⒌ Consider the closed-loop system having the following open-loop transfer function:

GH(S)?K. ① Sketch the polar plot ( Nyquist diagram). ② Determine the

S(TS?1)stability of the closed-loop system. (12%)

⒍Sketch the root-locus plot. (18%) Im Im Re Im Im Re

⒎ Obtain the closed-loop transfer function

Im Re Re Im Re Re C(S). （15%） R(S)G4 R G1 G2 G3 H2 H1 C ⒈

G1G2G3G4?G1G2G4G5(1?G3H1)C(S)? R(S)1?G3H1?G2G3H2?G1G2G3G4H2?G1G2G4G5H3?G3H1G1G2G4G5H3?G4H3?H2G2G4G5H3E(S)? N(S)1?G3H1?G2G3H2?G1G2G3G4H2?G1G2G4G5H3?G3H1G1G2G4G5H3⒉0?K?3.45

⒌S: N=1 P=1 Z=0; the closed-loop system is stable ⒎

G1G2G3?G1G4C(S)? R(S)1?G1G2H1?G1G2G3?G1G4?G2G3H2?G4H2AUTOMATIC CONTROL THEOREM (10)

⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function

C(S)C(S), . （16%） R(S)N(S)N G3 G2 G4 G5 H C

R G1

Fig.1

⒉ The characteristic equation is given

1?GH(S)?S4?20KS3?5S2?10S?15?0. Discuss the condition of stability. (14%)

⒊ Consider a unity-feedback control system whose open-loop transfer function is

G(S)?0.4S?1 . Obtain the response to a unit-step input. What is the rise time for

S(S?0.6)this system? What is the maximum overshoot? （10%）

⒋ Sketch the root-locus plot for the system GH(S)?K(1?0.5s). (The gain K is

S(1?0.25s)assumed to be positive.)

③ Determine the breakaway point and K value.

④ Determine the value of K at which root loci cross the imaginary axis. Discuss the stability. (15%)

⒌ The system transfer function isG(s)?4,H(s)?1. ①Determine the

s(s?5)steady-state output c(t) when input is unit step1(t)、unit ramp t. ②Determine the

KVand Ka, obtain the steady-state error eSS when input is r(t)?2t. KP 、（12%）

⒍ Consider the closed-loop system whose open-loop transfer function is given by:

KKK①GH(S)?; ②GH(S)?; ③GH(S)?. Examine the stability

1?TS1?TSTS?1of the system. （15%）

⒎ Sketch the root-locus plot。 （18%） Im Re Im Re

Im Re Im Re Im Re Im Re