1 (209)

Prévia do material em texto

Problem 6.24PP
The Nyquist plot for some actual control systems resembles the one shown in Fig. What are the 
gain and phase margin(s) for the system of Fig., given that a = 0.4, /5 = 1.3. and 0 = 40*. 
Describe what happens to the stability of the system as the gain goes from zero to a very large 
value. Sketch what the corresponding root locus must look like for such a system. Also, sketch 
what the corresponding Bode plots would look like for the system.
Figure Nyquist plot
Im [C (j)]
I
I
1 \
^ U-a..
1
/ n 
/ 1 
/ 1 
/ 1 
X 1 
/ 1 
/ 1 
/ 1 
-1
t / W t f /
V l l Re[G(s)]
S tep -by-s tep s o lu tio n
Step 1 of 2
P M = q )= Aiy
G a fl = - = — =2.5 a n f 2 = - = 0.77
2 0.4
If gain lies between 0.77 and 2.5 system is stable 
If gain > 2.5 system becomes unstable 
Root locus will look like
Step 2 of 2
Re(s)