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AUTOMATIC CONTROL THEOREM (8)
⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function
C(S)E(S), . （16%） R(S)R(S) R E
G1 G2 C G3 G4 Fig.1 ⒉ The characteristic equation is given 1?GH(S)?S3?3KS2?(2?K)S?4?0. Discuss the condition of stability. (12%)
⒊ Draw the root-locus plot for the system GH(S)?K;H(s)?1.
(S?1)2(S?4)2Observe that values of K the system is overdamped and values of K it is underdamped. (16%)
⒋ The system transfer function isG(s)?K(1?0.5s),H(s)?1. Determine the
s(1?2s)(1?s)steady-state error eSS when input is unit impulse?(t)、unit step1(t)、unit ramp t and unit parabolic function
12t. (16%) 2
⒌ ① Calculate the transfer function (minimum phase);
② Draw the phase-angle versus ? dB -40 -20dB/dec w (12%) w1 w2 w3 -40 ⒍ Draw the root locus for the system with open-loop transfer function.
GH(s)?K(1?s) (14%)
s(s?2)(s?3)
⒎ GH(s)?(14%)
K Draw the polar plot and determine the stability of system. 3s(Ts?1)⒈
C(S)G1G2?G3G4?1?G1G2G3G4? R(S)G1G2?G3G4?G1G2G3G4⒉0.528?K??
⒊S:0 11⒋S: ?(t) ess?0; 1(t) ess?0; t ess?; t2ess?? K2?1?2(⒌S:K??1?2; G(s)?s?1?1) ss2()?3?1 AUTOMATIC CONTROL THEOREM (9) ⒈ Consider the system shown in Fig.1. Obtain the closed-loop transfer function C(S)E(S), . （12%） R(S)N(S) R E N G1 G2 G3 H1 H2 H3 ⒉ The characteristic equation is given G5 C G4 Fig.1 1?GH(S)?S3?34.5S2?7500S?7500K?0. Discuss the condition of stability. (16%) ⒊ Sketch the root-locus plot for the system GH(S)?(s?a)4. (The gain a is s2(s?1)assumed to be positive.) ① Determine the breakaway point and a value. ② Determine the value of aat which root loci cross the imaginary axis. ③ Discuss the stability. (12%) ⒋ Consider the system shown in Fig.2. G1(s)?Kis?1, G2(s)?K. Assume s(Ts?1)that the input is a ramp input, or r(t)?at where a is an arbitrary constant. Show that by properly adjusting the value of Ki, the steady-state error eSS in the response to ramp inputs can be made zero. (15%) E(s) R(s) G1(s) G2(s) C(s) Fig.2