Advanced control engineering (S.R. Burns, 2001)

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K

Im

ω = ∞

ω = 0

Re

–45°

0.707K

ω =

l

T

(a) Polar Plot

G(jω)

G(jω)

(degrees)

K

0

0.707K

– 45

– 90

l

ω (rad/s)

l

ω (rad/s)

T

(c)

T

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2.5

0.25

ζ =

2K

2

G(jω)

1.5

ζ = 0.5

K

1

ζ = 1.0

0.5K 0.5

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

ωn

ω

(rad/s)

(a) Modulus

0

–20

ζ =

–40

0.25

ζ =

0.5

G(jω) –60

ζ = 1.0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

ωn

ω (rad/s)

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R (jω)

G2(jω)

C (jω)

G1(jω)

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$ #

$ # $ #

$

–6 dB/octave

(–20 dB/decade)

1

log ω

T

G(jω)

(degrees)

LF Asymptote

0

MF Asymptote

–45

HF Asymptote

–90

1

1

10

log ω

10T

T

T

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|G(jω)|

dB

Slope = +6 dB/octave

(+20 dB/decade)

3 dB

K

1

log ω

T

G(jω)

90

(degrees)

45

0

log ω

1

T

(b) Phase

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