(b)
G1(s)?K1(T1s?1)s,
G2(s)?K2s(T2s?1), T1?T2
Solution: (a) In this case the system is of second-order and must be stable. The transfer function from disturbance to error is given by ?e.d(s)??G21?G1G2??K2s(Ts?1)?K1K21s1s2
The corresponding steady-state errors are ?ss.p ?ss.a?lims?s?0?K2s(Ts?1)?K1K2?K2s(Ts?1)?K1K2???1K1
?lims?s?0???
(b) Now, the transfer function from disturbance to error is given by ?e.d(s)??K2ss(T2s?1)?K1K2(T1s?1)2
and the characteristic polynomial is
?(s)?T2s3?s2?K1K2T1s?K1K2 Using L-C criterion,
D2?1T2K1K2K1K2T1?K1K2(T1?T2)?0
the system is stable. The corresponding steady-state errors are ?ss.p ?ss.a
?lims?s?0?K2s2s(T2s?1)?K1K2(T1s?1)s?1?0
1K1?lims?s?0?K2s2?12??s(T2s?1)?K1K2(T1s?1)s