Análise de Sistema de Feedback

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Problem 3.30PP
A feedback system has the following response specifications;
• Percent overshoot Wp M
: * 1
step 3 of 5
Refer Figure 3.24 in the text book, the value of damping ratio ^ is 0.5 for maximum overshoot 
of
Refer Figure 3.20 in textbook. For damping ratio ( f ) ° f 0 .5 , the location of the pole is 30®. 
Draw the sketch of s- plane as shown In Figure 1.
Figure 1
Thus, the simple second order acceptable closed loop poles in the s plane shown in Figure 1.
sten 4 of 5
(b)
Refer Figure 1, locate the points where and line meet ^x)whlch Is the damping ratio. So 
damping ratio ^ is 0.66.
Write the formula for overshoot.
M = e '
Substitute 0.66 for f •
-irriU*
= 0.063
Step 5 of 5
Find the value of percentage of 
Percentageof x 100
Substitute 0.063 for A/, 
Percentageof =0.063x100
= 6.3%
Thus, the percentage overshoot is |6.3%l •