Page 377 - The Mechatronics Handbook

0066_Frame_C18 Page 13 Wednesday, January 9, 2002 5:14 PM

FIGURE 18.20 Frequency response magnitude for second-order system.

FIGURE 18.21 Frequency response phase angle for second-order system.

is the amplitude ratio (a dimensionless quantity), and

−1 2ζω/ω n )
(
Φ = – tan ----------------------------
1 ( ω /ω n )
2
2
–
is the phase angle.
Figures 18.20 and 18.21 are plots of the magnitude response M dB = 20 log 10 (M) and the phase angle
Φ for the second-order system as a function of damping ratio, ζ. The peak value in the magnitude
response, M P , can be found by taking the derivative of M with respect to ω and setting the result to zero
to find (Nise, 1995)

1
M P = ------------------------
2
2ζ 1 ζ–
This peak value in M occurs at the frequency ω P given by

ω P = ω n 12ζ 2
–

©2002 CRC Press LLC

©2002 CRC Press LLC