LAG COMPENSATOR
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LAG COMPENSATOR DESIGN. Bode Diagrams. 20. 0. -20. -40. -60. Phase (deg); Magnitude (dB). -100. -150. -200. -180 o. -250. -1. 0. 1. 10. 10. 10. Frequency (rad/sec). Idea:. ω g. Shift gain crossover left. by pulling gain down. without changing low freq.

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LAG COMPENSATOR DESIGN

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Lag compensator design

LAG COMPENSATOR

DESIGN

10.4 Phase-Lag Compensation


Lag compensator design

Bode Diagrams

20

0

-20

-40

-60

Phase (deg); Magnitude (dB)

-100

-150

-200

-180o

-250

-1

0

1

10

10

10

Frequency (rad/sec)

Idea:

ωg

Shift gain crossover left

by pulling gain down

without changing low freq.

Using a phase-lag compensator

PM

PM

also introduces lagging phase

10.4 Phase-Lag Compensation


Lag compensator design

Thus

Must introduce a lag compensator such that

Sufficient amount of attenuation is obtained at the desired frequency

while keeping the phase effects small

10.4 Phase-Lag Compensation


Properties of phase l ag compensator

-20loga

0 dB

-1/T

-1/aT

ωm

0O

Properties of phase-lag compensator

a<1

|Gc|dB

Attenuation is “almost” -20loga

Phase is “almost” zero

at “high” frequencies

Gc

10.4 Phase-Lag Compensation


Procedure

Procedure:

Specs: steady-state error & phase margin

Determine the gain compensation for desired st.st. error

1

K

10.4 Phase-Lag Compensation


Lag compensator design

|KGH|dB

0 dB

KGH

180o

Find the frequency yielding sufficient phase

20 log a

ω’g

ω’g

Determine the necessary attenuation

Hence calculate “a”

ΦD

a

20loga=|KGH(jω’g)|

10.4 Phase-Lag Compensation


Lag compensator design

|KGH|dB

0 dB

1/a

1 decade

KGH

180o

Place the zero at 1/10 of (a decade below) ’g

ω’g

Place the pole at 1/a of the zero

10.4 Phase-Lag Compensation


Lag compensator design

10.4 Phase-Lag Compensation


Lag compensator design

|KGH|dB

0 dB

KGH

180o

Draw Bode for KGcGH

ω’g

10.4 Phase-Lag Compensation


Check and modify as necessary

20 log a

D

Check and modify as necessary!

10.4 Phase-Lag Compensation


Fails if

FAILS IF

Gain

A LARGE a

VALUE IS REQUIRED

20 log a

Phase

OBSERVE!

10.4 Phase-Lag Compensation


Fails if1

20 log a

’g

D

FAILS IF

Gain

GAIN IS STEEP

MEANS LARGE a

Phase

10.4 Phase-Lag Compensation


Fails if2

’g

D

FAILS IF

PHASE IS FLAT

Gain

MEANS LARGE a

Phase

10.4 Phase-Lag Compensation


Lag compensator design

Phase

D

BEWARE !

MAY CAUSE STABILITY PROBLEMS !

10.4 Phase-Lag Compensation


End of section

End of Section

Next section

Restart section

Restart chapter

i

The

End

General index

End show

10.4 Phase-Lag Compensation


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