WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–25
B and γ 1 can be expressed in either degrees or radians as convenient. However, since ω n
and ω d are both computed in units of rad/s, σ must be in radians for Eq. 32 to be evaluated
properly.
Figure 15 gives plots of θ/γ 1 for various values of ξ. Asξ increases, the amount of overshoot
decreases, and the distance between zero crossings increases. This means that the damped
frequency ω d is decreasing as ξ is increasing.
Figure 15: Second-order system response to a step input
It is common to define a natural period τ n and a damped period τ d from the corresponding
radian frequencies.
τ n = 2π
ω n
τ d = 2π
ω d
=
2π
ω n
√
1 − γ 2 =
τ n
√
1 − γ 2
The damped period is the time required to go from one peak to the next, or twice the time
required to go from one zero crossing to the next.
(36)
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001