Frequency-Domain Analysis of Control Systems

(1)

Frequency-Domain Analysis of

Control Systems

Seong

Seong--Ho SongHo Song 자동제어시스템자동제어시스템자동제어자동제어 시스템시스템

(2)

Frequency Response

q Output for Sinusoidal Input

q Frequency Response

1. Magnitude : 2. Phase :

q Bandwidth : -3 dB

q Resonant Peak : Maximum magnitude, frequency

( ) ^t ^M ^M ⁽ ^w ⁾ ^cos( ^wt ^A ^A ⁽ ^w ⁾⁾

c =

_i _G

+

_i

+

_G

( ) ^jw ^M ⁽ ^w ⁾ ^A ⁽ ^w ⁾

G =

_G

Ð

_G

( ) ^t ^M

_i

^cos( ^wt ^A

_i

⁾

r = +

Seong 2

Seong--Ho SongHo Song Frequency Domain AnalysisFrequency Domain Analysis

q Output for Sinusoidal Input

q Frequency Response

1. Magnitude : 2. Phase :

q Bandwidth : -3 dB

q Resonant Peak : Maximum magnitude, frequency

( ) ^jw ^M ⁽ ^w ⁾ ^A ⁽ ^w ⁾

G =

_G

Ð

_G

)

(w M

_G

)

(w

A

_G

(3)

Ideal Low Pass Filter

Seong 3

(4)

Resonant Peak :

n

Damping ratio 가 크면, Resonant Peak 도 작아진다.

Seong 4

M

r

(5)

M

_r

versus Damping Ratio

n M_r versus damping ratio for the prototype second-order system

Seong 5

(6)

Normalized resonant frequency versus damping ratio for the prototype second-order system

n Normalized resonant frequency versus damping ratio for the prototype second-order system

Seong 6

(7)

Bandwidth/ω

_n

versus damping ratio

n Bandwidth/ω_n versus damping ratio for the prototype second-order system.

Seong 7

(8)

Seong 8

(9)

Adding zeros

n Bandwidth of a second-order system with open-loop transfer function G(s) = (1 + Ts)/[s(s + 1.414)]

Seong 9

(10)

Unit-step responses with Added zero

n Unit-step responses of a second-order system with a forward-path transfer function G(s).

Seong 10

(11)

Adding pole ; Magnification curves

Seong 11

(12)

Adding a Pole : Unit-step responses

Seong 12

(13)

Nyquist Plot of L(s)

Seong 13

(14)

Gain Margin & Phase Margin

Seong 14

(15)

Relative Stability

Seong 15

(16)

Gain Margin & Phase Margin in Bode Plot

Seong 16

(17)

Bode plot of L(s) =

( 5)( 50)^. 2500

+

+ s

s s

Seong 17

Frequency-Domain Analysis of Control Systems