Example 5.3.1: Given the open-loop transfer function please draw the root locus. G(SH(S k(s+3) (S+1)(S+2 ↑/o k=5.18°poek=02 ±0(2k+=士1801 2± Break (6如如马平2 breaka way 2)+3 s+pn-m a+1a+2 k at 上潇人字 SHANGHAI ILAO TONG UNIVIRSITY 2021/1/262021/1/26 6 3.5.Asymptote Symmetry 6.Breakaway and break-in points 1.Draw the open 4. Segments on real axis -loop poles and zeros -3 -2 -1 2. Two segments pole pole zero   180 2 1 180 (2 1) =  −  + = k  ( ) ( ) 0 2 1 1 1 ( 1 2) 3 = − − − + = − − − − =   = = n m p z n j m i j i  breaka way Break￾in a = −3 2 a a − a + − = − 2 1 1 1 3 1 Example 5.3.1: Given the open-loop transfer function, please draw the root locus. ( 1)( 2) ( 3) ( ) ( ) + + + = s s k s G s H s 3 1 2 1 1 + + + = + + =   = = a a a s z s p k m i i n j j k =5.818 k =0.172