QI@ system is stable

@ Eyput substitution ,

⑨start :

eco ) - It CA- '

B

-

- Itf -2434%10,9*5/1)-

- Itf ' -2431-1 ? ! (I )= I - 6=-5

④Raarphrpnteanti. it:;= finna f - 5 t t 27 .

5]= - D

Q2 i

⑤Tls) =It GIST

characteristic Eg. It KGISIHISKO¥E¥i;nmK ( s'

-125g - too )It- =o

S't 155 450

④guy ,

KC s - es --

,

§tlo)CS-#K CS - 3.5 ) ( s -128)-

( s -110) ( s -15 ) toes= #t#

i:¥#Ii

truth Test-

K ( s'

-125g - too )

-110=5't 155 4504k ( s ' -125g - too )

K ( s'

-125g - too )-

114115 -145*+1515-1150 - look)

§ K -11 50 - look

s' 25kt 15

soMi entire row O :

-25kt, K -- - Is5 : ' (Kt 1) s - + 50 - look -_ o

f- 5=-1105=115y

'

0-3

⑦Los - of{ =-lnCEosaF%oT

=

-411011€

Ft- 0.59

Wn -- too -- 14, I n

¢÷±×.

K = 90 ( from matlab )

④make Tp -- 0,2 = 5=0.59Wn -- 19.5 Wd

-

- 15.7 ( Imaginary Part)

" * ii. ⇒ Hat:3co - K . Cst 7 )

Gds) ---S . ( St co) ( St 20)

K --33.2 closed - loop :• 11.5-115.75

poles

con. a. . .

±÷i¥

⑨

- compensated- uncompensated

compensated version only has

32 overshoot , not desired 10%.

This is because the 2nd order

approximation is not accurate

enough .

To adjust, one can

move the zero further negative( but not crossing - lo pole ) so that

the asymptote is more negative .This way ,

the cross.y with the

damping factor 's line matches the10% OS requirement .

⑨ Els) -- RNC l - Tls ) ) pls) -- fTls ) =#

I t Gls )

I - Tls ) =#It Gls )

Rls)Els ) =-

I -1 Gls )

thanGls ) = -

S - Ls -110) ( HLF

I-

SEls ) =-900"-

s ( Sto) ( s -120 )

s-

t 30 S t zoo=-

S3 t 30 s't 200 s t 900@ system is stable ( see ⑨ )

@ Apply KVT :

eld ) = Lim s - Els)s -so

34305242005= ( im#s -so 53-130521-2005-1900

= 0

-compensated332 - ( s -17)

Gls) =-S . ( St lo ) ( s -120)

E- ( D=332 ( St 7 )i t-

S - Cst co) ( St 20)

L

5¥30 S t 200 S-

53+3054532 s t 2324

@ system stable seen from ⑨@ Apply FVT ,

@ (D) = Lims . Els)s -70

= 0

Qfwsefignrelo.9dlotenormalizat.in#-@Gls7--s(5tll'Cstloo)

-

I-

- - --

,-20dBIdea

uzodtldec idy.

- vodka .I '

'

I

0.1 A b too radsAngleton

90S

45 190 deyldeco " ?45dg%¥uT

-180#sD. I 1 to Ipo 1000

④ G. Cs) =60 -

S ' ( s t / o o ,

40 (Stl

,

db?

yudbldec"

"

^,

St l

90 - -

✓,-454dm .

°

- 90#m

"