1 (254)

Prévia do material em texto

Problem 6.69PP
Consider the system shown in Fig.
(a) Construct an inverse Nyquist plot of [Y(jo))/E(yojj]-1. (See Appendix W6.9.2.)
(b) Show how the value of K for neutral stability can be read directly from the inverse Nyquist 
plot.
(c) For K =A ,2 , and 1. determine the gain and phase margins.
(d) Construct a root-locus plot for the system, and identify corresponding points in the two plots. 
To what damping ratios ^do the GM and PM of part (c) correspond?
(d) Construct a root-locus plot for the system, and identify corresponding points in the two plots. 
To what damping ratios ^do the GM and PM of part (c) correspond?
Figure Control system
Step-by-step solution
step 1 of 4
a. KG(s)=- 3K
(s+l)(s+3)
Step 2 of 4
b. K is intersection with real axis
Step 3 of 4
c. K=4;GM=0dBPM=0"
K*2;GM=6.02dB ,PM=18.3" 
K=1;GM=12dB J>M=38.1"
Step 4 of 4
d for K=4. ^
forK=2 , ^ .1 8 3 
for K=l, 5=0.381