1 (215)

Prévia do material em texto

Problem 6.30PP
If a system has the open-loop transfer function
G (s) = -
s(s + 2(o>n)
with unity feedback, then the closed-loop transfer function is given by 
Q)i
T (s) = - ^ "--------y.
+ 2f0)nS +
Verify the values of the PM shown in Fig. fo r^ = 0.1,0.4, and 0.7. 
Figure Damping ratio versus PM
Step-by-step solution
step 1 of 2
G ( 0 = -
s(s+2? f t+ 2 x 0 .f - 2 x - 0 .f 
2x0.4
.VVl+2x0.4" -2X -0.4V 
2x0.7
_>/V n-2x0.7*-2x-0.7^ 
All these values matche closely with fig: 6.36
= 110.42*1 
= 1 ^ 
= 170.33*1