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 < with h r ( f ) Exercise 16.10 a) D r w tbc pale-zero diagram of H ( s ) when G ( s ) = Is H ( s ) hca'nle in this CiW? b) To stabilise H(Y) proportional feedback is prwidccl by G(8) (with real amplification K ) h w the root lociis of H ( s ) for < h: < cm.Fox what values of Ii' does the ~ ~ ~ ~ ~ i l siic.ceett? is~tiar~ Exercise 16,d H ( s ) is as in Excrcise 16.10, although F ( s ) = s2 - 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