AUTOMATIC CONTROL THEOREM (5)
⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function
C(S)E(S), . （18%） R(S)R(S) H2
E R G1 G2
H1
H4 Fig.1
⒉ The characteristic equation is given
C G3 H3 1?GH(S)?S5?3S4?12S3?24S2?32S?48?0. Discuss the distribution of the closed-loop poles. (16%)
⒊ Sketch the root-locus plot for the system GH(S)?K. (The gain
S(S?1)(0.5S?1)K is assumed to be positive.)
① Determine the breakaway point and K value.
② Determine the value of K at which root loci cross the imaginary axis. ③ Discuss the stability. (18%)
⒋ The system block diagram is shown Fig.2. G1?K1K2, G2?. ①T1S?1T2S?1Suppose r?0, n?1. Determine the value of eSS. ②Suppose r?1, n?1. Determine the value of eSS. (14%)
N R E C G1 G2 Fig.2
⒌ Sketch the Bode diagram for the following transfer function. GH(s)?K,
s(1?Ts)K?7, T?0.087. (10%)
⒍ A system with the open-loop transfer function GH(S)?K is inherently 2s(TS?1)unstable. This system can be stabilized by adding derivative control. Sketch the polar plots for the open-loop transfer function with and without derivative control. (14%)
⒎ Draw the block diagram and determine the transfer function. (10%)
R C U2(s) U1(s)
⒈
C(S)G1G2G3? R(S)?⒉R=0, L=3,I=2 ⒋①ess??K21?K2②ess?
1?K1K21?K1K2⒎
U2(s)1? U1(s)RCs?1
AUTOMATIC CONTROL THEOREM (6)
⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function
C(S)E(S), . （18%） R(S)R(S)C E R G1 G2 H1 H2 H3
⒉The characteristic equation is given
Fig.1 1?GH(S)?25S5?105S4?120S3?122S2?20S?1?0. Discuss the distribution of the closed-loop poles. (12%)
⒊ Sketch the root-locus plot for the system GH(S)?K(S?1). (The gain K is
S(S?3)assumed to be positive.)
① Determine the breakaway point and K value.
② Determine the value of K at which root loci cross the imaginary axis. ③ Discuss the stability. (15%)
⒋ The system block diagram is shown Fig.2. G1?101, G2?. Suppose
S(0.25S?1)Sr?1?t, n?0.1. Determine the value of eSS. (12%) R E
N G1 0.5 G2 C Fig.2
