Transcript

Bode Plot for G1(s) with Gain Margin (GM) and Phase Margin (øM)

Bode Plot for G2(s) with Gain Margin (GM) and Phase Margin (øM)

Mag

nitu

de (d

B)

-60

-50

-40

-30

-20

-10

0

10

10-1 100 101

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 12 dB (at 1.73 rad/s) , Pm = 67.6 deg (at 0.766 rad/s)

Frequency (rad/s)

Mag

nitu

de (d

B)

-120

-100

-80

-60

-40

-20

0

20

10-2 10-1 100 101 102

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 4.86 dB (at 1.73 rad/s) , Pm = 22.3 deg (at 1.38 rad/s)

Frequency (rad/s)

Bode Plot for G3(s) with Gain Margin (GM) and Phase Margin (øM)

Step Response for G1(s) and a 2nd order approximation of G1(s) in Unity Feedback (T1(s))

Mag

nitu

de (d

B)

-140

-120

-100

-80

-60

-40

-20

0

20

10-2 10-1 100 101 102 103

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 19.9 dB (at 5.07 rad/s) , Pm = 89.4 deg (at 1.08 rad/s)

Frequency (rad/s)

0 2 4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9T1 (Original)T1 (2nd Order)

Step Response

Time (seconds)

Ampl

itude

Step Response for G2(s) and a 2nd order approximation of G2(s) in Unity Feedback (T2(s))

Step Response for G3(s) and a 2nd order approximation of G3(s) in Unity Feedback (T3(s))

0 5 10 15 20 25 30 35 400

0.2

0.4

0.6

0.8

1

1.2T2 (Original)T2 (2nd Order)

Step Response

Time (seconds)

Ampl

itude

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8T3 (Original)T3 (2nd Order)

Step Response

Time (seconds)

Ampl

itude

Bode Plot for G(s) with Gain Margin (GM) and Phase Margin (øM)

Mag

nitu

de (d

B)

-160-140-120-100

-80-60-40-20

02040

10-4 10-3 10-2 10-1 100 101 102 103

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 30.4 dB (at 7.11 rad/s) , Pm = 63.5 deg (at 0.921 rad/s)

Frequency (rad/s)

Bode Plot for GCG(s) with GC(s) = 10 (s / 0.03 + 1) / (s / 0.003 + 1).

Step Response for G(s) (eSS = 0.01) and GCG(s) (eSS = 0.001) in unity feedback.

Mag

nitu

de (d

B)

-150

-100

-50

0

50

100

10-4 10-3 10-2 10-1 100 101 102 103

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 30 dB (at 6.99 rad/s) , Pm = 61.8 deg (at 0.921 rad/s)

Frequency (rad/s)

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

1.2TTc

Step Response

Time (seconds)

Ampl

itude

Bode Plot for GCG(s) with GC(s) = 10 (s / 0.3 + 1) / (s / 0.03 + 1) (to meet øM ≈ 45°).

Step Response for G(s) (eSS = 0.01) and GCG(s) (eSS = 0.001) in unity feedback.

Mag

nitu

de (d

B)

-150

-100

-50

0

50

100

10-4 10-3 10-2 10-1 100 101 102 103

Phas

e (d

eg)

-270

-225

-180

-135

-90

-45

0

Bode DiagramGm = 27.1 dB (at 5.98 rad/s) , Pm = 46.9 deg (at 0.958 rad/s)

Frequency (rad/s)

0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

1.2

1.4TTc

Step Response

Time (seconds)

Ampl

itude

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

UncompensatedCompensated

Step Response

Time (seconds)

Am

plit

ud

e

Time0 0.5 1 1.5 2 2.5 3 3.5

Va

lue

0

0.2

0.4

0.6

0.8

1

1.2

y(t)u(t)

Time

0 0.5 1 1.5 2 2.5 3 3.5

Valu

e

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

k1x1

k2x2

k3x3


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