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Fig.5 23 Frequency-response parameters.
LINEAR SYSTEMS, THEORY, AND DESIGN: A BRIEF REVIEW 485
To determine the peak amplitude M p and the corresponding frequency COp, take
the squares on both sides ofEq. (5.147), differentiate with respect to to, and equate
the resulting expression to zero to obtain
1
(5.148)
Mp = 2"j2_~
(Op = tOn,n-=2T7- (5.149)
Equations (5.148) and (5.149) show that Mp and COp of the closed-loop frequency
response are directly related to the damping ratio C. The percent overshoot Os and
damping ratio < are related through Eq. (5.75), which is reproduced here in the
following:
- ~,( Os/l00)
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PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL3(60)
