自动控制原理（双语教学）：9.10.3.9

Solution 9.10.3.9 S G a = a G @G @a = a a 2 (s + a) 2 @ @a a 2 (s + a) 2 = (s + a) 2 a " ;a 2 (2s +2a) (s 2 +2as + a 2 ) 2 + 2a s 2 +2as + a 2 # = (s 2 +2as + a 2 ) " ;a(2s +2a)+2(s 2 +2as + a 2 ) (s 2 +2as + a 2 ) 2 # = 2s(s + a) (s + a) 2 = 2s (s + a) S T c a = a T c @T c @a = a a 2 s 2 +2as +2a 2 @ @a a 2 s 2 +2as +2a 2 = s 2 +2as +2a 2 a " ;a 2 (2s +4a) (s 2 +2as +2a 2 ) 2 + 2a s 2 +2as +2a 2 # = s 2 +2as +2a 2 " ;a(2s +4a)+2(s 2 +2as +2a 2 ) (s 2 +2as +2a 2 ) 2 # = 2s(s + a) s 2 +2as +2a 2 S G K = S T c K =0;; since there is no dependence on K.