 90 100

Input(%)

Output(RPM)

DLF9-1-05

300 RPM-1500 RPM

20 %-90 %

Step Response Input-Output Relationship

Ke-t0

M(t)

Input(%)

C(t)

Output

(RPM)

800

900

1000

1100

1200

1300

3 5 7 9 11 13 15 17 1945

50

55

60

65

70

75

3 5 7 9 11 13 15 17 19

τ – Time Constant (s) = 0.2 t0 – Dead Time (s) = 0.1 K – Gain (RPM/%) = 17

Frequency Response Input-Output Relationship

Ke-t0

M(t)

Input(%)

C(t)

Output

(RPM)τ – Time Constant (s)t0 – Dead Time (s)

K – Gain (RPM/%)

45

55

65

75

2 4 6 8 10 12500

700

900

1100

1300

1500

2 4 6 8 10 12

tau - t0 - tau -0.2 s

t0 – 0.1 s

Step and Frequency Response Experiments Conclusions FOPDT Parameters

= 0.2 s to = 0.1 s K = 17 RPM/%

order about 1st fu = 3.5 Hz

Kcu= 0.3%/RPM

Feedback Controller

Characteristic Equation (CE)

st

st

e st

21

21

0

0

0

Padés Approximation

Control Gain Locations

KC-CD=0.02 %/RPM

KCU=0.3 %/RPMKQD=0.19 %/RPM

Over-dampedUnder-damped Unstable

fu = 24/2Π = 3.82 Hz

Root Locus Conclusions Ultimate Kcu= 0.3

Quarter Decay Kc = 0.19

Critically Damping KCD = 0.02

Underdamped 0.02<Kc<0.3

Overdamped 0<Kc<0.02

*all units are % / RPM

Determination of fu Bode plots

fu = 3.5 Hz

Characteristic Equation (CE) fu = 4 Hz

Root Locus fu = 3.8 Hz

0171)85.025.0(1.0 22 cuucuu KiKi

P-only Controller Analysis ModelFOPDT Parameters

= 0.2 s to = 0.1 s K = 17 RPM/%

Values found for Ultimate (Marginal Stability) Quarter Decay Critical Damping Overdamped

Speed System Proportional Controller Model Response: Base 1100RPM, Delta R 300RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

TIME (sec)

OU

TP

UT

/SE

T P

OIN

T (

RP

M)

Kc = 0.3 %/RPM

SIW11-04-05

Decay Ratio – 1OscillatorySettling Time – NeverOffset - CBD

Set Point

Output

Speed System Proportional Controller Model Response: Base 1100RPM, Delta R 300RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

TIME (sec)

OU

TP

UT

/SE

T P

OIN

T (

RP

M)

Kc = 0.19 %/RPM

SIW11-04-05

Decay Ratio – 0.25OscillatorySettling Time – 1.25 sOffset – 71 RPM

Set Point

Output

Speed System Proportional Controller Model Response: Base 1100RPM, Delta R 300RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

TIME (sec)

OU

TP

UT

/SE

T P

OIN

T (

RP

M)

Kc = 0.022 %/RPM

SIW11-04-05

Decay Ratio – 0MonotonicSettling Time – 0.5 sOffset – 219 RPM

Set Point

Output

Speed System Proportional Controller Model Response: Base 1100RPM, Delta R 300RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

TIME (sec)

OU

TP

UT

/SE

T P

OIN

T (

RP

M)

Kc = 0.018 %/RPM

SIW11-04-05

Decay Ratio – 0MonotonicSettling Time – 0.5 sOffset – 230 RPM

Set Point

Output

Model Decay Ratio & Offset as Function of Kc For 1100-1400 RPM

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3

Kc (%/RPM)

Dec

ay R

atio

0

40

80

120

160

200

240

Off

set

(RP

M)

Decay Ratio Offset (RPM)

SIW11-5-05

Controller Operating Curve for Model

)()()(

)()(

tctrte

teKmtm c

m bar = 63%r(t) = 1100 RPMdelta r = 300 RPM

Speed Controller Operating CurveBase 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

40 50 60 70 80 90 100

Input(%)

Ou

tpu

t (R

PM

)

DLF9-1-05

Delta R = 300 RPM

Offset = 50 RPM

SSOC

Controller Operating Line

Kc = 0.3 %/RPM

Speed Controller Operating CurveBase 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

40 50 60 70 80 90 100

Input(%)

Ou

tpu

t (R

PM

)

DLF9-1-05

Delta R = 300 RPM

Offset = 75 RPM

SSOC

Controller Operating Line

Kc = 0.19 %/RPM

Speed Controller Operating CurveBase 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

40 50 60 70 80 90 100

Input(%)

Ou

tpu

t (R

PM

)

DLF9-1-05

Delta R = 300 RPMOffset = 225 RPM

SSOC

Controller Operating Line

Kc = 0.022 %/RPM

Speed Controller Operating CurveBase 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

40 50 60 70 80 90 100

Input(%)

Out

put (

RPM

)

DLF9-1-05

Delta R = 300 RPMOffset = 250 RPM

SSOC

Controller Operating Line Kc = 0.018 %/RPM

P-only Controller Analysis ExperimentalFOPDT Parameters

= 0.2 s to = 0.1 s K = 17 RPM/%

Values found for Ultimate (Marginal Stability) Quarter Decay Critical Damping Overdamped

Speed System Proportional Controller Exper. Base 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

Time (sec)

Ou

tpu

t/S

et

Po

int

(RP

M) Kc = 0.3 %/RPM

Decay Ratio - 1OscillatorySettling Time - neverOffset - ?

Set Point

Output

SIW11-5-05

RPM

Speed System Proportional Controller Exper. Base 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

Time (sec)

Ou

tpu

t/S

et

Po

int

(RP

M) Kc = 0.19 %/RPM

Decay Ratio - 0.4OscillatorySettling Time - 5 secOffset - 75 RPM

Set Point

Output

SIW11-5-05

RPM

Speed System Proportional Controller Exper. Base 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

Time (sec)

Ou

tpu

t/S

et

Po

int

(RP

M) Kc = 0.022 %/RPM

Decay Ratio - 0MonotonicSettling Time - 0.25 secOffset - 220 RPM

Set Point

Output

SIW11-5-05

Speed System Proportional Controller Exper. Base 1100 RPM, Delta R 300 RPM

1000

1100

1200

1300

1400

1500

4 5 6 7

Time (sec)

Ou

tpu

t/S

et

Po

int

(RP

M) Kc = 0.018 %/RPM

Decay Ratio - 0MonotonicSettling Time - 0.25 secOffset - 225 RPM

Set Point

Output

SIW11-5-05

Experimental Decay Ratio & Offset as Function of Kc For 1100-1400 RPM

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3

Kc (%/RPM)

Dec

ay R

atio

0

50

100

150

200

250

Off

set

(RP

M)

Decay Ratio Offset (RPM)

SIW11-5-05could not

be determined

Model vs. Experimental Decay Ratio Settling Offset

Comparison of Average Decay Ratio

0

0.2

0.4

0.6

0.8

1

1.2

0.3 0.19 0.022 0.018

Kcu (%/RPM)

Dec

ay R

atio

Model Experimental

SIW11-5-05

Comparison of Average Settling Time

0

1

2

3

4

5

6

0.3 0.19 0.022 0.018

Kcu (%/RPM)

Set

tling

Tim

e (s

ec)

Model Experimental

∞

∞

SIW11-5-05

∞

Comparison of Average Offset

0

50

100

150

200

250

300

0.3 0.19 0.022 0.018

Kcu (%/RPM)

Off

set

(RP

M)

Model Experimental Controller Curve FVT

SIW11-5-05

Could Not Be Determined

FVT = delta R*(1-KCK/(1+KCK))

Conclusions Low Kc values

Model and experimental responses are analogous

Higher Kc values Experimental responses never settle

Recommended Kc = 0.19 (%/RPM) High offset (75 RPM)

Proportional-Integral Feedback Controller