⒌ Calculate the transfer function for the following Bode diagram of the minimum phase. (15%) dB w 0.1 1 4 8 16 -40 -20 0dB/dec 20 0 ⒍ For the system show as follows, G(s)?4,H(s)?1, (16%)
s(s?5)① Determine the system output c(t) to a unit step, ramp input.
② Determine the coefficient KP, KV and the steady state error to r(t)?2t.
⒎ Plot the Bode diagram of the system described by the open-loop transfer function elements G(s)?
10(1?s), H(s)?1. (12%)
s(1?0.5s)⒈
G1G2?(1?G2H2)C(S)? R(S)1?G1H1?G2H2?G1G2H3?H2?G1G2H1H2?G2H2H3⒉R=0, L=5
s0.05(10s?1)(s?1)(?1)4⒌G(s)? 12s(1?s)1641541⒍c(t)?1?e?t?e?4t c(t)?t??e?t?e?4t KP??, KV?0.8,
3ess?2.5
34312AUTOMATIC CONTROL THEOREM (7)
⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function R C(S)E(S), . （16%） R(S)R(S)C G3 Fig.1 G1 G2
⒉ The characteristic equation is given
E 1?GH(S)?S6?4S5?4S4?4S3?7S2?8S?10?0. Discuss the distribution of the closed-loop poles. (10%)
⒊ Sketch the root-locus plot for the system GH(S)?K(S?1). (The gain K is S3assumed 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 Show that the steady-state error in the response to ramp inputs can be made zero, if the closed-loop transfer function is given by:
an?1s?anC(s)?n ;H(s)?1 （12%） R(s)s?a1sn?1???an?1s?an
⒌ Calculate the transfer function for the following Bode diagram of the minimum phase.
-40 dB -20dB/dec
w （15%）
w1 w2 w3
-40
⒍ Sketch the Nyquist diagram (Polar plot) for the system described by the open-loop transfer function GH(S)?0.1s?1, and find the frequency and phase such that
s(0.2s?1)magnitude is unity. （16%）
⒎ The stability of a closed-loop system with the following open-loop transfer function GH(S)?K(T2s?1) depends on the relative magnitudes of T1 and T2. 2s(T1s?1)Draw Nyquist diagram and determine the stability of the system. ( K?0T1?0T2?0) ⒈
C(S)G1?G1G2G3R(S)?2?GG 1?1G2?G2G3?G1G2G3⒉R=2, I=2,L=2
?22(s?1)⒌G(s)??1s2(s
??1)3⒍??0.986rad/s???95.5o
16%） （