B–7–18.Consider the unity-feedback control system with
the following open-loop transfer function G(s):Plot Nyquist diagrams of G(s)forK=1, 10, and 100.B–7–19.Consider a negative-feedback system with the fol-
lowing open-loop transfer function:Plot the Nyquist diagram of G(s).If the system were a pos-
itive-feedback one with the same open-loop transfer func-
tionG(s),what would the Nyquist diagram look like?B–7–20.Consider the control system shown in Figure 7–160.
Plot Nyquist diagrams of G(s),wherefork=0.3, 0.5, and 0.7.=
10
s^3 +6s^2 +(5+10k)sG(s)=10
sC(s+1)(s+5)+10kDG(s)=2
s(s+1)(s+2)G(s)=K(s+2)
s(s+1)(s+10)564 Chapter 7 / Control Systems Analysis and Design by the Frequency-Response Methodk1
s10
+– +– (s+ 1) (s+ 5)Figure 7–160
Control system.B–7–22.Referring to Problem B–7–21, it is desired to plot
only for v>0. Write a MATLAB program
to produce such a plot.
If it is desired to plot for –q<v<q,
what changes must be made in the MATLAB program?B–7–23.Consider the unity-feedback control system whose
open-loop transfer function isDetermine the value of aso that the phase margin is 45°.
B–7–24.Consider the system shown in Figure 7–161. Draw
a Bode diagram of the open-loop transfer function G(s).
Determine the phase margin and gain margin.G(s)=as+ 1
s^2Y 1 (jv)U 1 (jv)Y 1 (jv)U 1 (jv)G(s)25
s(s+ 1) (s+ 10)+–Figure 7–161
Control system.G(s)20(s+ 1)
s(s^2 + 2 s+ 10) (s+ 5)+Figure 7–162
Control system.B–7–21.Consider the system defined byThere are four individual Nyquist plots involved in this sys-
tem. Draw two Nyquist plots for the input u 1 in one dia-
gram and two Nyquist plots for the input u 2 in another
diagram. Write a MATLAB program to obtain these two
diagrams.B
y 1
y 2R = B
1
0
0
1
RB
x 1
x 2R + B
0
0
0
0
RB
u 1
u 2R
B
x# 1
x# 2R = B
- 1
6.5
- 1
0
RB
x 1
x 2R +B
1
1
1
0
RB
u 1
u 2R
B–7–25.Consider the system shown in Figure 7–162.
Draw a Bode diagram of the open-loop transfer function
G(s). Determine the phase margin and gain margin with
MATLAB.Openmirrors.com