Wiley signals and systems e book TLFe BO 417

16. Stabilitv and Feedback Systems

402

b)

S1 will

now Iw iiicorporated into a feotlback loop,
X(s)

Give the net*: traiisfcr functior-t Hr i s ) =
a) For what viiliips of

#$.

II is the feedback systcm srable?

d) Test the stability for K < 0 with h r ( f ) .

Exercise 16.10

a) D r w tbc pale-zero diagram of

H ( s ) when G ( s ) = 0. Is H ( s ) hca'nle in this

CiW?

b) To stabilise H(Y)
proportional feedback is prwidccl by G(8) (with real amplification K ) . 1 h w the root lociis of H ( s ) for 0 < h: < cm.Fox what values
of Ii' does the ~ ~ ~ ~ ~ i l siic.ceett?

is~tiar~

Exercise 16,d. 1

H ( s ) is as in Excrcise 16.10, although F ( s ) =

s2

1
- 2s 4-5 '

a) Draw the root lociis for G(s) = h . Can the system be stabilised'?

b) If G(s) is changed to provide differeritial feedback with K real, can the system
then be s t a ~ i ~ i ~ If
e dyes,
? Lor what values of Kf
Note: consider t,he Hnrwitx test.